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The Effects of initially high error tasks on short term learning for mildly handicapped students

Material Information

Title:
The Effects of initially high error tasks on short term learning for mildly handicapped students
Creator:
Gerent, Michele C., 1948- ( Dissertant )
Wolking, William D. ( Thesis advisor )
Mercer, Cecil ( Reviewer )
Bolduc, Elroy J. ( Reviewer )
Morsink, Catherine ( Reviewer )
Algozzine, Robert ( Reviewer )
Place of Publication:
Gainesville, Fla.
Publisher:
University of Florida
Publication Date:
Copyright Date:
1984
Language:
English
Physical Description:
ix, 136 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Celebrations ( jstor )
Error rates ( jstor )
High school students ( jstor )
Learning ( jstor )
Learning disabilities ( jstor )
Learning rate ( jstor )
Mathematics ( jstor )
Special education ( jstor )
Special needs students ( jstor )
Students ( jstor )
Children with mental disabilities -- Education -- Florida ( lcsh )
Children with mental disabilities -- Education -- Curricula ( lcsh )
Dissertations, Academic -- Special Education -- UF
Learning, Psychology of ( lcsh )
Special Education thesis Ph. D
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Abstract:
This investigation compares the learning of mildly handicapped students in initially low and initially high error environments. It studies the effects of curriculum leap-ups on short term learning rates. A curriculum leap-up is defined as an upward curriculum change that results in a student making at least 10% more errors than correct responses. The dependent measures are celerations for correct responses and errors, improvement index, accuracy improvement, and fluency. Frequency (movements per minute) is the basic measure for all the dependent variables. Single subject designs are used to compare the learning rates of students on preleap-up skills with leap-up skills. Both a Leap and Keep and a Leap and Leave Design are used. The Leap and Keep design involves continuing the preleap-up skill when the leap-up skill is introduced. The Leap and Leave design involves dropping the preleap-up skill when the leap-up skill begins. Sixteen students in elementary and middle school resource room programs were included. The students ranged in age from seven to fourteen. Both reading and m.ath leap-ups were used. Twenty-four of twenty-nine experiments produced effects favoring learning during the leap-up condition. In most experiments celeration for correct responses and errors, the improvement index, and accuracy all increased. Findings for fluency were mixed. Results were replicated across subjects, skills, teachers, and settings. Implications for future placement and instruction, and recommendations for continuing research are presented.
Thesis:
Thesis (Ph. D.)--University of Florida, 1984.
Bibliography:
Bibliography: leaves 133-135.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Michele C. Gerent.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
030501762 ( AlephBibNum )
11665418 ( OCLC )
ACN8983 ( NOTIS )

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THE EFFECTS OF INITIALLY HIGH ERROR TASKS ON
SHORT TERN LEARNING FOR MILDLY HANDICAPPED STUDENTS



BY



MICHELE C. GERENT












A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE
UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA
198














ACKNOWLEDGEMENTS


Many individuals have contributed to the completion of

this research. First, thanks go to Dr. Bill Wolking whose

training in precision teaching and single case analysis

research enabled me to undertake this project. His help in

conceptualizing the study, and support and guidance through-

out its course are most appreciated.

Second, thanks are due to my committee members,

Dr. Catherine Morsink, Dr. Bob Algozzine, Dr. Roy Bolduc,

and Dr. Cecil Mercer, for their input and ideas during the

early stages of its development. I would also like to thank

the practicum teachers from the Fall of 1983 and their

learners for their help. They were a terrific group of

young teachers with whom to work.

Finally, thanks go to my family and friends who sup-

ported me throughout this research. I want to thank my son

Eric for coping so well with our hectic life style, my

mother who gave unselfishly of her time and support when I

needed it, and my friend Mary Mehn whose interest and

enthusiasm were often what I needed to keep me working.















TABLE OF CONTENTS


Page


ACKNOWLEDGEMENTS . . . .

LIST CF TABLES . . . .

LIST OF FIGURES . . . .


ABSTRACT .


CHAPTER I. INTRODUCTION . . . . . .

Significance . . . . . . . .
Rationale . . . . . . . . .
Statement of the Problem . . . . .
Question Under Investigation . . . .
Delimitations . . . . . . . .
Definition of Terms . . . . . .

CHAPTER II. REVIEW OF RELATED LITERATURE . .

Studies from Precision Teaching on Learning
Tasks with Initially High Error Rates/
Curriculum Leap-Ups . . . . . .
Studies from Applied Behavior Analysis and
Learning Theory on Learning Tasks with
Initially High Error Rates . . . .
Summary . . . . . . . . .

CHAPTER III. METHOD . . . . . . .


Setting . . . . . .
Subjects . . .
Variables Under Investigation

Dependent Variables .
Independent Variable . .

Experimental Design . . .

Leap and Keep Design . .
Leap and Leave Design .


. . Vii


vii

. . viii

. . 1


10


S 23
S 24

26


. . 26
. . 27
. . 31


S . . . 31
S . . . 31






Page


Procedure . . . . . . . . . . 36

Pre-experimental Phase . . . . .. 36
Experimental Phase . . . . . ... 36

Materials . . . . . . . . . . 3

Curricular Materials . . . . . . 38
Data Recording Form . . . . ... 38
Standard Celeration Chart . . . .. 39

Measurement . . . . . . . . ... 39
Data Recording and Analysis . . . . .. 43

Data Recording . . . . . . . 43
Data Analysis . . . . . . ... 44

CHAPTER IV. RESULTS . . . . . . . ... 45

Leap and Keep . . . . ... . . . 45
Reading Example: J.V. Ginn Phrases . . .. .55
Systematic Replications on Other Reading
Leap-Ups . . . . . . . . . 58
Systematic Replications with Math Leap-Ups . 60
Math Example: Add Facts/Rounding Numbers . . 61
Replications With the Same Math Skills . . 64
Systematic Replications with Other Math Skills 64
During Phases . . . . . . . .. . 65
Summary of Leap and Keeps . . . . . .. .66
Leap and Leave . . . . . . . . 67
Reading Example: Oral Reading . . . . 67
Systematic Replications with Math Skills . .. 75
Math Example: Add Facts/2 Digit Addition with
Carrying . . . . . . . . .. 76
Systematic Replications With Other Math Skills .76
Summary of Leap and Leave Leap-Ups ...... .78

CHAPTER V. DISCUSSION . . . . . . ... 79

Experimental Question . . . . . ... 79

Leap and Keep Design . . . . ... 79
Leap and Leave Design . . . . . 81
Summary . . . . . . . ... 82

Replications . . . . . . .. . . 82

Replications Across Leap and Keep and Leap
and Leave Designs ........... 83
Replications With Studies Already in the
Literature . . . . . . . . 83

_M__.... M I ......










Practical Implications


Benefits . . . . . .
Guidelines . . . . .


. . 85
. . 87


Problems and Limitations of the Study . . .
Recommendations for Future Research . . .

Longer Leap-Up Phases and Fluency . .
Chunk-Ups . . . . . . . .
Step Size . . . . . . . .
Strategies for Reducing Errors . . .
Anxiety and Resistance to Errors .. ..


APPENDICES
A DEFINITION OF TERMS . . . . . .
B. ALACHUA COUNTY CRITERIA FOR ELIGIBILITY IN
LEARNING DISABILITY, EMOTIONALLY HANDI-
CAPPED, AND EDUCABLY MENTALLY RETARDED
CLASSES . . . . . . . . .
C. DECISION AND OUTCOME FORM . . . . .
D. RAW DATA: CORRECT AND INCORRECT FREQUENCIES
FOR ALL PHASES OF THE LEAP AND KEEP AND
LEAP AND LEAVE DESIGNS . . . . .


REFERENCES . ..

BIOGRAPHICAL SKETCH


87
S 88

S 89
89
S 90
S 91
. 91


93



99
105


107

131

134


Page


. 35














LIST OF TABLES


Table Page

1. Review of Selected Studies on Learning Tasks
With Initially High Error Rates/Curriculum
Leap-Ups . . . . . . . . . . 12

2. Demographic Data for Subjects . . . .... .. 28

3. Examples of Frequency Multipliers from
Preleap-Postleap Comparisions . . . . .. 41

4. Leap and Keep Design: Learning Outcomes by
Subject, Teacher, and Skill . .. . . . 46

5. Leap and Keep Design: Frequency Multipliers for
All the Preleap-Postleap-Up Comparisons ... .52

6. Leap and Leap Design: Learning Outcomes by
Subject, Teacher, and Skill . . . . . 68

7. Leap and Leave Design: Frequency Multipliers
for All Preleap-Postleap-Up Comparisons. . . 72


__ ...'J .I -------*1.- ------ li;














LIST OF FIGURES


Figure Page

1. Type One Leap-Ups: Slow Growth . . . ... 29

2. Type Two Leap-Ups: Below Grade Level . . . 30

3. Examples of Dependent Variable Measures . .. 32

4. Diagrams of Experimental Arrangements ...... 35

5. The Reading Leap and Keep Example . . . .. 56

6. The Math Leap and Keep Example . . . .. 62

7. The Reading Leap and Leave Example . . . 74

8. The Math Leap and Keep Example . . . . 77


r














Abstract of Dissertation Presented to the Graduate School
of The University of Florida in Partial Fulfillment of the
Requirements for the Degree of Dcctor of Philosophy



THE EFFECTS OF INITIALLY HIGH ERROR TASKS ON
SHORT TERM LEARNING FOR MILDLY HANDICAPPED STUDENTS

By

Michele C. Gerent

August 1984

Chairperson: William D. Wolking
Major Department: Special Education

This investigation compares the learning of mildly

handicapped students in initially low and initially high

error environments. It studies the effects of curriculum

leap-ups on short term learning rates. A curriculum leap-up

is defined as an upward curriculum change that results in a

student making at least 10% more errors than correct

responses. The dependent measures are celebrations for

correct responses and errors, improvement index, accuracy

improvement, and fluency. Frequency (movements per minute)

is the basic measure for all the dependent variables.

Single subject designs are used to compare the learning

rates of students on preleap-up skills with leap-up skills.

Both a Leap and Keep and a Leap and Leave Design are used.

The Leap and Keep design involves continuing the preleap-up

skill when the leap-up skill is introduced. The Leap and


VIII







Leave design involves dropping the preleap-up skill when the

leap-up skill begins.

Sixteen students in elementary and middle school

resource room programs were included. The students ranged

in age from seven to fourteen. Both reading and math

leap-ups were used.

Twenty-four of twenty-nine experiments produced effects

favoring learning during the leap-up condition. In most

experiments celebration for correct responses and errors, the

improvement index, and accuracy all increased. Findings for

fluency were mixed.

Results were replicated across subjects, skills,

teachers, and settings. Implications for future placement

and instruction, and recommendations for continuing research

are presented.














CHAPTER I

INTRODUCTION



The problem addressed in this study is the relationship

between task difficulty and learning outcomes. A review of

recent history and the status of programs for mildly handi-

capped students indicates that what is done instructionally

for the mildly handicapped occurs in the context of instruc-

tional protectiveness. There is a tendency to avoid placing

students in high expectation situations where they might

encounter failure (Meyen & Lehr, 1980). The consequence of

this protection from possible failure may also limit oppor-

tunities for growth. The use of teaching strategies that

fail to challenge students may play a part in accounting for

some of the failures and limited successes of programs for

the mildly handicapped.

Traditionally, instruction in special education has

differed from regular education in the use of several

important teaching strategies. These strategies include

allowing extra time for students to complete their academic

assignments, moving more slowly through curriculum

sequences, and giving them curricular material on which they

achieve initially low error rates. It is obvious that these

strategies have both the potential of protecting the learner

1








from failure, but also of limiting growth. These strategies

may also provide indirect messages to learners that could

affect their self-concept and general motivation for aca-

demic learning. This research explores one of these issues

by studying the learning of mildly handicapped students

taught in both initially low and high error instructional

environments.



Significance

There are indications that special education is inef-

fective and inefficient in fostering learning for the mildly

handicapped student (Dunn, 1968; Semmel, 1979). Although,

there has been a concerted effort by some educators

(Deshler, Shumaker, Alley, Warner, & Clark, 1982; Englemann

& Carnine, 1982) to develop more effective teaching methods,

common practice is that special educators have become overly

concerned with the labeling and placement of special educa-

tion students, rather than in looking for methods that

foster their learning.

Conclusions from a six-year study of the performance of

over 1300 mildly handicapped students (Neely, 1978) revealed

that using teaching strategies which allowed the students to

make some errors initially and charted daily performance was

the most effective way to improve student learning rates.

The students' label or whether or not they were taught in

special education settings or regular classrooms had no

direct bearing on their learning rates. Yet Neely found,








that in the three school districts he surveyed, the majority

of time and effort was spent on the labeling of students and

deciding on their placement, rather than on training

teachers in using charting and teaching strategies to

promote high rate learning.

After looking at the current teaching practices in

special education classrooms, Glazzard (1984) recommended

that special educators should restructure these settings to

make them more like general education classrooms. She

concluded that in many classrooms special education teachers

are limiting the academic growth of their students by

continually giving them academic material which is too easy.

Also, because of a tendency to use teaching strategies that

protect students from failure and emphasize immediate

reinforcement, teachers may be limiting the generalization

of skill learning to regular classroom settings.

Howell, Kaplan, and O'Connell (1979) point out that

many of the popular methods for teaching handicapped stu-

dents actually guarantee that they will remain behind their

peers rather than emphasizing strategies that allow special

education students to "go like mad" in order to catch up.

In an effort to implement appropriate instructional

programs to meet individual needs, teaching strategies that

challenge the learner may have been overlooked by special

educators. In many cases the consequence of this may be

passive learners who never reach their potential. It may be

that our emphasis should be on devising teaching strategies








that promote rapid learning of material closer to the

student's grade placement and potential. There are at least

three advantages of rapid learning. One, it allows the

special student a good chance of mastering everything which

is essential for competing with other students. Two, it

raises the special student to the criteria of regular

students so that there is no built-in guarantee of future

failure. Three, it allows the student, maybe for the first

time, to experience the joy of new learning.

Tawney and Gast (1984) note that the field of special

education faces greater challenges today than it has at any

other time in the past. The altruism that provided past

impetus for special education programs is gone. Arguments

for programs based on equal opportunity interpretations of

the Constitution have been overshadowed by the decline of

the economy. Programs for the handicapped are increasingly

being called upon to justify their existence. Only by

implementing a technology of education that uses student

learning as a basic datum for justifying its existence can

special educators become more accountable to parents of

handicapped students and to the public at large. As part of

this accountability it is imperative that special educators

prove that they have the strategies to help students learn

faster and the data to show how it is being done.








Rationale

There is little research on the learning of handicapped

students who are given academic tasks with initially high

error rates. As an outcome of this special education may be

producing students who fail to develop high rate learning

skills (the skills that are associated with making many

errors initially but reducing them quickly), or stay on the

same skill level for long periods of time without making

gains or reaching proficiency levels.

A rapidly developing technology of teaching and learn-

ing, Precision Teaching (See Appendix A for a definition),

is making it possible for teachers to begin to accumulate

data on student learning rates. Average classrooms in

America produce around 10% learning per week (O.R. Lindsley

personal communication August, 1981), while classrooms that

are precision taught average around 25% per week learning

(R. Beck personal communication March, 1980) and there are

data to show that some precision teachers continually

produce 100% learning per week (W.D. Wolking personal

communication May, 1983). But even precision teachers fell

into the "easy task" approach to teaching exceptional

students. McGreevy, Thomas, Lacy, Krantz, and Salisbury

(1982) report that for many years precision teachers charted

student performance, while continuing to implement

traditional public school curricular strategies. These

strategies produced initial correct performances that were

relatively high with very few incorrect responses (high








accuracy), but subsequent rates of learning remained

relatively low.

Few teachers introduce skills at levels that provided

high error rates. Yet it is at these levels that intensive

teaching is most appropriate if students are to experience

academic growth. Teaching skills on which accuracy is

already high places an emphasis on practice, requiring

little of the teacher, other than that opportunities for

practice are provided. This type of teaching has the

potential of developing bored teachers who become frustrated

by the lack of progress of their students. It may also

contribute to the high rate of burn-out during a teacher's

first few years in the classroom (Wells, Schmid, Algozzine,

& Maher, 1984).

In 1978, Lindsley (cited in McGreevy, 1980) began to

question the effectiveness of curricular strategies that

emphasized highly accurate initial performance and

apparently provided less opportunity for learning. Neely

(1978), one of Lindsley's students at Kansas, analyzed

student learning from four different teaching strategies

over a six year period. Results indicated that giving

students tasks with initial error rates at 5 to 10 per

minute was more effective at producing steeper error

decelerations than was giving students tasks with initial

error rates below 5 per minute. His study fell short of

gathering any conclusive data on another teaching strategy,

that of giving students tasks with the initial errors above








the correct responses, because teachers were reluctant to

teach this way in many cases. However, other precision

teachers (Bower & Orgal, 1981; Eaton & Whittman, 1982;

McGreevy, 1978, 1980; Stromberg & Chappel, 1980) then began

to look at the initially high error or leap-up teaching

strategy (with initial errors above the correct responses)

and data began to accumulate that showed steep celebrations

for both correct responses and errors resulted when this

strategy was used.

The investigator in this study became interested in the

leap-up teaching strategy for two reasons. First, it is a

means for motivating a large group of mildly handicapped

students who were making slow progress in special education

classrooms. Second, it is a way of training graduate

practicum students to use high error teaching strategies in

teaching academic skills. The opportunity to investigate

the strategy was aided by the fact that graduate practicum

students at the university are trained in precision

teaching.



Statement of the Problem

Many special education students fail to make gains or

improve very slowly on academic tasks that have initially

low error rates. This study explores the relative effects

of initially low and high error teaching environments on

four dimensions of student performance and learning. A








change from low-to-high error rates, while holding other

features as constant as possible, is called a leap-up.

This study extends the work on leap-ups or high error

learning by (1) further quantifying the definition of a

leap-up first used by McGreevy, Thomas, Lacy, Krantz, and

Salisbury (1982), (2) identifying two kinds of leap-ups,

(3) extending the sample studied to include elementary age

mildly handicapped students, and (4) including more work on

reading skills.

The design of this investigation is single subject.

The teaching strategy of a curricular leap-up is used with

students who are not meeting performance standards or who

are working on skills below their grade level or both.



Question Under Investigation

This study examined the effect of curriculum leap-ups

on four dimensions of academic performance. The major

concern in this study was a comparison of rates of learning

under preleap and leap-up conditions. Celeration for

corrects and errors, improvement index, and accuracy

improvement were compared for the preleap-up and leap-up

conditions. Fluency measures were also reported. Defini-

tions of these four measures are listed in Appendix A.

Also, a more detailed explanation and a graphic display of

their meanings are presented in Chapter 3 under the Measure-

ment section and in Figure 3.








The following question was investigated: What are the

effects of leaping-up to tasks that initially produce at

least 10% more errors than correct responses, on celebration,

improvement index, accuracy improvement, and fluency? (See

Chapter 3 for definitions of pre- and post-leap-up phases.)



Delimitation

The subjects in this investigation are elementary and

middle school mildly handicapped students; therefore the

findings cannot be generalized without systematic

replications to mildly handicapped high school students or

to normal high school students.



Definition of Terms

Many technical terms frcm precision teaching and

behavior analysis were used in reporting this investigation.

Some of the terms where introduced in this chapter and

others will be introduced throughout the study. The terms

have all been defined in Appendix A; so the reader may refer

to them as needed.















CHAPTER II

REVIEW OF RELATED LITERATURE



This review has two sections. The first section

reviews the literature from Precision Teaching on high error

learning usually conceptualized under the label of curricu-

lum leap-ups. The second section reviews relevant research

and theory on learning with initially high errors from the

published work of behavior analysts and learning theorists.



Studies from Precision Teaching on Learning
Tasks with Initially High Error Rates/
Curriculum Leap-Ups

To complete this section all the articles from the

Journal of Precision Teaching and "All the Known Precision

Teaching/Standard Chart References" (Eshleman, 1983) were

reviewed. "All the Kncwn Precision Teaching/Standard Chart

References" is a database of over 700 references pertaining

to precision teaching and/or standard celebration charting.

It spans the years of 1965 to the present. The database was

compiled from all the published and unpublished sources in

precision teaching that the author could locate. The

references in the database include those found through an

ERIC search, journal sources, private sources, presentations

from Precision Teaching Conferences and presentations from


... ..... .- ..... ... .....


_ ~I 1 __ _I


i ll l .,


........... .. - .








the Applied Behavior Analysis conferences that dealt with

precision teaching. Much of the literature from Precision

Teaching is in the form of unpublished work and personal

communication because O.R. Lindsley has promoted this

approach to professional communication in building a

research base. All the Known References from Precision

Teaching is continually being updated in order to provide a

research base for those conducting research in the Precision

Teaching field.

The major concern in this investigation was the rate of

learning tasks under initially high and initially low error

conditions. Precision Teachers have always been interested

in the provision of curricular and other environmental

arrangements that accelerate the mastery of skills (Bower &

Orgal, 1981). When data began to accumulate that showed

that tasks with initially high error rates provided more

opportunities for learning (Neely, 1978), the field began to

address the issue. It first looked at tasks that were

initially hard to learn (had high error rates) and then

moved to the leap-up concept which involves "leaping a

student up" to more difficult material.

Seven studies were located that addressed the issue of

giving students tasks with initially high error rates or of

giving them curriculum leap-ups in an attempt to accelerate

learning. Table 1 presents a description of these studies

beginning with the earliest and moving up to the most

recent.










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The earliest study that looked at errors as learning

opportunities was reported by Neely (1978). The basis for

this study was the analysis of six years of data on the

learning of students in special education programs. Approx-

imately, 62,320 celebrations and 630,000 frequencies were

collected from 1300 mildly handicapped students. The

analysis looked at three aspects of educational practice.

The aspects were a description of reading, the effects cf

curricula on learning, and the effects of teaching strate-

gies on learning. The last two aspects of this investiga-

tion dealt with initial error rates and relate to the

hard-to-do or leap-up concept.

The results of the analysis across different curricula

and teaching strategies indicated that curricula materials

that provided students with high initial error rates

promoted higher rates of learning than those which had

students beginning with relatively few errors. There were

also preliminary data that suggested crossover learning

pictures (where the errors are initially higher than the

corrects) were the most desirable learning pictures to aim

for because they produced the fastest learning. Crossover

learning pictures were also the most difficult to get

teachers to try.

In conclusion, Neely suggests that students are being

cheated out of a appropriate education if curricula and

teaching strategies that promote rapid learning are not

implemented in special education classrooms. Choosing a








curricula which has an initially high error rate, viewing

errcrs as learning opportunities, and the daily charting of

performance were seen as the most efficient ways to meet

high rate learning goals. Further, his study indicates that

most basal reading series do not support the concept of high

error learning; rather they support the idea that a student

needs to be 90-95% correct when initially "learning" a new

task.

In 1978, McGreevy conducted a two-year study that

examined the effectiveness of a remedial resource program

which used a traditional "easy skill" approach. One hundred

and 22 students labeled as mildly handicapped were involved

in the investigation. Seventy five of the students were

administered a one minute see-say reading task, and 47 of

the students were administered a one minute see-write math

task. This was done for ten days. The content of these

tasks was grade level specific and corresponded to the

district curricula in which the students lived. Initial

error rates on these tasks were relatively high. Each day,

after the one minute timing, the students were made aware of

their errors and verbally supplied with the answers, but no

instruction was given.

The students were later placed in a remedial program

and their progress was monitored with the use of daily

timings on remedial reading and math tasks. For reading it

was found that students learned more during the screening

phase without instruction than they did during the








remediation phase. For math, the results showed the same

amount of learning had taken place during both phases.

Conclusions drawn from this study were that the easy

tasks used during the remedial program did not allow enough

room for growth (initial errors on the tasks were too low),

and that the remedial program was ineffective in providing

for a high rate of learner change. This appears to be a

common occurrence in many programs where students are placed

on relatively easy skill levels as a means of "remediating

their skill deficits." They frequently make slow gains

because of the "easy task" approach.

In McGreevy's (1980) second project, an eighteen year

old moderately retarded boy was given a see-say task (see

the word, say the word) on the first 29 words of Wilson's

essential vocabulary. The initial frequencies indicated

that the task was very difficult for the student--he began

by making many more errors than corrects. But he learned

the task easily--his correct rate went up quickly and his

error rate went down quickly. In other words, the task was

"hard-to-do" initially, but "easy-to-learn."

Stromberg and Chappell (1980) attempted to teach an

entire second grade class a math curriculum at a pace

suggested by the adopted math text. Pairing the text with

precision teaching methods (daily timings and the use of

probes) resulted in the students achieving initially high

correct rates while they made almost no errors. The stu-

dents learned the material at an acceptable rate. After








4 months the investigators "leaped-up" the entire class to

all the math operations contained in the second grade math

book by giving the students mixed worksheets (problems with

all the operations to be learned in the second grade on

them). This leap up in curriculum produced lower initial

performance for correct responses with the students making a

lot of errors. However, results of learning measures

indicated that the students learned the material very

rapidly. Conclusions were that following logical curriculum

sequences may unnecessarily slow students down, and that

students should be challenged to see how fast they can

learn.

Bower and Orgal (1981) used the concept of high error

learning with college students. They set very high aims for

the students to meet in learning psychology terms. The

students were told to learn all the terms at one time and

not to be concerned with their high initial error rates.

Results indicated that the students' high initial error

rates led to steep celebrations (rapid learning) and satis-

factory accuracy and fluency rates at the end of the course.

Conclusions were that students can learn to view errors as

learning opportunities instead of something to be avoided.

Another investigation by McGreevy, Thomas, Lacy,

Krantz, and Salisbury (1982) found that neither learning nor

variability can be predicted from low initial performance by

students. These conclusions were based on the data from the

learning of difficult tasks by 24 severely handicapped

students over a four week period. In order to qualify as a








difficult task, there had to be at least 10% more errors

than correct responses on the initial timing the student

took on a task. Sixty-six tasks met this criterion and were

then divided into those that were hard-to-do and those that

were extremely-hard-to-do depending on how many errors the

student initially made on them.

The results of several comparisons between the

two groups of tasks clearly indicated that, although the

difficulty range varied within the range of hard tasks,

there was no relationship between how hard the task was

initially and the rate of learning or variability (bounce of

the performance). The students learned all the tasks at

fairly high rates even when they began with only one or

two corrects and many errors.

The most recent investigation which used the leap-up

approach was done by Eaton and Wittman (1982). This inves-

tigation examined the effects of the leap-up teaching

strategy on the learning rates of three learning disabled

junior high school students. All three students were

accurate in performance of the multiplication and division

tables but were not meeting fluenc'., aims (not doing the

problems quickly enough). They were considered "reluctant

learners" b" the invest igators w.:ho wa:ntd them tC. :nv.'. i&.

quickly through the math curriculum. When the'.' v-r c:i":: .

leap-up to fractions where their initial error rates were

high, they all responded well by increasing their rate of

learning. Eventually they all began to meet fluency ?.ims.







Conclusions were that the leap-up approach appears to

be an effective way to motivate students with slow growth

learning and that special education teachers should guard

against using small curriculum steps in teaching students

who are not meeting fluency aims.



Studies from Applied Behavior Analysis
and Learning Theory on Learning Tasks
with Initially High Error Rates

The intent in this section was to review teaching

strategies from the applied behavior analysis and learning

theory that allowed mildly handicapped students to experi-

ence learning tasks with initially high error rates, or

tasks that were hard for them in the beginning stages. A

computer search using the key words applied behavior analy-

sis, learning theory, high error learning, difficult tasks,

teaching strategies, curriculum strategies, mildly handi-

capped students (EM, LD, BD) was done. Also, a search using

the same key words was done in the Exceptional Child Index,

CIJE, Education Index, and the Annual Review of Psychology

for the years 1974 to 1983. No studies were located.

Since the first searchers were unproductive, a search

of the titles in the table of contents was completed for the

Journal of Learning Disabilities, LD Quarterly, Teaching

Exceptional Students, The Journal of Applied Behavior

Analysis, and Exceptional Education Quarterly. This search

reviewed titles from these journals for the years 1975 to








present. The same key words as in the computer and indices

searches were used. Again, no studies were located.

It appears there is little, if any, research on this

topic.



Summary

Research evidence that normal learners as well as

handicapped learners have more opportunities for learning

when they are placed in "high error" generating situations

is beginning to accumulate. Precision teaching techniques

that emphasize this approach are curriculum leap-ups and

hard-to-do tasks. There is growing evidence that these

strategies may be successful with handicapped and nonhandi-

capped students as well as with adults.

The hard-to-do or leap-up approach to learning repre-

sents a change from the traditional approach of giving

students tasks with initially low error rates. Studies

using precision teaching have shown that (1) errors can

serve as learning opportunities, (2) curriculum leap-ups and

hard-to-do tasks are effective ways of increasing student

performance, (3) motivation for learning may be improved by

giving "reluctant learners" curriculum leap-ups, (4) teach-

ing and learning in initially high error learning environ-

mental need further study.

A search of the research literature from Applied

Behavior Analysis and learning theory failed to locate any








studies which looked at the learning of mildly handicapped

students in high error environments.

Continued research in naturalistic settings is needed

to validate strategies that promote initially high error

learning. Special educators need to expand their knowledge

of the motivating factors of hard-to-do tasks for popula-

tions of students who are accustomed to being presented

relatively easy tasks under the guise of remediation and

protection from failure and its pressures.














CHAPTER III

METHOD



This work attempts to advance the understanding of

teaching and learning under high initial error conditions

while teaching mildly handicapped students. This experiment

investigated the effects of curriculum leap-ups on four

learning outcomes. Specifically, the effects on celebration,

improvement index, accuracy improvement, and fluency were

explored. The study was a series of clinical investigations

conducted in ongoing classrooms with graduate practicum

students serving as teachers.



Setting

The study was carried out in Alachua County, a north-

central Florida school district of 22,000 students. The

system has special education resource and/or self-contained

rooms in all elementary and middle schools. The data were

gathered by the investigator and by graduate students as

part of their practicum assignment in resource rooms for the

mildly handicapped. The typical student teacher was indi-

vidualizing instruction on about 25 separate skills at any

one time. The skills that were taught were chosen to


I1








satisfy the Individual Education Plan (IEP) for each stu-

dents as determined by the special education teacher and the

student teacher jointly. Teaching procedures were selected

with the idea of maximizing student learning.



Subjects

There were sixteen subjects in this investigation. The

subjects were all learning disabled, emotionally handi-

capped, severely language impaired, or educably mentally

retarded students. They ranged in age from 7-14. Ten were

males and six were females. One subject attended a self-

contained program for the severely language impaired, five

attended an elementary school resource room program for the

mildly handicapped, and ten attended a middle school

resource room program for the mildly handicapped. See

Table 2 for demographic data on the subjects. All subjects

in the study met the Department of Education and the local

school district special education placement guidelines (See

Appendix B).

Subjects chosen to participate in the experiments met

the criteria for type one or type two leap-ups or both. See

Figures 1 and 2 for the rationale and criteria for each type

of leap-up. Type One leap-ups were used with learners who

were making little or no progress in meeting performance

standards. Type Two leap-ups were used to allow students

working on below grade level skills to experience learning

at or near their grade level placement.









Table 2

Demographic Data for Subjects


Subject Sex Grade Exceptionality Age Race Teacher


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.


L.A.

Y.B.

C.B.

E.B.

A.F.

J.R.

R.J.

C.J.

A.K.

D.P.

N.R.

G.R.

O.S.

W.T.

E.C.

J.V.


L.D.

EMR

L.D.

Lang

SLD

E.H.

EMR

EMR

EMR

L.D.

L.D.

L.D.

L.D.

EMR

E.H.

E.H.


Imp


W. 0.

S.B.

B. M.

M. G.

W.O.

B. M.

S.B.

S.B.

J.R.

C.F.

C.F.

B. M.

B. M.

J.R.

B. M.

S.L.









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Variables Under Investigation



Dependent Variables

The four dependent variables in this investigation were

celebration, improvement index, accuracy improvement, and

fluency. All are measures of academic performance.

Previous work indicates that celebration, accuracy, and

fluency are sensitive dimensions (Koenig, 1972) likely to

detect changes in the independent variable being manipu-

lated. The improvement index was included because it is a

convenient way of looking at the celebration for correct

responses and errors at one time.

Figure 3 presents an example of each of the dependent

variables. The figure illustrates both a preleap-up and

leap-up phase. Figure 3 and the measures used in this

investigation are explained fully under the measurement

section of this chapter.



Independent Variable

The independent variable is a curriculum leap-up (See

Figures 1 and 2). A curriculum leap-up is a change from a

skill with an initially low error rate to a skill with an

initially high error rate. The size of a leap-up depends on

the individual subject, rather than on the skill. For some

subjects a leap to the next level in a curriculum ladder met

the error requirements; for others a much larger leap up the

curriculum ladder was required in order for the error










/


/


2"


0 7 4 21 28 Dvys35 42 49 56 6:


Symbol Name


Formula


Value
Preleap-up Leap-up


A Initial Perf.
B Initial Perf.
C Final Pref.
(Fluency)
D Final Perf.
(Fluency)
E Cel for Corr.
(Learning)
F Cel for Err.
(Learning)
G Improvement
Index
H Accuracy Impr.


Frequency for
Frequency for


Corr.
Errors


Frequency for Corr.

Frequency for Errors

mov/min/week for Corr.

mov/min/week for Err.
cel for corr x ceel for
errors
Final accuracy ratio/
initial accuracy' ratio


of Dependent Variable Measures.


/


x 1 / 1 5

xl. 0

x1.15

xl1.12


x8.40

/5.80

x50

x160


Figure 3. Examples








criteria to be met. Both Slow Growth and Below Grade level

types of leap-ups, as mentioned under the subject section,

were used.



Experimental Design

The experimental design in this study is single sub-

ject. Single subject designs make it feasible to demon-

strate within subject control because the unit of analysis

is the individual. Replications across subjects, teachers,

skills, and settings were done to demonstrate the relia-

bility and generality of the findings (Tawney & Gast, 1984).

This investigation presented a special design chal-

lenge. In educational settings, designs that require the

repeated withdrawal or reversal of the independent variable

may not be practical (Tawney & Gast, 1984). In these

experiments, it is not meaningful to return to a baseline

after a leap-up because the student is learning new material

during the leap-up.

The designs used in this investigation do not com-

pletely fit any of the standard design descriptions. They

do have elements in common with the AB, multiple baseline,

and alternating treatment designs. The two designs used in

this investigation meet the unique needs of the real world

teaching situation (Alberto & Troutman, 1982; Haring,

Lovitt, Eaton, & Hansen, 1978). They are referred to as

Leap and Keep and Leap and Leave designs.








Leap and Keep Design

The Leap and Keep designs are illustrated in Figure 4.

Every vertical line (change line) gives the opportunity to

observe an experimental effect. Because the baseline A is

continued when the treatment B is introduced, the design

controls for maturation and correlated historical variables.



Leap and Leave Design

The Leap and Leave designs are illustrated in Figure 4.

There is one opportunity (change line) with this design for

an experimental effect to be observed. This design is most

like the AB design.

The AB design provides a structure for drawing experi-

mentally valid conclusions when certain conditions are met

(Tawney & Gast, 1984). Optimal conditions include

(1) Behaviorally defined target behavior.

(2) Collection of continuous baseline data (at least

3 days).

(3) Introduction of the independent variable only

after the baseline trend is stabilized.

(4) Continuous collection of baseline data on the

target behavior during the intervention.

(5) Replicate the experimental effects with similar

subjects.

This design can provide a convincing demonstration that

outcomes are not a function of other variables (time,

maturation, experience, unobserved correlated events) when








Leap and Keep

(1) Leap 1


PL IDuring

(2) Leap 2


Leap 1


PL I During

(3) Leap 3

Leap 2

Leap 1
r-------------
PL During

(4) Leap 2

Leap 1 ---------------

PL During 1 iDuring 2

(5) Leap 3

Leap 2

Leap 1 J


PL During 1 During 2 During 3


Leap and Leave

(6) Leap 1


PL

(7) Leap 2

Leap I j

PL

Figure 4. Diagrams of Experimental Arrangements.








behavioral changes measured following the intervention are

immediate and abrupt following a stable baseline.

Conclusions drawn by AB designs may be limited by

threats to internal validity and/or external validity. The

lack of data on the natural course of the preleap-up

behavior during the intervention phase or a novelty affect

were concerns in this experiment. Therefore, several

replications were done. Several replications of the

experimental effect with this design are usually quite

convincing. The design has certainly served very well in

medicine over the past 150 years.



Procedure



Pre-experimental Phase

During this phase the practicum teachers received

training in identifying students and skills for the leap-up

strategy during their weekly practicum sessions. They were

also trained in using the Decision and Outcome form and in

using the quarter intersect method to draw learning lines.

With the aid of the investigator pinpoints for possible

leap-ups were selected. Techniques for teaching in high

initial error environments were discussed.



Experimental Phase

During this phase the practicum teachers selected

students to participate in the investigation according to








the criteria for the two types of leap-ups and gathered the

daily data for inclusion in the investigation. The fol-

lowing procedure was used for Leap and Keep experiments.

1. Students whose learning met the criteria for a

Slow Growth or Below Grade Level leap-up were

chosen to participate in the investigation.

2. A stable baseline on the preleap-up phase was

verified with the investigator.

3. A skill related to the preleap-up skill but higher

in the curriculum sequence was chosen for the

student. The skill had to meet the requirement of

having initially 10% more errors than correct

responses or another skill was tried.

4. Both the preleap-up skill and the leap-up skill

were continued. Daily timings were taken and

charted on both skills. The leap-up skills were

continued until experimental results were seen or

an aim was met.

5. In some instances one or more additional leap-up

skills were also added, making within teacher,

learner, and skill replication possible.

The procedure for the experimental phase for the Leap

and Leave investigations was identical to the above pro-

cedure with one exception. In Step 4 the preleap-up skill

was dropped when the leap-up skill was started with a

student.








