Citation
Frequency, celeration, and variability of academic performance as predictors of learning

Material Information

Title:
Frequency, celeration, and variability of academic performance as predictors of learning
Creator:
Trifiletti, John J. ( John Junior ), 1947- ( Thesis advisor )
Wolking, William D. ( Thesis advisor )
Forgnone, Charles ( Reviewer )
Mercer, Cecil D. ( Reviewer )
Algozzine, Bob ( Reviewer )
Hodgson, Thom J. ( Reviewer )
Place of Publication:
Gainesville, Fla.
Publisher:
University of Florida
Publication Date:
Copyright Date:
1980
Language:
English
Physical Description:
vi, 130 leaves ; 28 cm.

Subjects

Subjects / Keywords:
Academic achievement ( jstor )
Academic learning ( jstor )
Celebrations ( jstor )
Frequency standards ( jstor )
Learning ( jstor )
Learning disabilities ( jstor )
Mathematics ( jstor )
Pedagogy ( jstor )
Precision teaching ( jstor )
Special education ( jstor )
Learning, Psychology of ( lcsh )
Prediction of scholastic success ( lcsh )
Special education ( lcsh )
City of Clearwater ( local )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Abstract:
This study examined the predictive ability of frequency, celeration, and variability measures of academic performance during assessment for predicting celerations during instruction. Data from 360 separate teacher-learner-task triads in reading, spelling, writing, and mathematics were evaluated. Learners were assessed over a five day period, then received twenty days of instruction during which daily timed samples of their academic performance were recorded. The amount of variance in celerations explained by baseline predictor variables was generally small. Moderate amounts of variance were explained by predictor variables for phonics sounds tasks and see to say tasks.
Thesis:
Thesis (Ph. D.)--University of Florida, 1980.
Bibliography:
Includes bibliographical references (leaves 100-107).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by John J. Trifiletti.

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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:
023446878 ( AlephBibNum )
07382206 ( OCLC )
AAL5803 ( NOTIS )

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FREQUENCY, CELEBRATION, AND VARIABILITY OF
ACADEMIC PERFORMANCE AS PREDICTORS OF LEARNING












By

John J. Trifiletti


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



UNIVERSITY OF FLORIDA


1980





















To Diane, my wife and best friend,

and to the expression of our love,

John Cristopher, III.













ACKNOWLEDGMENTS


I wish to express my sincere appreciation to all

my committee members for their support, encouragement,

and for their constructive suggestions, with special

thanks to Dr. William Wolking for his encouragement,

guidance, and intellectual stimulation throughout my

program of studies. Deserving of special acknowledgment

is Dr. Cecil Mercer for advice, support, and writing

skills.

I would also like to extend my appreciation to

Dr. Thom Hodgson for his guidance in the systems

engineering area and programming skills.

Finally, I wish to acknowledge my wife, Diane,

who has given me the emotional and intellectual

support I've needed throughout my program.


iii














TABLE OF CONTENTS


ACKNOWLEDGMENTS


ABSTRACT .

CHAPTER I INTRODUCTION

Importance of the Study
Rationale .
Statement of the Problem


vi




2
8
. 8


CHAPTER II REVIEW OF RELATED LITERATURE . . 12

Early Identification Research . . . 14
Prediction-Performance Comparison Matrix . 15
Single Instruments as Predictors . . 19
Multiple Instrument Batteries as Predictors 23
Teacher Ratings as Predictors . . . 27
Areas of Assessment for Prediction . . 28
Frequency Measurement of Academic Performance .30
Frequency versus Percentage Statements . 33
Considerations for Measurement of Frequency 35
Record Floor 36
Record Ceiling 37
Performance Ceiling . . 38
Studies of Frequency Performance Standards 41
Math Frequency Standards . . . 42
Reading Frequency Standards . 44
Spelling Frequency Standards . . . 52
Writing Frequency Standards . . . 53
A Frequency Model of Learning . . . 56
Predictive Studies Using Frequency Measurement . 59
Predictive Studies 61


CHAPTER III METHOD .


. . 70


Subjects .
Equipment .
Setting .
Procedure .
Training Procedures . . .
Initial Precision Assessment .
Instruction .
Experimental Design . . .
Data Collection ..
Data Analysis .


. 70
. 71
. 72
. 72
S . 73
. 73
S 76
. 76
. 77
.* 77
* S 77


iii










CHAPTER IV RESULTS . . .

Reliability .
Analyses of Prediction Results

CHAPTER V DISCUSSION . .


Findings .
Interpretation of the Findings . . .
Problems and Limitations of the Study . .
Practical Implications .
Suggestions for Further Research . . .

REFERENCES .

APPENDICES

A. DEFINITIONS .

B. DESCRIPTION OF SPARK II INSTRUMENT

C. FORTRAN PROGRAM FOR COMPUTERIZED CHARTS
AND SUMMARY STATISTICS . . .

D. SAMPLE FREQUENCY CHART . .

E. SYLLABUS OF TEACHER TRAINING SESSION .

BIOGRAPHICAL SKETCH .


S 100



108

111


S 114

125

S 128

129


*









Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of
the Requirements for the Degree of
Doctor of Philosophy



FREQUENCY, CELEBRATION, AND VARIABILITY OF
ACADEMIC PERFORMANCE AS PREDICTORS OF LEARNING

By

John J. Trifiletti

December, 1980


Chairman: William D. Wolking
Major Department: Special Education

This study examined the predictive ability of

frequency, celebration, and variability measures of

academic performance during assessment for predicting

celebrations during instruction. Data from 360 separate

teacher-learner-task triads in reading, spelling,

writing, and mathematics were evaluated. Learners

were assessed over a five day period, then received

twenty days of instruction during which daily timed

samples of their academic performance were recorded.

The amount of variance in celebrations explained

by baseline predictor variables was generally small.

Moderate amounts of variance were explained by

predictor variables for phonics sounds tasks and see

to say tasks.













CHAPTER I

INTRODUCTION


There are multiple dimensions to the academic

performance of learners in the classroom. Accuracy of

performance, expressed in terms of percentage statements,

has traditionally been used as the primary measure of

academic performance. Recently, other dimensions of

academic performance have received attention (Haughton,

1971a; White, 1972a; White Haring, 1976). These include

frequency, the speed of performance; celebration, the

rate of change in performance over days; and variability,

the variation in frequency about a trend line.

The problem of interest to this study is the use of

frequency, celebration, and variability measures of

performance during assessment to predict subsequent

academic performance during instruction.


Importance of the Study

Schools are designed to change the behavior of child-

ren. Ideally, learners progress from little or no knowledge

or skill to a desired level of academic performance. This

change occurs as a direct or indirect result of instruction.

The general purpose of assessment is to determine whether

a learner's performance is changing appropriately.

Assessment for instruction or teaching refers to the process

1









of obtaining information about a student's instructional

needs (Wiederholt, Hammill, S Brown, 1978). To facilitate

instructional programming the assessment must provide

information in two areas. First, it must help the teacher

select what to teach the individual student. Second, it

must help the teacher determine how to teach the student

for optimal progress (Mercer & Mercer, 1980).

Of equal importance is the use of assessment to

predict and prevent failure. Such prediction depends

upon the sensitivity of educational measurement and

the examination of multiple dimensions of performance.

This study is aimed at determination of the utility

of frequency, celebration, and variability of academic

performance during assessment for predicting subsequent

performance during instruction. As such, it builds and

extends upon previous research which has explored the use

of multiple dimensions of academic performance to predict

subsequent learning (White, 1972a).

Rationale

Traditionally, educational assessment has been of

limited success and has progressed little beyond

assumtions and concepts from the 19th century. The ideas

of Galton, Simon, Binet, Terman, and others with respect

to global variables and group measurement techniques

remain relatively unchanged except for the development of

new statistical procedures for the evaluation of group

performance data. Statistical evaluation has not









compensated for the inaccurate and incomplete measurement

of academic performance fostered by reliance on accuracy

as a single dimension of academic performance.

Traditional educational measurement is based upon

norm-referenced comparison. An individual's performance

is converted to a norm-referenced variable such as

grade level, age level, or percentile. Sensitivity is thus

limited by the dimensions and units used in measuring.

An additional problem with traditional educational

measurement is the reliance on percentage accuracy

statements to describe a single dimension of performance.