The Leap and Keep and Leap and Leave field experiments

by the practicum students were monitored by the investigator

both in the classroom and in weekly chart share sessions.

At the end of the investigation the teachers discussed their

teaching procedures and results on the leap-up skills with

the investigator.



Materials



Curricular Materials

The curricular materials used were based on the szu-

dents' current academic program. Resource rooms in Alachua

County use county adopted materials for each grade level

along with remedial materials. Materials currently used

include the Ginn and SRA reading series and the Heath math

program. Most teachers used adaptations of the materials

for precision teachers available from the Alachua Learning

and Resource Center.



Data Recording Form

The Decision and Outcome Form was used to record all

the specifics of the program and the outcomes. The infor-

mation on the Form was combined with the charted data to

obtain a complete picture of the learning in each phase.

See Appendix C for a copy of the form.








Standard Celeration Chart

The Standard Celeration Chart (Pennypacker, Koenig, &

Lindsley, 1972) was used to display and analyze all the data

from the investigation. Precision teachers have made an

attempt to standardize graphic displays of data by using

this chart.



Measurement

Frequency, movements per minute (Pennypacker, Koenig, &

Lindsley, 1972) was chosen as the basic unit of measurement

in this investigation. For many academic and social

behaviors, frequency yields more informations than other

standard educational measurements (Haring, Lovitt, Eaton, &

Hasen, 1978). Frequency, when used to measure both correct

responses and errors, gives a measure of both the accuracy

and fluency of a student's performance. Fluency, the rate

at which a student performs a skill, is often the discrimi-

nating factor between a student who is acquiring a skill and

one who is proficient at a skill. Percent scores, most

often used in educational settings, provide only a measure

of the accuracy of a student's performance and give no

indication of fluency. When using percent data there is no

way to discriminate between the student who is just accurate

and the student who is both accurate and proficient. For

example, if one student completes 50 math facts (100 digits)

correctly in 20 minutes with no errors he is accurate but

not proficient. If another one completes 50 math facts








(100 digits) correctly in 1 minute he is both accurate and

proficient.

Frequency multipliers (the ratio between two frequen-

cies) were used to analyze the data from this study. A

frequency multiplier can be visualized as the distance

between two frequencies on the Standard Celeration Chart.

There are two levels of frequency multipliers. The first

level is a ratio comparison between two frequencies on the

chart. The second level is a comparisons between

two ratios. Both types were used in this study and are

illustrated below.

Figure 3 presents the data from a sample preleap-up and

leap-up phase. The name of the behavior being measured, the

formula for calculating it, and the value of the behavior

being measured are given. If a multiplication sign (x)

precedes the value, it indicates that the frequency of the

behavior was accelerating. If a division sign (/) precedes

the value, it indicates that the frequency of the behavior

was decelerating. In Figure 3 the initial frequencies for

correct responses and errors and the value for each of the

dependent measures in this study were calculated for both

the preleap-up and leap-up phases. These values were then

used as the basis for the ratio comparisons done in Table 3.

In Figure 3, A and B represent the initial frequency

for the corrects and errors in the two phases. The initial

frequency is the point where the learning lines (one for

correct responses, one for errors) cross the first day line








Table 3

Examples of Frequency Multipliers
from Preleap-Postleap Comparisons


Measure Value Multiplier
Preleap-Up Leap-Up


Celeration For Correct
Responses xl.15 x8.40 x7.30

Celeration For Errors xl.00 /5.80 x5.80

Improvement Index xl.15 x50 x43

Accuracy Improvement x1.62 x160 x99

Final Performance
For Correct Responses 52 60 xl.15

Final Performance
For Errors 0 0 xl.00








in a phase. The letters C and D represent the final fre-

quencies for correct responses and errors on the learning

lines. The final frequency is alsc know as fluency.

The letters E and F mark the celebrations for corrects

and errors. The unit for celebration is movements per minute

per week. It describes the rate at which frequencies change

in a week. Celeration is also called learning.

The letter G represents the improvement index. The

improvement index is a ratio between the celebration for the

corrects and the celebration for the errors. The measure

conveniently% summarizes improvement in correct and error

responding into one number. Graphically, it can be vis-

ualized as the size of the angle between the celebration for

the corrects and celebration for the errors.

The letter H represents accuracy improvement. Accuracy

improvement is calculated by determining the ratio of the

corrects to the errors at the beginning of a phase, and then

comparing that value to the ratio of the corrects to the

errors at the end of a phase. It is a measure of change in

accuracy over time.

Table 3 presents the values for the comparisons between

the preleap-up and the leap-up phases in Figure 3. These

ratios are always calculated by dividing the smaller fre-

quency into the larger frequency. For example, in the

comparison for celebrations for corrects in Table 3 the

frequency multiplier is a x7.30. This was calculated by

dividing x8.40 (c for corrects for leap-up phase) by xl.15








(c for corrects for preleap-up phase). The x sign indicates

that the rate of learning was in favor of the leap-up phase.

Within the field of precision-teaching there are,

unfortunately, two ways in which the multiply and divide

sign are used. The signs may be used to identify movement

on the chart: x for acceleration and / for deceleration.

The sign may also be used to signify the direction of an

experimental effect: x for an increase, and / for a decrease

by the indicated factor.

For making comparisons in this investigation, the x

sign before the frequency multiplier was used to indicate

that the leap-up phase is better than the preleap-up phase

on the comparison measure. The / sign was used to indicate

that the leap-up phase worsened by the factor indicated on

the comparison measure.



Date Recording and Analysis



Data Recording

Daily data were recorded on the Academic Behavior

Chart-3 (Wolking, 1983) by the practicum teachers and their

students. Each time a phase change was made the data for

the completed phase was recorded on the Decision and Outcome

sheets by the teachers and the forms were given to the

investigator.

For purposes of analysis, the data from the preleap-up

and leap-ups were plotted on the Standard Behavior Chart








using frequency for correct responses and errors. This

allowed for visual analysis of the preleap-up and leap-up

phases of learning. The scale on the Standard Behavior

chart is a ratio scale. Most measurement in educational

research occurs at the nominal, ordinal, and interval levels

because it is difficult to find variables that lend them-

selves to ratio measurements (Glass & Stanley, 1970). Patio

scales are considered to be the most sensitive scales of

measurement because they allow for interval comparison and

for an absolute zero--which indicates the total absence of

the movement being measured. Further, plots of human

behavior frequencies, as they change over time, on a ratio

scale, tend to be linear and thus permit relatively easy

predictions (Pennypacker, 1974).



Data Analysis

Visual inspection of all the data and frequency multi-

pliers were both used for data analysis. Frequency multi-

pliers add quantification to the visual inspection procedure

by making it easier to compare results across subjects,

settings, skills, and teachers. No test of statistical

significance exists for these ratios. Rather, they are

evaluated in the context of expert judgment cf their prac-

tical importance.














CHAPTER IV

RESULTS



The results for the two types of leap-ups, Leap and

Keep and Leap and Leave, are presented separately. An

example of a reading leap-up and a math leap-up are pre-

sented in detail for each type. Other cases are presented

as replications within each type of experimental condition.



Leap and Keep

The results for the Leap and Keep experiments are

presented in two tables. Table 4 is a summary of all the

data on the Leap and Keeps. Leap and Keep leap-ups involve

continuing the preleap-up phase after the introduction of a

leap-up. Both skills are taught and measured daily.

Eight subjects and five teachers in five settings were

included in the Leap and Keep experiments. The subjects

experienced sixteen leap-ups. Eight of the leap-ups were

reading related and eight were on math skills.

The four dependent variables celebrationn for correct

responses and errors, improvement index, accuracy improve-

ment, and fluency) were determined for each preleap-up,

during, and leap-up phase. Preleap-up phases include all

the data taken before a leap-up began. During phases


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include all the data from the continuation of the preleap-up

skill after the introduction of the leap-up skill, and

leap-up phases include all the data from the leap-up skill.

The number of data points in each phase and whether the

leap-up was a Slow Growth or Below Grade Level leap-up are

also reported in Table 4.

Following is a brief explanation of how to read the

results presented in Table 5. Table 5 presents comparisons

between the celebrations, improvement index, accuracy

improvement, and fluency for the preleap-up, during, and

leap-up phases. The comparisons were done using frequency

multipliers. If the change represents an improvement, the

value is assigned a multiplication sign (x). If it repre-

sents a worsening situation, the value is assigned a divi-

sion sign (/).

By subtracting 1 from the frequency multiplier, and

moving the decimal point 2 places to the right, comparisons

between the phases can be discussed as percentages. Looking

at the first leap-up in Table 5, for subject W.T., the fre-

quency multiplier for the celebrations for the correct

responses between the preleap-up and the first leap-up phase

is a x1.24. This means that the correct responses acceler-

ated 24% faster in the leap-up phase than in the preleap-up

phase. For the error celebration the frequency multiplier is

/1.04. This means that the errors decelerated 4% slower in

the leap-up phase than in the preleap-up phase. For the

improvement index the frequency multiplier indicates that

















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the leap-up phase was improving 38% faster, while accuracy

improvement was 391% better for the leap-up phase. Fluency

was 10% better for the correct responses and 6% better for

the errors in the preleap-up phase, compared with the

leap-up phase.



Reading Experiment: J.V. Ginn Phrases

J.V. was a 5th grade student classified as emotionally

disturbed. He was working on Ginn level 7 phrases and

vocabulary. The teacher decided to leap J.V. up to a higher

level of Ginn (see Figure 5) because he was working below

his grade level placement and had expressed an interest in

doing "harder work." His preleap-up celebration for correct

responses indicated that he was progressing at 23% per week,

while his errors were going down at 82% per week (see

Table 4). For J.V. a leap-up to Ginn Level 8 produced the

required error rate of 10% more errors than correct

responses.

Table 5 shows the comparison between the preleap-up

phase for J.V. on Level 7 Ginn and three separate leap-ups

to Level 8 Ginn. The celebration for the correct responses

was 18% faster for the first leap-up, 51% faster for the

second leap-up, and 95% faster for the third leap-up when

compared to the preleap-up phase. For error deceleration,

the effect of the leap-up teaching strategy grows as the

teacher learns to teach to errors. In the first leap-up,

the error celebration was 25% faster during the preleap-up




















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Figure 5. Continued.


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phase. During the second leap-up it was 65% faster for the

leap-up phase, and for the third leap-up, it was 153% faster

for the leap-up phase.

The improvement index was almost equal for the first

leap-up, but much faster for the leap-up phases in leaps two

and three. The improvement index for the first leap-up was

6% faster for the preleap-up phase, the second was 149%

faster for the leap-up phase, and the third was 393% faster

for the leap-up phase. Accuracy improvement across the

three leap-up phases was much better for the leap-up phases

than for the preleap-up phase ranging from 58% to 1300%

better. J.V. obtained better fluency in the preleap-up

phase for two of the three leap-ups.

When comparing the 3 leap-ups to the during phases the

findings for celebration, improvement index, and accuracy

ratio were similar to the preleap-up comparisons. The

leap-up phases provided faster celebrations, more improve-

ment, and higher accuracy improvement. Fluency was better

in the during phase for the first leap-up, but better in the

leap-up phases for the second and third leap-ups.



Systematic Replications on Other Reading Leap-Ups

Similar results were found for subject W.T., a first

grade EMR student in a resource room. This subject experi-

enced two leap-ups (see Table 4). The preleap-up phase was

learning to say the alphabet and the two leap-ups were to








Ginn Level 2 and then Ginn Level 5 vocabulary. Her begin-

ning celebrations for the preleap-up phase indicated slow

growth for correct responses and a fairly good deceleration

of errors (see Table 4). Results were similar to J.V.'s

results. Here celebrations for correct responses were

steeper in both leap-up phases. Error deceleration was

almost equal for the comparison between the first preleap-up

and leap-up phases and 9% faster for the leap-up phase

during the second leap-up.

The improvement index was faster and accuracy improve-

ment was higher for both leap-ups. Fluency was better

during the preleap-up phase when compared with the first

leap-up, but better in the leap-up phase for the second.

For D.P., a 5th grade learning disabled student working

on Ginn vocabulary and phrases, mixed results were obtained.

But the findings were generally in favor of the preleap-up

phases. D.P. was given two grade level leap-ups from Ginn

Level 8 to Ginn Level 11 vocabulary. His rate of learning

was already quite high on his preleap-up phase (see

Table 4). For the two leap-ups, celebration for correct

responses was 7% in favor of the preleap-up phase for the

first leap-up and 14% in favor of the preleap-up phase

during the second leap-up. Error deceleration was faster

for the preleap-up phases. It was 73% faster for the first

leap-up and 40% faster for the second-leap-up in favor of

the preleap phases. The improvement index and accuracy








improvement measures were also better for the preleap-up

phase.

On the reading phrases the preleap-up rate of learning

was also greater. In D.P.'s case his preleap-up condition

was unique in that his correct and error celebrations were

both very high before the leap-up. Although these results

favor the preleap condition, it is important to note that

D.P. continues to learn very well on the Level 11 Ginn

phrases, an increase in three levels over the preleap

material.



Systematic Replications with Math Leap-ups

The comparisons for N.R., an educably mentally retarded

student, were similar to J.V.'s results (see Table 5). In

his first leap-up all the measures for rate of learning were

better for the leap-up phase except error deceleration which

was 20% in favor of the preleap-up phase. In his second

leap-up all the measures for learning increased dramatically

in favor of the leap-up phase including error deceleration.

Results show that acceleration for corrects was better b. a

factor of 175, error deceleration was better by a factor of

11, the improvement index was 1960 times better, and

accuracy improvement was 57 times better during the leap-up

phase. Fluency was better in the preleap-up phase for the

first leap-up, and for the leap-up phase for the second

leap-up.







A.K., an emotionally handicapped student, C.J., an

educably mentally retarded student, and G.R. and Y.B.,

learning disabled students, were given a total of six math

leap-ups. They all showed an increase in learning following

the leap-up condition for celebration, growth, and accuracy

improvement (see Table 5). Results show that celebrations

for increasing correct responses and decreasing errors were

higher, improvement was faster, and accuracy improvement was

higher. Fluency was better for two of the leap-ups when

compared with the preleap condition and for two of the

leap-ups when compared with the during conditions.



Math Example: Add Facts/Rounding Numbers

C.J., a middle school educably mentally retarded

student, was given a leap-up from add facts to rounding

numbers (see Figure 6). C.J. had been working on add facts

in order to build up her fluency in adding number facts.

Her celebration for corrects was a xl.03 and for errors a

xl.0. It was decided to leap-up because her progress was

slow and she was bored practicing the facts.

A comparison of the celebrations for the two phases (see

Table 5) for her first leap-up show that the leap-up condi-

tion produced faster celebration for the corrects by a factor

of 2 and errors were reduced faster by a factor of 8. The

improvement index and accuracy improvement were improved by

factors of 17 and 27 respectively. Fluency was 4% better


















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for the leap-up phase. Results from the during phase

comparison were very similar.

Two more leap-ups were then done with C.J. in order to

replicate the experimental effects within subject. They

were two place addition with carrying and two place sub-

traction with borrowing. Both leap-ups showed an increased

rate of learning as measured by celebration, improvement

index and accuracy improvement similar to the first leap-up.

Both leap-up phases were short. Fluency was higher for

corrects during the preleap-up condition and was the same

for errors across both conditions.



Replications With the Same Math Skills

Two of the leap-ups from C.S. were replicated with

another student, N.R., an EMR student was given a leap-up

from add facts to rounding numbers. Results were similar to

C.J.'s. Her comparisons for celebration for correct

responses, improvement index, and accuracy improvement, and

fluency were all higher in the leap-up phase when compared

with the preleap-up or during phase. Her second leap-up to

subtraction with borrowing also resulted in higher rates of

learning on all the measures including error deceleration.

Celeration, improvement index, and accuracy improvement were

all better in the leap-up phase while fluency was better in

the preleap-up phase. Her error decelerations were not as

high as C.J.'s.








Systematic Replications with Other Math Skills

Three other leap-ups were done with students on math

skills. The first one was a leap-up for A.K., an elementary

emotionally handicapped student. The leap was from add

facts to 2-digit adding with carrying. His celebration,

improvement index and accuracy improvement increased during

the leap-up phase but his fluency level was lower. G.R., an

emotionally handicapped student, was given a leap-up from

multiplication facts to square roots. His learning on the

leap-up skill was faster on all measures including fluency.

Another student, Y.B., was given a leap-up from multiplica-

tion facts to one place division. Her learning rates were

better on all measures except celebration for correct

responses. Fluency was better in the preleap-up phase.



During Phases

The Leap and Keep Design controls for maturation and

correlated historical events by continuing the preleap-up

phase when the leap-up begins. The results from these

experiments indicate that learning rates were faster as

measured by celebration for correct responses and errors,

improvement index, and accuracy improvement during the

leap-up phases compared with the during phases. These

results were replicated 9 times across subjects, skills,

teachers, and settings. Fluency for correct responses was

generally in favor of the during phases compared with the

leap-up phases, and fluency for errors was mixed, some of








the leap-up phases achieving higher fluency and some of the

during phases achieving better results for errors. These

results indicate that maturation and outside events were not

responsible for the higher rate of learning during the

leap-up condition.



Summary of Leap and Keeps

A total of 16 Leap and Keep Leap-ups were done with

S students. Nineteen of twenty-eight comparisons across all

the preleap-up, during, and leap-up phases showed an

increase in student rate of learning as measured by celera-

tion, improvement index, and accuracy improvement in the

leap-up phase. Three of the comparisons indicated better

error deceleration for the preleap-up phases, which was

subsequently followed by additional leap-ups with the same

students in which the errors decelerated more rapidly in the

leap-up phases. For one comparison, the celebration for

correct responses was better for the preleap-up phase, but

all other measures were better for the leap-up phases.

Five comparisons were in favor of the preleap-up phases

on rate of learning comparisons. These were all reading

leap-ups in which the student began with high initial

acceleration for correct responses and deceleration for

errors. The results for the fluency measure were mixed with

some of the preleap-up and during phases achieving a higher

terminal frequency than the leap-up phases.








The findings that the leap-up teaching strategy pro-

duces a higher rate of learning as measured by celebration

for correct responses and errors, improvement index, and

accuracy improvement was replicated across 3 teachers,

3 settings, 6 students, and 9 skills using the Leap and Keep

Design. Possible factors involved in replication failures

will be discussed in the next chapter.



Leap and Leave

Table 6 presents a summary of all the data on the Leap

and Leave experiments. Leap and Leave leap-ups use the

procedure of dropping the skill with low error rate when the

leap-up skill starts. Nine subjects and five teachers in

five settings were included in the Leap and Leave experi-

ments. The subjects experienced 13 leap-ups. Two of the

leap-ups were on reading skills and the other eleven were

math skills. The five dependent measures are presented for

each preleap-up and leap-up phase. The number of data

points in the phase and whether the leap-up is a Slow Growth

or Below Grade Level leap-up are also given.

Table 7 presents the comparisons between the celera-

tions, improvement index, accuracy improvement, and fluency

for the preleap-up and leap-up phases. The comparisons were

done using frequency multipliers, as in Table 5.














































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74



Reading Example: Oral Reading

E.B., an elementary school language disabled student,

was given a leap-up from a first grade reading book to a

college level astronomy text (see Figure 7). Several leaps

to lower level reading material were tried but the error

rate criteria could only be reached at this level. The

preleap-up phase had a correct celebration of xl.42 and an

error celebration of xl.00.

A comparison of the celebrations for the two phases (see

Table 7) shows that the leap-up condition was better by a

factor of 17 for the correct responses and a factor of 11

for the errors. The improvement index was better by a

factor of 136 and accuracy improvement was better by a

factor of more than 4. Fluency was 33% better for the

preleap-up phase for correct responses and it doubled for

the errors. E.B.'s second leap-up on reading vocabulary

produced similar results.



Systematic Replications with Math Skills

Eleven math replications of leap and leaves replicated

the findings of E.B.'s leap-up. Three leap-ups in math were

done for L.A., a middle school learning disabled student.

The three leap-ups had faster celebration for correct

responses by factors of 10, 3.3, and 14 and for errors by

4.19, 6.19, and 16. The improvement index for the three

leap-ups ranged from a factor of 20 to a factor of 125

better. Accuracy improvement ranged from a factor of a






















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0 7 14 21 20 Days 35 42 49 56 63

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T,7***h .-Investigator-. Lvp-,p I .College level astronomy text
s.tvit _Home_


Figure 7.


The Reading Leap and Leave Example.


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little more than 2 to a factor of 24 better. Fluency was

better in the preleap-up phases.

Four other leap-ups with middle school students R.V.,

A.F., O.S., and R.J. had similar results. Although the

celebrations for the correct responses were not as fast as

E.B.'s leap-up, the other measures were comparable.

Further, students who experienced two math leap-ups had

faster learning as measured by celebration, improvement

index, and accuracy improvement and also had higher fluency

in their leap-up phases compared with their preleap-up

phases.



Math Example: Add Facts/2 Digit Addition with Carrying

W.T., a mentally retarded student, was given a leap-up

from learning add facts to 6 to doing two place addition

with carrying (see Figure 8). Her preleap-up phase had a

correct celebration at xl.39 and error celebration at xl.46.

She was not achieving fluency on the addition facts even

though her errors were going down.

A comparison of the celebrations for the two phases (see

Table 7) shows that the leap-up phase produced faster

celebration for the corrects by a factor of 13 and that the

error-learning improved by a factor of 5.4. The improvement

index was better by x78, while accuracy improvement was

better by a factor of 67 in the leap-up phase. Fluency was

also higher in the leap-up phase.





















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0 2 4 Weeks 6 8
500



200


100


Io
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0 7 14 21 28 Days 35 42 49 56 63

L-.Cr _W T rL_______ p nonvn,_1t ee Write Add FacLs sums to 5
T*.ch*r _J R Leep-up I .Two column addIUon wtIUiout carrying
serint .Stepnen Foster_


Figure 8. The Math Leap and Leave Example.


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4








Systematic Replications With Other Math Skills

One math leap-up replicated the findings on all the

measures of W.T.'s leap-up. Comparisons for R.J.'s leap-up

(see Table 7) show that the celebration for the correct

responses was 55% faster and improved error learning by a

factor of 2.4 during the leap-up phase. The improvement

index was better by x3.7 and accuracy improvement was better

by a factor of 6.6. Fluency for correct responses was 11%

better for the leap-up phase than for the preleap-up phase.

Nine math leap-ups replicated the findings of W.T.'s

leap-up on all the measures except fluency. A comparison of

the celebrations for the correct responses shows that the

leap-up phases produced better learning by factors between

1.3 and 16.8. Errors learning improved by factors between

1.5 and 58.3. The improvement index was better by factors

between 1.9 and 615. Accuracy improvement changed by

factors between 2.1 and 1659. Fluency was better in the

preleap-up phases. The range for fluency was between x1.3

and xll in favor of the preleap-up phases.



Summary of Leap and Leave Leap-Ups

A total of 13 Leap and Leave leap-ups were done with

8 students. Across all the preleap-ups and leap-up phases

results show an increase in student rate of learning as

measured by celebration, improvement index, and accuracy

improvement. Three of the leap-ups resulted in higher

fluency for the leap-up phase compared with the preleap-up




79



phase, while the remaining 10 leap-ups produced higher

fluency during the preleap-up phases.

The findings that the leap-up teaching strategy pro-

duces a higher rate of learning as measured by celebration

for correct responses and errors, improvement index, and

accuracy improvement were replicated across 4 teachers,

4 settings, 8 students, and 12 skills using the Leap and

Leave Design.













CHAPTER V

DISCUSSION



The discussion is organized around the experimental

question, replications and previous knowledge, practical

implications for special education and regular education,

problems and limitations of the study, and recommendations

for future research.



Experimental Question



Leap and Keep Design

Celeration, improvement index, and accuracy improve-

ment. The findings of this study suggest that the curricu-

lum leap-up can be an effective teaching strategy for

elementary and middle school students in special education

resource rooms who are not making gains on lower level

materials. Leap-ups to skills with initially high error

rates generally produced faster learning as measured by

celebration, improvement index, and accuracy improvement.

There is also evidence to suggest that this teaching

strategy can benefit students who are making gains on below

grade level material. Results indicate that when a student








is experiencing medium to rapid growth on below grade level

skills, leap-ups may not accelerate learning above the

preleap-up phase, but can produce medium to high rate

learning on the leap-up skill.

There were also some indications of "learning to learn"

and "learning to teach" occurrences during these experi-

ments. In three cases in particular students and teachers

did better decelerating errors on each successive leap-up.

Fluency. In looking across all the frequency multi-

pliers (see Table 4) for the preleap, during, and leap-up

phases, fluency for correct responses was split fairly

evenly between the preleap and during phases compared with

the leap-up phases. In over half, the fluency for the

errors reached zero across the preleap-up, during, and

leap-up phases. In the remaining leap-ups fluency was

generally in favor of the preleap-up phases. Achieving

fluency is a matter of how long the leap-up continues. In

some cases the student failed to reach higher fluency on the

leap-up skill because the teacher dropped the skill as soon

as the data stabilized. This was often due to time limita-

tions in the classroom and the fact that the leap-up was

done specifically for experimental purposes. There was no

difference in fluency for the leap-ups across low growth and

below grade level leap-ups.








Leap and Leave Design

Celeration, improvement index, and accuracy improve-

ment. The findings from this group of experiments indicate

that skills that have an initially higher error rate (10%

more than correct responses) generally produce higher rates

of learning than those which begin with lower initial error

rates. There was no difference in the results across Low

Growth leap-ups and Below Grade Level leap-ups. These

findings suggest that students in special education resource

rooms should be given tasks with errors initially above the

correct responses when they are making slow gains on skills

with low or no errors or when they are working on skills

below their grade level with low to medium rates of

learning.

Fluency. The frequency multipliers for fluency (see

Table 7) indicate that fluency for corrects was generally

better in the preleap-up phases than in the leap-up phases.

The fluency for errors was the same in all but one leap-up.

This indicates that the errors in all but the one leap-up

reached 0. Again, in many cases the fluency on the correct

responses in the leap-up phases was not higher because of

the fact that the primary purpose of the investigation was

to look for learning rates. Once it was established that

the student could learn the skill rapidly, the teacher often

dropped it and tried another skill. Fluency was not

affected by the type of leap-up (Low Growth or Below Grade

Level).








Summary

Both the Leap and Keep and Leap and Leave experiments

generally produced higher rates of learning during the

leap-up phases. While three leap-ups did not get results,

many of the leap-ups do show large differences on the

learning measure comparisons. These findings could have

significant implications for the education of handicapped

learners. Probably some proportion of all handicapped

learners' curriculum should be high initial error instruc-

tion.



Replications

One reason replications are done is to demonstrate the

reliability and generality of data (Tawney and Gast, 1984).

Another reason is that replications reduce the scientists'

margin of error and insure that the findings can withstand

repeated tests (Sidman, 1960). In this investigation,

replications were done across subjects, teachers, skills,

and settings within each experimental design as described in

Chapter 4.

For the Leap and Keep designs three leap-ups failed to

replicate the results of higher rates of learning that were

generally found for the other 13 leap-ups in the study.

There are at least two possible explanations for this

failure to replicate. First, the initial celebrations for

correct responses and errors for these leap-ups were already

high. Second the same teacher taught the same learner all








three leap-up skills. The data indicate that she had some

trouble teaching to errors in the leap-up phases.



Replications Across Leap and Keep and Leap and Leave
Designs

Generally, higher rates of learning during the leap-up

phases were found for both the Leap and Keep and the Leap

and Leave designs. This replication across designs serves

to strengthen confidence in the findings of the less power-

ful Leap and Leave design.



Replications With Studies Already in the Literature

Subjects in this study generally experienced steeper

learning rates under the initially high error rate condi-

tion. One of the early studies on learning rates from

precision teaching (Neely, 1978) found that error

deceleration rates were greater when students were given

tasks on which they were making at least 5 to 10 errors per

minute. No differences in correct celebration rates were

found. However, Neely introduced the idea that crossover

learning pictures (with initial error frequencies above

correct responses) could produce steeper celebrations for

correct responses. McGreevy (1980) became interested in the

concept that tasks with initially high errors could produce

steeper learning and introduced the idea of "hard to do,"

"easy to learn." He studied the learning of a severely

retarded teenager on a vocabulary task with the initial

error frequency above the correct responses. The student








achieved rapid acceleration for correct responses and rapid

deceleration for errors on the task. Bower and Orgal (1981)

taught college students psychology terms on which they

initially made many more errors than corrects. Their rates

of learning were steep for both corrects and errors.

Stromberg and Chappell (1980) taught a second grade class

math tasks on which they made little or no initial errors.

He then gave them a leap-up to all the math operations in

the curriculum to learn at one time. The students' initial

error frequencies were very high for the leap-up math tasks,

but their rate of learning was much better than it had been

on the easier math tasks. Eaton and Wittman (1982) found

the learning rates for three junior high school mildly

handicapped students could be accelerated by giving them

math leap-ups to skills with initially high error rates.

This investigation studied the learning rates of mildly

handicapped students in resource rooms who were given math

and reading leap-ups. Results replicated across subjects,

teachers, skills, and settings generally found higher

learning rates on skills with at least 10% more errors than

correct responses compared with skills that had initially

very low error rates. These results replicate the findings

in the above studies and add a new sample population and

different skills.








Practical Implications

May students fail to make gains in special education

classes (Glazzard, 1984). These classes often focus on

skills with initially low error rates so that students can

experience success. There is also evidence that the type of

instruction used in the majority of classrooms may fail to

challenge the learner or to give them skills that will

generalize to mainstream classes (Glazzard, 1984).

Further, some teaching strategies that have come from

applied behavior analysis, like task analysis (Eaton and

Wittman, 1982; Howell, Kaplan, & O'Connell, 1981) or

errorless learning may be overused with handicapped

learners. The steps in task analysis can be made so excru-

tiatingly small that the student becomes bored with learning

the task. Errorless learning, while an excellent teaching

method, does not allow students to experience the learning

that comes from viewing errors as learning opportunities

(Alberto & Troutman, 1982). The results of overusing these

strategies may be that we are producing passive learners who

become bored with easy unchallenging tasks or don't know how

to learn from errors.

The use of the high error teaching strategy offers many

benefits to classroom teachers and their students. These

are discussed below along with some guidelines.








Benefits

Results from this study indicate that when teachers use

the leap-up teaching strategy students rate of learning may

increase. Students tend to become more active learners and

teachers become involved in actually teaching skills on

which students need instruction rather than just practice.

From a practical point of view, special education

students who are behind in school need to be taught using

teaching strategies that promote high rate learning. This

is the only way that they can hope to catch up with their

peers and/or reach any level of competency in basic skills

when they complete their education. It is apparent that we

must not be content to see these students fall further, and

further behind grade level skills as they progress through

special education programs.

As evidenced in these experiments, by teaching students

to accept making many errors when they begin to learn a new

skill, it is possible to accelerate learning and to move

students closer to grade level skills. Students appear to

be motivated by learning more difficult skills and skills

closer to those that their peers are learning. Leap-up

strategies may be a contribution to the successful main-

streaming of mildly handicapped students.

Also, these findings may have implications for school

psychologist and placement committee members responsible for

developing IEP's for handicapped students. The tendency is

to write long and short term objectives for students which







emphasize skills with fairly high initial accuracy rates.

While this may be done to "let the student experience

success," educators should be aware that tasks with ini-

tially high error rates must also be included in a student's

program in order to insure that maximum learning is taking

place and that the student is getting experience in learning

from errors.



Guidelines

The high error teaching strategy is one way to acceler-

ate the learning of skills for those students who are making

slow progress and/or who are working on skills below their

grade level placement. However, it would probably not be

appropriate to go overboard on leap-ups. More work is

needed to determine what proportion of the curriculum should

be initially high error rate skills. Also, more ways to

reduce errors rapidly need to be developed and ways of

overcoming learner resistance to making errors need to be

explored before the high error teaching strategy can be

fully appreciated.



Problems and Limitations of the Study

One problem appeared during the course of this study.

This was due to the fact that many of the practicum teachers

were young and inexperienced. They received little or no

support from their directing teachers in using the leap-up

teaching strategy. They were eager to become involved in







the leap-up experiments, but were reluctant to take the

chance of leaping their students to skills with very high

error rates. Many of them were concerned that the students

still needed practice on the lower level skills and would

"miss out on learning." It was interesting to note, how-

ever, as they became involved in the experiments two things

happened. First, they became excited about the learning

taking place on the leap-up skills and actually felt they

were teaching instead of just providing opportunities for

practice. Second, they began to defend the leap-up concept

to their directing teachers and wanted to cease teaching the

lower level skills.

A limitation of this study was that the leap-ups

generally consisted of math skills, and of reading vocabu-

lary skills. This was because these skills were the easiest

to define and were the skills being taught in the practicum

sites. A problem was found in trying to do leap-ups on oral

reading. Because of the connecting words in oral reading it

was very difficult to meet the high initial error rate

criterion. The error rate was only achieved for one leap-up

and this entailed leaping a student from first grade reader

to a college level text book. It may be that the leap-up

concept will have to be defined more precisely for a broader

range of skills.







Recommendations for Future Research

The curriculum leap-up is an effective teaching

strategy when used as part of the instructional approach

with mildly handicapped learners. Future research on

curriculum leap-ups should focus on five areas: (1) the

effects of longer leap-up phases on fluency, (2) chunk-ups,

(3) the effects of step-size on learning rates in leap-up

phases, (4) strategies for reducing errors, and (5) pro-

cedures for reducing anxiety and overcoming resistance to

errors.



Longer Leap-Up Phases and Fluency

In this investigation the major concern was rate of

learning under leap-up conditions compared with preleap-up

conditions. Many of the leap-up phases were short. Future

research should focus on the attainment of fluency following

a leap-up. Since fluency is dependent on time, the leap-up

phases would have to be lengthened and strategies that build

fluency could be blended with the error reduction pro-

cedures.



Chunk-Ups

A second suggestion for future research is on the

concept of chunk-ups. Chunk-ups are special cases of

leap-ups. They involve adding more unique problems or units

to the teaching set. For example, if a student usually is








given 10 words per week, he could be given a chunk-up to

20 words per week.

Chunk-ups are related to leap-ups in that the student

is expected to learn more at one time. The idea is that if

the same rate of learning or a faster rate of learning is

noted then the "chunk-up" is way of expediting learning for

students who need to catch up or who are challenged by

learning more at one time.

This investigation intended to study the chunk-up

concept. However, preliminary work with chunk-ups led to

some problems. Specifically, (1) the chunk-up was not

empirically defined in such a way that the concept could be

easily understood by those trying to explore its value and

(2) there was resistance on the part of the practicum

teachers and the directing teachers to try the strategy.

Reports from the practicum teachers indicated that directing

teachers felt that the chunk size that they were already

using was adequate. They were not interested in exploring

learning under large chunk conditions.

The small amount of data that was obtained did not show

clear enough evidence of control to warrant conclusions

about the effectiveness of chunk-ups. Recently, teachers

who have tried chunk-ups have reported informally that it is

working effectively as a teaching strategy. This concept

should be studied further and documented more carefully.




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PAGE 1

THE EFFECTS OF INITIALLY HIGH ERROR TASKS ON SHORT TERM LEARNING FOR MILDLY HANDICAPPED STUDENTS BY MICHELE C. GERENT A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA | i 1984 I

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ACKNOWLEDGEMENTS Many individuals have contributed to the completion of this research. First, thanks go to Dr. Bill Wolking whose training in precision teaching and single case analysis research enabled me to undertake this project. His help in conceptualizing the study, and support and guidance throughout its course are most appreciated. Second, thanks are due to my committee members, Dr. Catherine Morsink, Dr. Bob Algozzine, Dr. Roy Bolduc, and Dr. Cecil Mercer, for their input and ideas during the early stages of its development. I would also like to thank the practicum teachers from the Fall of 1983 and their learners for their help. They were a terrific group of young teachers with whom to work. Finally, thanks go to my family and friends who supported me throughout this research. I want to thank my son Eric for coping so well with our hectic life style, my mother who gave unselfishly of her time and support when I needed it, and my friend Mary Mehn whose interest and enthusiasm were often what I needed to keep me working. 11

PAGE 3

TABLE OF CONTENTS Page ACKNOWLEDGEMENTS ii LIST OF TABLES vi LIST OF FIGURES .' vii ABSTRACT viii CHAPTER I. INTRODUCTION 1 Significance 2 Rationale 4 Statement of the Problem 7 Question Under Investigation 8 Delimitations 8 Definition of Terms 9 CHAPTER II. REVIEW OF RELATED LITERATURE 10 Studies from Precision Teaching on Learning Tasks with Initially High Error Rates/ Curriculum Leap-Ups 10 Studies from Applied Behavior Analysis and Learning Theory on Learning Tasks with Initially High Error Rates 23 Summary 2 4 CHAPTER III. METHOD 26 Setting 25 Subjects 27 Variables Under Investigation 31 Dependent Variables 31 Independent Variable 31' Experimental Design 33 Leap and Keep Design 34 Leap and Leave Design 3 4 in

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Page Procedure 3 6 Pre-experimental Phase 36 Experimental Phase 36 Materials 38 Curricular Materials 38 Data Recording Form 38 Standard Celeration Chart 39 Measurement 3 9 Data Recording and Analysis 43 Data Recording 43 Data Analysis 44 CHAPTER IV. RESULTS 45 Leap and Keep 4 5 Reading Example: J.V. Ginn Phrases 55 Systematic Replications on Other Reading Leap-Ups 58 Systematic Replications with Math Leap-Ups ... 60 Math Example: Add Facts/Rounding Numbers .... 61 Replications With the Same Math Skills 64 Systematic Replications with Other Math Skills . 64 During Phases 65 Summary of Leap and Keeps 66 Leap and Leave 67 Reading Example: Oral Reading 67 Systematic Replications with Math Skills .... 75 Math Example: Add Facts/2 Digit Addition with Carrying 76 Systematic Replications With Other Math Skills . 76 Summary of Leap and Leave Leap-Ups 78 CHAPTER V. DISCUSSION 79 Experimental Question 79 Leap and Keep Design 79 Leap and Leave Design 81 Summary 82 Replications 82 Replications Across Leap and Keep and Leap and Leave Designs 83 Replications With Studies Already in the Literature 83 IV

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Page Practical Implications 85 Benefits 85 Guidelines 87 Problems and Limitations of the Study 87 Recommendations for Future Research 88 Longer Leap-Up Phases and Fluency 89 Chunk-Ups 8 9 Step Size 90 Strategies for Reducing Errors 91 Anxiety and Resistance to Errors 91 APPENDICES A DEFINITION OF TERI-IS 93 B. ALACHUA COUNTY CRITERIA FOR ELIGIBILITY IN LEARNING DISABILITY, EMOTIONALLY HANDICAPPED, AND EDUCABLY MENTALLY RETARDED CLASSES 99 C. DECISION AND OUTCOME FORM 105 D. RAW DATA: CORRECT AND INCORRECT FREQUENCIES FOR ALL PHASES OF THE LEAP AND KEEP AND LEAP AND LEAVE DESIGNS 107 REFERENCES 131 BIOGRAPHICAL SKETCH 134

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LIST OF TABLES Table Page 1. Review of Selected Studies on Learning Tasks With Initially High Error Rates/Curriculum Leap-Ups 12 2. Demographic Data for Subjects 28 3. Examples of Frequency Multipliers from Preleap-Postleap Comparisions 41 4. Leap and Keep Design: Learning Outcomes by Subject, Teacher, and Skill 46 5. Leap and Keep Design: Frequency Multipliers for All the Preleap-Postleap-Up Comparisons 52 6. Leap and Leap Design: Learning Outcomes by Subject, Teacher, and Skill 68 7. Leap and Leave Design: Frequency Multipliers for All Preleap-Postleap-Up Comparisons 72 2^

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LIST OF FIGURES Figure Page 1. Type One Leap-Ups: Slow Growth 2 9 2. Type Two Leap-Ups: Below Grade Level 3 3. Examples of Dependent Variable Measures 3 2 4. Diagrams of Experimental Arrangements 3 5 5. The Reading Leap and Keep Example 56 6. The Math Leap and Keep Example 62 7. The Reading Leap and Leave Example 74 8. The Math Leap and Keep Example 7 7 vij.