Percentage statements are subject to a number of measurement

problems (Haughton, 1969; White & Haring, 1976). These

include an arbitrary ceiling effect and inadequate descrip-

tion of performance. When percentage accuracy statements

alone are used to describe academic performance, changes

beyond 100 percent cannot be reflected by the measurement.

Yet there are many ways in which learners can increase

performance beyond 100 percent accuracy. For instance, the

latency (time to onset) of the performance can decrease, or

the speed of performance can increase. Furthermore,

accuracy statements inadequately describe academic

performance when there are multiple ways to obtain the same

unit of measurement. For instance, a student who correctly

answers three out of four questions during a class period









might be compared with a student who correctly answers

30 out of 40 questions. The latter student's performance

far exceeds the former, yet using percentage accuracy

statements alone, both students will be equated at

75 percent correct.

Lindsley (1971) has developed alternative measurement

procedures within an instructional system of precision

teaching. In this model, frequency measurement is

employed to describe multiple dimensions of academic

performance. Frequency measures have been found to be

more sensitive for description of individual behavior

than evaluation using percentage criteria (Pennypacker,

1972). With frequency measurement, both speed and

accuracy dimensions of performance are considered.

As such, frequency is a better measure of the fluency

of performance.

It is believed that high frequencies of performance

facilitate acquisition and retention of academic behavior

(Starlin, 1971; Haughton, 1971a). The rationale for high

rates of accurate responding during instruction is that

they insure against practicing errors and rapid loss of

skills due to inadequate learning. Key differences between

precision teaching and traditional educational measurement

include emphasis on frequency as a standard measurement unit,

emphasis on multiple dimensions of performance, the use of









criterion-referenced as opposed to norm-referenced

comparison, and frequent direct measurement (see Table 1).

Lindsley's (1971) precision teaching begins with

measurement of the frequency of performance prior to

instruction. This baseline measurement serves as a

reference point for comparison with subsequent measure-

ments during instruction. Following baseline measurement,

specific skills are identified as targets for instruction,

and instruction begins. During the course of instruction,

daily measurements of the performance of each skill are

obtained and graphically displayed on standard behavior

charts. Integral to precision teaching is a system of

instructional decision-making and optimization based on

observation of the daily measurements.

White and Haring (1976) have recently expanded upon

the baseline aspects of precision teaching with their

procedures for precision assessment. Precision assessment

provides for examination of a wide range of skills in the

learner's repertoire through the use of mixed skill probes.

A mixed skill probe is similar to a traditional achievement

test in that the items from many skills are presented. The

difference is that frequency of performance is measured,

and the assessment does not end at this point. Next,

single skill probes are used to obtain speed and accuracy

measures of skills in need of instruction. A single skill

probe differs from a mixed skill probe in that it contains










Table 1

A Comparison of Traditional
Measurement and Precision Teaching


Traditional Precision Teaching
Psycho-Educational Behavior-Analytic
Measurement Measurement




Norm-referenced Criterion-referenced

Measurement before and after Daily or frequent
instruction, infrequent measurement

Measurement direct or Measurement always
indirect direct

Individuals are compared to Individuals are
a group compared with
themselves

Considers accuracy dimension Considers multiple
of academic performance dimensions of
performance

No standard unit of measurement Frequency used as
standard unit of
measurement









items from only one skill domain. Additionally, single

skill probes contain many items representing a single

skill, and thus constitute a better sample of the

movement than the mixed skill probe or an achievement

test. A third type of skill, the tool skill probe,

is used to assess skills such as saying digits, writing

digits, saying letters, writing letters, and saying

letter sounds. These skills are considered prerequisite

to more advanced skills which build upon them (see Table 2).

An additional dimension of academic performance is

celebration, the rate of change in frequency across days.

Celeration has been used as a criterion measure to

evaluate performance during instruction. White and

Haring (1976) recommend a number of possible procedures

for determining acceptable performance during instruction,

one of which is the standard celebration. The standard

celebration procedure is based on research by Liberty (1975).

In a working paper from the University of Washington, Liberty

analyzed several hundred programs dealing with all types of

skills and children of all ages. Liberty observed that,

of the children whose programs showed some progress, about

53 percent accelerated at a rate of X1.25 (25 percent

improvement in frequency per week). About 66 percent of

the children achieved a -1.25 for deceleration targets

(25 percent improvement in frequency per week). In the

absence of other criteria, White and Haring recommend









minimum celebration values of X1.25 for acceleration

targets and -1.25 for deceleration targets.

In summary, the sensitivity of measurement

provided by precision teaching and precision assessment

is seen by many educators as an improvement over

traditional educational measurement. The use of

multiple measures of performance, criterion-referenced

evaluation, and continuous daily measurement holds

great promise for increased instructional control and

subsequent increased academic performance. The use of

frequency and multiple dimensions of academic performance

to predict learning is a relatively new area for research.

This study explores the use of frequency and multiple

dimensions of initial academic performance to predict

performance during instruction.


Statement of the Problem

The problem of interest to this study is the use

of frequency, celebration, and variability dimensions of

performance during baseline assessment to predict

academic performance during instruction. The specific

questions this study will address are:

(1) Can frequency, celebration, and variability of

baseline performance on tool skill probes be used to

predict the rate of learning during instruction?

(2) Can frequency, celebration, and variability of

baseline performance on single skill probes be used to









Table 2

The Relationship ,of Tool Skills To
Complex Academic Skills


Prerequisite Tool Skills


Write Digits 0 9


Complex Academic Skills


Write

Write

Write

Write

Write

Write


Write
words

Write

Write

Write
words


Write Letters A Z


digits for addition

digits for subtraction

digits for multiplication

digits for division

digits for fractions

digits to record time


letters for basic sight


letters for texted words

letters for name

letters for spelling









predict the rate of learning during instruction?

(3) Can frequency, celebration, and variability

of baseline performance on mixed skill probes be used

to predict the rate of learning during instruction?

(4) Is there a differential predictive relationship

by academic task stimuli from baseline performance to

performance during instruction? The different academic

task stimuli of interest include letters, digits, phonics

sounds, sight words, texted words, number problems,

phonics words, and spelling words.

(5) Is there a differential predictive relationship

by input and output modality of learners from baseline

performance to performance during instruction? The

different input and output modalities of interest include

see to say, see to write, see to do, hear to say, hear to

write, hear to do, think to say, think to write, think to do.

For each of the above questions, the rate of learning

will be measured by celebration. Celeration is defined as

the percent of change in frequency per week.

The answers to these questions increase our knowledge

of how academic skills are learned. This study also

extends our knowledge of measurement procedures. History

makes clear that the development of accurate observation

and measurement procedures inevitably leads to an explosion

of technology and knowledge. The telescope in astronomy,

the microscope in biology, x-rays and blood counts in

medicine, the Geiger counter in physics, Neilson ratings









in television advertising, and the cumulative recorder

in psychology are illustrative. Following each of these

technological achievements in measurement was a rapid

upgrading of the discipline involved.

The consequence of refined and sensitive educational

measurement may be a technology of education in which the

effects of a given instructional procedure on a given

individual are predictable and replicable. The questions

under investigation in this study are a small step toward

the development of such a technology of educational

measurement.













CHAPTER II

REVIEW OF RELATED LITERATURE


The review of literature is presented in three

parts. The related area of early identification

research is reviewed in the first section. The focus

here is on early identification studies concerned with

the prediction of learning failure.

The second section contains the theoretical and

research basis for the use of frequency as a measurement

datum for academic performance. Consideration was given

to major theoretical landmarks in the literature, as

well as experimental works. Studies of frequency

performance criteria for academic behaviors in reading,

writing, computational math, and spelling are reviewed

in this section.

The final section of the literature review contains

predictive studies using frequency measurement. These

studies are similar in nature to the present research

and are the foundation from which this research extends.

In order to survey the related literature, an ERIC

document search was made using key words "frequency,"

"rate," and "learning." In addition, the following

journals were searched from their initial publications

to date, with the exception of Review of Educational










Research

1.

2.

3.


which was searched from 1960 to present.

Academic Therapy

Exceptional Children

Educational Technology


4. Journal of Applied Behavior Analysis


Journal of Applied Psychology

Journal of Educational Measurement

Journal of Educational Psychology

Journal of Educational Research

Journal of Experimental Analysis of Behavior

Journal of Experimental Psychology

Journal of Learning Disabilities

Journal of Measurement and Evaluation

Journal of Personalized Instruction

Journal of Research and Development in Education

Journal of School Health

Journal of School Psychology


In order


to locate important theoretical discussion,


the reference lists of selected journal articles were

searched for relevant texts. Personal communication with

experimenters added to the literature review.