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Abstract of Dissertation Presented to the Graduate School of The University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy THE EFFECTS OF INITIALLY HIGH ERROR TASKS ON SHORT TERM LEARNING FOR MILDLY HANDICAPPED STUDENTS By Michele C. Gerent August 1984 Chairperson: William D. Wolking Major Department: Special Education This investigation compares the learning of mildly handicapped students in initially low and initially high error environments. It studies the effects of curriculum leap-ups on short term learning rates. A curriculum leap-up is defined as an upward curriculum change that results in a student making at least 10% more errors than correct responses. The dependent measures are celerations for correct responses and errors, improvement index, accuracy improvement, and fluency. Frequency (movements per minute) is the basic measure for all the dependent variables. Single subject designs are used to compare the learning rates of students on preleap-up skills with leap-up skills. Both a Leap and Keep and a Leap and Leave Design are used. The Leap and Keep design involves continuing the preleap-up skill when the leap-up skill is introduced. The Leap and vili

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Leave design involves dropping the preleap-up skill when the leap-up skill begins. Sixteen students in elementary and middle school resource room programs were included. The students ranged in age from seven to fourteen. Both reading and m.ath leap-ups were used. Twenty-four of twenty-nine experiments produced effects favoring learning during the leap-up condition. In most experiments celeration for correct responses and errors, the improvement index, and accuracy all increased. Findings for fluency were mixed. Results were replicated across subjects, skills, teachers, and settings. Implications for future placement and instruction, and recommendations for continuing research are presented. IX

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CHAPTER I INTRODUCTION The problem addressed in this study is the relationship between task difficulty and learning outcomes. A review of recent history and the status of programs for mildly handicapped students indicates that what is done instructionally for the mildly handicapped occurs in the context of instructional protectiveness . There is a tendency to avoid placing students in high expectation situations where they might encounter failure (Meyen & Lehr, 1980) . The consequence of this protection from possible failure may also limit opportunities for growth. The use of teaching strategies that fail to challenge students may play a part in accounting for some of the failures and limited successes of programs for the mildly handicapped. Traditionally, instruction in special education has differed from regular education in the use of several important teaching strategies. These strategies include allowing extra time for students to complete their academic assignments, moving more slowly through curriculum sequences, and giving them curricular material on which they achieve initially low error rates. It is obvious that these strategies have both the potential of protecting the learner 1

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from failure, but also of limiting growth. These strategies may also provide indirect messages to learners that could affect their self-concept and general motivation for academic learning. This research explores one of these issues by studying the learning of mildly handicapped students taught in both initially low and high error instructional environments . Significance There are indications that special education is ineffective and inefficient in fostering learning for the mildly handicapped student (Dunn, 1968; Semmel, 1979). Although, there has been a concerted effort by some educators (Deshler, Shumaker, Alley, Warner, & Clark, 1982; Englemann & Carnine, 1982) to develop more effective teaching methods, common practice is that special educators have become overly concerned with the labeling and placement of special education students, rather than in looking for methods that foster their learning. Conclusions from a six-year study of the performance of over 1300 mildly handicapped students (Neely, 1978) revealed that using teaching strategies which allowed the students to make some errors initially and charted daily performance was the most effective way to improve student learning rates. The students' label or whether or not they were taught in special education settings or regular classrooms had no direct bearing on their learning rates. Yet Neely found.

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that in the three school districts he surveyed, the majority of time and effort was spent on the labeling of students and deciding on their placement, rather than on training teachers in using charting and teaching strategies to promote high rate learning. After looking at the current teaching practices in special education classrooms, Glazzard (1984) recommended that special educators should restructure these settings to make them more like general education classrooms. She concluded that in many classrooms special education teachers are limiting the academic growth of their students by continually giving them academic material which is too easy. Also, because of a tendency to use teaching strategies that protect students from failure and emphasize immediate reinforcement, teachers may be limiting the generalization of skill learning to regular classroom settings. Howell, Kaplan, and O'Connell (1979) point out that many of the popular methods for teaching handicapped students actually guarantee that they will remain behind their peers rather than emphasizing strategies that allov/ special education students to "go like mad" in order to catch up. In an effort to implement appropriate instructional programs to meet individual needs, teaching strategies that challenge the learner may have been overlooked by special educators. In many cases the consequence of this may be passive learners who never reach their potential. It may be that our emphasis should be on devising teaching strategies

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that promote rapid learning of material closer to the student's grade placement and potential. There are at least three advantages of rapid learning. One, it allows the special student a good chance of mastering everything which is essential for competing with other students. Two, it raises the special student to the criteria of regular students so that there is no built-in guarantee of future failure. Three, it allows the student, maybe for the first time, to experience the joy of new learning. Tawney and Cast (1984) note that the field of special education faces greater challenges today than it has at any other time in the past. The altruism that provided past impetus for special education programs is gone. Arguments for programs based on equal opportunity interpretations of the Constitution have been overshadowed by the decline of the economy. Programs for the handicapped are increasingly being called upon to justify their existence. Only by implementing a technology of education that uses student learning as a basic datum for justifying its existence can special educators become more accountable to parents of handicapped students and to the public at large. As part of this accountability it is imperative that special educators prove that they have the strategies to help students learn faster and the data to show how it is being done.

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Rationale There is little research on the learning of handicapped students who are given academic tasks with initially high error rates. As an outcome of this special education may be producing students who fail to develop high rate learning skills (the skills that are associated with making many errors initially but reducing them quickly) , or stay on the same skill level for long periods of time without making gains or reaching proficiency levels. A rapidly developing technology of teaching and learning. Precision Teaching (See Appendix A for a definition) , is making it possible for teachers to begin to accumulate data on student learning rates. Average classrooms in America produce around 10% learning per week (O.R. Lindsley personal communication August, 1981), while classrooms that are precision taught average around 25% per week learning (R. Beck personal communication March, 1980) and there are data to show that some precision teachers continually produce 100% learning per week (W.D. Wolking personal communication May, 1983) . But even precision teachers fell into the "easy task" approach to teaching exceptional students. McGreevy, Thomas, Lacy, Krantz, and Salisbury (1982) report that for many years precision teachers charted student performance, while continuing to implement traditional public school curricular strategies. These strategies produced initial correct performances that were relatively high with very few incorrect responses (high

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accuracy) , but subsequent rates of learning remained relatively low. Few teachers introduce skills at levels that provided high error rates. Yet it is at these levels that intensive teaching is most appropriate if students are to experience academic growth. Teaching skills on which accuracy is already high places an emphasis on practice, requiring little of the teacher, other than that opportunities for practice are provided. This type of teaching has the potential of developing bored teachers who become frustrated by the lack of progress of their students. It may also contribute to the high rate of burn-out during a teacher's first few years in the classroom (Wells, Schmid, Algozzine, & Maher, 1984) . In 1978, Lindsley (cited in McGreevy, 1980) began to question the effectiveness of curricular strategies that emphasized highly accurate initial performance and apparently provided less opportunity for learning. Neely (1978), one of Lindsley's students at Kansas, analyzed student learning from four different teaching strategies over a six year period. Results indicated that giving students tasks with initial error rates at 5 to 10 per minute was more effective at producing steeper error decelerations than was giving students tasks with initial error rates below 5 per minute. His study fell short of gathering any conclusive data on another teaching strategy, that of giving students tasks with the initial errors above

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the correct responses, because teachers were reluctant to teach this v;ay in many cases. However, other precision teachers (Bower & Orgal, 1981; Eaton & Whittman, 1982; McGreevy, 1978, 1980; Stromberg & Chappel, 1980) then began to look at the initially high error or leap-up teaching strategy (with initial errors above the correct responses) and data began to accumulate that showed steep celerations for both correct responses and errors resulted when this strategy was used. The investigator in this study became interested in the leap-up teaching strategy for two reasons. First, it is a means for motivating a large group of mildly handicapped students who were making slow progress in special education classrooms. Second, it is a way of training graduate practicum students to use high error teaching strategies in teaching academic skills. The opportunity to investigate the strategy was aided by the fact that graduate practicum students at the university are trained in precision teaching. Statement of the Problem Many special education students fail to make gains or improve very slowly on academic tasks that have initially low error rates. This study explores the relative effects of initially low and high error teaching environments on four dimensions of student performance and learning. A

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change from low-to-high error rates, while holding other features as constant as possible, is called a leap-up. This study extends the work on leap-ups or high error learning by (1) further quantifying the definition of a leap-up first used by McGreevy, Thomas, Lacy, Krantz , and Salisbury (1982), (2) identifying two kinds of leap-ups, (3) extending the sample studied to include elementary age mildly handicapped students, and (4) including more work on reading skills. The design of this investigation is single subject. The teaching strategy of a curricular leap-up is used with students who are not meeting performance standards or who are working on skills below their grade level or both. Question Under Investigation This study examined the effect of curriculum leap-ups on four dimensions of academic performance. The major concern in this study was a comparison of rates of learning under preleap and leap-up conditions. Celeration for corrects and errors, improvement index, and accuracy improvement were compared for the preleap-up and leap-up conditions. Fluency measures were also reported. Definitions of these four measures are listed in Appendix A. Also, a more detailed explanation and a graphic display of their meanings are presented in Chapter 3 under the Measurement section and in Figure 3.

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The following question was investigated: What are the effects of leaping-up to tasks that initially produce at least 10% more errors than correct responses, on celeration, improvement index, accuracy improvement, and fluency? (See Chapter 3 for definitions of preand post-leap-up phases.) Delimitation The subjects in this investigation are elementary and middle school mildly handicapped students; therefore the findings cannot be generalized without systematic replications to mildly handicapped high school students or to normal high school students. Definition of Terms Many technical terms from precision teaching and behavior analysis were used in reporting this investigation. Some of the terms where introduced in this chapter and others will be introduced throughout the study. The terms have all been defined in Appendix A; so the reader may refer to them as needed.

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CHAPTER II PEVIEW OF RELATED LITERATURE This review has two sections. The first section reviews the literature from Precision Teaching on high error learning usually conceptualized under the label of curriculum leap-ups . The second section reviews relevant research and theory on learning with initially high errors from the published work of behavior analysts and learning theorists. Studies from Precision Teaching on Learning Tasks with Initially High Error Rates/ Curriculum Leap-Ups To complete this section all the articles from the Journal of Precision Teaching and "All the Known Precision Teaching/Standard Chart References" (Eshleman, 19 83) were reviewed. "All the Known Precision Teaching/Standard Chart References" is a database of over 700 references pertaining to precision teaching and/or standard celeration charting. It spans the years of 1965 to the present. The database was compiled from all the published and unpublished sources in precision teaching that the author could locate. The references in the database include those found through an ERIC search, journal sources, private sources, presentations from Precision Teaching Conferences and presentations from 10

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11 the Applied Behavior Analysis conferences that dealt with precision teaching. Much of the literature from Precision Teaching is in the form of unpublished work and personal communication because O.R. Lindsley has promoted this approach to professional communication in building a research base. All the Known References from Precision Teaching is continually being updated in order to provide a research base for those conducting research in the Precision Teaching field. The major concern in this investigation was the rate of learning tasks under initially high and initially low error conditions. Precision Teachers have always been interested in the provision of curricular and other environmental arrangements that accelerate the mastery of skills (Bower & Orgal, 1981) . When data began to accumulate that showed that tasks with initially high error rates provided more opportunities for learning (Neely, 1978) , the field began to address the issue. It first looked at tasks that were initially hard to learn (had high error rates) and then moved to the leap-up concept which involves "leaping a student up" to more difficult material. Seven studies were located that addressed the issue of giving students tasks with initially high error rates or of giving them curriculum leap-ups in an attempt to accelerate learning. Table 1 presents a description of these studies beginning with the earliest and moving up to the most recent.

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12

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13

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14

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15

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16

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17

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18 The earliest study that looked at errors as learning opportunities was reported by Neely (1978). The basis for this study was the analysis of six years of data on the learning of students in special education programs. Approximately, 62,820 celerations and 630,000 frequencies v;ere collected from 1300 mildly handicapped students. The analysis looked at three aspects of educational practice. The aspects were a description of reading, the effects of curricula on learning, and the effects of teaching strategies on learning. The last two aspects of this investigation dealt with initial error rates and relate to the hard-to-do or leap-up concept. The results of the analysis across different curricula and teaching strategies indicated that curricula materials that provided students with high initial error rates promoted higher rates of learning than those which had students beginning with relatively few errors. There were also preliminary data that suggested crossover learning pictures (where the errors are initially higher than the corrects) were the most desirable learning pictures to aim for because they produced the fastest learning. Crossover learning pictures were also the most difficult to get teachers to try. In conclusion, Meely suggests that students are being cheated out of a appropriate education if curricula and teaching strategies that promote rapid learning are not implemented in special education classrooms. Choosing a

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19 curricula which has an initially high error rate, viewing errors as learning opportunities, and the daily charting of performance were seen as the most efficient ways to meet high rate learning goals. Further, his study indicates that most basal reading series do not support the concept of high error learning; rather they support the idea that a student needs to be 90-95% correct when initially "learning" a new task. In 1978, McGreevy conducted a two-year study that examined the effectiveness of a remedial resource program which used a traditional "easy skill" approach. One hundred and 22 students labeled as mildly handicapped were involved in the investigation. Seventy five of the students were administered a one minute see-say reading task, and 47 of the students were administered a one minute see-write math task. This was done for ten days. The content of these tasks was grade level specific and corresponded to the district curricula in which the students lived. Initial error rates on these tasks were relatively high. Each day, after the one minute timing, the students were made aware of their errors and verbally supplied with the answers, but no instruction was given. The students were later placed in a remedial program and their progress was monitored with the use of daily timings on remedial reading and math tasks. For reading it was found that students learned more during the screening phase without instruction than they did during the

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20 remediation phase. For math, the results showed the same amount of learning had taken place during both phases. Conclusions drawn from this study were that the easy tasks used during the remedial program did not allow enough room for growth (initial errors on the tasks were too low) , and that the remedial program was ineffective in providing for a high rate of learner change. This appears to be a common occurrence in many programs where students are placed on relatively easy skill levels as a means of "remediating their skill deficits." They frequently make slow gains because of the "easy task" approach. In McGreevy's (1980) second project, an eighteen year old moderately retarded boy was given a see-say task (see the word, say the word) on the first 29 words of Wilson's essential vocabulary. The initial frequencies indicated that the task was very difficult for the student — he began by making many more errors than corrects. But he learned the task easily — his correct rate went up quickly and his error rate v/ent down quickly. In other words, the task was "hard-to-do" initially, but "easy-to-learn. " Stromberg and Chappell (1980) attempted to teach an entire second grade class a math curriculum at a pace suggested by the adopted math text. Pairing the text with precision teaching methods (daily timings and the use of probes) resulted in the students achieving initially high correct rates while they made almost no errors. The students learned the material at an acceptable rate. After

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O 1 4 months the investigators "leaped-up" the entire class to all the math operations contained in the second grade math book by giving the students mixed worksheets (problems with all the operations to be learned in the second grade on them) . This leap up in curriculum produced lower initial performance for correct responses with the students making a lot of errors. However, results of learning measures indicated that the students learned the material very rapidly. Conclusions were that following logical curriculum sequences may unnecessarily slow students down, and that students should be challenged to see how fast they can learn. Bower and Orgal (1981) used the concept of high error learning with college students. They set very high aims for the students to meet in learning psychology terms. The students were told to learn all the terms at one time and not to be concerned with their high initial error rates. Results indicated that the students' high initial error rates led to steep celerations (rapid learning) and satisfactory accuracy and fluency rates at the end of the course. Conclusions were that students can learn to view errors as learning opportunities instead of something to be avoided. Another investigation by McGreevy, Thomas, Lacy, Krantz, and Salisbury (1982) found that neither learning nor variability can be predicted from low initial performance by students. These conclusions were based on the data from the learning of difficult tasks by 24 severely handicapped students over a four week period. In order to qualify as a

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22 difficult task, there had to be at least 10% more errors than correct responses on the initial timing the student took on a task. Sixty-six tasks met this criterion and were then divided into those that were hard-to-do and those that were extremely-hard-to-do depending on how many errors the student initially made on them. The results of several comparisons between the two groups of tasks clearly indicated that, although the difficulty range varied within the range of hard tasks, there was no relationship between how hard the task was initially and the rate of learning or variability (bounce of the performance) . The students learned all the tasks at fairly high rates even when they began with only one or two corrects and many errors. The most recent investigation which used the leap-up approach was done by Eaton and Wittman (1982). This investigation examined the effects of the leap-up teaching strategy on the learning rates of three learning disabled junior high school students. All three students were accurate in performance of the multiplication and division tables but were not meeting fluency aims (not doing the problems quickly enough) . They were considered "reluctant learners" by the investigators who wanted them to move :nDr'5 quickly through the math curriculum. When they v^-er-^ cive:; a leap-up to fractions where their initial error rates were high, they all responded well by increasing their rate of learning. Eventually they all began to meet fluency aims.

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23 Conclusions were that the leap-up approach appears to be an effective way to motivate students with slow growth learning and that special education teachers should guard against using small curriculum steps in teaching students who are not meeting fluency aims. Studies from Applied Behavior Analysis and Learning Theory on Learning Tasks with Initially High Error Rates The intent in this section was to review teaching strategies from the applied behavior analysis and learning theory that allowed mildly handicapped students to experience learning tasks with initially high error rates, or tasks that were hard for them in the beginning stages. A computer search using the key words applied behavior analysis, learning theory, high error learning, difficult tasks, teaching strategies, curriculum strategies, mildly handicapped students (EM, LD , BD) was done. Also, a search using the same key words was done in the Exceptional Child Index , CUE , Education Index , and the Annual Review of Psychology for the years 1974 to 1983. No studies were located. Since the first searchers were unproductive, a search of the titles in the table of contents was completed for the Journal of Learning Disabilities , LD Quarterly , Teaching Exceptional Students , The Journal of Applied Behavior Analysis , and Exceptional Education Quarterly . This search reviewed titles from these journals for the years 1975 to

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24 present. The same key words as in the computer and indices searches were used. Again, no studies were located. It appears there is little, if any, research on this topic. Summary Research evidence that normal learners as well as handicapped learners have more opportunities for learning when they are placed in "high error" generating situations is beginning to accumulate. Precision teaching techniques that emphasize this approach are curriculum leap-ups and hard-to-do tasks. There is growing evidence that these strategies may be successful with handicapped and nonhandicapped students as well as with adults. The hard-to-do or leap-up approach to learning represents a change from the traditional approach of giving students tasks with initially low error rates. Studies using precision teaching have shown that (1) errors can serve as learning opportunities, (2) curriculum leap-ups and hard-to-do tasks are effective ways of increasing student performance, (3) motivation for learning may be improved by giving "reluctant learners" curriculum leap-ups, (4) teaching and learning in initially high error learning environmental need further study. A search of the research literature from Applied Behavior Analysis and learning theory failed to locate any

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25 studies which looked at the learning of mildly handicapped students in high error environments. Continued research in naturalistic settings is needed to validate strategies that promote initially high error learning. Special educators need to expand their knowledge of the motivating factors of hard-to-do tasks for populations of students who are accustomed to being presented relatively easy tasks under the guise of remediation and protection from failure and its pressures.

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CHAPTER III METHOD This work attempts to advance the understanding of teaching and learning under high initial error conditions while teaching mildly handicapped students. This experiment investigated the effects of curriculum leap-ups on four learning outcomes. Specifically, the effects on celeration, improvement index, accuracy improvement, and fluency were explored. The study was a series of clinical investigations conducted in ongoing classrooms with graduate practicum students serving as teachers. Setting The study was carried out in Alachua County, a northcentral Florida school district of 22,000 students. The system has special education resource and/or self-contained rooms in all elementary and middle schools. The data were gathered by the investigator and by graduate students as part of their practicum assignment in resource rooms for the mildly handicapped. The typical student teacher was individualizing instruction on about 25 separate skills at any one time. The skills that v/ere taught were chosen to 2L,

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27 satisfy the Individual Education Plan (lEP) for each students as determined by the special education teachex" and the student teacher jointly. Teaching procedures were selected with the idea of maximizing student learning. Subjects There were sixteen subjects in this investigation. The subjects were all learning disabled, emotionally handicapped, severely language impaired, or educably mentally retarded students. They ranged in age from 7-14. Ten were males and six were females. One subject attended a selfcontained program for the severely language impaired, five attended an elementary school resource room program for the mildly handicapped, and ten attended a middle school resource room program for the mildly handicapped. See Table 2 for demographic data on the subjects. All subjects in the study met the Department of Education and the local school district special education placement guidelines (See Appendix B) . Subjects chosen to participate in the experiments met the criteria for type one or type two leap-ups or both. See Figures 1 and 2 for the rationale and criteria for each type of leap-up. Type One leap-ups were used with learners who were making little or no progress in meeting performance standards. Type Two leap-ups were used to allow students working on below grade level skills to experience learning at or near their grade level placement.

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28 Table 2 Demographic Data for Subjects Subject Sex Grade Exceptionality Age Race Teacher 1.

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30 S StiOOti QUOOiU s z i _ cs

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31 Variables Under Investigation Dependent Variables The four dependent variables in this investigation were celeration, improvement index, accuracy improvement, and fluency. All are measures of academic performance. Previous work indicates that celeration, accuracy, and fluency are sensitive dimensions (Koenig, 1972) likely to detect changes in the independent variable being manipulated. The improvement index was included because it is a convenient way of looking at the celeration for correct responses and errors at one time. Figure 3 presents an example of each of the dependent variables. The figure illustrates both a preleap-up and leap-up phase. Figure 3 and the measures used in this investigation are explained fully under the measurement section of this chapter. Independent Variable The independent variable is a curriculum leap-up (See Figures 1 and 2). A curriculum leap-up is a change from a skill with an initially low error rate to a skill with an initially high error rate. The size of a leap-up depends on the individual subject, rather than on the skill. For some subjects a leap to the next level in a curriculum ladder met the error requirements; for others a much larger leap up the curriculum ladder was required in order for the error

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32 y ^ y V c

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33 criteria to be met. Both Slow Growth and Below Grade level types of leap-ups, as mentioned under the subject section, were used. Experimental Design The experimental design in this study is single subject. Single subject designs make it feasible to demonstrate within subject control because the unit of analysis is the individual. Replications across subjects, teachers, skills, and settings were done to demonstrate the reliability and generality of the findings (Tawney & Gast, 1984). This investigation presented a special design challenge. In educational settings, designs that require the repeated v/ithdrawal or reversal of the independent variable may not be practical (Tawney & Gast, 1984) . In these experiments, it is not meaningful to return to a baseline after a leap-up because the student is learning new material during the leap-up. The designs used in this investigation do not completely fit any of the standard design descriptions. They do have elements in common with the AB, multiple baseline, and alternating treatment designs. The two designs used in this investigation meet the unique needs of the real world teaching situation (Alberto & Troutman, 1982; Haring, Levitt, Eaton, & Hansen, 1978). They are referred to as Leap and Keep and Leap and Leave designs.

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34 Leap and Keep Design The Leap and Keep designs are illustrated in Figure 4. Every vertical line (change line) gives the opportunity to observe an experimental effect. Because the baseline A is continued when the treatment B is introduced, the design controls for maturation and correlated historical variables. Leap and Leave Design The Leap and Leave designs are illustrated in Figure 4, There is one opportunity (change line) with this design for an experimental effect to be observed. This design is most like the AB design. The AB design provides a structure for drawing experimentally valid conclusions when certain conditions are met (Tawney & Cast, 1984) . Optimal conditions include (1) Behaviorally defined target behavior. (2) Collection of continuous baseline data (at least 3 days) . (3) Introduction of the independent variable only after the baseline trend is stabilized. (4) Continuous collection of baseline data on the target behavior during the intervention. (5) Replicate the experimental effects with similar subjects. This design can provide a convincing demonstration that outcomes are not a function of other variables (time, maturation, experience, unobserved correlated events) when

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35 Leap and Keep (1) Leap 1 PL (2) (3) (4) PL (5) PL During Leap 1 PL I During Leap 1 r PL 1 During Leap 1 During 1 Leap 2 Leap 3 Leap 2 Leap 2 J"" During 2 Leap 2 Leap 1 During 1 Leap 3 During 2 During 3 Leap and Leave (6) Leap 1 PL (7) Leap 2 Leap 1 J PL Figure 4. Diagrams of Experimental Arrangements

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36 behavioral changes measured following the intervention are iiranediate and abrupt following a stable baseline. Conclusions drawn by AE designs may be limited by threats to internal validity and/or external validity. The lack of data on the natural course of the preleap-up behavior during the intervention phase or a novelty affect were concerns in this experiment. Therefore, several replications were done. Several replications of the experimental effect with this design are usually quite convincing. The design has certainly served very well in medicine over the past 150 years. Procedure Pre-experimental Phase During this phase the practicum teachers received training in identifying students and skills for the leap-up strategy during their weekly practicum sessions. They were also trained in using the Decision and Outcome form and in using the quarter intersect method to draw learning lines. With the aid of the investigator pinpoints for possible leap-ups were selected. Techniques for teaching in high initial error environments were discussed. Experimental Phase During this phase the practicum teachers selected students to participate in the investigation according to

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37 the criteria for the two types of leap-ups and gathered the daily data for inclusion in the investigation. The following procedure was used for Leap and Keep experiments. 1. Students whose learning met the criteria for a Slow Growth or Below Grade Level leap-up were chosen to participate in the investigation. 2. A stable baseline on the preleap-up phase was verified with the investigator. 3. A skill related to the preleap-up skill but higher in the curriculum sequence was chosen for the student. The skill had to meet the requirement of having initially 10% more errors than correct responses or another skill was tried. 4. Both the preleap-up skill and the leap-up skill were continued. Daily timings were taken and charted on both skills. The leap-up skills were continued until experimental results were seen or an aim was met. 5. In some instances one or more additional leap-up skills were also added, making within teacher, learner, and skill replication possible. The procedure for the experimental phase for the Leap and Leave investigations was identical to the above procedure with one exception. In Step 4 the preleap-up skill was dropped when the leap-up skill was started with a student.

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38 The Leap and Keep and Leap and Leave field experiments by the practicum students were monitored by the investigator both in the classroom and in weekly chart share sessions. At the end of the investigation the teachers discussed their teaching procedures and results on the leap-up skills with the investigator. Materials Curricular Materials The curricular materials used were based on the students' current academic program. Resource rooms in Alachua County use county adopted materials for each grade level along with remedial materials. Materials currently used include the Ginn and SRA reading series and the Heath math program. Most teachers used adaptations of the materials for precision teachers available from the Alachua Learning and Resource Center. Data Recording Form The Decision and Outcome Form was used to record all the specifics of the program and the outcomes. The information on the Form was combined with the charted data to obtain a complete picture of the learning in each phase. See Appendix C for a copy of the form.

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39 Standard Celeration Chart The Standard Celeration Chart (Pennypacker , Koenig, & Lindsley, 1972) was used to display and analyze all the data from the investigation. Precision teachers have made an attempt to standardize graphic displays of data by using this chart. Measurement Frequency, movements per minute (Pennypacker, Koenig, & Lindsley, 1972) was chosen as the basic unit of measurement in this investigation. For many academic and social behaviors, frequency yields more informations than other standard educational measurements (Haring, Lovitt, Eaton, & Hasen, 1978). Frequency, when used to measure both correct responses and errors, gives a measure of both the accuracy and fluency of a student's performance. Fluency, the rate at which a student performs a skill, is often the discriminating factor between a student who is acquiring a skill and one who is proficient at a skill. Percent scores, most often used in educational settings, provide only a measure of the accuracy of a student's performance and give no indication of fluency. When using percent data there is no way to discriminate between the student who is just accurate and the student who is both accurate and proficient. For example, if one student completes 50 math facts (100 digits) correctly in 20 minutes with no errors he is accurate but not proficient. If another one completes 50 math facts

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40 (100 digits) correctly in 1 minute he is both accurate and proficient. Frequency multipliers (the ratio between two frequencies) were used to analyze the data from this study. A frequency multiplier can be visualized as the distance between two frequencies on the Standard Celeration Chart. There are two levels of frequency multipliers. The first level is a ratio comparison between two frequencies on the chart. The second level is a comparisons between two ratios. Both types were used in this study and are illustrated below. Figure 3 presents the data from a sample preleap-up and leap-up phase. The name of the behavior being measured, the formula for calculating it, and the value of the behavior being measured are given. If a multiplication sign (x) precedes the value, it indicates that the frequency of the behavior was accelerating. If a division sign (/) precedes the value, it indicates that the frequency of the behavior was decelerating. In Figure 3 the initial frequencies for correct responses and errors and the value for each of the dependent measures in this study were calculated for both the preleap-up and leap-up phases. These values were then used as the basis for the ratio comparisons done in Table 3. In Figure 3, A and B represent the initial frequency for the corrects and errors in the two phases. The initial frequency is the point where the learning lines (one for correct responses, one for errors) cross the first day line

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Table 3 Examples of Frequency Multipliers from Preleap-Postleap Comparisons 41 Measure Value Multiplier Preleap-Up Leap-Up Celeration For Correct Responses Celeration For Errors Improvement Index Accuracy Improvement Final Performance For Correct Responses Final Performance For Errors xl.15 xl.OO xl.15 xl.62 52 X8.40 /5.80 x50 xl60 60 X7.30 x5.80 x43 x99 xl.15 xl.OO

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42 in a phase. The letters C and D represent the final frequencies for correct responses and errors on the learning lines. The final frequency is also know as fluency. The letters E and F mark the celerations for corrects and errors. The unit for celeration is movements per minute per week. It describes the rate at which frequencies change in a week. Celeration is also called learning. The letter G represents the improvement index. The improvement index is a ratio between the celeration for the corrects and the celeration for the errors. The measure conveniently summarizes improvement in correct and error responding into one number. Graphically, it can be visualized as the size of the angle between the celeration for the corrects and celeration for the errors. The letter H represents accuracy improvement. Accuracy improvement is calculated by determining the ratio of the corrects to the errors at the beginning of a phase, and then comparing that value to the ratio of the corrects to the errors at the end of a phase. It is a measure of change in accuracy over time. Table 3 presents the values for the comparisons between the preleap-up and the leap-up phases in Figure 3. These ratios are always calculated by dividing the smaller frequency into the larger frequency. For example, in the comparison for celerations for corrects in Table 3 the frequency multiplier is a x7.30. This was calculated by dividing x8.40 (c for corrects for leap-up phase) by xl.l5

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43 (c for corrects for preleap-up phase) . The x sign indicates that the rate of learning was in favor of the leap-up phase. V7ithin the field of precisionteaching there are, unfortunately, two ways in which the multiply and divide sign are used. The signs may be used to identify movement on the chart: x for acceleration and / for deceleration. The sign may also be used to signify the direction of an experimental effect: x for an increase, and / for a decrease by the indicated factor. For making comparisons in this investigation, the x sign before the frequency multiplier was used to indicate that the leap-up phase is better than the preleap-up phase on the comparison measure. The / sign was used to indicate that the leap-up phase worsened by the factor indicated on the comparison measure. Date Recording and Analysis Data Recording Daily data were recorded on the Academic Behavior Chart-3 (Wolking, 1983) by the practicum teachers and their students. Each time a phase change was made the data for the completed phase was recorded on the Decision and Outcome sheets by the teachers and the forms were given to the investigator. For purposes of analysis, the data from the preleap-up and leap-ups were plotted on the Standard Behavior Chart

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44 using frequency for correct responses and errors. This allov/ed for visual analysis of the preleap-up and leap-up phases of learning. The scale on the Standard Behavior chart is a ratio scale. Most measurement in educational research occurs at the nominal, ordinal, and interval levels because it is difficult to find variables that lend themselves to ratio measurements (Glass & Stanley, 1970) . Ratio scales are considered to be the most sensitive scales of measurement because they allow for interval comparison and for an absolute zero — which indicates the total absence of the movement being measured. Further, plots of human behavior frequencies, as they change over time, on a ratio scale, tend to be linear and thus permit relatively easy predictions (Pennypacker , 1974) . Data Analysis Visual inspection of all the data and frequency multipliers were both used for data analysis. Frequency multipliers add quantification to the visual inspection procedure by making it easier to compare results across subjects, settings, skills, and teachers. No test of statistical significance exists for these ratios. Rather, they are evaluated in the context of expert judgment of their practical importance.