5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.









Early Identification Research


There is currently a great interest in screening

infants and preschool children to predict which ones

are at risk for experiencing difficulty with subsequent

learning. This interest is based on the assumption

that treatment initiated prior to schooling will

alleviate school-related problems. The studies of

Kirk (1958) and Skeels (1966) and the reviews by

Tjossem (1976) and Mercer, Algozzine, and Trifiletti

(1979) have formed a basis for continued research in

early identification and prediction.

Proponents of prediction procedures to identify

preschoolers at risk of school problems suggest several

advantages of early identification. First, they believe

early identification efforts are more likely to be

successful due to the belief that the behavior of young

children is more suceptable to change than that of older

children (Hayden, 1974; Stimbert, 1971). Secondly, early

identification enables preventive interventions during

optimal developmental periods when personality charac-

teristics are forming (Hayden, 1974; Stimbert, 1971).

Finally, early identification enables earlier family

adjustments and acceptance, providing additional support

for intervention strategies (Hayden, 1974). Disadvantages

of early identification are primarily concerned with the

effect of misdiagnosis and labeling (Keogh & Smith, 1970).









Prediction-Performance Comparison Matrix

Mercer, Algozzine, and Trifiletti (1979) have

presented a model for interpreting the predictive

utility of standardized assessment instruments and

batteries in which both vertical and horizontal

percentages are analyzed. Integral to this model is

construction of a prediction-performance comparison

matrix which allows observation of predictions and

outcomes (see Figure 1). Levels of prediction in terms

of poor performance or good performance are compared

with poor or good levels of criterion performance.

Quadrant A of Figure 1 represents those students who

performed poorly and who were predicted to perform

poorly. Quadrant B refers to those students who

performed well on the criterion measure, but were

predicted to perform poorly. These are referred to

as false positives. Quadrant C refers to students who

were predicted to perform well, but in fact performed

poorly. These are referred to as false negatives.

Quadrant D refers to students predicted to perform

well, who in fact did perform well.

There are a number of ways of comparing prediction

with performance on the matrix. Mercer (1975) reported

that most prediction studies utilize the horizontal

method of comparison. In the horizontal method observed

values in each quadrant are compared with prediction














PERFORMANCE


Poor


Poor


Prediction



Good


Figure 1


Prediction-Performance Comparison Matrix


Good


Predicted Poor Predicted Poor
Performed Poor Performed Good

(valid positive) (false positive)
A B

Predicted Good Predicted Good
Performed Poor Performed Good

(false negative) (valid negative)
C D









levels. Figure 2 is an example of a prediction-

performance comparison from a hypothetical prediction

study. Percentage of correct and incorrect outcomes

can be obtained by applying the horizontal analysis

method. In this case, 80 of 100 children predicted to

perform poorly actually did so (80 percent), while

20 of 100 children predicted to perform poorly did

well (20 percent). Similarly, 270 of 300 children

predicted to perform well did so (90 percent), while

30 of 300 predicted to perform well actually performed

poorly (10 percent). The overall hit rate describes

the number of children who were correctly identified.

It can be figured by adding the poor predicted poor

in quadrant A with the good predicted good in quadrant

D and dividing by the sum of all quadrants. The

overall hit rate for the example in Figure 2 is 87.5

percent.

Although the horizontal method serves as a way

of organizing and evaluating prediction-performance

information, it neglects consideration of the

relationship between the observed values within the

quadrants and the actual performance levels. This

can be accomplished by vertically analyzing the matrix.

Figure 2 includes vertically computed percentages.

For example, 72.7 percent (80 of 110) of the poorly

performing students were predicted poor, and 14.5













PERFORMANCE


Poor


PREDICTION


Good


110
Performed
Poorly


100
Predicted
Poor



300
Predicted
Good


290
Performed
Well


Figure 2

Numerical Example of Prediction-
Performance Comparison Matrix


Poor


Good









percent (20 of 290) of the good performing students

were predicted to do poorly. Percentages generated

by the vertical method will obviously differ from

those figured by the horizontal method.