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CHAPTER IV RESULTS The results for the two types of leap-ups, Leap and Keep and Leap and Leave, are presented separately. An example of a reading leap-up and a math leap-up are presented in detail for each type. Other cases are presented as replications within each type of experimental condition. Leap and Keep The results for the Leap and Keep experiments are presented in two tables. Table 4 is a summary of all the data on the Leap and Keeps. Leap and Keep leap-ups involve continuing the preleap-up phase after the introduction of a leap-up. Both skills are taught and measured daily. Eight subjects and five teachers in five settings were included in the Leap and Keep experiments. The subjects experienced sixteen leap-ups. Eight of the leap-ups were reading related and eight were on math skills. The four dependent variables (celeration for correct responses and errors, improvement index, accuracy improvement, and fluency) were determined for each preleap-up, during, and leap-up phase. Preleap-up phases include all the data taken before a leap-up began. During phases 11

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46 (0 Eh CG c (0 o n) 0) Eh O i 0) (U e o o -p 3 o a •H c u O -P -H (T3 O C o c o u CO dJ = a; a, >i Eh U (U J= U rc QJ Eh I 4-> o 0) o m m o X -l (C > 0) )-l 0) m a h^i OS 1-3 O
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47

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48

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49

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50

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51 include all the data from the continuation of the preleap-up skill after the introduction of the leap-up skill, and leap-up phases include all the data from the leap-up skill. The number of data points in each phase and whether the leap-up was a Slow Growth or Below Grade Level leap-up are also reported in Table 4. Following is a brief explanation of how to read the results presented in Table 5. Table 5 presents comparisons between the celerations, improvement index, accuracy improvement, and fluency for the preleap-up, during, and leap-up phases. The comparisons were done using frequency multipliers. If the change represents an improvement, the value is assigned a multiplication sign (x) . If it represents a worsening situation, the value is assigned a division sign (/ ) . By subtracting 1 from the frequency multiplier, and moving the decimal point 2 places to the right, comparisons between the phases can be discussed as percentages. Looking at the first leap-up in Table 5, for subject W.T., the frequency multiplier for the celerations for the correct responses between the preleap-up and the first leap-up phase is a xl.24. This means that the correct responses accelerated 24% faster in the leap-up phase than in the preleap-up phase. For the error celeration the frequency multiplier is /1. 04. This means that the errors decelerated 4% slower in the leap-up phase than in the preleap-up phase. For the improvement index the frequency multiplier indicates that

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53

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55 the leap-up phase was improving 38% faster, while accuracy improvement was 391% better for the leap-up phase. Fluency was 10% better for the correct responses and 6% better for the errors in the preleap-up phase, compared with the leap-up phase. Reading Experiment: J.V. Ginn Phrases J.V. was a 5th grade student classified as emotionally disturbed. He was working on Ginn level 7 phrases and vocabulary. The teacher decided to leap J.V. up to a higher level of Ginn (see Figure 5) because he was working below his grade level placement and had expressed an interest in doing "harder work." His preleap-up celeration for correct responses indicated that he was progressing at 23% per week, while his errors were going down at 82% per week (see Table 4) . For J.V. a leap-up to Ginn Level 8 produced the required error rate of 10% more errors than correct responses. Table 5 shows the comparison between the preleap-up phase for J.V. on Level 7 Ginn and three separate leap-ups to Level 8 Ginn. The celeration for the correct responses was 18% faster for the first leap-up, 51% faster for the second leap-up, and 95% faster for the third leap-up when compared to the preleap-up phase. For error deceleration, the effect of the leap-up teaching strategy grows as the teacher learns to teach to errors. In the first leap-up, the error celeration was 25% faster during the preleap-up

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56 28 Days 35 T»«eh»t _S L_ PT»i»«piioTMT»««_s^ . Say Glnn Phrases, level 7. DoTifi^ 1 .Level 7, new phrases s#(tif
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57 .%> 500 200 100 50 r R E 20 q u f 10 N c V 3 We

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58 phase. During the second leap-up it was 65% faster for the leap-up phase, and for the third leap-up, it was 153% faster for the leap-up phase. The improvement index was almost equal for the first leap-up, but much faster for the leap-up phases in leaps two and three. The improvement index for the first leap-up was 6% faster for the preleap-up phase, the second was 149% faster for the leap-up phase, and the third was 393% faster for the leap-up phase. Accuracy improvement across the three leap-up phases was much better for the leap-up phases than for the preleap-up phase ranging from 58% to 1300% better. J.V. obtained better fluency in the preleap-up phase for two of the three leap-ups. When comparing the 3 leap-ups to the during phases the findings for celeration, improvement index, and accuracy ratio were similar to the preleap-up comparisons. The leap-up phases provided faster celerations, more improvement, and higher accuracy improvement. Fluency was better in the during phase for the first leap-up, but better in the leap-up phases for the second and third leap-ups. Systematic Replications on Other Reading Leap-Ups Similar results were found for subject W.T., a first grade EMR student in a resource room. This subject experienced two leap-ups (see Table 4). The preleap-up phase was learning to say the alphabet and the two leap-ups were to

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59 Ginn Level 2 and then Ginn Level 5 vocabulary. Her beginning celerations for the preleap-up phase indicated slow growth for correct responses and a fairly good deceleration of errors (see Table 4). Results were similar to J.V.'s results. Here celerations for correct responses were steeper in both leap-up phases. Error deceleration was almost equal for the comparison between the first preleap-up and leap-up phases and 9% faster for the leap-up phase during the second leap-up. The improvement index was faster and accuracy improvement was higher for both leap-ups . Fluency was better during the preleap-up phase when compared with the first leap-up, but better in the leap-up phase for the second. For D.P., a 5th grade learning disabled student working on Ginn vocabulary and phrases, mixed results were obtained. But the findings were generally in favor of the preleap-up phases. D.P. was given two grade level leap-ups from Ginn Level 8 to Ginn Level 11 vocabulary. His rate of learning was already quite high on his preleap-up phase (see Table 4). For the two leap-ups, celeration for correct responses was 7% in favor of the preleap-up phase for the first leap-up and 14% in favor of the preleap-up phase during the second leap-up. Error deceleration was faster for the preleap-up phases. It was 73% faster for the first leap-up and 40% faster for the second-leap-up in favor of the preleap phases. The improvement index and accuracy

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60 improvement measures were also better for the preleap-up phase. On the reading phrases the preleap-up rate of learning was also greater. In D.P.'s case his preleap-up condition was unique in that his correct and error celerations were both very high before the leap-up. Although these results favor the preleap condition, it is important to note that D.P. continues to learn very well on the Level 11 Ginn phrases, an increase in three levels over the preleap material. Systematic Replications with Math Leap-ups The comparisons for N.R., an educably mentally retarded student, were similar to J.V.'s results (see Table 5). In his first leap-up all the measures for rate of learning were better for the leap-up phase except error deceleration which was 20% in favor of the preleap-up phase. In his second leap-up all the measures for learning increased dramatically in favor of the leap-up phase including error deceleration. Results show that acceleration for corrects was better by a factor of 175, error deceleration was better by a factor of 11, the improvement index was 1960 times better, and accuracy improvement was 57 times better during the leap-up phase. Fluency was better in the preleap-up phase for the first leap-up, and for the leap-up phase for the second leap-up.

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61 A.K., an emotionally handicapped student, C.J., an educably mentally retarded student, and G.R. and Y.B., learning disabled students, were given a total of six math leap-ups . They all showed an increase in learning following the leap-up condition for celeration, growth, and accuracy improvement (see Table 5) . Results show that celerations for increasing correct responses and decreasing errors were higher, improvement was faster, and accuracy improvement was higher. Fluency was better for two of the leap-ups when compared with the preleap condition and for two of the leap-ups when compared with the during conditions. Math Example: Add Facts /Rounding Numbers C.J., a middle school educably mentally retarded student, was given a leap-up from add facts to rounding numbers (see Figure 6) . C.J. had been working on add facts in order to build up her fluency in adding number facts. Her celeration for corrects was a xl.03 and for errors a xl.O. It was decided to leap-up because her progress was slow and she was bored practicing the facts. A comparison of the celerations for the two phases (see Table 5) for her first leap-up show that the leap-up condition produced faster celeration for the corrects by a factor of 2 and errors were reduced faster by a factor of 8. The improvement index and accuracy improvement v/ere improved by factors of 17 and 27 respectively. Fluency was 4% better

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62 \y r 500 200 100 50 20 10 2 sy # f Week

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63 f sV^/ 9' r < sy .\3^ ,V I >A^ s^> (

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64 for the leap-up phase. Results from the during phase comparison were very similar. Two more leap-ups were then done with C.J. in order to replicate the experimental effects within subject. They were two place addition with carrying and two place subtraction with borrowing. Both leap-ups showed an increased rate of learning as measured by celeration, improvement index and accuracy improvement similar to the first leap-up. Both leap-up phases were short. Fluency was higher for corrects during the preleap-up condition and was the same for errors across both conditions. Replications With the Same Math Skills Two of the leap-ups from C.S. were replicated with another student, N.R., an EMR student was given a leap-up from add facts to rounding numbers. Results were similar to C.J.'s. Her comparisons for celeration for correct responses, improvement index, and accuracy improvement, and fluency were all higher in the leap-up phase when compared with the preleap-up or during phase. Her second leap-up to subtraction with borrowing also resulted in higher rates of learning on all the measures including error deceleration. Celeration, improvement index, and accuracy improvement were all better in the leap-up phase while fluency was better in the preleap-up phase. Her error decelerations were not as high as C.J.'s.

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65 Systematic Replications with Other Math Skills Three other leap-ups were done with students on math skills. The first one was a leap-up for A.K., an elementary emotionally handicapped student. The leap was from add facts to 2-digit adding with carrying. His celeration, improvement index and accuracy improvement increased during the leap-up phase but his fluency level was lower. G.R., an emotionally handicapped student, was given a leap-up from multiplication facts to square roots. His learning on the leap-up skill was faster on all measures including fluency. Another student, Y.B., v/as given a leap-up from multiplication facts to one place division. Her learning rates were better on all measures except celeration for correct responses. Fluency was better in the preleap-up phase. During Phases The Leap and Keep Design controls for maturation and correlated historical events by continuing the preleap-up phase when the leap-up begins. The results from these experiments indicate that learning rates were faster as measured by celeration for correct responses and errors, improvement index, and accuracy improvement during the leap-up phases compared with the during phases. These results were replicated 9 times across subjects, skills, teachers, and settings. Fluency for correct responses was generally in favor of the during phases compared with the leap-up phases, and fluency for errors was mixed, some of

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66 the leap-up phases achieving higher fluency and some of the during phases achieving better results for errors. These results indicate that maturation and outside events were not responsible for the higher rate of learning during the leap-up condition. Summary of Leap and Keeps A total of 16 Leap and Keep Leap-ups were done with 8 students. Nineteen of twenty-eight comparisons across all the preleap-up, during, and leap-up phases showed an increase in student rate of learning as measured by celeration, improvement index, and accuracy improvement in the leap-up phase. Three of the comparisons indicated better error deceleration for the preleap-up phases, which was subsequently followed by additional leap-ups with the same students in which the errors decelerated more rapidly in the leap-up phases. For one comparison, the celeration for correct responses was better for the preleap-up phase, but all other measures were better for the leap-up phases. Five comparisons were in favor of the preleap-up phases on rate of learning comparisons. These were all reading leap-ups in which the student began with high initial acceleration for correct responses and deceleration for errors. The results for the fluency measure were mixed with some of the preleap-up and during phases achieving a higher terminal frequency than the leap-up phases.

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67 The findings that the leap-up teaching strategy produces a higher rate of learning as measured by celeration for correct responses and errors, improvement index, and accuracy improvement was replicated across 3 teachers, 3 settings, 6 students, and 9 skills using the Leap and Keep Design. Possible factors involved in replication failures will be discussed in the next chapter. Leap and Leave Table 6 presents a summary of all the data on the Lean and Leave experiments. Leap and Leave leap-ups use the procedure of dropping the skill with low error rate when the leap-up skill starts. Nine subjects and five teachers in five settings were included in the Leap and Leave experiments. The subjects experienced 13 leap-ups. Two of the leap-ups were on reading skills and the other eleven were math skills. The five dependent measures are presented for each preleap-up and leap-up phase. The number of data points in the phase and whether the leap-up is a Slow Growth or Below Grade Level leap-up are also given. Table 7 presents the comparisons between the celerations, improvement index, accuracy improvement, and fluency for the preleap-up and leap-up phases. The comparisons were done using frequency multipliers, as in Table 5.

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68 CO c o (Ct Eh o (U o i3 3 CO >i J3 CO OJ E o o -p 3 O t3l H u 1-^ c en •H (0 0) Q > (0 (U J -o c a 1^ Cm u Hi o a o e < H e c H M tn O 4J -H (C o c -H +J •H -u c o u •H 0) =«= a; >i Eh u x: u (d (1) S-l 0) CQ O i-q o CO in 3 I O. (T3 U O 13 m o n

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69

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71

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73 o c a 3 u s < M 0) e c a c o •H 4-1 u 0) u u X

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74 Reading Example: Oral Reading E.B., an elementary school language disabled student, was given a leap-up from a first grade reading book to a college level astronomy text (see Figure 7). Several leaps to lower level reading material were tried but the error rate criteria could only be reached at this level. The preleap-up phase had a correct celeration of xl.42 and an error celeration of xl.OO. A comparison of the celerations for the two phases (see Table 7) shows that the leap-up condition was better by a factor of 17 for the correct responses and a factor of 11 for the errors. The improvement index was better by a factor of 186 and accuracy improvement was better by a factor of more than 4. Fluency was 38% better for the preleap-up phase for correct responses and it doubled for the errors. E.B.'s second leap-up on reading vocabulary produced similar results. Systematic Replications with Math Skills Eleven math replications of leap and leaves replicated the findings of E.B.'s leap-up. Three leap-ups in math were done for L.A. , a middle school learning disabled student. The three leap-ups had faster celeration for correct responses by factors of 10, 3.3, and 14 and for errors by 4.19, 6.19, and 16. The improvement index for the three leap-ups ranged from a factor of 20 to a factor of 125 better. Accuracy improvement ranged from a factor of a

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75 c

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76 little more than 2 to a factor of 24 better. Fluency was better in the preleap-up phases. Four other leap-ups with middle school students R.V. , A.F., O.S., and R.J. had similar results. Although the celerations for the correct responses were not as fast as E.B.'s leap-up, the other measures were comparable. Further, students who experienced two math leap-ups had faster learning as measured by celeration, improvement index, and accuracy improvement and also had higher fluency in their leap-up phases compared with their preleap-up phases . Math Example; Add Facts/2 Digit Addition with Carrying W.T. , a mentally retarded student, was given a leap-up from learning add facts to 6 to doing two place addition with carrying (see Figure 8) . Her preleap-up phase had a correct celeration at xl.39 and error celeration at xl.46. She was not achieving fluency on the addition facts even though her errors were going down. A comparison of the celerations for the two phases (see Table 7) shows that the leap-up phase produced faster celeration for the corrects by a factor of 13 and that the error-learning improved by a factor of 5.4. The improvement index was better by x78 , while accuracy improvement was better by a factor of 67 in the leap-up phase. Fluency was also higher in the leap-up phase.

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77 .S> •SiY 500 200 100 50 f R E 20 q u E 10 H C V 3 f vs. 4 .^' Weeks

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78 Systematic Replications With Other Math Skills One math leap-up replicated the findings on all the measures of W.T.'s leap-up. Comparisons for R.J.'s leap-up (see Table 7) show that the celeration for the correct responses was 55% faster and improved error learning by a factor of 2.4 during the leap-up phase. The improvement index was better by x3 . 7 and accuracy improvement was better by a factor of 6.6. Fluency for correct responses was 11% better for the leap-up phase than for the preleap-up phase. Nine math leap-ups replicated the findings of W.T.'s leap-up on all the measures except fluency. A comparison of the celerations for the correct responses shows that the leap-up phases produced better learning by factors between 1.3 and 16.8. Errors learning improved by factors between 1.5 and 58.3. The improvement index was better by factors between 1.9 and 615. Accuracy improvement changed by factors between 2.1 and 1659. Fluency was better in the preleap-up phases. The range for fluency was between xl.3 and xll in favor of the preleap-up phases. Summary of Leap and Leave Leap-Ups A total of 13 Leap and Leave leap-ups were done with 8 students. Across all the preleap-ups and leap-up phases results show an increase in student rate of learning as measured by celeration, improvement index, and accuracy improvement. Three of the leap-ups resulted in higher fluency for the leap-up phase compared with the preleap-up

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79 phase, while the remaining 10 leap-ups produced higher fluency during the preleap-up phases. The findings that the leap-up teaching strategy produces a higher rate of learning as measured by celeration for correct responses and errors, improvement index, and accuracy improvement were replicated across 4 teachers, 4 settings, 8 students, and 12 skills using the Leap and Leave Design.

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CHAPTER V DISCUSSION The discussion is organized around the experimental question, replications and previous knowledge, practical implications for special education and regular education, problems and limitations of the study, and recommendations for future research. Experimental Question Leap and Keep Design Celeration, improvement index, and accuracy improvement . The findings of this study suggest that the curriculum leap-up can be an effective teaching strategy for elementary and middle school students in special education resource rooms who are not making gains on lower level materials. Leap-ups to skills with initially high error rates generally produced faster learning as measured by celeration, improvement index, and accuracy improvement. There is also evidence to suggest that this teaching strategy can benefit students who are making gains on below grade level material. Results indicate that when a student 80

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81 is experiencing medium to rapid growth on below grade level skills, leap-ups may not accelerate learning above the preleap-up phase, but can produce medium to high rate learning on the leap-up skill. There were also some indications of "learning to learn" and "learning to teach" occurrences during these experiments. In three cases in particular students and teachers did better decelerating errors on each successive leap-up. Fluency . In looking across all the frequency multipliers (see Table 4) for the preleap, during, and leap-up phases, fluency for correct responses was split fairly evenly between the preleap and during phases compared with the leap-up phases. In over half, the fluency for the errors reached zero across the preleap-up, during, and leap-up phases. In the remaining leap-ups fluency was generally in favor of the preleap-up phases. Achieving fluency is a matter of how long the leap-up continues. In some cases the student failed to reach higher fluency on the leap-up skill because the teacher dropped the skill as soon as the data stabilized. This was often due to time limitations in the classroom and the fact that the leap-up was done specifically for experimental purposes. There was no difference in fluency for the leap-ups across low growth and below grade level leap-ups.

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82 Leap and Leave Design Celeration^ improvement index, and accuracy improvement . The findings from this group of experiments indicate that skills that have an initially higher error rate (10% more than correct responses) generally produce higher rates of learning than those which begin with lower initial error rates. There was no difference in the results across Low Growth leap-ups and Below Grade Level leap-ups. These findings suggest that students in special education resource rooms should be given tasks with errors initially above the correct responses when they are making slow gains on skills with low or no errors or when they are working on skills below their grade level with low to medium rates of learning. Fluency . The frequency multipliers for fluency (see Table 7) indicate that fluency for corrects was generally better in the preleap-up phases than in the leap-up phases. The fluency for errors was the same in all but one leap-up. This indicates that the errors in all but the one leap-up reached 0. Again, in many cases the fluency on the correct responses in the leap-up phases was not higher because of the fact that the primary purpose of the investigation was to look for learning rates. Once it was established that the student could learn the skill rapidly, the teacher often dropped it and tried another skill. Fluency was not affected by the type of leap-up (Low Growth or Below Grade Level) .

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83 Suminary Both the Leap and Keep and Leap and Leave experiments generally produced higher rates of learning during the leap-up phases. While three leap-ups did not get results, many of the leap-ups do show large differences on the learning measure comparisons. These findings could have significant implications for the education of handicapped learners. Probably some proportion of all handicapped learners' curriculum should be high initial error instruction. Replications One reason replications are done is to dem^onstrate the reliability and generality of data (Tawney and Cast, 1984) . Another reason is that replications reduce the scientists' margin of error and insure that the findings can withstand repeated tests (Sidman, 1960). In this investigation, replications were done across subjects, teachers, skills, and settings within each experimental design as described in Chapter 4. For the Leap and Keep designs three leap-ups failed to replicate the results of higher rates of learning that were generally found for the other 13 leap-ups in the study. There are at least two possible explanations for this failure to replicate. First, the initial celerations for correct responses and errors for these leap-ups were already high. Second the same teacher taught the same learner all

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84 three leap-up skills. The data indicate that she had some trouble teaching to errors in the leap-up phases. Replications Across Leap and Keep and Leap and Leave Designs Generally, higher rates of learning during the leap-up phases were found for both the Leap and Keep and the Leap and Leave designs. This replication across designs serves to strengthen confidence in the findings of the less powerful Leap and Leave design. Replications With Studies Already in the Literature Subjects in this study generally experienced steeper learning rates under the initially high error rate condition. One of the early studies on learning rates from precision teaching (Neely, 1978) found that error deceleration rates were greater when students were given tasks on which they were making at least 5 to 10 errors per minute. No differences in correct celeration rates were found. However, Neely introduced the idea that crossover learning pictures (with initial error frequencies above correct responses) could produce steeper celerations for correct responses. McGreevy (1980) became interested in the concept that tasks with initially high errors could produce steeper learning and introduced the idea of "hard to do," "easy to learn." He studied the learning of a severely retarded teenager on a vocabulary task with the initial error frequency above the correct responses. The student

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85 achieved rapid acceleration for correct responses and rapid deceleration for errors on the task. Bower and Orgal (1981) taught college students psychology terms on which they initially made many more errors than corrects. Their rates of learning were steep for both corrects and errors. Stromberg and Chappell (1980) taught a second grade class math tasks on which they made little or no initial errors. He then gave them a leap-up to all the math operations in the curriculum to learn at one time. The students' initial' error frequencies were very high for the leap-up math tasks, but their rate of learning was much better than it had been on the easier math tasks. Eaton and Wittman (1982) found the learning rates for three junior high school mildly handicapped students could be accelerated by giving them math leap-ups to skills with initially high error rates. This investigation studied the learning rates of mildly handicapped students in resource rooms who were given math and reading leap-ups. Results replicated across subjects, teachers, skills, and settings generally found higher learning rates on skills with at least 10% more errors than correct responses compared with skills that had initially very low error rates. These results replicate the findings in the above studies and add a new sample population and different skills.

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86 Practical Implications May students fail to make gains in special education classes (Glazzard, 1984) • These classes often focus on skills with initially low error rates so that students can experience success. There is also evidence that the type of instruction used in the majority of classroom.s may fail to challenge the learner or to give them skills that will generalize to mainstream classes (Glazzard, 1984) . Further, some teaching strategies that have come from applied behavior analysis, like task analysis (Eaton and Wittman, 1982; Howell, Kaplan, & O'Connell, 1981) or errorless learning may be overused with handicapped learners. The steps in task analysis can be made so excrutiatingly small that the student becomes bored with learning the task. Errorless learning, while an excellent teaching method, does not allow students to experience the learning that comes from viewing errors as learning opportunities (Alberto & Troutman, 1982) . The results of overusing these strategies may be that we are producing passive learners who become bored with easy unchallenging tasks or don't know how to learn from errors. The use of the high error teaching strategy offers many benefits to classroom teachers and their students. These are discussed below along with some guidelines.

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87 Benefits Results from this study indicate that when teachers use the leap-up teaching strategy students rate of learning may increase. Students tend to become more active learners and teachers become involved in actually teaching skills on which students need instruction rather than just practice. From a practical point of view, special education students who are behind in school need to be taught using teaching strategies that promote high rate learning. This is the only way that they can hope to catch up with their peers and/or reach any level of competency in basic skills when they complete their education. It is apparent that we must not be content to see these students fall further, and further behind grade level skills as they progress through special education programs. As evidenced in these experiments, by teaching students to accept making many errors when they begin to learn a new skill, it is possible to accelerate learning and to move students closer to grade level skills. Students appear to be motivated by learning more difficult skills and skills closer to those that their peers are learning. Leap-up strategies may be a contribution to the successful mainstreaming of mildly handicapped students. Also, these findings may have implications for school psychologist and placement committee members responsible for developing lEP's for handicapped students. The tendency is to write long and short term objectives for students which

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88 emphasize skills with fairly high initial accuracy rates. While this may be done to "let the student experience success," educators should be aware that tasks with initially high error rates must also be included in a student's program in order to insure that maximum learning is taking place and that the student is getting experience in learning from errors. Guidelines The high error teaching strategy is one way to accelerate the learning of skills for those students who are making slow progress and/or who are working on skills below their grade level placement. However, it would probably not be appropriate to go overboard on leap-ups. More work is needed to determine what proportion of the curriculum should be initially high error rate skills. Also, more ways to reduce errors rapidly need to be developed and ways of overcoming learner resistance to making errors need to be explored before the high error teaching strategy can be fully appreciated. Problems and Limitations of the Study One problem appeared during the course of this study. This was due to the fact that many of the practicum teachers were young and inexperienced. They received little or no support from their directing teachers in using the leap-up teaching strategy. They were eager to become involved in

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89 the leap-up experiments, but were reluctant to take the chance of leaping their students to skills with very high error rates. Many of them were concerned that the students still needed practice on the lower level skills and. would "miss out on learning." It was interesting to note, however, as they became involved in the experiments two things happened. First, they became excited about the learning taking place on the leap-up skills and actually felt they were teaching instead of just providing opportunities for practice. Second, they began to defend the leap-up concept to their directing teachers and wanted to cease teaching the lower level skills. A limitation of this study was that the leap-ups generally consisted of math skills, and of reading vocabulary skills. This was because these skills were the easiest to define and were the skills being taught in the practicum sites. A problem was found in trying to do leap-ups on oral reading. Because of the connecting words in oral reading it was very difficult to meet the high initial error rate criterion. The error rate was only achieved for one leap-up and this entailed leaping a student from first grade reader to a college level text book. It may be that the leap-up concept will have to be defined more precisely for a broader range of skills.

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90 Recommendations for Future Research The curriculum leap-up is an effective teaching strategy when used as part of the instructional approach with mildly handicapped learners. Future research on curriculum leap-ups should focus on five areas: (1) the effects of longer leap-up phases on fluency, (2) chunk-ups , (3) the effects of step-size on learning rates in leap-up phases, (4) strategies for reducing errors, and (5) procedures for reducing anxiety and overcoming resistance to errors. Longer Leap-Up Phases and Fluency In this investigation the major concern was rate of learning under leap-up conditions compared with preleap-up conditions. Many of the leap-up phases were short. Future research should focus on the attainment of fluency following a leap-up. Since fluency is dependent on time, the leap-up phases would have to be lengthened and strategies that build fluency could be blended with the error reduction procedures . Chunk-Ups A second suggestion for future research is on the concept of chunk-ups . Chunk-ups are special cases of leap-ups. They involve adding more unique problems or units to the teaching set. For example, if a student usually is

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91 given 10 words per week, he could be given a chunk-up to 20 words per week. Chunk-ups are related to leap-ups in that the student is expected to learn more at one time. The idea is that if the same rate of learning or a faster rate of learning is noted then the "chunk-up" is way of expediting learning for students who need to catch up or who are challenged by learning more at one time. This investigation intended to study the chunk-up concept. However, preliminary work with chunk-ups led to some problems. Specifically, (1) the chunk-up was not empirically defined in such a way that the concept could be easily understood by those trying to explore its value and (2) there was resistance on the part of the practicum teachers and the directing teachers to try the strategy. Reports from the practicum teachers indicated that directing teachers felt that the chunk size that they were already using was adequate. They were not interested in exploring learning under large chunk conditions. The small amount of data that was obtained did not show clear enough evidence of control to warrant conclusions about the effectiveness of chunk-ups. Recently, teachers who have tried chunk-ups have reported informally that it is working effectively as a teaching strategy. This concept should be studied further and documented more carefully.

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92 Step Size Step is a measure of the iranediate change in the frequency for correct responses and errors when a new phase begins. In going from the preleap-up to the leap-up phase a step down in correct responses and a step up in errors occurs. Further research should focus on the size of these steps and their correlation with learning rates in leap-up phases . McGreevy et al. (1982) have already looked at the effect on variability of learning within a range of difficult tasks and found little differences. This research would extend his conclusions by looking at the rate of learning within a range of step sizes. Strategies for Reducing Errors Effective strategies for reducing errors rapidly need to be explored. Current behavior analysis research on new ways to reduce errors using stimulus control procedures give hope that new tools may be developing in this area. Anxiety and Resistance to Errors At present teachers, parents, and learners are often reluctant and anxious about learning a task that generates high initial errors. Previous experience, with errors viewed as failures, may account for large part of this resistance. Research needs to focus on ways to help individuals view high initial errors as "learning

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GO opportunities." Handicapped persons may produce more than expected errors in their "natural" interaction with the world. It may be especially important for them to learn hov; to cope with, and keep trying through, the stage of initially high error production.

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APPENDIX A DEFINITION OF TERMS

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standard Glossary and Charting Procedures Accelerating Target — a movement the behaver, manager, advisor, or supervisor expects to accelerate; the frequency is symbolized by placing a dot on the Chart. Accuracy Improvement — a measure of change in accuracy over time; celeration correct/celeration incorrect. Accuracy Multiplier — measure of accuracy: frequency correct/ frequency incorrect; distance from frequency incorrect to frequency correct; also called the accuracy ratio. Accuracy Pair — two movements, usually correct and incorrect, charted simultaneously. Add-Subtract Scale — any measurement scale on which adding and subtracting by a constant amount is represented by a constant distance; the "up the left" scale on a equal interval chart. Advisor -per son who advises a manager, usually viewing Charts on a weekly basis. Behaver — person whose behavior is displayed on the Chart. Behavior Floor — the lowest daily frequency possible for a particular behavior; 1/number of minutes behavior can occur; symbolized by drawing a solid horizontal line on the Chart. Bounced Around Celeration up bounce and down bounce combined; the range of deviations of frequencies from the celeration line. Celeration --basic unit of measurement of behavior change; change in frequency per unit time. Celeration Aim — the expected celeration for a given movement. Celeration Line — straight line constructed through continuous Frequencies for a given movement on the Standard Behavior Chart. For purposes of this investigation, celeration lines were drawn using the quarter intersect method (White & Haring, 1980) . Celeration Multiplier (turn up or turn down) — value by which one celeration is multiplied or divided to obtain a second .

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96 Change Day --first day of a phase change; symbolized by drawing a vertical line covering that day line on the Chart. Change Line — 'A line to demark a change of instructional conditions. Goes in the space before first day of new condition. Chunk — Change in frequency per week. Number of units in the teaching set. Counting Period Ceiling — the highest frequency observable under a given counting procedure; symbolized by drawing a dash line on the Chart connecting the Saturday and Monday lines. Counting Period Floor — the lowest frequency detectable by a given counting procedure; 1 /number of minutes spent counting; symbolized by drawing a dash line on the Chart connecting the Tuesday and Thursday lines. Cycle — distance on the Chart betv/een consecutive powers of 10. Day line — vertical line on the Daily Standard Behavior Chart. Decelerating Target — a movement the behaver, manager, advisor, or supervisor expects to decelerate; the frequency is symbolized by placing an "x" on the Chart. Double Improvement Learning Picture — both movements of an accuracy pair with celerations in the expected direction; for example. Down Bounce — the distance from the celeration line to the frequency farthest below it. Duration — the amount of time it takes to complete one occurrence of a behavior; 1/number of minutes spent behaving. Errorless learning — a teaching procedure in which cues and prompts are arranged so as to occasion only correct responses . Event-Following Celeration Line — a celeration line drawn through all frequencies for a given movement just prior to a phase change. Fluency — final performance for correct responses and errors. Freehand Method — a method of visually estimating and drawing celeration lines.

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97 Frequency — basic unit of behavioral measurement; the number of movements per unit time. Frequency Aim — the expected phase-ending frequency for ? given movement; s^^^mbolized by drawing "A" at the expected frequency on the day the aim was set. Frequency Line — a horizontal line on the Chart; also called a counting line. Frequency Multiplier (jump up or jump down) — value by which one frequency is multiplied or divided to obtain a second. Geometric Mean — the appropriate method for obtaining an average on a multiply-divide scale. Ignored Day — a day on which the behavior being measured occurs but is not charted. Latency — the amount of time between the occurrence of a signal and the beginning of a movement; 1/time from signal to start of movement. Learning — a change in performance per unit time, also called celeration. Learning Picture — the celeration lines of both movements of an accuracy pair viewed together; for example. Manager -per son who works with the behaver on a daily basis. Median Celeration --the middle celeration in a celeration distribution; symbolized by drawing a "<" on the Chart. Median Frequency --the middle frequency in a frequency distribution; symbolized by drawing a "<" on the Chart. Most Recent Celeration Line — a celeration line drawn through the last 7-10 frequencies for a given movement. Movement — recorded behavioral event; usually specified in terms of a movement cycle with a beginning, middle and end. Multiply-divide Scale --any measurement scale on which multiplying and dividing by a constant amount is represented by a constant distance; the "up the loft" scale on the Standard Behavior Chart. No Chance Day — a day on which the behavior being measured has no chance to occur.

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98 Overall Celeration Line — a celeration line drawn through all frequencies for a given movement. Performance -the number of movements per unit time; also called frequency. Periodic Celeration Line — a celeration line drawn through all frequencies for a given movement in a specific time period such as bi-weekly or monthly. Phase --A period in which a particular set of conditions is in effect. Phase Change — a deliberate alternation made to the behaver's environment in an effort to improve the behavior being measured. Precision Teaching — a comprehensive instructional system for accelerating learning and maintaining high proficiency, based on direct and continuous meas procedures. Quarter-Intersect Method — a method for computing and constructing celeration lines. Recorded Day — a day on which the behavior being measured as the opportunity to and is recorded. Single Improvement Learning Picture — one movement of an accuracy pair with a celeration in the expected direction; for example. Split-middle Line — a line drawn parallel to a quarterintersect celeration line, such that half the data points fall on or above the line and half the data points fall on or below the line. Standard Behavior Chart — a standard, six-cycle semilogarithmic chart that measures frequency as movements/ time and celeration as movements/time/time; Daily, Weekly, Monthly, Yearly and Summary versions are available; also called the Standard Celeration Chart. Step — the ratio between the frequency of two learning lines that intersect the same change line. Supervisor — a person who views the Charts on a monthly basis. Total Bounce — distance from the highest to the lowest frequency; analogous to range of an add-subtract scale. Trend-following Celeration Line — a celeration line drawn through visible trends for a given movement.

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99 Up Bounce — distance from the celeration line to the frequency farthest above it.

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APPENDIX B ALACHUA COUNTY CRITERIA FOR ELIGIBILITY IN LEARNING DISABILITY, EMOTIONALLY HANDICAPPED, AND EDUCABLY MENTALLY RETARDED CLASSES

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SPECIFIC LEARNING DISABILITIES Specific Learning Disabilities — one who exhibits a disorder in one (1) or more of the basic psychological processes involved in understanding or in using spoken and written language. These may be manifested in disorders of listening, thinking, reading, talking, writing, spelling, or arithmetic. They do not include learning problems which are due primarily to visual, hearing, or motor handicaps, to mental retardation, emotional disturbance, or to an environmental deprivation. Criteria for Eligibility A student is eligible if the following criteria are met : a. Evidence of a disorder in one (1) or more of the basic psychological process areas. Basic psychological process areas include visual, auditory, motor and language processes. Only tests or subtests appropriate for the student's chronological age shall be used for placement purposes. Hereafter, the Illinois Test of Psycholinguistic Abilities shall be abbreviated as ITPA; the Detroit Tests of Learning Aptitude as DTLA. Required batteries appropriate to age and by process cluster are as follows: (1) Chronological ages 5.0 through 10.0 (a) Visual ITPA Reception ITPA Association ITPA Closure ITPA Memory ITPA Manual Expression (b) Auditory ITPA Reception ITPA Association ITPA Grammatic Closure ITPA Memory ITPA Verbal Expression (c) Visual Motor Beery Developmental Test of Visual Motor Integration (Beery) Bender Motor Gestalt Test 101

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102 (2) Chronological ages above 10.0 (a) Visual DTLA Memory for Objects DTLA Memory for Letters DTLA Disarranged Pictures (b) Auditory DTLA Memory for Words DTLA Memory for Sentences DTLA Verbal Opposites DTLA Oral Directions (c) Visual Motor Beery DTLA Memory for Design Disorders shall be defined according to the instructions of each test's author(s). b. Evidence of academic achievement which is significantly below the student's level of intellectual functioning. (1) For students below age seven (7), evidence must be presented that the student exhibits a discrepancy of one (1) standard deviation or more between an intellectual standard score and an achievement standard score (s) in thinking, reading, talking, writing, spelling or arithmetic. Students with deficits in reading, arithmetic, and/or spelling may be considered for exceptional student placement if other applicable criteria are met. Students with deficits in other areas may be offered consultative services. (2) For students ages seven (7) through ten (10), evidence must be presented that the student exhibits a discrepancy of one (1) standard deviation or more between an intellectual standard score and academic standard score (s) in reading, writing, arithmetic or spelling. (3) For students ages eleven (11) and above, evidence must be presented that the student exhibits a discrepancy of one and one-half (1 1/2) standard deviations or more between an intellectual standard score and academic standard score in reading, writing, arithmetic or spelling.

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103 (4) For students ages seven (7) and above with deficits in reading, arithmetic, and/or spelling, exceptional student placement may be considered if other applicable criteria are met. (5) If more than one academic instrument is used to docum.ent a weakness, the results must consistently show deficits in the same academic area. If more than one level of functioning is obtained, the mean level of functioning will be used to establish a deficit. (6) For eligible students functioning at or above their current grade levels, consultative services may be offered. c. Evidence that learning problems are not due primarily to other handicapping conditions. (1) For students with intellectual deficits, evidence that intellectual functioning is no more than one (1) standard deviation below the mean on an individual test of intellectual functioning, or evidence that a score below one (1) standard deviation below the mean is not a reliable indicator of the student's potential. Intellectual functioning will be determined by the use of the full scale score derived from the standard battery instrument. (2) For students with visual processing deficits, evidence that visual acuity is at least 20/70 in the better eye with best possible correction, or evidence that the student's inability to perform adequately on tasks which require visual processing is not due to poor visual acuity. (3) For students with auditory processing or language deficits, evidence that the loss of auditory acuity is no more than 30 decibles in the better ear unaided or evidence that the student's inability to perform adequately on tasks which require auditory processing of language is not due to poor auditory acuity. (4) For students with a motor handicap, evidence that their inability to perform adequately on tasks which assess the basic psychological process is not due to the motor handicap.

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104 (5) For students with an emotional handicap, evidence that their inability to perform adequately on tasks which assess the basic psychological processes is not due to the emotional handicap. d. Documented evidence which indicates that general educational alternatives have been attempted and found to be ineffective in meeting the student's educational needs. EMOTIONALLY HANDICAPPED Emotionally Handicapped — one, who after receiving supportive educational assistance and counseling services available to all students, still exhibits a persistent and consistent severe emotional handicap which consequently disrupts the student's own learning process. This is the student whose inability to achieve adequate academic progress or satisfactory interpersonal relationships cannot be attributed primarily to physical, sensory or intellectual deficits. This term does not include children who are socially maladjusted unless it is determined that they are also emotionally handicapped. Severely Emotionally Disturbed — one who meets the criteria stated above and, in addition, requires a special program^ for the full school week and extensive supportive services. 1 . Criteria for Eligibility a. Emotionally Handicapped (1) Evidence that the student, after receiving appropriate supportive educational assistance and counseling, still exhibits a severe emotional handicap. (2) Evidence that the student exhibits a persistent and consistent severe emotional handicap as determined by documented observations and psychological evaluation. (3) Evidence that the behavior disrupts the student's ability to achieve adequate academic progress or develop satisfactory interpersonal relationships. (4) Evidence that the primary problem of the student cannot be attributed primarily to physical, sensory, or intellectual deficits.

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105 b. Severely Emotionally Disturbed In addition to the criteria stated above in (1) through (4) , the following shall be used to determine each student's eligibility: (1) Evidence that the student requires a program for the full school week which provides a highly structured cognitive and affective curriculum; individual or group counseling and parent counseling or education; and (2) Evidence that a program provided in a less restrictive environment has not met the individual student's needs. EDUCABLE MENTALLY HANDICAPPED Educable Mentally Handicapped — one who is mildly im.paired in intellectual and adaptive behavior and whose development reflects a reduced rate of learning. The measured intelligence of an educable mentally handicapped student generally falls between two (2) and three (3) standard deviations below the m.ean, and the assessed adaptive behavior falls below age and cultural expectations. Criteria for Eligibility a. The measured level of intellectual functioning, as determined by performance on an individual test of intelligence, is between two (2) and (3) standard deviations below the mean. The standard error of measurement may be considered in individual cases. The profile of intellectual functioning shows consistent sub-average performance in a majority of areas evaluated. b. The assessed level of adaptive behavior is below age and cultural expectation. c. Sub-average performance on a standardized measure of academic achievement is demonstrated.

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APPENDIX C DECISION AND OUTCOME FORM

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l-» i 1 fvj LJ C O M I Teacher_ Learner Setting n F Age_ Dates to Program Skill Name X 3tC s^< ill CZI— ± FD-tx CDI-I :«c 3tc Phase

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APPENDIX D RAW DATA: CORRECT AND INCORRECT FREQUENCIES FOR ALL PHASES OF THE LEAP AND KEEP AND LEAP AND LEAVE DESIGNS

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Learner: E 8 Tegcher: Investigator Movement Cuc!s: 5ee--Sau Textsd Words Fho5T Coiiendor Frrqijenoy Fr^qurricy Norr* Dc u * Crjrf'="jt Error; Pr*l*op-Up >>>>>>>>>>>>>>>>>>>> 2 S-g 3 96 4 1 0G 5 1 09 6 110 LfOp-Up >>>>>>>>>>>>>>>>>>>>> 7 9 11 9 24 3 9 57 4 10 64 2 11 72 2 109

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110 Learner: E B Teacher: Investigator Movement C u ds: See — Say Vocabulary Words FtiOfr Colendor Frrquency Frrqurncy f-Jiirn^' [in ij *^ Corf frit ErTor* Prri«"2C-Up > > > > >

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Ill Learner: L A Teacher: W Movernent C y cie: See — Write Add Facts, sums to 18 Phos* Coi^ndor Frequrrioy Frrqurncy PCrlrOp-Up >>>>>>>>>>>>> 3 34 L^-op-Up I'.r. * < 4 5 6 7 8 9 10 11 12 >• > > 36 37 38 39 40 41 43 43 NC NC 40' 59 59 43 2 68 Q >>>>>>>>>;>> > 1 NC NC ^ ^ .' v* NC 7 9 9 NC NC 4 NC NC NC Lt-op-Up '2 >>>>>>>>>>>>>>>>>>;> 43 44 45 46 47 43 49 3 NC 13 16 13 NC NC 6 NC NC NC 50 SI 5^: 53 22 NC NC NC -lAP-i.iP "3 NC NC NC NC 55 NC NC 56 NC NC >>>>>>>>>>>>>>>>>>>> 57 15 Se 2 59 5 60 5 61 7

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112 Learner: W T Teachsr: J R Movement C y cle: See — Write Add Facts, sums to 5 F'ho:"'? Coirfidor Freqij^-ricy Frtqu-jncu Ni:rri» Do u " Corri?ct Error? 3 24 • 4 19 2 5 NC NC 6 NC NC 7 NC NC S 31

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113 fS^l5[<)SlIJ(iJus ©s i?Q[KL &ii (Leap Qffiti] (Lsq^q [ls[pecrO[iD@0{l3 Learner: R J Teacher: 5 B Movement C y cle: See — Write Add Facts, sums to 18 Phofr Coler.dor

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114 R J iCuniinuijd) 61

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115 Appendix D: Section A: Leap and Leave Experiments Learner: S Teacher: B M Movement Cucie: See — Write Add Facts, sums to 18 Phasi

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116 Appendix D: Ssction A: Leep end Leave Experiments Learner: J R Teacher; B M Movement C u cie: See--Write Add Facts, sums to 10 Pho.-* Colsndor 4 5 6 S g Id il 12 13 14 15 10 17 18 19 20 24 2y 30 Frsqusncq

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117 Appendix D: Section A: Leap and Leave Experiments Learner: A F Teacher: W Movement C y cle: See — Write Subtraction Facts Phofe Calender

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Ill Appendix D: Section A: Leap and Leave Experiments Learner: R V Teacher: B fl Movement C y cle : See — Write Mixed Math Facts Fhcse CalsnciGr Frequi^nc'^ Frequency Fr9leop-Up > > > > > > > > ;• > >>>>>>>> 5 31 6 NC WC 7 NC NC S 33 . 9 35 10 33 It 39 12 NC NC 1 3 NC NC 1 4 NC NC 1 5 40 15 42 17 NC NC 13 44 19 45 20 NC NC 21 NC NC Lt-op-Up > ;• ; > > > > > > > > > > > ;>>>>; 22 1 1 23 22 1 24 27 25 NC NC 25 34

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119 Appendix D: Section A: Leap and Leave Experiments Lesrner: C B Teacher: B M ilQvement C u cie: See — Write Nultipiication Facts, X 4 tabie Fha.-*' Coleridar

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120 C S (Ccritinusd) 51

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iS 121 !2sij5[psaj(ij3s Sis \Piiu^ ©s iLsQi? sfflCi} Keep ^^^©[rOEefflSg iBQrnsr. W T Teacher: J R Movement C y cle: See — Sey Alphabet Phosi Coirfidor Fr^qu'-ricg Fre^qiji'Ticy F'ho:"r Fr^qurncg Fr*qijt-ricy Norn* Doy " Corrs'cts Errors Ncrri'? Corrifots Error; Prrleop-Up > > > > >

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V T (ContiriUH.j) 122 46 47 43 49 50 54 59 60 61 52 53 64 65 56 67 5S 69 70 71 72 73 74 75 10

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tej)3[D(ijOs< Ss [Pstrtl ®o Heap esfl [Se@[p [lapsirOasesae Learner: J V Teacher: 5 L riovement C u cie: See — Say Ginn Phrases, level ? 123 F'rS'it'Op Durifrj *1 Colrridor Fr'?qij«-ricij Fr^qu^jnoy PhofsFrrqueriog Frequency Dog ^ Corrects Error.-Noroi? Correct." Error; Up >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 3 56 5 4 5 6 7 3 9 10 11 12 13 14 15 16 17 18 19 20 21 23 24 25 2i< i. > 25 29 50 31 32 33 34 35 36 3y 40 41 42 42 43 44 59

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t V (ContiYiued) 124 Durinq *2 > [JuririQ «-.. 45

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^[PipssdiSa ®s ipi]^ Ss iGGiD aECi] Essip [la[j)Q[r3uiieLDils 125 Learner: D P Teacher: C F ilovement C uc!e: Sss— Say Ginn Vocabulary, level 6 F'ho5e Col^ndor-

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P (Continued) 126 4Q NC ric

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i^^(?(pSffia]3s ®S [PSir^ Ss [LS2iTeffiCi] KSQfT] [IS<[>)3[fO[i2S[!]a9 Learner: D P Teacher: C F novement. C u ds: 58e--S8y Ginn Phrases, ievel S 127 Colrri'jor Fri?>]'jt'ricy Fr^qu^noy Pho;? Frequrririy Freqij^noij Doy * Corr^-cti ErroriNomsCc'rrijc.t; Error? Up >>>>>>>>.'>>>>>;>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1 34 3 3 NC 1 NC NC NC Durinq 2 3 4 5 6 7 9 10 11 12 13 14 15 ID 17 IS 19 20 21 NC 63 NC NC NC >>>>>:>>> 76 > > > > > /LS'Op-Up > >>>>>> > > > > >

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12! (appsffitilSs ©= [?s[r^ Es deep qhkiI [Seep [IspGirOmcDEGs Learner: N R Teacher: S B ilovement C u cle: See Write Add Facts, sums to 18 Phofe Cole'ridor Frequrncij Frrqiji^ricq F'hofe Fr^qui?ricij Ffirquencij Nomi? Dog " Corr^ot." Error; Momi Ccrr^o\s Error? ^ ^ ^ y y 1

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(ii:iiJ}[?GffiCiiSE2 ®S PSQ^ ©S a=eS[? EffiCiJ iSGSfjj dESpeCr^ SDE^as 129 Lssrner: C J Teacher: 5 B Movement C u cis: 5ee-V/r1te Add Facts, sums to 18 Colrndof Frrqurficij Fr^qijenoij Dag ' Corr^ots Errors -IJo > > > > > > ; ;• > > >>?> > > > > > > 4 3S 5 39 NC NC 1 NC NC NC NC NC 1 1 NC NC PhOfr

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130 •iijrpssH^js ®s \f-iiu*l So [Leap QECii IEgqi]) [IspsfrOiiDSGDilQ Learner: A K Teacher: J R Movemsnt Cucie: See — Write Add Facts, sums to 10 Pho;-'? Calirndor Fr^-qut'ricy Fr^qu^ncg Pho?'? N'orne No.Ti'?

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T31 Leorner: Y B Tegcher: B M Movemgnt C q cie: See — Write hultipiication Feels Phof* Col^ridor Ft^quirocy Frequrnog Phoj^ Fre-qurncy Frequency iN'om^Doy " Correct." Error; Nome Correct; Error; F'releop-Llp >>>>>>>>:>>>>>>>>>>>>>>>>>•'>>>>>>>>>>•'>>>>>> 1 37 1 2 49 3 51 4 NC NC 5 53 6 NC NC 7 NC NC Durino >>>>>>>>>>>>>>>>>>>> >Leop'-'Jp >>>>>>>>>>>>>>>>>>>> S 51 9 55 1 57 1 1 60 12 13 14 15 16 17 13 I'l-i 20 21 22 2o 24 26 2':l 29 30 31 32 2

PAGE 141

iS5iprp3K(L^^3 ®s \pQ\rl Ss iL©Ep QffiCLi [Eee[p [Isijje[rO[ii]S[DlL3 132 Learner: 6 R Teacrier: B M Movement Cue

PAGE 142

REFERENCES Alberto, P., & Troutman, A. Applied behavior analysis for teachers. Columbus, Ohio: Charles Merrill, 1982. Alley, G. , & Deshler, D. Teaching the learning disabled adolescent: Strategies and methods . Denver, Colorado: Love Publishing Co., 1979. Bower, B., & Orgal, R. To err is divine. Journal of Precision Teaching , 1981, _2(1)' 3-12. Deshler, D., Shumaker, J., Alley, G., Warner, M., & Clark, R. Learning disabilities in adolescent and young adult populations: Research implicatios. Focus on Exceptional Children , 1982, 15(1). Dunn, L. Special education for the mildly retarded: Is much of it justified? Exceptional Children , 1968, 35 , 5-22. Eaton, M. , & Wittman, V. Leap ups: Acceleration of learning through increasing material difficulty. Journal of Precision Teaching , 1982, 2(2), 29-33. Engelmann, S., & Carnine, D. Theory of Instruction: Principles and Applications . New York, New York: Irvington Publishers Inc., 1982. Eshleman, J. All the known precision teaching/standard chart references. Journal of Precision Teaching , 1983, 4^(3) , 56-66. Glass, G., & Stanley, N.J. Statistical methods in education and psychology . Englewood Cliffs, N.J.: PrenticeHall, 1970. Glazzard, P. Are our expectations of special students high enough? Teaching Exceptional Students , 1984, 16 , 136-9. Haring, N., Lovitt, T., Eaton, M. , & Hansen, C. The Fourth R Research in the Classroom . Columbus, Ohio: Charles E. Merrill, 1978. 133

PAGE 143

134 Johnston, J., & Pennypacker, H. Strategies and tactics of human behavior research . Princeton, N.J.: Lawrence Erlbaum Associates, 1980. Howell, K., Kaplan, J., & O'Connell, C. Evaluating exceptional children . Columbus, Ohio: Charles E. Merrill, 1979. Koenig, C. Charting the future course of behavior . Kansas City, Kansas: Precision Media, 1972. McGreevy, P. District-wide learning screening compared with average learning and learning picture products of resource teachers. (Doctoral dissertation, Kansas University, 1978). Dissertation Abstracts International , 1979, 3_9' 4183A. (University Microfilms No. 78-24854) McGreevy, P. Hard to do becomes easy to learn. Journal of Precision Teaching , 1980, ^(1), 27-29. McGreevy, P., Thomas, J., Lacy, L., Krantz, S., & Salisbury, C. Can learning or variability be predicted from low initial performance: Implications for precision teachers and equal interval charters? Journal of Precision Teaching , 1982, 2(3), 63-68. Meyen, E., & Lehr, D. Least restrictive environments: Instructional implications. Focus on Exceptional Children, 1980, jj_, 1-8. Neely, M. Six years of supervising a special education program by learning products. (Doctoral dissertation, University of Kansas, 1978). Dissertation Abstracts International, 1979, 3_2.' 6443A. (University Microfilms No. 79-10622) Pennypacker, H. The relation of teacher competence in charting to changes in pupil performance in mathematics . Gainesville, FL Precision Media, 1974. Pennypacker, H. , Koenig, C. , & Lindsley, 0. Handbook of the standard behavior chart . Kansas City, Kansas: Precision Media, 1972. Semmel, M. Expanded role of regular class teaching: Implications for teacher education. McGill Journal of Education, 1979, 14_, 327-41. Sidman, M. Tactics of scientific research — Evaluating experimental data in psychology . New York: Basic Books, 1960.

PAGE 144

135 Stromberg, G. , & Chappell, M. Poster session at the Association for Behavior Analysis Fifth Annual Convention, 1980. Tawney, J., & Gast, D. Single subject research in special education . Columbus, Ohio: Charles E. Merrill, 1984. Wells, D., Schmid, R., Algozzine, B., & Maher, M. Teaching LD Adolescents: A study of selected teacher and teaching characteristics. Teacher Education and Special Education , 1983, 6_(4), 227-234. White, 0., & Haring, G. Exceptional teaching . Columbus, Ohio: Charles E. Merrill Publishing Co., 1980. Wolking, W. Academic behavior chart (ABC-3) . Gainesville, FL: Performance Data Co., 1983. (b)

PAGE 145

BIOGRAPHICAL SKETCH Michele C. Cerent was born April 23, 1948, in Schenectady, New York. She was graduated from the University of Florida in 1970, with a Bachelor of Arts in Education degree. In 1974, she received a Master of Education degree from Florida Atlantic University at Boca Raton, Florida, with an emphasis in learning disabilities. She was employed as a special education teacher for a total of 11 years in Palm Beach, Broward, and Indian River County school systems. During those years she taught mentally retarded, emotionally handicapped, learning disabled, and gifted students. Michele came to the University of Florida in the spring of 1981 to work on a Ph.D in special education. Her major area was learning disabilities with an emphasis in precision teaching and microcomputers in education. 136

PAGE 146

I certify that I have read this study and that in my )pinion it conforms to acceptable standards of scholarly )resentation and is fully adequate, in scope and quality, as dissertation for the degree of Doctor of Philosophy. William D. Wo Iking , Chairman Professor of Special Education I certify that I have read this study and that in my )pinion it conforms to acceptable standards of scholarly )resentation and is fully adequate, in scope and quality, as dissertation for the degree of Doctor of Philosophy. Cecil Mercer Professor of Special Education I certify that I have read this study and that in my jpinion it conforms to acceptaole standards of scholarly iresentation and is fully adequate, in scope and quality, as dissertation for the degree of Doctor of Philosophy. Elroy J. 3(i) 1 due , Jr Professor , ^Department o Subject Specialization Teacher Education

PAGE 147

I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Catherine Mors: Professor of Special Education I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Robert Al^ozzi^e Professor of al Education This dissertation was submitted to the Graduate Faculty of the Department of Special Education in the College of Education and to the Graduate School, and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. August 19 84 Dean for Graduate Studies and Research


THE EFFECTS OF INITIALLY HIGH ERROR TASKS ON
SHORT TERM LEARNING FOR MILDLY HANDICAPPED STUDENTS
BY
MICHELE C. GERENT
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE
UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA

ACKNOWLEDGEMENTS
Many individuals have contributed to the completion of
this research. First, thanks go to Dr. Bill Wolking whose
training in precision teaching and single case analysis
research enabled me to undertake this project. His help in
conceptualizing the study, and support and guidance through¬
out its course are most appreciated.
Second, thanks are due to my committee members,
Dr. Catherine Morsink, Dr. Bob Algozzine, Dr. Roy Bolduc,
and Dr. Cecil Mercer, for their input and ideas during the
early stages of its development. I would also like to thank
the practicum teachers from the Fall of 1983 and their
learners for their help. They were a terrific group of
young teachers with whom to work.
Finally, thanks go to my family and friends who sup¬
ported me throughout this research. I want to thank my son
Eric for coping so well with our hectic life style, my
mother who gave unselfishly of her time and support when I
needed it, and my friend Mary Mehn whose interest and
enthusiasm were often what I needed to keep me working.
ii

TA3LE OF CONTENTS
Page
ACKNOWLEDGEMENTS ii
LIST OF TABLES vi
LIST OF FIGURES vii
ABSTRACT viii
CHAPTER I. INTRODUCTION 1
Significance 2
Rationale 4
Statement of the Problem 7
Question Under Investigation 8
Delimitations 8
Definition of Terms 9
CHAPTER II. REVIEW OF RELATED LITERATURE 10
Studies from Precision Teaching on Learning
Tasks with Initially High Error Rates/
Curriculum Leap-Ups 10
Studies from Applied Behavior Analysis and
Learning Theory on Learning Tasks with
Initially High Error Rates 23
Summary 2 4
CHAPTER III. METHOD 2 6
Setting 26
Subjects 27
Variables Under Investigation 31
Dependent Variables 31
Independent Variable 31'
Experimental Design 33
Leap and Keep Design 3 4
Leap and Leave Design 3 4
.11.1

Page
Procedure 36
Pre-experimental Phase 36
Experimental Phase 36
Materials 38
Curricular Materials 38
Data Recording Form 38
Standard Celeration Chart 39
Measurement 39
Data Recording and Analysis 43
Data Recording 43
Data Analysis 44
CHAPTER IV. RESULTS 45
Leap and Keep 4 5
Reading Example: J.V. Ginn Phrases 55
Systematic Replications on Other Reading
Leap-Ups 58
Systematic Replications with Math Leap-Ups ... 60
Math Example: Add Facts/Rounding Numbers .... 61
Replications With the Same Math Skills 64
Systematic Replications with Other Math Skills . 64
During Phases 65
Summary of Leap and Keeps 66
Leap and Leave 67
Reading Example: Oral Reading 67
Systematic Replications with Math Skills .... 75
Math Example: Add Facts/2 Digit Addition with
Carrying 76
Systematic Replications With Other Math Skills . 76
Summary of Leap and Leave Leap-Ups 78
CHAPTER V. DISCUSSION 79
Experimental Question 79
Leap and Keep Design 79
Leap and Leave Design 81
Summary 82
Replications 82
Replications Across Leap and Keep and Leap
and Leave Designs 83
Replications With Studies Already in the
Literature 83
iv

Page
Practical Implications 85
Benefits 85
Guidelines 87
Problems and Limitations of the Study 87
Recommendations for Future Research 88
Longer Leap-Up Phases and Fluency 89
Chunk-Ups 8 9
Step Size 90
Strategies for Reducing Errors 91
Anxiety and Resistance to Errors 91
APPENDICES
A DEFINITION OF TERMS 93
B. ALACHUA COUNTY CRITERIA FOR ELIGIBILITY IN
LEARNING DISABILITY, EMOTIONALLY HANDI¬
CAPPED, AND EDUCABLY MENTALLY RETARDED
CLASSES 99
C. DECISION AND OUTCOME FORM 10 5
D. RAW DATA: CORRECT AND INCORRECT FREQUENCIES
FOR ALL PHASES OF THE LEAP AND KEEP AND
LEAP AND LEAVE DESIGNS 107
REFERENCES 131
BIOGRAPHICAL SKETCH 134
V

LIST OF TABLES
Table Page
1. Review of Selected Studies on Learning Tasks
With Initially High Error Rates/Curriculum
Leap-Ups 12
2. Demographic Data for Subjects 28
3. Examples of Frequency Multipliers from
Preleap-Postleap Comparisions 41
4. Leap and Keep Design: Learning Outcomes by
Subject, Teacher, and Skill 46
5. Leap and Keep Design: Frequency Multipliers for
All the Preleap-Postleap-Up Comparisons 52
6. Leap and Leap Design: Learning Outcomes by
Subject, Teacher, and Skill 68
7. Leap and Leave Design: Frequency Multipliers
for All Preleap-Postleap-Up Comparisons 72

LIST OF FIGURES
Figure Page
1. Type One Leap-Ups: Slow Growth 2 9
2. Type Two Leap-Ups: Below Grade Level 30
3. Examples of Dependent Variable Measures 32
4. Diagrams of Experimental Arrangements 35
5. The Reading Leap and Keep Example 56
6. The Math Leap and Keep Example 6 2
7. The Reading Leap and Leave Example 7 4
8. The Math Leap and Keep Example 7 7

Abstract of Dissertation Presented to the Graduate School
of The University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
THE EFFECTS OF INITIALLY HIGH ERROR TASKS ON
SHORT TERM LEARNING FOR MILDLY HANDICAPPED STUDENTS
By
Michele C. Gerent
August 1984
Chairperson: William D. Wolking
Major Department: Special Education
This investigation compares the learning of mildly
handicapped students in initially low and initially high
error environments. It studies the effects of curriculum
leap-ups on short term learning rates. A curriculum leap-up
is defined as an upward curriculum change that results in a
student making at least 10% more errors than correct
responses. The dependent measures are celerations for
correct responses and errors, improvement index, accuracy
improvement, and fluency. Frequency (movements per minute)
is the basic measure for all the dependent variables.
Single subject designs are used to compare the learning
rates of students on preleap-up skills with loap-up skills.
Both a Leap and Keep and a Leap and Leave Design are used.
The Leap and Keep design involves continuing the preleap-up
skill when the leap-up skill is introduced. The Leap and
V I ( j

Leave design involves dropping the preleap-up skill when the
leap-up skill begins.
Sixteen students in elementary and middle school
resource room programs were included. The students ranged
in age from seven to fourteen. Both reading and math
leap-ups were used.
Twenty-four of twenty-nine experiments produced effects
favoring learning during the leap-up condition. In most
experiments celeration for correct responses and errors, the
improvement index, and accuracy all increased. Findings for
fluency were mixed.
Results were replicated across subjects, skills,
teachers, and settings. Implications for future placement
and instruction, and recommendations for continuing research
are presented.
IX

CHAPTER I
INTRODUCTION
The problem addressed in this study is the relationship
between task difficulty and learning outcomes. A review of
recent history and the status of programs for mildly handi¬
capped students indicates that what is done instructionally
for the mildly handicapped occurs in the context of instruc¬
tional protectiveness. There is a tendency to avoid placing
students in high expectation situations where they might
encounter failure (Meyen & Lehr, 1980). The consequence of
this protection from possible failure may also limit oppor¬
tunities for growth. The use of teaching strategies that
fail to challenge students may play a part in accounting for
some of the failures and limited successes of programs for
the mildly handicapped.
Traditionally, instruction in special education has
differed from regular education in the use of several
important teaching strategies. These strategies include
allowing extra time for students to complete their academic
assignments, moving more slowly through curriculum
sequences, and giving them curricular material on which they
achieve initially low error rates. It is obvious that these
strategies have both the potential of protecting the learner
1

2
from failure, but also of limiting growth. These strategies
may also provide indirect messages to learners that could
affect their self-concept and general motivation for aca¬
demic learning. This research explores one of these issues
by studying the learning of mildly handicapped students
taught in both initially low and high error instructional
environments.
Significance
There are indications that special education is inef¬
fective and inefficient in fostering learning for the mildly
handicapped student (Dunn, 1968; Semmel, 1979). Although,
there has been a concerted effort by some educators
(Deshler, Shumaker, Alley, Warner, & Clark, 1982; Englemann
& Camine, 1982) to develop more effective teaching methods,
common practice is that special educators have become overly
concerned with the labeling and placement of special educa¬
tion students, rather than in looking for methods that
foster their learning.
Conclusions from a six-year study of the performance of
over 1300 mildly handicapped students (Neely, 1978) revealed
that using teaching strategies which allowed the students to
make some errors initially and charted daily performance was
the most effective way to improve student learning rates.
The students' label or whether or not they were taught in
special education settings or regular classrooms had no
direct bearing on their learning rates. Yet Neely found,

3
that in the three school districts he surveyed, the majority
of time and effort was spent on the labeling of students and
deciding on their placement, rather than on training
teachers in using charting and teaching strategies to
promote high rate learning.
After looking at the current teaching practices in
special education classrooms, Glazzard (1984) recommended
that special educators should restructure these settings to
make them more like general education classrooms. She
concluded that in many classrooms special education teachers
are limiting the academic growth of their students by
continually giving them academic material which is too easy.
Also, because of a tendency to use teaching strategies that
protect students from failure and emphasize immediate
reinforcement, teachers may be limiting the generalization
of skill learning to regular classroom settings.
Howell, Kaplan, and O'Connell (1979) point out that
many of the popular methods for teaching handicapped stu¬
dents actually guarantee that they will remain behind their
peers rather than emphasizing strategies that allow special
education students to "go like mad" in order to catch up.
In an effort to implement appropriate instructional
programs to meet individual needs, teaching strategies that
challenge the learner may have been overlooked by special
educators. In many cases the consequence of this may be
passive learners who never reach their potential. It may be
that our emphasis should be on devising teaching strategies

4
that promote rapid learning of material closer to the
student's grade placement and potential. There are at least
three advantages of rapid learning. One, it allows the
special student a good chance of mastering everything which
is essential for competing with other students. Two, it
raises the special student to the criteria of regular
students so that there is no built-in guarantee of future
failure. Three, it allows the student, maybe for the first
time, to experience the joy of new learning.
Tawney and Gast (1984) note that the field of special
education faces greater challenges today than it has at any
other time in the past. The altruism that provided past
impetus for special education programs is gone. Arguments
for programs based on equal opportunity interpretations of
the Constitution have been overshadowed by the decline of
the economy. Programs for the handicapped are increasingly
being called upon to justify their existence. Only by
implementing a technology of education that uses student
learning as a basic datum for justifying its existence can
special educators become more accountable to parents of
handicapped students and to the public at large. As part of
this accountability it is imperative that special educators
prove that they have the strategies to help students learn
faster and the data to show how it is being done.

5
Rationale
There is little research on the learning of handicapped
students who are given academic tasks with initially high
error rates. As an outcome of this special education may be
producing students who fail to develop high rate learning
skills (the skills that are associated with making many
errors initially but reducing them quickly), or stay on the
same skill level for long periods of time without making
gains or reaching proficiency levels.
A rapidly developing technology of teaching and learn¬
ing, Precision Teaching (See Appendix A for a definition),
is making it possible for teachers to begin to accumulate
data on student learning rates. Average classrooms in
America produce around 10% learning per week (O.R. Lindsley
personal communication August, 1981), while classrooms that
are precision taught average around 25% per week learning
(R. Beck personal communication March, 1980) and there are
data to show that some precision teachers continually
produce 100% learning per week (W.D. Wolking personal
communication May, 1983). But even precision teachers fell
into the "easy task" approach to teaching exceptional
students. McGreevy, Thomas, Lacy, Krantz, and Salisbury
(1982) report that for many years precision teachers charted
student performance, while continuing to implement
traditional public school curricular strategies. These
strategies produced initial correct performances that were
relatively high with very few incorrect responses (high

6
accuracy), but subsequent rates of learning remained
relatively low.
Few teachers introduce skills at levels that provided
high error rates. Yet it is at these levels that intensive
teaching is most appropriate if students are to experience
academic growth. Teaching skills on which accuracy is
already high places an emphasis on practice, requiring
little of the teacher, other than that opportunities for
practice are provided. This type of teaching has the
potential of developing bored teachers who become frustrated
by the lack of progress of their students. I.t may also
contribute to the high rate of burn-out during a teacher's
first few years in the classroom (Wells, Schmid, Algozzine,
& Maher, 1984) .
In 1978, Lindsley (cited in McGreevy, 1980) began to
question the effectiveness of curricular strategies that
emphasized highly accurate initial performance and
apparently provided less opportunity for learning. Neely
(1978), one of Lindsley's students at Kansas, analyzed
student learning from four different teaching strategies
over a six year period. Results indicated that giving
students tasks with initial error rates at 5 to 10 per
minute was more effective at producing steeper error
decelerations than was giving students tasks with initial
error rates below 5 per minute. His study fell short of
gathering any conclusive data on another teaching strategy,
that of giving students tasks with the initial errors above

7
the correct responses, because teachers were reluctant to
teach this way in many cases. However, other precision
teachers (Bower & Orgal, 1981; Eaton & Vihittman, 1982;
McGreevy, 1978, 1980; Stromberg & Chappel, 1980) then began
to look at the initially high error or leap-up teaching
strategy (with initial errors above the correct responses)
and data began to accumulate that showed steep celerations
for both correct responses and errors resulted when this
strategy was used.
The investigator in this study became interested in the
leap-up teaching strategy for two reasons. First, it is a
means for motivating a large group of mildly handicapped
students who were making slow progress in special education
classrooms. Second, it is a way of training graduate
practicum students to use high error teaching strategies in
teaching academic skills. The opportunity to investigate
the strategy was aided by the fact that graduate practicum
students at the university are trained in precision
teaching.
Statement of the Problem
Many special education students fail to make gains or
improve very slowly on academic tasks that have initially
low error rates. This study explores the relative effects
of initially low and high error teaching environments on
four dimensions of student performance and learning. A

8
change from low-to-high error rates, while holding other
features as constant as possible, is called a leap-up.
This study extends the work on leap-ups or high error
learning by (1) further quantifying the definition of a
leap-up first used by McGreevy, Thomas, Lacy, Krantz, and
Salisbury (1982), (2) identifying two kinds of leap-ups,
(3) extending the sample studied to include elementary age
mildly handicapped students, and (4) including more work on
reading skills.
The design of this investigation is single subject.
The teaching strategy of a curricular leap-up is used with
students who are not meeting performance standards or who
are working on skills below their grade level or both.
Question Under Investigation
This study examined the effect of curriculum leap-ups
on four dimensions of academic performance. The major
concern in this study was a comparison of rates of learning
under preleap and leap-up conditions. Celeration for
corrects and errors, improvement index, and accuracy
improvement were compared for the preleap-up and leap-up
conditions. Fluency measures were also reported. Defini¬
tions of these four measures are listed in Appendix A.
Also, a more detailed explanation and a graphic display of
their meanings are presented in Chapter 3 under the Measure¬
ment section and in Figure 3.

9
The following question was investigated: What are the
effects of leaping-up to tasks that initially produce at
least 10% more errors than correct responses, on celeration,
improvement index, accuracy improvement, and fluency? (See
Chapter 3 for definitions of pre- and post-leap-up phases.)
Delimitation
The subjects in this investigation are elementary and
middle school mildly handicapped students; therefore the
findings cannot be generalized without systematic
replications to mildly handicapped high school students or
to normal high school students.
Definition of Terms
Many technical terms from precision teaching and
behavior analysis were used in reporting this investigation.
Some of the terms where introduced in this chapter and
others will be introduced throughout the study. The terms
have all been defined in Appendix A; so the reader may refer
to them as needed.

CHAPTER II
REVIEW OF RELATED LITERATURE
This review has two sections. The first section
reviews the literature from Precision Teaching on high error
learning usually conceptualized under the label of curricu¬
lum leap-ups. The second section reviews relevant research
and theory on learning with initially high errors from the
published work of behavior analysts and learning theorists.
Studies from Precision Teaching on Learning
Tasks with Initially High Error Rates/
Curriculum Leap-Ups
To complete this section all the articles from the
Journal of Precision Teaching and "All the Known Precision
Teaching/Standard Chart References" (Eshleman, 1983) were
reviewed. "All the Known Precision Teaching/Standard Chart
References" is a database of over 700 references pertaining
to precision teaching and/or standard celeration charting.
It spans the years of 1965 to the present. The database was
compiled from all the published and unpublished sources in
precision teaching that the author could locate. The
references in the database include those found through an
ERIC search, journal sources, private sources, presentations
from Precision Teaching Conferences and presentations from

11
the Applied Behavior Analysis conferences that dealt with
precision teaching. Much of the literature from Precision
Teaching is in the form of unpublished work and personal
communication because O.R. Lindsley has promoted this
approach to professional communication in building a
research base. All the Known References from Precision
Teaching is continually being updated in order to provide a
research base for those conducting research in the Precision
Teaching field.
The major concern in this investigation was the rate of
learning tasks under initially high and initially low error
conditions. Precision Teachers have always been interested
in the provision of curricular and other environmental
arrangements that accelerate the mastery of skills (Bower &
Orgal, 1981). When data began to accumulate that showed
that tasks with initially high error rates provided more
opportunities for learning (Neely, 1978) , the field began to
address the issue. It first looked at tasks that were
initially hard to learn (had high error rates) and then
moved to the leap-up concept which involves "leaping a
student up" to more difficult material.
Seven studies were located that addressed the issue of
giving students tasks with initially high error rates or of
giving them curriculum leap-ups in an attempt to accelerate
learning. Table 1 presents a description of these studies
beginning with the earliest and moving up to the most
recent.

Table 1
Review of Selected Studies on Learning Tasks
With Initially High Error Rates/Curriculum Leap-Ups
Author(s) Subjects Invervention Measures Results Conclusions
Neely (1978)
1300
1. Different
1. Frequencies 1.
Curricula 1.
Special Edu¬
special
curricula
for correct
that allow
cation
education
2. Different
responses and
higher ini¬
Students
students
teaching
strate¬
gies .
errors.
2 . Celerations
for correct
responses 2.
and errors.
tial error
rates produce
higher rates.
Teaching
strategies
that empha- 2 .
size reducing
errors produce
higher error
decelerations.
should be
given mate¬
rials with
high error
rates.
Teaching
strategies
that empha¬
size teaching
to errors
should be
used to
increase
learning.

Table 1
Continued
Author(s)
Subjects
Invervention
Measures
Results
Conclusions
McGreevy
122
1 . Screening
1.
Initial fre-
1.
Screening
Remediation
(1978)
mildly
tasks for
quencies for
tasks pro-
efforts were
handicapped
10 days w/o
corrects.
duced lower
relatively in-
students
instruction.
2 .
Celerations
initial
effective for
2. Resource
for corrects.
correct
this group of
teacher
frequencies
students because
remedial
and higher
the tasks were
program with
correct
too easy.
instruction.
2.
celerations.
Remediation
tasks produced
high initial
correct fre-
quencies but
low correct
celerations.
McGreevy
(1) moderately
See/say task
1.
Initial
1 .
Initial
The task was
(1980)
retarded
Wilson's sight
accuracy
accuracy
initially
boy
vocabulary
ratio
ratio
"hard to do"
(29) words)
2 .
Celeration
/19
but proved
high initial
for
2.
Cel for
to be "easy
error task.
correct
corrects
to learn."
responses
x2.6 .
and errors.
3 .
Cel for
errors
/ 12.6 .

Table 1
Continued
Author(s)
Subjects
Invervention
Measures
Results
Conclusions
Stromberg
Regular
1. O.P.T. timing
1.
Initial
Intervention #1
The presen-
& Chappel
Second
of second
accuracy
1.
Initial accu-
tation of
(1980)
grade
grade math
ratios.
racy ratio
all the math
students
operations
2.
Median
xl to x65.
curriculum
Following the
correct
2 .
Median
at one time
curriculum
celera-
correct
was "hard to
steps (probes)
•
tions.
celeration
do" but
2. Leap-Up to all
3.
Median
xl. 4 .
"easy to
of the 2nd
error
3.
Median error
learn."
grade curricu-
celera-
celeration
lum at one
tions.
xl. 0.
time (mixed
Intervention #2
probes).
1.
Initial accu-
racy ratio
x6 to /1.6.
2. Median
correct
celeration
x2.0.
3. Median error
celeration
/ 2.4 .

Table 1
Continued
Author(s) Subjects Invervention Measures Results Conclusions
Bower & Orgal College
(1981) students
enrolled
in an
undergrad¬
uate psy-
cology
class
(3 groups).
1. High aims for 1.
correct re¬
sponses set
(40 per min¬
ute) when
learning psy- 2.
cology terms.
2. High initial
performance
with few correct
many errors
presented as
a model for
class.
3 . Snapping
fingers at
60 per minute
during
timings
in class.
4. Consequating
any correct
answers.
5. Setting grade
criteria as
only the num¬
ber of correct
responses.
Frequen¬
cies for
correct
responses
& errors.
Learning
pictures
generated.
1. All three
groups pro¬
duced more
errors than
correct
responses.
2. Majority of
learning
pictures
were jaws or
crossovers.
1 . Attention
to errors
may retard
the rate
at which
people
learn.
2. Students
can enjoy
high error
learning
situations.

Table 1
Continued
Author(s)
Subjects
Invervention
Measures
Results
Conclusions
McGreevy,
24 severely
1.
66 tasks that
1
. Initial
1.
Inital
Neither
Thomas, Lacy
handicapped
were "hard to
number
number
learning
Krantz. &
students
do" or
correct.
correct
nor varia-
Salisbury
"extremely
2
. Initial
Median = 1
bility can
(1982)
hard to do"
number
Range - 0-15.
be predicted
were chosen
incorrect.
2.
Initial
from low
for students
3
. Initial
number
initial per-
on the basis
Accuracy
incorrect
formance.
of high ini-
ratio.
Median = 9
tial error
4
. Celeration
Range = 2-54.
rates. The
for cor-
3.
Initial
initial error
rect
accuracy
rates had to
responses.
ratio
be at least
5
. Celeration
Median = 16
10% more than
for errors.
Range xl.5-128
the correct
6
. Bounce
4 .
No relation-
responses.
around
ship between
2.
Daily timings
correct
how difficult
& teaching of
celeration.
the task was
the tasks by
7
. Bounce
(low initial
classroom
around
performance)
teachers.
celeration
& learning or
for errors.
variability.

Table 1
Continued
Author(s) Subjects Invervention Measures Results
Conclusions
Eaton &
3 junior
Curriculum
Celerations
Leáp-Up skills
Leap-Ups are
Wittman
high L.D.
Leap-Up
for correct
produced higher
an effective
(1982)
students
responses
and errors.
learning rates
for all 3 stu¬
dents when com¬
pared with
preleap-up skill
learning.
strategy for
motivating
students and
increasing
learning.