Gallagher and Bradley (1972) advocated using

the horizontal method for establishing false positives

and the vertical method for computing false negatives.

They also favored evaluating the overall hit rate and

visually inspecting the entire matrix.


Single Instruments as Predictors

The majority of prediction studies use single

instruments as predictive measures. General readiness

tests (Ferinden & Jacobson, 1970; Lessler & Bridges, 1973),

intelligence tests (Lessler & Bridges, 1973), language

tests (Lyons & Bangs, 1972), perceptual-motor tests (Keogh

& Smith, 1970), and general physical factors such as

unusual birth history (Galante, Flye, S Stephens, 1972)

have been used as single predictors. An analysis of

these studies using horizontal and vertical percentages

is presented in Table 3.

As illustrated in Table 3, the Metropolitan Reading

Readiness Test (MRRT) yielded favorable percentages in

both short-term and long-term analyses. In comparing

this instrument to the Lee-Clark Readiness Test (LC) and

the California Test of Mental Maturity (CTMM), Lessler

and Biidgeo (1973) Coneluded that the MRT is th bnt






20





Table 3


An Analysis of Single Instruments as Predictors Using
Horizontal (H) and Vertical (V) Percentages




Study Sample Prediction Length of Performance Valid False False Valid
Instrument Prediction Test Positives Positives Negatives Negatives Overall


II V II V II V II V


lillt


Ferinden & 67 kinder- Evanston
.lacobson garden Early
(1970) children Identifica-
tion Scale
Ferinden & 64 kinder- WRAT
Jacobson garten Reading
(1970) children
Ferindcn & 67 kinder- MRIRT
JarobFon gartei
(1970) thillhen
Keogh & 2') kinder- Bender
Smith garten
(19701 children
Kenlh & 26 kinder- Bender
Smith .arten
(1970) children
Galante, 71 kinder- Unusual
Fle. & garden birth
Stephens children history
(1972j
Galante 71 kinder. Birth


Flye. &
Stephens
(1972)
Lyons &
Bangs
(1072)
Lyrnn| &

(1972)

Lyons &
Bangis
(1972)

Lyons &
Bangs
(1972)

l.r'sler &
lBlndqes
(1973)
Lessler &
Brikls
(1973)


garten
children


35 1st


order



LLAT


H month; WRAT


Reading



,8 months WRAT
8 months WRAT


Reading
6 ywais CAT
Reading


6 years CAT
Arllhmeilc


7 years Stanford
Aciievenment
& I lorn
Expectancy
7 years Sl.iford
Achievement
& Horn
Expectancy
I 2 years SRA


grader with special Arithmetic

23: 1t1 LI.AT 11/2 years SRA

special
intervention
35 11 LLAT '1/2 years SRA
graders with Rcading
special
intervention
23 1st LLAT IV'. years SRA
graders without leading
special
Intervention
293 Isl MRII 9 months CAT &
graders Teacher
Rating
196 Isl MRRT End of 2nd CAT &
graders grade Teacher
follow-up 21 month Ratiny


56 50 44 17 20 50 80 83


63 100 37


27 0


0 100 73


57 85 43 28 8 15 92 72 76


47 8: 53 44 9 13 91 56 65


40 100 60 45 0


0 100 55


56 41 44 14 24 59 76 S6 72




25 27 75 37 34 73 66 63 52




67 35 33 33 65 65 35 67 46


91 71 9 11 33 29 67 .'l


30 70 70 64 25


82 75 18


18 25


30 75 35




25 75 82


78




46


R6 87 14 14 13 13 87 86



91 62 9 10 39 38 61 90











Table 3 continued


Study Sample Prediction Length of Performance Valid False False Valid
Instrument Prediction Teat Posltlve@ Positives Negatives Negatives Overall
H V H V H V H V Hit"


Lessler & 293 1st Lee Clark 9 months CAT &
Bridges graders Heading Teacher
(1973) Readlrnss Rating
Test
Lessler & 293 1st California 9 months CAT &
Brldqes gralers Te!t of Teacher
(l1'73) Mental Raling
M.altlrlty


82 77 18 17 22 23 78 83



82. 78 18 18 22 22 78 82


Note. From "Early Identification An Analysis of the
Research". By C.D. Mercer, B. Algozzine, and J. Trifiletti,
Learning Disability Quarterly, 1979, 2, 12-24.


aThe median overall hit rate is 73.