18
The earliest study that looked at errors as learning
opportunities was reported by Neely (1978). The basis for
this study was the analysis of six years of data on the
learning of students in special education programs. Approx¬
imately, 62,820 celerations and 630,000 frequencies were
collected from 1300 mildly handicapped students. The
analysis looked at three aspects of educational practice.
The aspects were a description of reading, the effects of
curricula on learning, and the effects of teaching strate¬
gies on learning. The last two aspects of this investiga¬
tion dealt with initial error rates and relate to the
hard-to-do or leap-up concept.
The results of the analysis across different curricula
and teaching strategies indicated that curricula materials
that provided students with high initial error rates
promoted higher rates of learning than those which had
students beginning with relatively few errors. There were
also preliminary data that suggested crossover learning
pictures (where the errors are initially higher than the
corrects) were the most desirable learning pictures to aim
' for because they produced the fastest learning. Crossover
learning pictures were also the most difficult to get
teachers to try.
In conclusion, Neely suggests that students are being
cheated out of a appropriate education if curricula and
teaching strategies that promote rapid learning are not
implemented in special education classrooms. Choosing a

19
curricula which has an initially high error rate, viewing
errors as learning opportunities, and the daily charting of
performance were seen as the most efficient ways to meet
high rate learning goals. Further, his study indicates that
most basal reading series do not support the concept of high
error learning; rather they support the idea that a student
needs to be 90-95% correct when initially "learning" a new
task.
In 1978, McGreevy conducted a two-year study that
examined the effectiveness of a remedial resource program
which used a traditional "easy skill" approach. One hundred
and 22 students labeled as mildly handicapped were involved
in the investigation. Seventy five of the students were
administered a one minute see-say reading task, and 47 of
the students were administered a one minute see-write math
task. This was done for ten days. The content of these
tasks was grade level specific and corresponded to the
district curricula in which the students lived. Initial
error rates on these tasks were relatively high. Each day,
after the one minute timing, the students were made aware of
their errors and verbally supplied with the answers, but no
instruction was given.
The students were later placed in a remedial program
and their progress was monitored with the use of daily
timings on remedial reading and math tasks. For reading it
was found that students learned more during the screening
phase without instruction than they did during the

20
remediation phase. For math, the results showed the same
amount of learning had taken place during both phases.
Conclusions drawn from this study were that the easy
tasks used during the remedial program did not allow enough
room for growth (initial errors on the tasks were too low),
and that the remedial program was ineffective in providing
for a high rate of learner change. This appears to be a
common occurrence in many programs where students are placed
on relatively easy skill levels as a means of "remediating
their skill deficits." They frequently make slow gains
because of the "easy task" approach.
In McGreevy's (1980) second project, an eighteen year
old moderately retarded boy was given a see-sav task (see
the word, say the word) on the first 29 words of Wilson's
essential vocabulary. The initial frequencies indicated
that the task was very difficult for the student—he began
by making many more errors than corrects. But he learned
the task easily—his correct rate went up quickly and his
error rate went down quickly. In other words, the task was
"hard-to-do" initially, but "easy-to-learn."
Stromberg and Chappell (1980) attempted to teach an
entire second grade class a math curriculum at a pace
suggested by the adopted math text. Pairing the text with
precision teaching methods (daily timings and the use of
probes) resulted in the students achieving initially high
correct rates while they made almost no errors. The stu¬
dents learned the material at an acceptable rate. After

21
4 months the investigators "leaped-up" the entire class to
all the math operations contained in the second grade math
book by giving the students mixed worksheets (problems with
all the operations to be learned in the second grade on
them). This leap up in curriculum produced lower initial
performance for correct responses with the students making a
lot of errors. However, results of learning measures
indicated that the students learned the material very
rapidly. Conclusions were that following logical curriculum
sequences may unnecessarily slow students down, and that
students should be challenged to see how fast they can
learn.
Bower and Orgal (1981) used the concept of high error
learning with college students. They set very high aims for
the students to meet in learning psychology terms. The
students were told to learn all the terms at one time and
not to be concerned with their high initial error rates.
Results indicated that the students' high initial error
rates led to steep celerations (rapid learning) and satis¬
factory accuracy and fluency rates at the end of the course.
Conclusions were that students can learn to view errors as
learning opportunities instead of something to be avoided.
Another investigation by McGreevy, Thomas, Lacy,
Krantz, and Salisbury (1982) found that neither learning nor
variability can be predicted from low initial performance by
students. These conclusions were based on the data from the
learning of difficult tasks by 24 severely handicapped
students over a four week period. In order to qualify as a

22
difficult task, there had to be at least 10% more errors
than correct responses on the initial timing the student
took on a task. Sixty-six tasks met this criterion and were
then divided into those that were hard-to-do and those that
were extremely-hard-to-do depending on how many errors the
student initially made on them.
The results of several comparisons between the
two groups of tasks clearly indicated that, although the
difficulty range varied within the range of hard tasks,
there was no relationship between how hard the task was
initially and the rate of learning or variability (bounce of
the performance). The students learned all the tasks at
fairly high rates even when they began with only one or
two corrects and many errors.
The most recent investigation which used the leap-up
approach was done by Eaton and Wittman (1982). This inves¬
tigation examined the effects of the leap-up teaching
strategy on the learning rates of three learning disabled
junior high school students. All three students were
accurate in performance of the multiplication and division
tables but were not meeting fluency aims (not doing the
problems quickly enough). They were considered "reluctant
learners" by the investigators who wanted them to move more
quickly through the math curriculum. When they were given a
leap-up to fractions where their initial error rates were
high, they all responded well by increasing their rate of
learning. Eventually they all began to meet fluency aims.

23
Conclusions were that the leap-up approach appears to
be an effective way to motivate students with slow growth
learning and that special education teachers should guard
against using small curriculum steps in teaching students
who are not meeting fluency aims.
Studies from Applied Behavior Analysis
and Learning Theory on Learning Tasks
with Initially High Error Rates
The intent in this section was to review teaching
strategies from the applied behavior analysis and learning
theory that allowed mildly handicapped students to experi¬
ence learning tasks with initially high error rates, or
tasks that were hard for them in the beginning stages. A
computer search using the key words applied behavior analy¬
sis, learning theory, high error learning, difficult tasks,
teaching strategies, curriculum strategies, mildly handi¬
capped students (EM, LD, BD) was done. Also, a search using
the same key words was done in the Exceptional Child Index,
CIJE, Education Index, and the Annual Review of Psychology
for the years 1974 to 1983. Mo studies were located.
Since the first searchers were unproductive, a search
of the titles in the table of contents was completed for the
Journal of Learning Pisabilities, LD Quarterly, Teaching
Exceptional Students, The Journal of Applied Behavior
Analysis, and Exceptional Education Quarterly. This search
reviewed titles from these journals for the years 1975 to

present. The same key words as in the computer and indices
searches were used. Again, no studies were located.
It appears there is little, if any, research on this
topic.
Summary
Research evidence that normal learners as well as
handicapped learners have more opportunities for learning
when they are placed in "high error" generating situations
is beginning to accumulate. Precision teaching techniques
that emphasize this approach are curriculum leap-ups and
hard-to-do tasks. There is growing evidence that these
strategies may be successful with handicapped and nonhandi¬
capped students as well as with adults.
The hard-to-do or leap-up approach to learning repre¬
sents a change from the traditional approach of giving
students tasks with initially low error rates. Studies
using precision teaching have shown that (1) errors can
serve as learning opportunities, (2) curriculum leap-ups and
hard-to-do tasks are effective ways of increasing student
performance, (3) motivation for learning may be improved by
giving "reluctant learners" curriculum leap-ups, (4) teach¬
ing and learning in initially high error learning environ¬
mental need further study.
A search of the research literature from Applied
Behavior Analysis and learning theory failed to locate any

25
studies which looked at the learning of mildly handicapped
students in high error environments.
Continued research in naturalistic settings is needed
to validate strategies that promote initially high error
learning. Special educators need to expand their knowledge
of the motivating factors of hard-to-do tasks for popula¬
tions of students who are accustomed to being presented
relatively easy tasks under the guise of remediation and
protection from failure and its pressures.

CHAPTER III
METHOD
This work attempts to advance the understanding of
teaching and learning under high initial error conditions
while teaching mildly handicapped students. This experiment
investigated the effects of curriculum leap-ups on four
learning outcomes. Specifically, the effects on celeration,
improvement index, accuracy improvement, and fluency were
explored. The study was a series of clinical investigations
conducted in ongoing classrooms with graduate practicum
students serving as teachers.
Setting
The study was carried out in Alachua County, a north-
central Florida school district of 22,000 students. The
system has special education resource and/or self-contained
rooms in all elementary and middle schools. The data were
gathered by the investigator and by graduate students as
part of their practicum assignment in resource rooms for the
mildly handicapped. The typical student teacher was indi¬
vidualizing instruction on about 25 separate skills at any
one time. The skills that were taught were chosen to

27
satisfy the Individual Education Plan (IEP) for each stu¬
dents as determined by the special education teacher and the
student teacher jointly. Teaching procedures were selected
with the idea of maximizing student learning.
Subjects
There were sixteen subjects in this investigation. The
subjects were all learning disabled, emotionally handi¬
capped, severely language impaired, or educably mentally
retarded students. They ranged in age from 7-14. Ten were
males and six were females. One subject attended a self-
contained program for the severely language impaired, five
attended an elementary school resource room program for the
mildly handicapped, and ten attended a middle school
resource room program for the mildly handicapped. See
Table 2 for demographic data on the subjects. All subjects
in the study met the Department of Education and the local
school district special education placement guidelines (See
Appendix B).
Subjects chosen to participate in the experiments met
the criteria for type one or type two leap-ups or both. See
Figures 1 and 2 for the rationale and criteria for each type
of leap-up. Type One leap-ups were used with learners who
were making little or no progress in meeting performance
standards. Type Two leap-ups were used to allow students
working on below grade level skills to experience learning
at or near their grade level placement.

28
Table 2
Demographic Data for Subjects
Subject
Sex
Grade
Exceptionality
Age
Race
Teacher
1.
L. A.
M
7
L.D.
12
W
VI. 0.
2.
Y.B.
F
7
EMR
13
B
S.B.
3.
C.B.
M
7
L.D.
13
W
B.M.
4.
E.B.
M
O
Lang Imp
8
W
M.G.
5.
A.F.
M
7
SLD
12
B
W.O.
6.
J.R.
F
6
E.H.
12
W
B.M.
7.
R. J.
F
7
EMR
13
B
S.B.
8.
C. J.
F
8
EMR
14
B
S.B.
9.
A.K.
M
2
EMR
8
B
J.R.
10.
D.P.
M
5
L.D.
11
B
C.F.
11.
N.R.
F
8
L.D.
14
B
C.F.
12.
G.R.
M
7
L.D.
13
W
B.M.
13.
O.S.
M
6
L.D.
12
B
B.M.
14.
W.T.
F
1
EMR
7
B
J.R.
15.
E.C.
M
6
E.H.
12
W
B.M.
16.
J.V.
M
5
E.H.
11
W
S.L.

Rationale: To motivate students who are not reaching aims or performance standards on
skills. These are students with medium to high accuracy, but maintaining or slightly
worsening learning pictures (see A, B, C above).
Criteria for Leap-Ups:
Preleap-Up Phase
1- Medium to high accuracy with low growth for corrects (celeration < X 1.15).
2. Corrects not at aim: Reading 100 words p.m. Math £ 50 digits p.m.
Spelling <_ 50 transitions p.m.
3. Low growth errors—errors at aim or celeration /1.15.
Leap-Up Phase
1. First day accuracy ratio _< 1.1 (at least 10% more errors).
2. If the accuracy ratio is not met, try a larger leap.
Figure 1. Type One Leap-Ups: Slow Growth
NJ
LD
RECORD FLOORS

tfl
cc
O
O
o
cc
O
o
ai
cc
+
MIN HRS
• lili l! llitil -1-L 1-1 ; , , , U -T— , ^ f | , , 1 : . I,-..!!!-, , . . I ) . ...lili,, —t-i . . ■* * 4 t ■ i i » » 4 I I » ■ » t » i t "» ♦ 1 t ♦ ! I'f T f
Rationale: To motivate students who are working on skills below their grade Level. These
students may be reaching performance standards on lower level skills, but they need to
experience learning skills above their grade level. Students have improving learning
pictures with slow growth or acceptable growth and medium to high accuracy (see D, K
above) .
Criteria for Leap-Ups:
Preleap-Up Phase
1. High accuracy with slow or acceptable grwoth for corrects (celeration X i.15).
2. Corrects at or near aim for skills below the student's grade placement.
3. Errors at or near aim.
Leap-Up Phase
1. First day accuracy ration <_ 1.1 (at least 10% more errors).
2. If the accuracy ratio is not met, take a larger leap.
Figure 2. Type Two Leap-Ups: Below Grade Level.
U)
o

31
Variables Under Investigation
Dependent Variables
The four dependent variables in this investigation were
celeration, improvement index, accuracy improvement, and
fluency. All are measures of academic performance.
Previous work indicates that celeration, accuracy, and
fluency are sensitive dimensions (Koenig, 1972) likely to
detect changes in the independent variable being manipu¬
lated. The improvement index was included because it is a
convenient way of looking at the celeration for correct
responses and errors at one time.
Figure 3 presents an example of each of the dependent
variables. The figure illustrates both a preleap-up and
leap-up phase. Figure 3 and the measures used in this
investigation are explained fully under the measurement
section of this chapter.
Independent Variable
The independent variable is a curriculum leap-up (See
Figures 1 and 2). A curriculum leap-up is a change from a
skill with an initially low error rate to a skill with an
initially high error rate. The size of a leap-up depends on
the individual subject, rather than on the skill. For some
subjects a leap to the next level in a curriculum ladder met
the error requirements; for others a much larger leap up the
curriculum ladder was required in order for the error

32
Symbol Name
Formula Value
Preleap-up Leap-up
A
B
C
D
E
F
G
H
Initial Perf.
Initial Perf.
Final Pref.
(Fluency)
Final Perf.
(Fluency)
Cel for Corr.
(Learning)
Cel for Err.
(Learning)
Improvement
Index
Accuracy Impr.
Frequency for Corr. 32
Frequency for Errors 0
Frequency for Corr. 52
Frequency for Errors 0
mov/min/week for Corr. xl/15
mov/min/week for Err. xl.O
cel for corr x cel for
errors x1.15
Final accuracy ratio/
initial accuracy ratio xl.12
3
8
60
0
x8.40
/ 5.80
x50
x 1 60
Figure 3. Examples of Dependent Variable Measures

33
criteria to be met. Both Slow Growth and Below Grade level
types of leap-ups, as mentioned under the subject section,
were used.
Experimental Design
The experimental design in this study is single sub¬
ject. Single subject designs make it feasible to demon¬
strate within subject control because the unit of analysis
is the individual. Replications across subjects, teachers,
skills, and settings were done to demonstrate the relia¬
bility and generality of the findings (Tawney & Gast, 1984).
This investigation presented a special design chal¬
lenge. In educational settings, designs that require the
repeated withdrawal or reversal of the independent variable
may not be practical (Tawney & Gast, 1984). In these
experiments, it is not meaningful to return to a baseline
after a leap-up because the student is learning new material
during the leap-up.
The designs used in this investigation do not com¬
pletely fit any of the standard design descriptions. They
do have elements in common with the AB, multiple baseline,
and alternating treatment designs. The two designs used in
this investigation meet the unique needs of the real world
teaching situation (Alberto & Troutman, 1982; Haring,
Lovitt, Eaton, & Hansen, 1978). They are referred to as
Leap and Keep and Leap and Leave designs.

34
Leap and Keep Design
The Leap and Keep designs are illustrated in Figure 4.
Every vertical line (change line) gives the opportunity to
observe an experimental effect. Because the baseline A is
continued when the treatment B is introduced, the design
controls for maturation and correlated historical variables.
Leap and Leave Design
The Leap and Leave designs are illustrated in Figure 4.
There is one opportunity (change line) with this design for
an experimental effect to be observed. This design is most
like the AB design.
The AB design provides a structure for drawing experi¬
mentally valid conclusions when certain conditions are met
(Tawney & Gast, 1984). Optimal conditions include
(1) Behaviorally defined target behavior.
(2) Collection of continuous baseline data (at least
3 days).
(3) Introduction of the independent variable only
after the baseline trend is stabilized.
(4) Continuous collection of baseline data on the
target behavior during the intervention.
(5) Replicate the experimental effects with similar
subjects.
This design can provide a convincing demonstration that
outcomes are not a function of other variables (time,
maturation, experience, unobserved correlated events) when

35
Leap and Keep
(1) Leap 1
PL
During
(2)
Leap 1
Leap 2
1
PL 1
During
(3)
Leap 1
Leap 3
Leap 2
J
PL
During
(4)
Leap 1
Leap 2
1
PL
i
During 1 iDuring 2
cu
in
Leap 1
During 1
Leap 3
Leap 2 j
During 2 During 3
Leap and Leave
(6) Leap 1
I
PL¡
(7) Leap 2
Leap 1
Figure 4. Diagrams of Experimental Arrangements.

36
behavioral changes measured following the intervention are
immediate and abrupt following a stable baseline.
Conclusions drawn by AE designs may be limited by
threats to internal validity and/or external validity. The
lack of data on the natural course of the preleap-up
behavior during the intervention phase or a novelty affect
were concerns in this experiment. Therefore, several
replications were done. Several replications of the
experimental effect with this design are usually quite
convincing. The design has certainly served very well in
medicine over the past 150 years.
Procedure
Pre-experimental Phase
During this phase the practicum teachers received
training in identifying students and skills for the leap-up
strategy during their weekly practicum sessions. They were
also trained in using the Decision and Outcome form and in
using the quarter intersect method to draw learning lines.
With the aid of the investigator pinpoints for possible
leap-ups were selected. Techniques for teaching in high
initial error environments were discussed.
Experimental Phase
During this phase the practicum teachers selected
students to participate in the investigation according to

37
the criteria for the two types of leap-ups and gathered the
daily data for inclusion in the investigation. The fol¬
lowing procedure was used for Leap and Keep experiments.
1. Students whose learning met the criteria for a
Slow Growth or Below Grade Level leap-up were
chosen to participate in the investigation.
2. A stable baseline on the preleap-up phase was
verified with the investigator.
3. A skill related to the preleap-up skill but higher
in the curriculum sequence was chosen for the
student. The skill had to meet the requirement of
having initially 10% more errors than correct
responses or another skill was tried.
4. Both the preleap-up skill and the leap-up skill
were continued. Daily timings were taken and
charted on both skills. The leap-up skills were
continued until experimental results were seen or
an aim was met.
5. In some instances one or more additional leap-up
skills were also added, making within teacher,
learner, and skill replication possible.
The procedure for the experimental phase for the Leap
and Leave investigations was identical to the above pro¬
cedure with one exception. In Step 4 the preleap-up skill
was dropped when the leap-up skill was started with a
student.

38
The Leap and Keep and Leap and Leave field experiments
by the practicum students were monitored by the investigator
both in the classroom and in weekly chart share sessions.
At the end of the investigation the teachers discussed their
teaching procedures and results on the leap-up skills with
the investigator.
Materials
Curricular Materials
The curricular materials used were based on the stu¬
dents' current academic program. Resource rooms in Alachua
County use county adopted materials for each grade level
along with remedial materials. Materials currently used
include the Ginn and SRA reading series and the Heath math
program. Most teachers used adaptations of the materials
for precision teachers available from the Alachua Learning
and Resource Center.
Data Recording Form
The Decision and Outcome Form was used to record all
the specifics of the program and the outcomes. The infor¬
mation on the Form was combined with the charted data to
obtain a complete picture of the learning in each phase.
See Appendix C for a copy of the form.

39
Standard Celeration Chart
The Standard Celeration Chart (Pennypacker, Koenig, &
Lindsley, 1972) was used to display and analyze all the data
from the investigation. Precision teachers have made an
attempt to standardize graphic displays of data by using
this chart.
Measurement
Frequency, movements per minute (Pennypacker, Koenig, &
Lindsley, 1972) was chosen as the basic unit of measurement
in this investigation. For many academic and social
behaviors, frequency yields more informations than other
standard educational measurements (Haring, Lovitt, Eaton, &
Hasen, 1978). Frequency, when used to measure both correct
responses and errors, gives a measure of both the accuracy
and fluency of a student's performance. Fluency, the rate
at which a student performs a skill, is often the discrimi¬
nating factor between a student who is acquiring a skill and
one who is proficient at a skill. Percent scores, most
often used in educational settings, provide only a measure
of the accuracy of a student's performance and give no
indication of fluency. When using percent data there is no
way to discriminate between the student who is just accurate
and the student who is both accurate and proficient. For
example, if one stude;nt completes 50 math facts (100 digits)
correctly in 20 minutes with no errors he is accurate but
not proficient. If another one completes 50 math facts

40
(100 digits) correctly in 1 minute he is both accurate and
proficient.
Frequency multipliers (the ratio between two frequen¬
cies) were used to analyze the data from this study. A
frequency multiplier can be visualized as the distance
between two frequencies on the Standard Celeration Chart.
There are two levels of frequency multipliers. The first
level is a ratio comparison between two frequencies on the
chart. The second level is a comparisons between
two ratios. Both types were used in this study and are
illustrated below.
Figure 3 presents the data from a sample preleap-up and
leap-up phase. The name of the behavior being measured, the
formula for calculating it, and the value of the behavior
being measured are given. If a multiplication sign (x)
precedes the value, it indicates that the frequency of the
behavior was accelerating. If a division sign (/) precedes
the value, it indicates that the frequency of the behavior
was decelerating. In Figure 3 the initial frequencies for
correct responses and errors and the value for each of the
dependent measures in this study were calculated for both
the preleap-up and leap-up phases. These values were then
used as the basis for the ratio comparisons done in Table 3.
In Figure 3, A and B represent the initial frequency
for the corrects and errors in the two phases. The initial
frequency is the point where the learning lines (one for
correct responses, one for errors) cross the first day line

41
Table 3
Examples of Frequency Multipliers
from Preleap-Postleap Comparisons
Measure
Value
Preleap-Up
Leap-Up
Multiplier
Celeration For Correct
Responses
xl.15
x8.40
x7.30
Celeration For Errors
xl.00
/5.80
x5.80
Improvement Index
xl.15
x50
x43
Accuracy Improvement
xl. 62
xl60
x99
Final Performance
For Correct Responses
52
60
xl.15
Final Performance
For Errors
0
0
xl. 00

42
in a phase. The letters C and D represent the final fre¬
quencies for correct responses and errors on the learning
lines. The final frequency is alsc know as fluency.
The letters E and F mark the celerations for corrects
and errors. The unit for celeration is movements per minute
per week. It describes the rate at which frequencies change
in a week. Celeration is also called learning.
The letter G represents the improvement index. The
improvement index is a ratio between the celeration for the
corrects and the celeration for the errors. The measure
conveniently summarizes improvement in correct and error
responding into one number. Graphically, it can be vis¬
ualized as the size of the angle between the celeration for
the corrects and celeration for the errors.
The letter H represents accuracy improvement. Accuracy
improvement is calculated by determining the ratio of the
corrects to the errors at the beginning of a phase, and then
comparing that value to the ratio of the corrects to the
errors at the end of a phase. It is a measure of change in
accuracy over time.
Table 3 presents the values for the comparisons between
the preleap-up and the leap-up phases in Figure 3. These
ratios are always calculated by dividing the smaller fre¬
quency into the larger frequency. For example, in the
comparison for celerations for corrects in Table 3 the
frequency multiplier is a x7.30. This was calculated by
dividing x8.40 (c for corrects for leap-up phase) by xl.15

43
(c for corrects for preleap-up phase). The x sign indicates
that the rate of learning was in favor of the leap-up phase.
Within the field of precision-teaching there are,
unfortunately, two ways in which the multiply and divide
sign are used. The signs may be used to identify movement
on the chart: x for acceleration and / for deceleration.
The sign may also be used to signify the direction of an
experimental effect: x for an increase, and / for a decrease
by the indicated factor.
For making comparisons in this investigation, the x
sign before the frequency multiplier was used to indicate
that the leap-up phase is better than the preleap-up phase
on the comparison measure. The / sign was used to indicate
that the leap-up phase worsened by the factor indicated on
the comparison measure.
Date Recording and Analysis
Data Recording
Daily data were recorded on the Academic Behavior
Chart-3 (Wolking, 1983) by the practicum teachers and their
students. Each time a phase change was made the data for
the completed phase was recorded on the Decision and Outcome
sheets by the teachers and the forms were given to the
investigator.
For purposes of analysis, the data from the preleap-up
and leap-ups were plotted on the Standard Behavior Chart

44
using frequency for correct responses and errors. This
allowed for visual analysis of the preleap-up and leap-up
phases of learning. The scale on the Standard Behavior
chart is a ratio scale. Most measurement in educational
research occurs at the nominal, ordinal, and interval levels
because it is difficult to find variables that lend them¬
selves to ratio measurements (Glass & Stanley, 1970). Ratio
scales are considered to be the most sensitive scales of
measurement because they allow for interval comparison and
for an absolute zero—which indicates the total absence of
the movement being measured. Further, plots of human
behavior frequencies, as they change over time, on a ratio
scale, tend to be linear and thus permit relatively easy
predictions (Pennypacker, 1974).
Data Analysis
Visual inspection of all the data and frequency multi¬
pliers were both used for data analysis. Frequency multi¬
pliers add quantification to the visual inspection procedure
by making it easier to compare results across subjects,
settings, skills, and teachers. No test of statistical
significance exists for these ratios. Rather, they are
evaluated in the context of expert judgment of their prac¬
tical importance.

CHAPTER IV
RESULTS
The results for the two types of leap-ups, Leap and
Keep and Leap and Leave, are presented separately. An
example of a reading leap-up and a math leap-up are pre¬
sented in detail for each type. Other cases are presented
as replications within each type of experimental condition.
Leap and Keep
The results for the Leap and Keep experiments are
presented in two tables. Table 4 is a summary of all the
data on the Leap and Keeps. Leap and Keep leap-ups involve
continuing the preleap-up phase after the introduction of a
leap-up. Both skills are taught and measured daily.
Eight subjects and five teachers in five settings were
included in the Leap and Keep experiments. The subjects
experienced sixteen leap-ups. Eight of the leap-ups were
reading related and eight were on math skills.
The four dependent variables (celeration for correct
responses and errors, improvement index, accuracy improve¬
ment, and fluency) were determined for each preleap-up,
during, and leap-up phase. Preleap-up phases include all
the data taken before a leap-up began.
Li
During phases

Table 4
Leap and Keep Design: Learning Outcomes by Subject, Teacher, and Skill
Sub¬
ject
Teacher
Type
Leap
# Skill i
Condition
# of
Data
Points
CC
CE
Imp
Ind
Acc
Imp
FL/C
FL/E
W.T.
J.R.
Below
Grade
Level
Alphabet
Preleap
9
xl.05
/1.52
xl. 59
x2.3
20
0
Alphabet
During
12
xl .18
11.22
xl. 44
x2.9
40
0
1
Vocab Ginn
Level 2
Leap-up
12
xl.51
/1.4 6
x2.20
xll.3
18
3.2
2
Vocab Ginn
Level 5
Leap-up
23
xl. 3
/1.66
x2.15
x61.9
38
0
J.V.
S.L.
Below
Grade
Level
Phrases &
Vocab Ginn
Level 7
Preleap
6
x 1.23
/1.82
x2.24
x5.14
90
0
During
16
xl. 20
/1.23
xl. 48
x5.17
90
0
1
Phrases &
Vocab Ginn
Level 8
Leap
11
xl. 45
/ 1.4 5
x2.10
x8.1
80
2.5
Ginn
Level 7
During
7
xl. 57
xl.O
x2.57
x2.63
100
3

Table 4
Continued
# of
Sub¬
ject
Teacher Type
Leap
# Skill
Condition
Data
Points
CC
CE
Imp
Ind
A cc
Imp
FL/C
FL/E
2
Ginn
Level 8
Leap
11
xl. 86
/3.0
x5.58
x68
130
0
Ginn
Level 7
During
7
xl. 46
/1.7
x2.48
x4.46
50
2
3
Ginn
Level 8
Leap
10
x2.4
/ 4.6
xll.04
x44
60
1.3
D. P.
C.F. Below
Grade
Level
Ginn Vocab
Level 8
Preleap
8
xl .45
/1.73
x2.50
xl 8
60
0
Level 8
During
3
xl. 05
/ 1.0 5
xl. 10
xl .12
65
0
Level 8
During
8
xl. 55
/1.27
xl. 97
x5.61
60
1.8
1
Ginn Vocab
Level 11
Leap-up
12
xl .35
xl.O
x 1.3 5
x3.11
59
2.5
2
Level 11
Leap-up
7
xl .65
/1. 24
x2.0 5
x4.71
37
2
D. P.
C.F. Below
Grade
Level
Ginn
Phrases
Level 8
Preleap
3
x6
/ 8.2
x 4 9.2
x6
68
0

Table 4
Continued
it of
Sub- Leap Data Imp Acc
ject
Teacher Type
#
Skill
Condition
Points
CC
CE
Ind
Imp
FL/C
FL/E
Level 8
During
3
xl. 72
/io
111
x2.4 1
88
0
Ginn
Phrases
Level 11
Leap-up
8
xl. 74
/1.9
x3.31
x 11
113
0
N.R.
S.B. Slow
Sums to
Growth
18
Preleap
5
xl. 25
/ 2.0
x2.5
xl. 41
22
0
During
10
xl. 00
xl. 0
xl. 00
xl
36
0
1
Rounding
Nos.
Leap-up
11
xl. 56
/ 1.6 6
x2.59
x9.8
49
0
2
2 column/
2 digit sub-
traction
Leap-up
5
xl. 40
/ 2 2.5
x3 150
x80
20
0
C. J.
S.B. Slow
Growth
Sums to
18
Preleap
10
xl .03
xl. 0
x 1.03
xl .06
48
0
During
5
xl. 14
xl. 0
xl .14
xl .23
59
0
1
Rounding
Nos.
Leap-up
9
x2.16
/ 8.0 6
x 17
x29
50
0

Table 4
Continued
# of
Sub- Leap Data Imp Acc
ject
Teacher Type
#
Skill
Condition
Points
CC
CE
Ind
Imp
FL/C
FL/E
2
Addition
2 column/
2 digit
w/b
Leap-up
5
xl.80
/3.25
x5.83
x3 2
23
0
3
Subtrac¬
tion 2 col/
digit w/b Leap-up
4
x3.5
/ 2 5
x86
x56
28
0
A. K.
J.R. Slow
Growth
Sums to 10
Preleap
6
xl.06
xl.O
xl.06
xl. 36
15
0
During
8
xl. 19
xl. 0
xl. 19
xl .16
14
8
Addition
2 digit
w/c
Leap-up
4
xl.95
/ 2.6
x5.07
x6.6
5
1.
Y.B.
B.M. Slow
Growth
Mult.
Facts
Preleap
4
xl. 60
/ 1.0 5
xl. 68
xl. 65
52
0
During
4
xl. 24
xl.O
xl. 24
xl. 11
59
0
1
One place
division
Leap-up
15
x 1.4 2
/ 4.2
x5.96
xl95
39
0

Table 4
Continued
# of
Teacher
Type
Leap
# Skill
Condition
Data
Points
CC
CE
Imp
Ind
A cc
Imp
FL/C
FL/E
B.M.
Slow
Growth
Mult.
Facts
Preleap
3
x 1.5 5
x 1.0 0
xl .55
x 1.4 2
61
0
During
6
xl. 40
xl. 00
xl .40
xl.38
90
0
1
Square
Root
Leap-up
19
xl.7 5
/3.50
x4.55
937
95
0

51
include all the data from the continuation of the preleap-up
skill after the introduction of the leap-up skill, and
leap-up phases include all the data from the leap-up skill.
The number of data points in each phase and whether the
leap-up was a Slow Growth or Below Grade Level leap-up are
also reported in Table 4.
Following is a brief explanation of how to read the
results presented in Table 5. Table 5 presents comparisons
between the celerations, improvement index, accuracy
improvement, and fluency for the preleap-up, during, and
leap-up phases. The comparisons were done using frequency
multipliers. If the change represents an improvement, the
value is assigned a multiplication sign (x). If it repre¬
sents a worsening situation, the value is assigned a divi¬
sion sign (/).
By subtracting 1 from the frequency multiplier, and
moving the decimal point 2 places to the right, comparisons
between the phases can be discussed as percentages. Looking
at the first leap-up in Table 5, for subject W.T., the fre¬
quency multiplier for the celerations for the correct
responses between the preleap-up and the first leap-up phase
is a xl.24. This means that the correct responses acceler¬
ated 24% faster in the leap-up phase than in the preleap-up
phase. For the error celeration the frequency multiplier is
/1.04. This means that the errors decelerated 4% slower in
the leap-up phase than in the preleap-up phase. For the
improvement index the frequency multiplier indicates that

Table 5
Leap and Keep Design: Frequency Multipliers for
All the Preleap-Postleap-Up Comparisons
Celeration Imp ACC Fluency
Subject
Condition
Skill
C
E
Index
Imp
C
E
WT
Preleap-Up
Alphabet
xl .24
/1.04
xl. 38
x4.91
/1.10
/1.06
Leap-Up 1
Ginn
L2
During
Alphabet
xl. 10
xl.19
xl .52
x3.8 9
/ 2.2
/ 3.2
Leap-Up 1
Ginn
L2
Preleap-Up
Alphabet
xl.44
xl .09
xl. 35
x26.9
xl .90
x3
Leap 2
Ginn
L5
JV
Preleap-Up
Ginn
L7
xl .18
/1.25
/1.06
xl .58
/1.30
/ 2.3
Leap-Up 1
Ginn
L8
During
Ginn
L7
xl. 20
xl .18
xl. 42
xl .56
/1.13
/ 2.3
Leap-Up
Ginn
L8
Preleap-Up
Ginn
L7
xl .51
xl .65
x2.49
xl 3
xl.44
xl
Leap-Up 2
Ginn
L8
During
Ginn
L7
xl. 18
x3
x2.17
x26
xl .30
x3
Leap-Up 2
Ginn
L8
Preleap-Up
Ginn
L7
xl. 95
x2.53
x4.93
xlO
/1.50
/1.30
Leap-Up 3
Ginn
L8
DP
Preleap-Up
Ginn
Phr.
Lll
/ 3.4 5
/4.31
/15
xl .78
xl .66
xl
Leap-Up 1
Ginn
Phr.
Lll
During
Ginn
Phr.
L8
xl. 01
/5.26
/ 5.10
x4.43
xl .28
xl
Leap-Up 1
Ginn
Phr.
Lll
DP
Preleap-Up
Ginn
V L8
xl .07
/1.73
/I .85
/5.61
xl
/ 2.5
Leap-Up 1
Ginn
V Lll

Table 5
Continued
Subject
Condition
Skill
Celeration
C E
Imp
Index
ACC
Imp
Fluency
C E
During 1
Ginn V L8
xl.29
xl.29
xl. 23
/ 2.50
/I
/ 2.5
Leap-Up 1
Ginn V LI1
During 2
Ginn V L8
/I .5
/1.27
/1.46
/1.18
xl
xl . 39
Leap-Up 1
Ginn V Lll
Preleap-Up
Ginn V L8
xl/14
/1.4 0
/ 1.21
/3.73
/1.62
/ 2
Leap-Up 2
Ginn V Lll
NR
Preleap-Up
Sums to 18
xl.95
/1.20
/ 2.34
/6.95
x2.22
X]
Leap-Up 1
Rounding Nos.
During
Sums to 18
xl .56
xl. 66
x2.59
x9.8
xl. 36
xl
Leap-Up 1
Rounding Nos.
Preleap-Up
Sums to 18
xl75
xll
xl969
x57
xll .1
xl
Leap-Up 2
2 digit sub
A.K
Preleap-Up
Sums to 10
xl .84
xl .50
x2.60
x4.78
/ 3
/1.50
Leap-Up 1
2 digit Add w/c
During
Sums to 10
xl .64
xl .50
x2.60
4.26
/ 2.8
/1.50
Leap-Up 1
2 digit Add w/c
C. J.
Preleap-Up
Sums to 18
x2.09
x8.06
xl7
x27
xl/04
xl
Leap-Up 1
Rounding Nos.
During
Sums to 18
xl. 89
x8.06
xl5
x24
/1.18
xl
Leap-Up 1
Rounding Nos.
Preleap-Up
Sums to 18
xl .75
x3.25
x5.67
x30
/2.08
xl
Leap-Up 2
2 digit Add w/c
Preleap-Up
Sums to 18
x3.40
x25
x83
x53
/1.71
xl
Leap-Up 3
2 digit Sub w/b
cn
u>

Table 5
Continued
Subject
Condition
Skill
Celeration
C E
Imp
Index
ACC
Imp
Fluency
C E
YB
Preleap-Up
Leap-Up 1
Mult. Facts
1 place div.
/l. 13
x4
x3.55
x58
/1.3 3
xl
During
Leap-Up 1
Mult. Facts
1 place div.
/l. 15
x2.40
x4.58
x86
xl. 51
xl
CR
Preleap-Up
Leap-Up 1
Mult. Facts
Square Root
xl. 13
x3.50
x2.9 4
x6 60
xl. 56
xl
During
Leap-Up 1
Mult. Facts
Square Root
xl.25
3.50
x3.2 5
x6 79
xl. 05
xl

55
the leap-up phase was improving 38% faster, while accuracy
improvement was 391% better for the leap-up phase. Fluency
was 10% better for the correct responses and 6% better for
the errors in the preleap-up phase, compared with the
leap-up phase.
Reading Experiment: J.V. Ginn Phrases
J.V. was a 5th grade student classified as emotionally
disturbed. He was working on Ginn level 7 phrases and
vocabulary. The teacher decided to leap J.V. up to a higher
level of Ginn (see Figure 5) because he was working below
his grade level placement and had expressed an interest in
doing "harder work." His preleap-up celeration for correct
responses indicated that he was progressing at 23% per week,
while his errors were going down at 82% per week (see
Table 4). For J.V. a leap-up to Ginn Level 8 produced the
required error rate of 10% more errors than correct
responses.
Table 5 shows the comparison between the preleap-up
phase for J.V. on Level 7 Ginn and three separate leap-ups
to Level 8 Ginn. The celeration for the correct responses
was 18% faster for the first leap-up, 51% faster for the
second leap-up, and 95% faster for the third leap-up when
compared to the preleap-up phase. For error deceleration,
the effect of the leap-up teaching strategy grows as the
teacher learns to teach to errors. In the first leap-up,
the error celeration was 25% faster during the preleap-up

< o
56
turrwr _j v pr»i»«t> Hor»m»nt_s^e . $37 Ginn Phrases, level 7
T»«ch»r _s l DoTínj i .Level 7, new phrases
s»«ifi4 _j J Flnley Elem— ihrring 2 .Level 7. new phrases
Figure 5. The Reading Leap and Keep Example.

57
Lnrwr _J V M.lr»? noT*m»nt_c(?* . Q|nn phrases |evel 7
T*»eh»r _s [ During i .Level 7, new phrases
s»mr* _J j Flhley E'em— d Figure 5.
Continued.

58
phase. During the second leap-up it was 65% faster for the
leap-up phase, and for the third leap-up, it was 153% faster
for the leap-up phase.
The improvement index was almost equal for the first
leap-up, but much faster for the leap-up phases in leaps two
and three. The improvement index for the first leap-up was
6% faster for the preleap-up phase, the second was 149%
faster for the leap-up phase, and the third was 393% faster
for the leap-up phase. Accuracy improvement across the
three leap-up phases was much better for the leap-up phases
than for the preleap-up phase ranging from 58% to 1300%
better. J.V. obtained better fluency in the preleap-up
phase for two of the three leap-ups.
When comparing the 3 leap-ups to the during phases the
findings for celeration, improvement index, and accuracy
ratio were similar to the preleap-up comparisons. The
leap-up phases provided faster celerations, more improve¬
ment, and higher accuracy improvement. Fluency was better
in the during phase for the first leap-up, but better in the
leap-up phases for the second and third leap-ups.
Systematic Replications on Other Reading Leap-Ups
Similar results were found for subject W.T., a first
grade EMR student in a resource room. This subject experi¬
enced two leap-ups (see Table 4). The preleap-up phase was
learning to say the alphabet and the two leap-ups were to

59
Ginn Level 2 and then Ginn Level 5 vocabulary. Her begin¬
ning celerations for the preleap-up phase indicated slow
growth for correct responses and a fairly good deceleration
of errors (see Table 4). Results were similar to J.V.'s
results. Here celerations for correct responses were
steeper in both leap-up phases. Error deceleration was
almost equal for the comparison between the first preleap-up
and leap-up phases and 9% faster for the leap-up phase
during the second leap-up.
The improvement index was faster and accuracy improve¬
ment was higher for both leap-ups. Fluency was better
during the preleap-up phase when compared with the first
leap-up, but better in the leap-up phase for the second.
For D.P., a 5th grade learning disabled student working
on Ginn vocabulary and phrases, mixed results were obtained.
But the findings were generally in favor of the preleap-up
phases. D.P. was given two grade level leap-ups from Ginn
Level 8 to Ginn Level 11 vocabulary. His rate of learning
was already quite high on his preleap-up phase (see
Table 4). For the two leap-ups, celeration for correct
responses was 7% in favor of the preleap-up phase for the
first leap-up and 14% in favor of the preleap-up phase
during the second leap-up. Error deceleration was faster
for the preleap-up phases. It was 73% faster for the first
leap-up and 40% faster for the second-leap-up in favor of
the preleap phases. The improvement index and accuracy

60
improvement measures were also better for the preleap-up
phase.
On the reading phrases the preleap-up rate of learning
was also greater. In D.P.'s case his preleap-up condition
was unique in that his correct and error celerations were
both very high before the leap-up. Although these results
favor the preleap condition, it is important to note that
D.P. continues to learn very well on the Level 11 Ginn
phrases, an increase in three levels over the preleap
material.
Systematic Replications with Math Leap-ups
The comparisons for N.R., an educably mentally retarded
student, were similar to J.V.'s results (see Table 5). In
his first leap-up all the measures for rate of learning were
better for the leap-up phase except error deceleration which
was 20% in favor of the preleap-up phase. In his second
leap-up all the measures for learning increased dramatically
in favor of the leap-up phase including error deceleration.
Results show that acceleration for corrects was better by a
factor of 175, error deceleration was better by a factor of
11, the improvement index was 1960 times better, and
accuracy improvement was 57 times better during the leap-up
phase. Fluency was better in the preleap-up phase for the
first leap-up, and for the leap-up phase for the second
leap-up.

61
A.K., an emotionally handicapped student, C.J., an
educably mentally retarded student, and G.R. and Y.B.,
learning disabled students, were given a total of six math
leap-ups. They all showed an increase in learning following
the leap-up condition for celeration, growth, and accuracy
improvement (see Table 5). Results show that celerations
for increasing correct responses and decreasing errors were
higher, improvement was faster, and accuracy improvement was
higher. Fluency was better for two of the leap-ups when
compared with the preleap condition and for two of the
leap-ups when compared with the during conditions.
Math Example: Add Facts/Rounding Numbers
C.J., a middle school educably mentally retarded
student, was given a leap-up from add facts to rounding
numbers (see Figure 6). C.J. had been working on add facts
in order to build up her fluency in adding number facts.
Her celeration for corrects was a xl.03 and for errors a
xl.O. It was decided to leap-up because her progress was
slow and she was bored practicing the facts.
A comparison of the celerations for the two phases (see
Table 5) for her first leap-up show that the leap-up condi¬
tion produced faster celeration for the corrects by a factor
of 2 and errors were reduced faster by a factor of 8. The
improvement index and accuracy improvement were improved by
factors of 17 and 27 respectively. Fluency was 4% better

O 2
62
r
2
si
Weeks
&
¿y
y
a
L'«™r _c J Prnnp Ho>>»míi\t_see. wrjte Add Facts, sums to 13
T**ch»r _s b Lnp-up i .Rounding numbers
Sitting .Lincoln Middle— L«p-«p 2 .Two column addition
Lup-tip 3 .Two digit, two place subtraction
Figure 6. The Math Leap and Keep Example

L'irtwr _c j ri»i»»p tio'i»m»nt_seo . write Add Fact
T»*eh*r _s g During ^«.Continuation of preleap-up
s.nine .Lincoln Middle
Figure 6
Continued

64
for the leap-up phase. Results from the during phase
comparison were very similar.
Two more leap-ups were then done with C.J. in order to
replicate the experimental effects within subject. They
were two place addition with carrying and two place sub¬
traction with borrowing. Both leap-ups showed an increased
rate of learning as measured by celeration, improvement
index and accuracy improvement similar to the first leap-up.
Both leap-up phases were short. Fluency was higher for
corrects during the preleap-up condition and was the same
for errors across both conditions.
Replications With the Same Math Skills
Two of the leap-ups from C.S. were replicated with
another student, N.R., an EMR student was given a leap-up
from add facts to rounding numbers. Results were similar to
C.J.'s. Her comparisons for celeration for correct
responses, improvement index, and accuracy improvement, and
fluency were all higher in the leap-up phase when compared
with the preleap-up or during phase. Her second leap-up to
subtraction with borrowing also resulted in higher rates of
learning on all the measures including error deceleration.
Celeration, improvement index, and accuracy improvement were
all better in the leap-up phase while fluency was better in
the preleap-up phase. Her error decelerations were not as
high as C.J.'s.

65
Systematic Replications with Other Math Skills
Three other leap-ups were done with students on math
skills. The first one was a leap-up for A.K., an elementary
emotionally handicapped student. The leap was from add
facts to 2-digit adding with carrying. His celeration,
improvement index and accuracy improvement increased during
the leap-up phase but his fluency level was lower. G.R., an
emotionally handicapped student, was given a leap-up from
multiplication facts to square roots. His learning on the
leap-up skill was faster on all measures including fluency.
Another student, Y.B., was given a leap-up from multiplica¬
tion facts to one place division. Her learning rates were
better on all measures except celeration for correct
responses. Fluency was better in the preleap-up phase.
During Phases
The Leap and Keep Design controls for maturation and
correlated historical events by continuing the preleap-up
phase when the leap-up begins. The results from these
experiments indicate that learning rates were faster as
measured by celeration for correct responses and errors,
improvement index, and accuracy improvement during the
leap-up phases compared with the during phases. These
results were replicated 9 times across subjects, skills,
teachers, and settings. Fluency for correct responses was
generally in favor of the during phases compared with the
leap-up phases, and fluency for errors was mixed, some of

66
the leap-up phases achieving higher fluency and some of the
during phases achieving better results for errors. These
results indicate that maturation and outside events were not
responsible for the higher rate of learning during the
leap-up condition.
Summary of Leap and Keeps
A total of 16 Leap and Keep Leap-ups were done with
8 students. Nineteen of twenty-eight comparisons across all
the preleap-up, during, and leap-up phases showed an
increase in student rate of learning as measured by celera-
tion, improvement index, and accuracy improvement in the
leap-up phase. Three of the comparisons indicated better
error deceleration for the preleap-up phases, which was
subsequently followed by additional leap-ups with the same
students in which the errors decelerated more rapidly in the
leap-up phases. For one comparison, the celeration for
correct responses was better for the preleap-up phase, but
all other measures were better for the leap-up phases.
Five comparisons were in favor of the preleap-up phases
on rate of learning comparisons. These were all reading
leap-ups in which the student began with high initial
acceleration for correct responses and deceleration for
errors. The results for the fluency measure were mixed with
some of the preleap-up and during phases achieving a higher
terminal frequency than the leap-up phases.

67
The findings that the leap-up teaching strategy pro¬
duces a higher rate of learning as measured by celeration
for correct responses and errors, improvement index, and
accuracy improvement was replicated across 3 teachers,
3 settings, 6 students, and 9 skills using the Leap and Keep
Design. Possible factors involved in replication failures
will be discussed in the next chapter.
Leap and Leave
Table 6 presents a summary of all the data on the Leap
and Leave experiments. Leap and Leave leap-ups use the
procedure of dropping the skill with low error rate when the
leap-up skill starts. Nine subjects and five teachers in
five settings were included in the Leap and Leave experi¬
ments. The subjects experienced 13 leap-ups. Two of the
leap-ups were on reading skills and the other eleven were
math skills. The five dependent measures are presented for
each preleap-up and leap-up phase. The number of data
points in the phase and whether the leap-up is a Slow Growth
or Below Grade Level leap-up are also given.
Table 7 presents the comparisons between the celera-
tions, improvement index, accuracy improvement, and fluency
for the preleap-up and leap-up phases. The comparisons were
done using frequency multipliers, as in Table 5.

Table 6
Leap and Leave Design: Learning Outcomes by Subject, Teacher, and Skill
# of
Sub¬
ject
Teacher
Leap
Type # Skill
Condition
Data
Points
CC
CE
Imp
Ind
Acc
Imp
FL/C
FL/E
E.B.
M.G.
Below
Grade
Level
Oral
Reading G1
Preleap
5
xl.42
xl. 00
xl.42
xl. 20
110
0
1
Oral
Reading CL
Leap-up
5
x2 4
/II
x264
x5.33
80
0
E.B.
M.G.
Below
Grade
Level
Vocabulary
2.2
Preleap
7
xl .37
xl.O
xl. 37
xl. 30
103
0
1
Vocabulary
8.0
Leap-up
7
xl. 83
/3.4
x2 5
x2 5
70
0
L. A.
W.O.
Slow
Growth
Sums to 18
Preleap
8
xl. 15
/ 1.0 5
xl. 2
xl. 30
63
0
1
Mult. Fract
x2 x3
Leap-up
4
xll. 7
/ 4.4
x51
x2.80
9
0
2
Mult Fract.
x4-x9
Leap-up
5
x3.90
/ 6.5
x2.5
xl 2
22
0
3
Changing
Dec. to %
Leap-up
5
xl6.5
/17
x276
x3 2
8
0

Table 6
Continued
# of
Sub- Leap Data
ject Teacher Type 4 Skill Condition Points
W.T.
J.R.
Below
Grade
Level
Sums to 6
Preleap
1
2 digit
Add w/c
Leap-up
R. J.
S.B.
Slow
Growth
Sums to 18
Preleap
1
Rounding
off nos.
Leap-up
O.S.
B.M.
Slow
Growth
Sums to 18
Preleap
1
One place
division
Leap-up
J.R.
B.M.
Below
Grade
Level
Sums to 10
Preleap
1
Telling Time
by 1/2 hour
Leap-up
7
CC
CE
Imp
Ind
Acc
Imp
FL/C
FL/E
xl.39
/l. 46
xl .90
x2.1
28
0
xl8.5
/ 8.0
xl48
xl40
35
0
xl. 13
xl.00
xl. 13
xl.80
90
0
x 1.7 5
/2.40
x4.2
xl. 20
100
0
xl. 09
xl. 00
xl. 09
xl. 15
54
0
xl. 46
/ 5.90
x8.61
xl. 54
18
0
xl. 20
/1.50
x2.4
x3.1
32
0
xl. 90
/2.59
x4.92
x 10
14
0

Table 6
Continued
# of
Sub- Leap Data Imp Acc
ject Teacher Type # Skill Condition Points CC CE Ind Imp FL/C FL/E
A.F. W.O. Below
Grade
Level
Sub Facts
Preleap
12
xl. 30
xl. 00
xl. 30
x2.03
55
0
1
Mult, of
Fractions
Leap-up
3
x4.00
19.6
x38
xlO
5
1
Below
Grade
Level
Mixed Facts
Preleap
9
xl. 27
x 1.00
xl. 27
xl. 55
45
0
1
Division of
Fractions
Leap-up
4
xl3
/ 583
x781
x26
36
0
o

Table 6
Continued
# of
Sub¬
ject
Teacher
Type
Leap
1/ Skill
Condition
Data
Points
CC
CE
Imp
Ind
Acc
Imp
FL/C
FL/E
C.B.
B.M.
Slow
Growth
Mult. Facts
Preleap
13
xl. 15
xl.O
xl .15
xl. 6
16
0
1
2 place
sub w/b
Leap-up
11
xl. 5
/1.5
x2.2 5
x6.7
12
0
2
Square Root
Leap-up
10
x2.03
/ 6.4
xl 3
X1320
22
0

Table 7
Leap and Leave Design: Frequency Multipliers for
All Preleap-Postleap-Up Comparisons
Celeration
Imp
ACC
Fluency
ibject Condition
Skill
C
E
Index
Imp
C
E
EB
Preleap-Up
Oral Reading G1
xl7
x 11
xl86
x4.44
/1.38
12.
Leap-Up
Oral Reading 12.0
EB
Preleap-Up
Vocabulary 2.2
Leap-Up
Vocabulary 8.0
x 1.3 4
xl3
xl8
xl9
/1.4 7
xl
L. A
Preleap-Up
Sums to 18
Leap-Up
Mult. Frac. x2-x3
xlO
x4.19
x43
x2.15
/ 7
xl
Preleap-Up
Sums to 18
Leap-Up
Mult. Frac. x4-x9
x3.39
x6.19
x20
x9.23
/ 2.8 6
xl
Preleap-Up
Sums to 18
Changing dec. to %
xl4
xl6
xl25
x24
/ 7.8 8
xl
W.T.
Preleap-Up
Sums to 6
Leap
2 digit Add w/c
xl3
x5.48
x78
x67
xl. 25
xl
R. J.
Preleap-Up
Sums to 18
Rounding of 10/100
xl.55
x2.4
x3.72
x6.67
xl. 11
xl
O.S.
Preleap-Up
Sums to 18
Leap-Up
One place division
xl.34
x5.9
x7.89
xl3 4
/ 3
xl
J.R.
Preleap-Up
Sums to 10
Leap-Up
Telling time
by 1/2 hour.
x 1.5 8
xl. 73
x2.05
x3.23
/ 2.29
xl

Table 7
Continued
Subject
Condition
i Skill
Celeration
C E
Imp
Index
ACC
Imp
Fluency
C E
A. F.
Preleap-Up
Leap-Up
Subtraction Facts
Mult, of Frac.
x3.07
x9.60
x29.2
x4.35
/II
xl
R. V.
Preleap-Up
Leap-Up
Mixed Facts
Div. of Fractions
xlO.55
x58.3
x615
x 17
/ 1.2 5
xl
C.B.
Preleap-Up
Leap-Up
Mult. Facts
2 place Sub w/b
xl.30
xl. 5
xl. 96
x4 . 19
/1.5
xl
Preleap-Up
Leap-Up
Mult. Facts
Square Root
x 177
x6.4
xll
x825
xl. 61
xl
u>

Reading Example: Oral Reading
E.B., an elementary school language disabled student,
was given a leap-up from a first grade reading book to a
college level astronomy text (see Figure 7). Several leaps
to lower level reading material were tried but the error
rate criteria could only be reached at this level. The
preleap-up phase had a correct celeration of xl.42 and an
error celeration of xl.OO.
A comparison of the celerations for the two phases (see
Table 7) shows that the leap-up condition was better by a
factor of 17 for the correct responses and a factor of 11
for the errors. The improvement index was better by a
factor of 186 and accuracy improvement was better by a
factor of more than 4. Fluency was 38% better for the
preleap-up phase for correct responses and it doubled for
the errors. E.B.'s second leap-up on reading vocabulary
produced similar results.
Systematic Replications with Math Skills
Eleven math replications of leap and leaves replicated
the findings of E.B.'s leap-up. Three leap-ups in math were
done for L.A., a middle school learning disabled student.
The three leap-ups had faster celeration for correct
responses by factors of 10, 3.3, and 14 and for errors by
4.19, 6.19, and 16. The improvement index for the three
leap-ups ranged from a factor of 20 to a factor of 125
better. Accuracy improvement ranged from a factor of a

75
Lturwr _e B pr»i»»p Texted Words - grade level 1
T««oh#r —Investigator L».p-np i .College level astronomy text
satire _Home
Figure 7. The Reading Leap and Leave Example.

76
little more than 2 to a factor of 24 better. Fluency was
better in the preleap-up phases.
Four other leap-ups with middle school students R.v.,
A.F., O.S., and R.J. had similar results. Although the
celerations for the correct responses were not as fast as
E.B.'s leap-up, the other measures were comparable.
Further, students who experienced two math leap-ups had
faster learning as measured by celeration, improvement
index, and accuracy improvement and also had higher fluency
in their leap-up phases compared with their preleap-up
phases.
Math Example; Add Facts/2 Digit Addition with Carrying
W.T., a mentally retarded student, was given a leap-up
from learning add facts to 6 to doing two place addition
with carrying (see Figure 8). Her preleap-up phase had a
correct celeration at xl.39 and error celeration at xl.46.
She was not achieving fluency on the addition facts even
though her errors were going down.
A comparison of the celerations for the two phases (see
Table 7) shows that the leap-up phase produced faster
celeration for the corrects by a factor of 13 and that the
error-learning improved by a factor of 5.4. The improvement
index was better by x78, while accuracy improvement was
better by a factor of 67 in the leap-up phase. Fluency was
also higher in the leap-up phase.

77
lormr _ w t Mn*«p notrm»nt_see . write Add Facts - sums to 5
T.«h»r _j r L..p-up i .Two column addition without carrying.
smini .Stephen Foster
Figure 8.
The Math Leap and Leave Example.

78
Systematic Replications With Other Math Skills
One math leap-up replicated the findings on all the
measures of W.T.'s leap-up. Comparisons for R.J.'s leap-up
(see Table 7) show that the celeration for the correct
responses was 55% faster and improved error learning by a
factor of 2.4 during the leap-up phase. The improvement
index was better by x3.7 and accuracy improvement was better
by a factor of 6.6. Fluency for correct responses was 11%
better for the leap-up phase than for the preleap-up phase.
Nine math leap-ups replicated the findings of W.T.'s
leap-up on all the measures except fluency. A comparison of
the celerations for the correct responses shows that the
leap-up phases produced better learning by factors between
1.3 and 16.8. Errors learning improved by factors between
1.5 and 58.3. The improvement index was better by factors
between 1.9 and 615. Accuracy improvement changed by
factors between 2.1 and 1659. Fluency was better in the
preleap-up phases. The range for fluency was between xl.3
and xll in favor of the preleap-up phases.
Summary of Leap and Leave Leap-Ups
A total of 13 Leap and Leave leap-ups were done with
8 students. Across all the preleap-ups and leap-up phases
results show an increase in student rate of learning as
measured by celeration, improvement index, and accuracy
improvement. Three of the leap-ups resulted in higher
fluency for the leap-up phase compared with the preleap-up

79
phase, while the remaining 10 leap-ups produced higher
fluency during the preleap-up phases.
The findings that the leap-up teaching strategy pro¬
duces a higher rate of learning as measured by celeration
for correct responses and errors, improvement index, and
accuracy improvement were replicated across 4 teachers,
4 settings, 8 students, and 12 skills using the Leap and
Leave Design.

CHAPTER V
DISCUSSION
The discussion is organized around the experimental
question, replications and previous knowledge, practical
implications for special education and regular education,
problems and limitations of the study, and recommendations
for future research.
Experimental Question
Leap and Keep Design
Celeration, improvement index, and accuracy improve¬
ment . The findings of this study suggest that the curricu¬
lum leap-up can be an effective teaching strategy for
elementary and middle school students in special education
resource rooms who are not making gains on lower level
materials. Leap-ups to skills with initially high error
rates generally produced faster learning as measured by
celeration, improvement index, and accuracy improvement.
There is also evidence to suggest that this teaching
strategy can benefit students who are making gains on below
grade level material. Results indicate that when a student
80

31
is experiencing medium to rapid growth on below grade level
skills, leap-ups may not accelerate learning above the
preleap-up phase, but can produce medium to high rate
learning on the leap-up skill.
There were also some indications of "learning to learn"
and "learning to teach" occurrences during these experi¬
ments. In three cases in particular students and teachers
did better decelerating errors on each successive leap-up.
Fluency. In looking across all the frequency multi¬
pliers (see Table 4) for the preleap, during, and leap-up
phases, fluency for correct responses was split fairly
evenly between the preleap and during phases compared with
the leap-up phases. In over half, the fluency for the
errors reached zero across the preleap-up, during, and
leap-up phases. In the remaining leap-ups fluency was
generally in favor of the preleap-up phases. Achieving
fluency is a matter of how long the leap-up continues. In
some cases the student failed to reach higher fluency on the
leap-up skill because the teacher dropped the skill as soon
as the data stabilized. This was often due to time limita¬
tions in the classroom and the fact that the leap-up was
done specifically for experimental purposes. There was no
difference in fluency for the leap-ups across low growth and
below grade level leap-ups.

82
Leap and Leave Design
Celeration, improvement index, and accuracy improve¬
ment . The findings from this group of experiments indicate
that skills that have an initially higher error rate (10%
more than correct responses) generally produce higher rates
of learning than those which begin with lower initial error
rates. There was no difference in the results across Low
Growth leap-ups and Below Grade Level leap-ups. These
findings suggest that students in special education resource
rooms should be given tasks with errors initially above the
correct responses when they are making slow gains on skills
with low or no errors or when they are working on skills
below their grade level with low to medium rates of
learning.
Fluency. The frequency multipliers for fluency (see
Table 7) indicate that fluency for corrects was generally
better in the preleap-up phases than in the leap-up phases.
The fluency for errors was the same in all but one leap-up.
This indicates that the errors in all but the one leap-up
reached 0. Again, in many cases the fluency on the correct
responses in the leap-up phases was not higher because of
the fact that the primary purpose of the investigation was
to look for learning rates. Once it was established that
the student could learn the skill rapidly, the teacher often
dropped it and tried another skill. Fluency was not
affected by the type of leap-up (Low Growth or Below Grade
Level) .

83
Summary
Both the Leap and Keep and Leap and Leave experiments
generally produced higher rates of learning during the
leap-up phases. While three leap-ups did not get results,
many of the leap-ups do show large differences on the
learning measure comparisons. These findings could have
significant implications for the education of handicapped
learners. Probably some proportion of all handicapped
learners' curriculum should be high initial error instruc¬
tion .
Replications
One reason replications are done is to demonstrate the
reliability and generality of data (Tawney and Gast, 1984) .
Another reason is that replications reduce the scientists'
margin of error and insure that the findings can withstand
repeated tests (Sidman, 1960). In this investigation,
replications were done across subjects, teachers, skills,
and settings within each experimental design as described in
Chapter 4.
For the Leap and Keep designs three leap-ups failed to
replicate the results of higher rates of learning that were
generally found for the other 13 leap-ups in the study.
There are at least two possible explanations for this
failure to replicate. First., the initial celerations for
correct responses and errors for these leap-ups were already
high. Second the same teacher taught the same learner all

84
three leap-up skills. The data indicate that she had some
trouble teaching to errors in the leap-up phases.
Replications Across Leap and Keep and Leap and Leave
Designs
Generally, higher rates of learning during the leap-up
phases were found for both the Leap and Keep and the Leap
and Leave designs. This replication across designs serves
to strengthen confidence in the findings of the less power¬
ful Leap and Leave design.
Replications With Studies Already in the Literature
Subjects in this study generally experienced steeper
learning rates under the initially high error rate condi¬
tion. One of the early studies on learning rates from
precision teaching (Neely, 1978) found that error
deceleration rates were greater when students were given
tasks on which they were making at least 5 to 10 errors per
minute. No differences in correct celeration rates were
found. However, Neely introduced the idea that crossover
learning pictures (with initial error frequencies above
correct responses) could produce steeper celerations for
correct responses. McGreevy (1980) became interested in the
concept that tasks with initially high errors could produce
steeper learning and introduced the idea of "hard to do,"
"easy to learn." He studied the learning of a severely
retarded teenager on a vocabulary task with the initial
error frequency above the correct responses. The student

85
achieved rapid acceleration for correct responses and rapid
deceleration for errors on the task. Bower and Orgal (1981)
taught college students psychology terms on which they
initially made many more errors than corrects. Their rates
of learning were steep for both corrects and errors.
Stromberg and Chappell (1980) taught a second grade class
math tasks on which they made little or no initial errors.
He then gave them a leap-up to all the math operations in
the curriculum to learn at one time. The students' initial
error frequencies were very high for the leap-up math tasks,
but their rate of learning was much better than it had been
on the easier math tasks. Eaton and Wittman (1982) found
the learning rates for three junior high school mildly
handicapped students could be accelerated by giving them
math leap-ups to skills with initially high error rates.
This investigation studied the learning rates of mildly
handicapped students in resource rooms who were given math
and reading leap-ups. Results replicated across subjects,
teachers, skills, and settings generally found higher
learning rates on skills with at least 10% more errors than
correct responses compared with skills that had initially
very low error rates. These results replicate the findings
in the above studies and add a new sample population and
different skills.

86
Practical Implications
May students fail to make gains in special education
classes (Glazzard, 1984) . These classes often focus on
skills with initially low error rates so that students can
experience success. There is also evidence that the type of
instruction used in the majority of classrooms may fail to
challenge the learner or to give them skills that will
generalize to mainstream classes (Glazzard, 1984) .
Further, some teaching strategies that have come from
applied behavior analysis, like task analysis (Eaton and
Wittman, 1982; Howell, Kaplan, & O'Connell, 1981) or
errorless learning may be overused with handicapped
learners. The steps in task analysis can be made so excru-
tiatingly small that the student becomes bored with learning
the task. Errorless learning, while an excellent teaching
method, does not allow students to experience the learning
that comes from viewing errors as learning opportunities
(Alberto & Troutman, 1982) . The results of overusing these
strategies may be that we are producing passive learners who
become bored with easy unchallenging tasks or don't know how
to learn from errors.
The use of the high error teaching strategy offers many
benefits to classroom teachers and their students. These
are discussed below along with some guidelines.

87
Benefits
Results from this study indicate that when teachers use
the leap-up teaching strategy students rate of learning may
increase. Students tend to become more active learners and
teachers become involved in actually teaching skills on
which students need instruction rather than just practice.
From a practical point of view, special education
students who are behind in school need to be taught using
teaching strategies that promote high rate learning. This
is the only way that they can hope to catch up with their
peers and/or reach any level of competency in basic skills
when they complete their education. It is apparent that we
must not be content to see these students fall further, and
further behind grade level skills as they progress through
special education programs.
As evidenced in these experiments, by teaching students
to accept making many errors when they begin to learn a new
skill, it is possible to accelerate learning and to move
students closer to grade level skills. Students appear to
be motivated by learning more difficult skills and skills
closer to those that their peers are learning. Leap-up
strategies may be a contribution to the successful main-
streaming of mildly handicapped students.
Also, these findings may have implications for school
psychologist and placement committee members responsible for
developing IEP's for handicapped students. The tendency is
to write long and short term objectives for students which

88
emphasize skills with fairly high initial accuracy rates.
While this may be done to "let the student experience
success," educators should be aware that tasks with ini¬
tially high error rates must also be included in a student's
program in order to insure that maximum learning is taking
place and that the student is getting experience in learning
from errors.
Guidelines
The high error teaching strategy is one way to acceler¬
ate the learning of skills for those students who are making
slow progress and/or who are working on skills below their
grade level placement. However, it would probably not be
appropriate to go overboard on leap-ups. More work is
needed to determine what proportion of the curriculum should
be initially high error rate skills. Also, more ways to
reduce errors rapidly need to be developed and ways of
overcoming learner resistance to making errors need to be
explored before the high error teaching strategy can be
fully appreciated.
Problems and Limitations of the Study
One problem appeared during the course of this study.
This was due to the fact that many of the practicum teachers
were young and inexperienced. They received little or no
support from their directing teachers in using the leap-up
teaching strategy. They were eager to become involved in

89
the leap-up experiments, but were reluctant to take the
chance of leaping their students to skills with very high
error rates. Many of them were concerned that the students
still needed practice on the lower level skills and would
"miss out on learning." It was interesting to note, how¬
ever, as they became involved in the experiments two things
happened. First, they became excited about the learning
taking place on the leap-up skills and actually felt they
were teaching instead of just providing opportunities for
practice. Second, they began to defend the leap-up concept
to their directing teachers and wanted to cease teaching the
lower level skills.
A limitation of this study was that the leap-ups
generally consisted of math skills, and of reading vocabu¬
lary skills. This was because these skills were the easiest
to define and were the skills being taught in the practicum
sites. A problem was found in trying to do leap-ups on oral
reading. Because of the connecting words in oral reading it
was very difficult to meet the high initial error rate
criterion. The error rate was only achieved for one leap-up
and this entailed leaping a student from first grade reader
to a college level text book. It may be that the leap-up
concept will have to be defined more precisely for a broader
range of skills.

90
Recommendations for Future Research
The curriculum leap-up is an effective teaching
strategy when used as part of the instructional approach
with mildly handicapped learners. Future research on
curriculum leap-ups should focus on five areas: (1) the
effects of longer leap-up phases on fluency, (2) chunk-ups,
(3) the effects of step-size on learning rates in leap-up
phases, (4) strategies for reducing errors, and (5) pro¬
cedures for reducing anxiety and overcoming resistance to
errors.
Longer Leap-Up Phases and Fluency
In this investigation the major concern was rate of
learning under leap-up conditions compared with preleap-up
conditions. Many of the leap-up phases were short. Future
research should focus on the attainment of fluency following
a leap-up. Since fluency is dependent on time, the leap-up
phases would have to be lengthened and strategies that build
fluency could be blended with the error reduction pro¬
cedures .
Chunk-Ups
A second suggestion for future research is on the
concept of chunk-ups. Chunk-ups are special cases of
leap-ups. They involve adding more unique problems or units
to the teaching set. For example, if a student usually is

given 10 words per week, he could be given a chunk-up to
20 words per week.
91
Chunk-ups are related to leap-ups in that the student
is expected to learn more at one time. The idea is that if
the same rate of learning or a faster rate of learning is
noted then the "chunk-up" is way of expediting learning for
students who need to catch up or who are challenged by
learning more at one time.
This investigation intended to study the chunk-up
concept. However, preliminary work with chunk-ups led to
some problems. Specifically, (1) the chunk-up was not
empirically defined in such a way that the concept could be
easily understood by those trying to explore its value and
(2) there was resistance on the part of the practicum
teachers and the directing teachers to try the strategy.
Reports from the practicum teachers indicated that directing
teachers felt that the chunk size that they were already
using was adequate. They were not interested in exploring
learning under large chunk conditions.
The small amount of data that was obtained did not show
clear enough evidence of control to warrant conclusions
about the effectiveness of chunk-ups. Recently, teachers
who have tried chunk-ups have reported informally that it is
working effectively as a teaching strategy. This concept
should be studied further and documented more carefully.

92
Step Size
Step .is a measure of the immediate change in the
frequency for correct responses and errors when a new phase
begins. In going from the preleap-up to the leap-up phase a
step down in correct responses and a step up in errors
occurs. Further research should focus on the size of these
steps and their correlation with learning rates in leap-up
phases.
McGreevy et al. (1982) have already looked at the
effect on variability of learning within a range of diffi¬
cult tasks and found little differences. This research
would extend his conclusions by looking at the rate of
learning within a range of step sizes.
Strategies for Reducing Errors
Effective strategies for reducing errors rapidly need
to be explored. Current behavior analysis research on new
ways to reduce errors using stimulus control procedures give
hope that new tools may be developing in this area.
Anxiety and Resistance to Errors
At present teachers, parents, and learners are often
reluctant and anxious about learning a task that generates
high initial errors. Previous experience, with errors
viewed as failures, may account for large part of this
resistance. Research needs to focus on ways to help
individuals view high initial errors as "learning

opportunities." Handicapped persons may produce more than
expected errors in their "natural" interaction with the
world. It may be especially important for them to learn how
to cope with, and keep trying through, the stage of
initially high error production.

APPENDIX A
DEFINITION OF TERMS

Standard Glossary and Charting Procedures
Accelerating Target—a movement the behaver, manager,
advisor, or supervisor expects to accelerate; the
frequency is symbolized by placing a dot on the Chart.
Accuracy Improvement—a measure of change in accuracy over
time; celeration correct/celeration incorrect.
Accuracy Multiplier—measure of accuracy: frequency
correct/frequency incorrect; distance from frequency
incorrect to frequency correct; also called the
accuracy ratio.
Accuracy Pair—two movements, usually correct and incorrect,
charted simultaneously.
Add-Subtract Scale—any measurement scale on which adding
and subtracting by a constant amount is represented by
a constant distance; the "up the left" scale on a equal
interval chart.
Advisor--person who advises a manager, usually viewing
Charts on a weekly basis.
Behaver—person whose behavior is displayed on the Chart.
Behavior Floor—the lowest daily frequency possible for a
particular behavior; 1/number of minutes behavior can
occur; symbolized by drawing a solid horizontal line on
the Chart.
Bounced Around Celeration up bounce and down bounce com¬
bined; the range of deviations of frequencies from the
celeration line.
Celeration--basic unit of measurement of behavior change;
change in frequency per unit time.
Celeration Aim--the expected celeration for a given move¬
ment.
Celeration Line—straight line constructed through con¬
tinuous Frequencies for a given movement on the
Standard Behavior Chart. For purposes of this inves¬
tigation, celeration lines were drawn using the quarter
intersect method (White & Haring, 1980).
Celeration Multiplier (turn up or turn down)--value by which
one celeration is'multiplied or divided to obtain a
second.

Change Day—first day of a phase change; symbolized by
drawing a vertical line covering that day line on the
Chart.
Change Line—A line to demark a change of instructional
conditions. Goes in the space before first day of new
condition.
Chunk—Change in frequency per week. Number of units in the
teaching set.
Counting Period Ceiling—the highest frequency observable
under a given counting procedure; symbolized by drawing
a dash line on the Chart connecting the Saturday and
Monday lines.
Counting Period Floor—the lowest frequency detectable by a
given counting procedure; 1/number of minutes spent
counting; symbolized by drawing a dash line on the
Chart connecting the Tuesday and Thursday lines.
Cycle—distance on the Chart between consecutive powers of
10.
Day line—vertical line on the Daily Standard Behavior
Chart.
Decelerating Target—a movement the behaver, manager,
advisor, or supervisor expects to decelerate; the
frequency is symbolized by placing an "x" on the Chart.
Double Improvement Learning Picture—both movements of an
accuracy pair with celerations in the expected direc¬
tion; for example.
Down Bounce—the distance from the celeration line to the
frequency farthest below it.
Duration—the amount of time it takes to complete one
occurrence of a behavior; 1/number of minutes spent
behaving.
Errorless learning—a teaching procedure in which cues and
prompts are arranged so as to occasion only correct
responses.
Event-Following Celeration Line—a celeration line drawn
through all frequencies for a given movement just prior
to a phase change.
Fluency—final performance for correct responses and errors.
Freehand Method—a method of visually estimating and drawing
celeration lines.

97
Frequency—basic unit of behavioral measurement; the number
of movements per unit time.
Frequency Aim—the expected phase-ending frequency for a
given movement; symbolized by drawing "A" at the
expected frequency on the day the aim was set.
Frequency Line—a horizontal line on the Chart; also called
a counting line.
Frequency Multiplier (jump up or jump down)—value by which
one frequency is multiplied or divided to obtain a
second.
Geometric Mean—the appropriate method for obtaining an
average on a multiply-divide scale.
Ignored Day—a day on which the behavior being measured
occurs but is not charted.
Latency—the amount of time between the occurrence of a
signal and the beginning of a movement; 1/time from
signal to start of movement.
Learning—a change in performance per unit time, also called
celeration.
Learning Picture—the celeration lines of both movements of
an accuracy pair viewed together; for example.
Manager—person who works with the behaver on a daily basis.
Median Celeration—the middle celeration in a celeration
distribution; symbolized by drawing a "<" on the Chart.
Median Frequency—the middle frequency in a frequency
distribution; symbolized by drawing a "<" on the Chart.
Most Recent Celeration Line—a celeration line drawn through
the last 7-10 frequencies for a given movement.
Movement—recorded behavioral event; usually specified in
terms of a movement cycle with a beginning, middle and
end.
Multiply-divide Scale--any measurement scale on which
multiplying and dividing by a constant amount is
represented by a constant distance; the "up the left"
scale on the Standard Behavior Chart.
No Chance Day—a day on which the behavior being measured
has no chance to occur.

98
Overall Celeration Line—a celeration line drawn through all
frequencies for a given movement.
Performance—the number of movements per unit time; also
called frequency.
Periodic Celeration Line—a celeration line drawn through
all frequencies for a given movement in a specific time
period such as bi-weekly or monthly.
Phase—A period in which a particular set of conditions is
in effect.
Phase Change—a deliberate alternation made to the behaver's
environment in an effort to improve the behavior being
measured.
Precision Teaching—a comprehensive instructional system for
accelerating learning and maintaining high proficiency,
based on direct and continuous meas procedures.
Quarter-Intersect Method—a method for computing and con¬
structing celeration lines.
Recorded Day—a day on which the behavior being measured as
the opportunity to and is recorded.
Single Improvement Learning Picture—one movement of an
accuracy pair with a celeration in the expected direc¬
tion; for example.
Split-middle Line--a line drawn parallel to a quarter-
intersect celeration line, such that half the data
points fall on or above the line and half the data
points fall on or below the line.
Standard Behavior Chart—a standard, six-cycle semi-
logarithmic chart that measures frequency as movements/
time and celeration as movements/time/time; Daily,
Weekly, Monthly, Yearly and Summary versions are
available; also called the Standard Celeration Chart.
Step—the ratio between the frequency of two learning lines
that intersect the same change line.
Supervisor—a person who views the Charts on a monthly
basis.
Total Bounce—distance from the highest to the lowest
frequency; analogous to range of an add-subtract scale.
Trend-following Celeration Line—a celeration line drawn
through visible trends for a given movement.

99
Up Bounce—distance from the celeration line to the
frequency farthest above it.

APPENDIX B
ALACHUA COUNTY CRITERIA FOR ELIGIBILITY IN LEARNING
DISABILITY, EMOTIONALLY HANDICAPPED, AND EDUCABLY
MENTALLY RETARDED CLASSES

SPECIFIC LEARNING DISABILITIES
Specific Learning Disabilities—one who exhibits a disorder
in one (1) or more of the basic psychological processes
involved in understanding or in using spoken and written
language. These may be manifested in disorders of listen¬
ing, thinking, reading, talking, writing, spelling, or
arithmetic. They do not include learning problems which are
due primarily to visual, hearing, or motor handicaps, to
mental retardation, emotional disturbance, or to an environ¬
mental deprivation.
Criteria for Eligibility
A student is eligible if the following criteria are
met:
a. Evidence of a disorder in one (1) or more of the
basic psychological process areas. Basic psycho¬
logical process areas include visual, auditory,
motor and language processes.
Only tests or subtests appropriate for the stu¬
dent's chronological age shall be used for place¬
ment purposes. Hereafter, the Illinois Test of
Psycholinguistic Abilities shall be abbreviated as
ITPA; the Detroit Tests of Learning Aptitude as
DTLA. Required batteries appropriate to age and
by process cluster are as follows:
(1) Chronological ages 5.0 through 10.0
(a) Visual
ITPA Reception
ITPA Association
ITPA Closure
ITPA Memory
ITPA Manual Expression
(b) Auditory
ITPA Reception
ITPA Association
ITPA Grammatic Closure
ITPA Memory
ITPA Verbal Expression
(c) Visual Motor
Beery Developmental Test of Visual -
Motor Integration (Beery)
Bender Motor Gestalt Test
101

102
(2) Chronological ages above 10.0
(a) Visual
DTLA Memory for Objects
DTLA Memory for Letters
DTLA Disarranged Pictures
(b) Auditory
DTLA Memory for Words
DTLA Memory for Sentences
DTLA Verbal Opposites
DTLA Oral Directions
(c) Visual Motor
Beery
DTLA Memory for Design
Disorders shall be defined according to the instructions of
each test's author(s).
b. Evidence of academic achievement which is signifi¬
cantly below the student's level of intellectual
functioning.
(1) For students below age seven (7), evidence
must be presented that the student exhibits a
discrepancy of one (1) standard deviation or
more between an intellectual standard score
and an achievement standard score(s) in
thinking, reading, talking, writing, spelling
or arithmetic. Students with deficits in
reading, arithmetic, and/or spelling may be
considered for exceptional student placement
if other applicable criteria are met.
Students with deficits in other areas may be
offered consultative services.
(2) For students ages seven (7) through ten (10),
evidence must be presented that the student
exhibits a discrepancy of one (1) standard
deviation or more between an intellectual
standard score and academic standard score (s)
in reading, writing, arithmetic or spelling.
(3) For students ages eleven (11) and above,
evidence must be presented that the student
exhibits a discrepancy of one and one-half (1
1/2) standard deviations or more between an
intellectual standard score and academic
standard score in reading, writing, arith¬
metic or spelling.

103
(4) For students ages seven (7) and above with
deficits in reading, arithmetic, and/or
spelling, exceptional student placement may
be considered if other applicable criteria
are met.
(5) If more than one academic instrument is used
to document a weakness, the results must
consistently show deficits in the same
academic area. If more than one level of
functioning is obtained, the mean level of
functioning will be used to establish a
deficit.
(6) For eligible students functioning at or above
their current grade levels, consultative
services may be offered.
c. Evidence that learning problems are not due
primarily to other handicapping conditions.
(1) For students with intellectual deficits,
evidence that intellectual functioning is no
more than one (1) standard deviation below
the mean on an individual test of intellec¬
tual functioning, or evidence that a score
below one (1) standard deviation below the
mean is not a reliable indicator of the
student's potential. Intellectual func¬
tioning will be determined by the use of the
full scale score derived from the standard
battery instrument.
(2) For students with visual processing deficits,
evidence that visual acuity is at least 20/70
in the better eye with best possible correc¬
tion, or evidence that the student's
inability to perform adequately on tasks
which reauire visual processing is not due to
poor visual acuity.
(3) For students with auditory processing or
language deficits, evidence that the loss of
auditory acuity is no more than 30 decibles
in the better ear unaided or evidence that
the student's inability to perform adequately
on tasks which require auditory processing of
language is not due to poor auditory acuity.
(4j For students with a motor handicap, evidence
that their inability to perform adequately on
tasks which assess the basic psychological
process is not due to the motor handicap.

104
(5) For students with an emotional handicap,
evidence that their inability to perform
adequately on tasks which assess the basic
psychological processes is not due to the
emotional handicap.
d. Documented evidence which indicates that general
educational alternatives have been attempted and
found to be ineffective in meeting the student's
educational needs.
EMOTIONALLY HANDICAPPED
Emotionally Handicapped—one, who after receiving supportive
educational assistance and counseling services available to
all students, still exhibits a persistent and consistent
severe emotional handicap which consequently disrupts the
student's own learning process. This is the student whose
inability to achieve adequate academic progress or satisfac¬
tory interpersonal relationships cannot be attributed
primarily to physical, sensory or intellectual deficits.
This term does not include children who are socially malad¬
justed unless it is determined that they are also emotion¬
ally handicapped.
Severely Emotionally Disturbed—one who meets the
stated above and, in addition, requires a special
for the full school week and extensive supportive
criteria
program
services.
1. Criteria for_Eligibility
a. Emotionally Handicapped
(1) Evidence that the student, after receiving
appropriate supportive educational assistance
and counseling, still exhibits a severe
emotional handicap.
(2) Evidence that the student exhibits a persis¬
tent and consistent severe emotional handicap
as determined by documented observations and
psychological evaluation.
(3) Evidence that the behavior disrupts the
student's ability to achieve adequate aca¬
demic progress or develop satisfactory
interpersonal relationships.
(4) Evidence that the primary problem of the
student cannot be attributed primarily to
physical, sensory, or intellectual deficits.

105
b. Severely Emotionally Disturbed
In addition to the criteria stated above in (1)
through (4), the following shall be used to
determine each student's eligibility:
(1) Evidence that the student requires a program
for the full school week which provides a
highly structured cognitive and affective
curriculum; individual or group counseling
and parent counseling or education; and
(2) Evidence that a program provided in a less
restrictive environment has not met the
individual student's needs.
EDUCABLE MENTALLY HANDICAPPED
Educable Mentally Handicapped—one who is mildly impaired in
intellectual and adaptive behavior and whose development
reflects a reduced rate of learning. The measured intelli¬
gence of an educable mentally handicapped student generally
falls between two (2) and three (3) standard deviations
below the mean, and the assessed adaptive behavior falls
below age and cultural expectations.
Criteria for Eligibility
a. The measured level of intellectual functioning, as
determined by performance on an individual test of
intelligence, is between two (2) and (3) standard
deviations below the mean. The standard error of
measurement may be considered in individual cases.
The profile of intellectual functioning shows
consistent sub-average performance in a majority
of areas evaluated.
b. The assessed level of adaptive behavior is below
age and cultural expectation.
c. Sub-average performance on a standardized measure
of academic achievement is demonstrated.

APPENDIX C
DECISION AND OUTCOME FORM

Teschi rig Sí I e s r- n i n g
DECISION S Sc OUTCOMES
Teacher Setting Dates to
Learner M F Age Program
Skill Name
Ski 1 1 Description **
Phase
Learning
Channel
Limits
of Class
Number
in Set •
Ai m
Focus
# Related
Skills
Performanee
Standard
1
2
3
A
** Dec i si on s and Act i on s
Learning
Picturel
Decisi on
Rule(s) Used
Describe Changes Made or
Record Comments or Questions
* Learning pictures need minimum of five data points.
>> DECISION RULES: Cl 3 At aim for 1 day confirmed C23 Three days flat
data C33 Minimum celeration < X1.25 for corrects C43 Corrects
decelerating C53 Less than previously projected celeration (5 days)
C6> Other
*: Ac
Outc CD l
D¿it a
Ac *:
Number
Timings
Last Day
Freqncy*
First Day
Freqncy#
Frequency
Change
Celerati on
for Phase
#
Days
Prf Stnd
Achvd
C
X f
Ves No
£
X 1-
C
X T
Yus No
f
X r
c
X f
Yes No
£
X f
C
X r-
Yes No
E
X f
Frequncies from intersections of learning lino with last and first days
107

APPENDIX D
RAW DATA: CORRECT AND INCORRECT FREQUENCIES
FOR ALL PHASES OF THE LEAP AND KEEP
AND LEAP AND LEAVE DESIGNS

£s(Plj)iBSSE3 ®S [PíDOÜ fa [L@ep HGGjÜ© lISpGCljGDGffitlS
Learner: E B Teacher: investigator
Movement Cuele: See--Sau Texted Words
Fhos?
rior¡>
Pr-rtecBUp1
LrOp-Up >
Cai*ndor
Frequency
Frequency
Dou 3
Correct
Errors
> > > > >
>>>>>>>>
>>>>>>>
O
SO
0
3
95
0
4
100
0
5
109
0
ft
110
0
•>>>>>
>>>>>>>>
>>>>>>
l*
0
11
9
24
Q
C-7
â– J 1
4
10
64
¿-
11
72
'¿
109

110
¿[ppQfficí'Íjs PeirQ ELsap qqxO keaüQ isjpstfilED©^©
Learner: E D Tsachen Investigator
Movement Cuds: See—Say Vocabuiaru Words
FtiOfr Colindar
Frequency
Friquincy
Norn? Dou *
Corroo*
Error?
PriiiOp-Un >>>>>>
>>>>>>>
> > > > > > >
c;
72
0
6
80
0
7
95
o
V.'
r.*7
O i
0
Q
NC
NC
10
101
0
11
100
0
12
101
o
13
100
o
LiGp-Up >>>>>>>>
> :• > > > ;• >
> > > > ;• >
14
12
15
5
16
40
5
17
49
2
I y
NC
NC
19
54
0
20
NC
NC
21
53
0
0‘*'
72
0
I

Ill
iPscra
0=3(DÍJ) QlD(j] H00E9 UspgOHEDQEGS
Learner: L A
Teacher: W 0
Movement Cucie: See-
-Write Add Facts, sums to 18
Phase Calendar
Frequency
Frequency
Name Da a 5
Correct
Errors
Preleap-Up >>>>>>
>>>>>>>>
>>>>>>
o
34
0
4
1
5
43
o
6
NO
NC
7
NC
NC
o
40'
0
Q
59
0
10
59
o
1 1
43
o
12
£ r‘
Do
0
Leap-Up a\ >>>>>>
>>>>>>>>
>>>;•>>
.¿Ft
0
4
•0“7
1
NC
NC
yy
7
o
39
9
0
40
9
0
41
NC
NC
42
NC
NC
Leap-Up ”2 >>>>>>
>>>>>>>:
>>>>>>>
43
3
Ft
44
NC
NC
45
13
0
4 ó
16
0
47
13
o
43
NC
NC
49
NC
NC
30
22
0
31
NC
Mr-
NC
ft If*
53
HL*
NC
• 4L-
X
5a
•
NC
cr
V'«*
NC
NC
cr¿
NC
NC
LE ^P~L*P **3 //>/'.
> ? > /â–  > ,> > >
> / > ' > > ✓ >
C"7
i
fi
15
39
<*,
Ci
59
5
0
60
~J
0
61
7
0

112
AppoaKOtls
fpatra £i=
(LqecD \Lmv©
Learner: W T
Teacher: J R
Movement Cue!
e: See-
-Write Add Facts, sums to 6
Phase Calendar
Frequency
Frequency
Nome Dan 0
Correct
Errors
Preleap-Up >>>>>>
>>>>>>>>
>>>>>>
3
24
0
’ 4
19
5
NC
NC
6
NC
NC
NC
NC
y
31
0
0
NC
NC
10
NC
NC
11
24
0
12
NC
NC
13
NC
NC
14
NC
NC
Leap-Up **1 >>>>>>
>>>>>>>>
\ \ \ \ v, N
15
0
24
16
o
0
17
0
0
1 o
o
6
19
NC
NC
20
NC
NC
21
NC
NC
22
NC
NC
2o
24
0
24
26
o
•" CT
28
o

113
AíPípeEtífós ©s Paira (Leap ama (Leaca [IspairaLiDaaaa
Learner: R J
Movement Cuele:
Teacher: 5 B
See—Write Add Facts, sums to IS
F hose
Nome
PfirirOp-Up
Leoo-Up* 31
Colendor
Dou n
Frequency
Correct
Frequí
Erroi
>>>>>>
>>>>>>>
> > > >
5
50
"0
6
NO
NC
1*
NC
NC
r.
o
NO
NC
9
NC
NC
10
54
1
11
54
0
12
C‘.
o
13
NC
NC
14
NC
NC
15
55
0
1
NC
NC
17
55
1
1 y
73
0
10
7d
0
20
NC
NC
21
NC
NC
71
0
'X'
NC
NC
'“l .4
73
0
25
75
0
26
NC
NC
O'?
L. 1
NC
NC
29
NC
NC
20
77
0
30
NC
NC
31
;jO
0
32
NC
NC
•2*0
NC
NC
34
NC
NC
'-.er
NC
NC
36
79
0
»• i
NC
NC
'■•r,
j*o
34
0
-.••>>>
> >.) > > >
> > • /
53
5
15
54
33
t
•t
cc
JO
37
56
NC
NC
57
NC
NC
53
54
0
50
NC
NC
50
52
0

114
R J (Continued 3
61
62
0
62
69
0
NO
NC
64
NC
NC
65
72
C
66
NC
NC
67
i {
Ü

115
Appendix D: Section A: Leap and Leave Experiments
Learner: 0 5 Teacher: B M
Movement Ciicie: See—Write Add Facts, sums to 18
Phase Calender
Frequency
Freque
Name C’ay s
Correct
Error
. i. t t_
• r rirUJ L'P
1
42
0
4c!
0
C*
49
0
4
50
0
5
51
0
6
NO
NC
7
NC
NC
8
52
0
9
Cj.-%
0
10
CO
JO
0
Leoo-tJ§ >>>>>>>
>>>>>>>>
> > > >
11
1
72
12
fi
OO
13
NO
NC
14
NC
NC
15
11
21
16
12
15
17
NC
NC
13
v
4
IQ
1
1
20
NC
NC
21
NC
NC
22
NC
NC
14
24
« *7
l 1
2d
21
o
2 ó
NC
NC
27
NC
NC
2ft
NC
NC
2Q
Í 5
0

116
Appendix D: Section A: Leap and Leave Experiments
Learner: J R Teacher: 6 M
Movement Cuele: See--Write Add Facts, sums to 10
Phase Calendar Frequency Frequency
Nome _Doy_f Correct Errors
Preleap-Up > > > > > >>>>>> > > > > > > > > >
g
or»
••u
G
4
“'■y
1
CT
â– J
25
5
NC
NC
NC
NC
8
28
1
9
NC
NC
10
NC
NC
1 1
NC
NC
12
NC
NC
13
NC
NC
14
NC
NC
15
2 í
Cl
16
30
0
17
GO
1
18
33
o
19
NC
NC
20
21
NC
NC
NC
NC
/ > / ?â–  >
;• ;• > :■
\ \ \ \ \ \ X
e / / / t * /
5
O";
o
D
24
i1
0
25
S
0
2d
NC
NC
4» 1
NC
NC
GO
NC
NC
29
NC
NC
to
o
1Ü
Ü
31
11
0
GG
13
0
15
o

117
Appendix D: Section A: Leap and Leave Experiments
Learner: A F Teacher: W 0
Movement Cycle: See—Write Subtraction Facts
Phaie
Calendar
Frequency
Frequency
Norn?
Pay *
Correct
Errar?
Preleap-Up
> > > > >
> B>>>>>>
> > > > > >
4
17
1
D
26
0
ó
NC
NC
1*
NC
NC
.5
28
0
9
31
0
10
oO
0
1 1
0"7
-* i
0
12
NC
NC
13
NC
NC
14
NC
NC
15
28
0
ID
0*7
•*»»
0
17
NC
NC
18
41
0
19
45
0
20
NC
NC
21
NC
NC
45
o
23
47
0
24
NC
NC
25
NC
NC
2d
NC
NC
ot
2. >
NC
NC
28
NC
NC
29
NC
NC
Lagp-Up >
/>>>>>
>>>>>>>>
>>>>>>
30
4
31
0
1
a
sJ

118
Appendix D: Section A: Leap end Leave Experiments
Learner:
n V
Teacher: 6 M
Movement Cuele: See--Write Mixed Math Facts
FhCSO
Nam*
Launder
Dau #
Frequency
Correct
Friqué
Error
> > > > > >
>>;•>>>>
> > > >
5
31
0
6
NO
NC
NO
NC
o
oo .
0
y
C‘l_i
0
10
OÓ
0
11
39
0
12
NC
NC
13
NC
NC
14
NC
NC
15
40
0
IS
42
0
1?
NC
NC
12
44
0
19
45
0
20
NC
NC
21
NC
NC
>>>>>>;â– 
>>>>>>>
> > > >
0
1 1
1
¿O
24
0
•-ccr
¿■J
NC
NC
26
34
o

119
Appendix D: Section A: Leap and Leave Experiments
Learner: C B Teacher: B M
Movement Cuele: See—Write Multiplication Facts, X 4 table
rhaxe
Nome
Preieop-Up
.‘oléndcr
Frequency
Frequency
Dou *
Correct
Error-.'
> > > > >
>>>>>>>>
>>>>>>
1
8
0
11
2
V
12
0
4
12
0
5
NC
NC
5
NC
NC
7
NC
NC
8
HC
NC
Q
13
0
1Ü
12
0
11
NC
NC
12
11
1
13
NC
NC
14
NC
NC
15
14
0
15
14
1
17
14
ij
13
15
0
19
Id
0
20
NC
NC
21
NC
NC
22
13
Ü
> > > > >
>>>>>>>>
>>/>>/â– 
23
2
D
24
NC
NC
â– ".C
6
1
¿.0
NC
NC
27
NC
NC
23
NC
NC
29
NC
NC
30
NC
NC
21
r.
32
c
.J
o
wiW
1
93
34
NC
NC
35
NC
NC
36
ft
0
37
9
0
12
1
29
13
0
> > > > '
>>>:>,>>
•>:;>>
46
4
i J
a?
NC
NC
43
NC
NC
49
50
30
4
55

120
C B (Continued)
51
9
oo
52
NC
NC
54
NC
NC
55
NC
NC
56
NC
NC
57
Q
IS
Cm
U«wl
12
16
5'?
NC
NC
60
14
1
61
17
0
62
NC
NC
63
NC
NC
64
NC
NC
65
NC
NC
66
IS
0
67
29
3

121
(25[]);jjSQj'i3'üES EíS [pQtrft (Ds kG0¡p Q12CÍ3 féQG[p HSPQirOCEGCDSS
Learner: W
T
Teacher: J R
Movement Cuc!e: See
—Say Alphabet
PhOS* CoSfndor
Frequency
Frequency Phase
Frequency Frequency
Norñf Doy 8
Corrects
Errors Name
Correo® Errors
Pr*!*op-ffii > > > > >
>>>>>>>>
>>>>>>>>>>>>>>>
> > > > > > > > > > > > :
1
12
Q
21
c
O
•■O
4
4
19
7
C
20
Mi
6
NC
NC
*7
i
NC
NC
y
21
C
9
26
5
10
^icr
3
11
21
C*
During >>>>>>>
>>>>>>>>
>>>>>>>> Leoo-Uo 81
>>>>>>>>>>>>>
12
NC
NC
3 11
1 O
NC
NC
NC NC
14
NC
NC
NC NC
15
24
y»,
o
6 8
15
27
O
x :?
17
19
1
9 3
* •*!
1 O
30
2
1 1 3
19
29
0
Mi rí
20
NC
NC
NC NC
21
NC
NC
NC NC
22
30
0
15 7
NC
NC
NC NC
24
NC
NC
NC NC
25
31
0
14 4
25
NC
NC
NC NC
27
NC
NC
NC NC
22
NC
NC
NC NC
29
32
o
15 0
o o
36
0
15 0
01
o y
o
16 4
o o
41
0
17 3
44
o
NC NC
04
NC NC
Leop_up a
NC NC
2 . > > ; > r ' / > >
26
0 10
37
5 11
0 10
39
6 10
40
NC NC
41
NC NC
42
NC NC
J3
NC NC
44
9 9

122
45
10
“?
1
46
16
Ü
47
18
10
43
NC
NC
49
NC
NC
50
17
I1
51
tr
52
19
5
0*1'
17
4
54
16
6
ere-
NC
NC
5u
NC
NC
57
17
4
C|C
20
v
59
NC
NC
60
26
61
4o
1
62
NC
NC
63
NC
NC
64
Z'd’
65
21
66
NC
NC
67
NC
NC
63
NC
NC
69
NC
NC
70
NC
NC
71
20
3
"7''1
— o
1 V
NC
NC
74
24
O
â– 7=;
1 -J
30
0

123
^{píp3CD(0Sa
Pajera ®o
[Leap mQ Keen] [IspsGl&süe
Learner: J V
Teacher: 5 L
Movement Cucie: See-
—Say Ginn Phrases, level ?
Phose Calender
Frequency
Frequency
Phase Frequency Frequency
Name Dag 3
Corrects
Errors
Name Corrects Errors
Preieop-Up >>>>>>
>>>>>>>;
>>>>>>
>>>>>>>>>>>>>>>>>>>>>>
<^i
55
O
4
50
2
5
NC
NC
5
NO
NC
Í
NC
NC
3
NC
NC
Q
NC
NC
10
NC
NC
11
NC
NC
12
NC
NC
13
NC
NC
14
NC
NC
15
í o
3
16
73
0
17
70
o
18
36
o
During °1 >>>>>>>
>>>>;â– >>
> > > > >
10
7
20
NC
NC
21
NC
NC
Leap-
Up 31 >>>>>>> >111 > >
22
40
z
8 1 1
23
42
0
23 23
•“> <
45
'Z
39 6
25
40
o
40 2
25
NC
NC
NC NC
27
NC
NC
NC NC
23
NC
NC
NC NC
20
50
40 6
30
53
0
46 2
31
57
O
c 1
1 —
32
NC
NC
NC NC
33
NC
NC
NC NC
34
NC
NC
NC NC
35
NC
NC
NC NC
36
NC
NC
NC NC
37
57
4
43 3
33
60
1
62 4
30
NC
NC
60 ?
40
C 4
0
o 1 3
41
NC
NC
NC NC
42
i«'C
NC
NC NC
Leap
Up n2 •'>>>>:.>
42
72
0
17 21
43
73
4
24 13
44
76
0
26 4

124
J V (Continued)
During **2
During #3
>
45
93
0
oo
tí
46
100
0
NO
NO
47
NO
NO-
NO
NO
43
NO
NO
NO-
NO
> > > >
>>>>>>>>
49
31
6
54
o
50
NO
NO
NO
NO
51
40
55
o
52
44
o
60
1
53
46
4
66
0
54
NO
NO
NO
NO
crc*
Jwi
NO
NO
NO
NO
56
51
4
63
0-
57
76
o
r z
0
53
103
o
tí 5
o
59
NO
NO
NO
NO
60
NO
NO
NO
NO
61
M»“
i «*—
NO
NO
NO
62
HC
NO
NO
NO
>>>>;•
>>>>>>>>
> > > ;L“Op-IJfi g
> > > > >> > j
: ;• ;• > > >
53
•/O
j
13
15
64
29
6
13
12
65
NO¬
NO
21
7D
66
NO
NO
25
O
67
NO
NO
3¡j
ft
63
NO
NO
NO
KC
63
NO
NO
NO
NO
70
4
34
o
71
35
Z
41
4
*70
i —
41
2
45
i
â– 70
i O
46
L.
49
0
74
C*.
JO
1
56

125
£>(L>rp3E(i]Sa ®=
\Pa?1 d3s
dGGij) (DCDCQ K00O) HS[jj9irí[iD0üDÍlS
Learner: D P
Teacher: C F
Movement Cue!
I g- See-
--Say Ginn Vocabulary,
level 8
Phase Colendar
Frequency
Frequency Phase Frequency
Frequency
Norr¡* Doy “
Corrects
Errors Nome Corrects
Errors
PfrlrOC—Up 5 > > > > >
>>>>>>>:
>>>>> >>>>>>>>>>>>>>> >
>>>>>>>>
c
13
45
6
NO
NC
?
HC
NC
y
Í i*
cr
0
NO
NC
10
NC
NC
11
25
o
12
36
2
13
NC
NC
14
NC
NC
| C
47
0
16
NC
NC
1?
NC
NC
1 O
HC
NC
19
NC
NC
20
NC
NC
21
NC
NC
NC
NC
03
c¡o
V
NC
NC
“C
¿.J
51
1
2 ó
cc
1
27
NC
NC
jy
NC
NC
jijriri'; 81 >>>>>>>
> > > > '/Lecp-Up 81 > >>>>>>>>
> > > > ><14
29
53
1 4
Q
30
NC
NC 13
c
,J
31
NC
NC 19
o
22
57
0 27
1
33
NC
NC HC
HC
34
NC
NC NC
NC
" C
NC
HC NC
NC
3 if.
65
0 29
2
Danny *2 >/•>>>>>
>.â– >>>>>
> ✓ > ’> >
I i
1
1 >-•
5 30
i
: c*
NC
NC NC
NC
39
21
NC
NC
40
24
4 34
2
41
NC
NC NC
NC
42
NC
HC NC
NC
4 3
34
2 34
•14
39
2 41
¿5
NC
NC NC
NC
46
NC
NC NC
NC
47
NC
NC NC
NC
4-3
NC
NC NC
HC

126
0 P (Continued)
49
NC
NC
NC
NC
50
42
40
2
51
49
O
43
O
NC
NC
NC
NC
5o
56
v
5t*
54
NC
NC
55
NC
NC
56
NC
NC
Leap-Up *2
>>>>>>>>>>>
)* > >
57
2
•I*
53
14
O
59
NC
NC
60
NC
NC
61
NC
NC
G-i
NC
' NC
63
NC
NC
64
NC
NC
65
13
66
NC
NC
D?
4
63
29
o
â– o
69
NC
NC
*7i-,
to
NC
NC
*7 1
■“.ET
i I
O-J
72
O l‘

127
^IPtPSffiíOüa (Pstrft ©s
(Lean) asá Ksep dspsírOíiESQüs
Learner: D P
Teacher: C F
Movement Cuele: See-
-Say Ginn Phrases, ieve
1 s
Pnoí* Coloridor Frequency
Frequency Phase Frequency
Frequency
Neme- Doy 3 Corrects
Errors Norn* Corrects
Errors
Freteop-Up >>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>
1 34
2 55
•3
3 NC
NC
4 68
1
5 NC
NC
6 NC
NC
7 NC
NC
During >>>>>>>>>>>>>>>>
> > >Uop-Up >>>>>>>>>>>>>>
>>>>>>
8 73
u *?f=
o
19
r i o
10 S3
0 48
1
11
54
]¿
12
NC
NC
lo
NO
NC
14
NC
NC
15
60
1
16
75
<
1
17
NC
NC
18
NC
NC
19
NC
NC
20
NC
NC
21
NC
NC
y o
31
V
OC;
115
1

Appeals ®= (Peirft Os ELeep ídeP Keep [lEBpGtrtaQGjüs
128
Learner: N R Teacher: S B
Movement Cycle: Bee Write Add Facts, sums to 18
Phase
Nome
Preieop-up
During > >
Calender
Frequency
Frequency
Phase
Frequency
Frequency
Day 9
Corrects
Errors
Name
Corrects
Errors
> > > :> >
>>>>>>>>
>>>>>>>>
> > > > >
} ) / ) s y > y y
y yy yyy.
1
27
1
2
NC
NC
31
4
21
0
5
19
0
6
NC
NC
7
NC
NC
8
31
o
g
NC
NC
> > > > >
>>>>>>>>
'/ > > >Leap-Up
#1 > > >
> >>>>>>>>
> > > > > >
10
32
0
12
2>;
11
36
0
NC
NC
12
NC
NC
NC
NC
13
NC
NC
NC
NC
14
NC
NC
NC
NC
15
35
0
21
1
16
NC
NC
NC
NC
17
27
0
34
2
18
NC
NC
NC
NC
19
NC
NC
NC
NC
20
NC
NC
NC
NC
21
NC
NC
NC
NC
¿'2
36
0
47
23
NC
NC
NC
NC
24
oo
0*0
0
44
0
â– * tr
35
0
52
1
¿.'J
35
0
43
Jim
27
NC
NC
NC
NC
26
NC
NC
NC
NC
29
36
0
44
30
NC
NC
NC
NC
31
NC
NC
44
0
32
NC
NC
49
o
Jo
39
0
NC
NC
Leap-Up
*2 > >
>>>>>>>>>
)) / )• y
50
0
6
51
NC
NC
52
4
1
CO
j/i
15
0
54
20

¿MppGEQjijS ®s PS(T2 ®= [Lesp EECl] GSGSíjj [liSPGtrtíLDGffiÜS
129
Learner: C J Teacher: 5 8
Movement Cucis: 5ee-V/ri te Add Facts, sums to 18
Phase Coloridor
Frequency
Frequency Phase
Frequency
Frequency
Nome Doy 3
Corrects
Errors Nome
Corrects
Errors
PfrirOO“'jO •' > > > > 3
>>>>>>>:
>>>>>>>>>>>>>>>
> > > > > > > >
>>>>>>>>
4
0
5
39
o
ó
41
o
7
NC
NC
o
NO
NC
9
44
1
10
NC
NC
11
43
0
12
49
o
13
NC
NC
14
NC
NC
15
NC
NC
16
55
0
17
NC
NC
IS
52
1
IQ
44
1
•*.r¡
45
0
2!
NC
NC
22
NC
NC
C'ijnno >>>>>>>>
>>>>>>>
> > > > > >L*op-Up 31 > >
> > > > > > > >
>>>>>>>>
22
40
0
16
**i 4
NC
NC
24
1
•” cr
c —
0
«2 l'
Ij
26
55
0
30
0
'-N“7
57
1
34
9
2y
NC
NC
NC
NC
¿y
NC
NC
NC
NC
30
59
0
41
0
31
NC
NC
32
46
0
-"V".
37
0
34
44
o
'I.c
NC
NC
36
NC
NC
Leop-Up 32 > > >
>>>>>>>>
>>>>>>>>
37
4
16
oc
w
16
1
39
NC
NC
40
NC
NC
41
17
1
42
NC
NC
43
NC
NC
44
NC
NC
45
NC
NC
46
NC
NC
47
NC
NC
43
19
0

130
©s i^sini ®= ©sap cdcdcO íEggp [IspatrOiiDGa©©
Learner: A K
Teacher: J R
Movement Cue!
e: 5ee-
—Write
Add Facts, sums
to 10
Phase Corridor
Frequency
Frequency
Phase Frequency
Frequency
Nome Doy *
Corrects
Errors
Nome Corrects
Errors
Preleop-üp >>>>>>
)•)’)/ / /
> >>>>>>
1
i
o
2
8
1
o
NC
NC
4
13
0
3
13
0
6
NC
NC
-»
»*
NC
NC
8
NC
NC
9
„ 15
0
10
16
0
During > > > > > > > >
>>>>>>>
> > > > > Leop-Up > > ;• > > > :• ;• > > > i
;• > ;• ;• ;• >
11
10
0
0
o
12
14
0
C
1
13
NC
NC
NC
NC
14
NC
NC
NC
NC
15
13
0
4
0
16
15
0
6
o

131
AíPípGüKüílS ®S
(Paira ©s
ÍLG0P GüXl] E©G[p ÜEpGCTOfZDSOüíiS
Learner: Y B
Teacher. B M
Movement Cuci
í e: See-
-Write Multiplication Facts
rhOf* Coloridor
Fr*qu&ncy
Frequency Phos* Frequency
Froqusncy
Horno Doy 3
Corrects
Errors Horno Corroéis
Errors
Pr*!*op-Up >>>>>>
>>>>>>>:
â–º>>>>>>>>>>>>>>>>>>>>>
>>>>>>>
1
37
1
2
49
0
o
51
o
4
HC
NC
5
53
0
5
NC
NC
7
HC
NC
During >>>>>>>>>
â– >>>>>>>
> > > > >Loop-Up >>>>>>>>>>>>
>>>>>>>
r«
•-»
51
0 2
41
9
55
0 5
53
10
57
0 7
30
11
60
0 9
37.
12
NC
NC
13
NC
NC
14
NC
NC
13
NC
NC
13
11
0\.\
17
NC
NC
13
10
"•1
jL l
19
10
c
wl
20
NC
NC
21
NC
NC
22
10
22
13
.1
*T
24
17
o
23
19
t
*T
23
NC
NC
27
NC
NC
23
22
2
29
■“ C
\
30
1
31
NC
NC
27
0

132
£[p!p3EGSÍií3S tPQCTÜ ©S O=00[p Qffiá C?G©[p dSp'Q^ÍIDGffiílS
Learner: 6 R Teacnsr: B M
Movement Cuele: See—Write Multiplication Facts
Phase Calendar
Frequency
Frequency Phase
Frequency
Frequency
Nome Doy s
Corrects
Errors Nome
Corrects
Errors.
Preleap-Up > > > > >
'->>>>>>>
>>>>>>>>>>>>
>>>>>>>
1
43
0
52
o
3
55
o
4
50
0
Leap-Up > >
;■ > ;• ;• > > > > > >
/ > > )â–  > > >
5
NC
NC
0
30
6
NC
NC
NC
NC
7
NC
NC
NC
NC
During >>>>>>>>
>>>>>>>>
> > > > >
o
60
0
“
12
9
64
0
10
21
10
67
0
13
z y
11
70
0
15
Z'd'
12
19
t;0
13
NC
NC
14
NC
NC
15
16
13
15
13
14
17
25
1 1
IS
NC
NC
19
¿¡*!
••y
20
NC
NC
21
NC
NC
v‘2
o--
0
Z3
NC
NC
Z^t
33
0
25
47
o
51
0
27
NC
NC
¿y
Mi--
i NC
20
59
o
yu
69
o
31
i* c<
0
ZZ
30
o
vO
79
1

REFERENCES
Alberto, P., & Troutman, A. Applied behavior analysis for
teachers. Columbus, Ohio: Charles Merrill, 1982.
Alley, G., & Deshler, D. Teaching the learning disabled
adolescent: Strategies and methods. Denver, Colorado:
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BIOGRAPHICAL SKETCH
Michele C. Gerent was born April 23, 1948, in
Schenectady, New York. She was graduated from the
University of Florida in 1970, with a Bachelor of Arts
in Education degree. In 1974, she received a Master of
Education degree from Florida Atlantic University at Boca
Raton, Florida, with an emphasis in learning disabilities.
She was employed as a special education teacher for a
total of 11 years in Palm Beach, Broward, and Indian River
County school systems. During those years she taught
mentally retarded, emotionally handicapped, learning
disabled, and gifted students.
Michele came to the University of Florida in the spring
of 1981 to work on a Ph.D in special education. Her major
area was learning disabilities with an emphasis in precision
teaching and microcomputers in education.
136

I certify that I have read this study and that in my
pinion it conforms to acceptable standards of scholarly
resentation and is fully adequate, in scope and quality, as
dissertation for the degree of Doctor of Philosophy.
William D. WoIking, Chairman
Professor of Special Education
I certify that I have read this study and that in my
pinion it conforms to acceptable standards of scholarly
resentation and is fully adequate, in scope and quality, as
dissertation for the degree of Doctor of Philosophy.
Cecil Mercer
Professor of Special Education
I certify that I have read this study and that in my
pinion it conforms to acceptaDle standards of scholarly
resentation and is fully adequate, in scope and quality, as
dissertation for the degree of Doctor of Philosophy.
Subject Specialization
Teacher Education

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Catherine Morsink\_
Professor of Special Education
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
This dissertation was submitted to the Graduate Faculty of
the Department of Special Education in the College of
Education and to the Graduate School, and was accepted as
partial fulfillment of the requirements for the degree of
Doctor of Philosophy.
Dean for Graduate Studiesand
Research
August 1984