--------~---









predictor of the three. Badian (1976) reported a

median correlation of .58 between the MRRT and subsequent

reading achievement and concluded that group-administered

readiness tests yield better prediction results than

group-administered ort individually administered

intelligence tests. In evaluating Badian's conclusion,

it is important to remember that the relationship

between predictive and criterion instruments is

crucial to the outcome of predictive studies, i.e., the

nature of the items on each test will greatly influence

the relationships between them. In support of this

qualification, Dykstra (1967) noted that letter naming

is one of the best predictors of reading achievement.

Analysis of studies using language tests as single

predictors indicates that educational intervention can

greatly influence achievement. Lyons and Bangs (1972)

used the Language and Learning Assessment for Training

Test (LLAT) to predict reading and mathematics achievement

with and without intervention. The overall hit rate of

the LLAT declined when children received intervention.

In other words, the predictive outcomes were influenced

by subsequent educational programming.

In a study using the Bender Visual-Motor Gestalt

Test (Bender) as a predictive instrument, Keogh and

Smith (1970) obtained good false negative percentages

but found a large percentage of false positives. Keogh









and Smith (1961) and Ferinden and Jacobson (1970)

suggested that a good score on the Bender is usually

followed by satisfactory achievement; however, low

scores tend not to be predictive.

While only one study of the predictive nature

of physical factors contained enough information to

obtain a horizontal and vertical analysis, many

investigations have been reported within this area.

Physical anomalies (Waldrop & Goering, 1971; Waldrop,

Pedersen, & Bell, 1968), developmental history (Denhoff,

Hainsworth, & Hainsworth, 1972; Hoffman, 1971; Pasamanick,

Rogers, S Lilienfeld, 1965; Wilborn & Smith, 1974), and

dental enamel defects (Cohen & Diner, 1970) have been

studied in attempts to establish their utility as

predictive measures. Mercer and Trifiletti (1977) have

examined the studies involving the predictive nature of

physical factors.


Multiple-Instrument Batteries as Predictors

A well-known multiple-instrument prediction study

was conducted by de Hirsch, Jansky, and Langford (1966).

A sample of 53 middle-class kindergarten children was used.

The battery consisted of 37 variables which were used to

predict reading performance. The authors concluded

that while background information is not useful as a

predictor, chronological age is a significant predictor.









Also, it was reported that predictions for girls are

more accurate than those for boys. An analysis of the

horizontal and vertical percentages obtained for the

de Hirsch et al. study and other multiple-battery

prediction studies is presented in Table 4. An overall

hit rate of 91 percent is indicated as are good percentages

in other categories, with the exception of false positives.

Gallagher and Bradley (1972) are critical of this study

and indicate that the results were obtained by applying

the index to the same group on whom it was developed.

Cross validation has not been as successful.

Feshbach, Adelman, and Fuller (1974) used the

de Hirsch Index to predict reading achievement in second

grade. As indicated in Table 4, the overall hit rate

was 73 percent and the number of false positives was

high. Likewise, Eaves, Kendall, and Critchton (1972)

administered the de Hirsch Predictive Index in a prediction

study and obtained positive results for prediction of

concurrent medical diagnosis of Minimal Brain Damage (MBD).

Eaves, Kendall, and Critchton (1974) used the de Hirsch

Modified Predictive Index (MPI) to predict teacher-

recommended grade placement. Their results were similar

to those of Feshbach et al. The overall hit rate was 76

percent and a high percentage of false positives was

found. The de Hirsch indices do not seem to have strong

empirical support.












Table 4


An Analysis of Multiple-Instrument Batterise as Predictors
Using Horizontal (H) and Vertical (V) Percentages



Study Sample Prediction Length of Performance Valid False False Valid
Instrument Prediction Test Poeltives Positives Negatives Negatives Overall
H V H V H V H V Hit"


de Hirsch. 53 kinder- de Hirsch
Jansky, & garden Index of 37
Langford children Variables
(1966)
Book 425 kin- MRT.
(1974) dergarten Bender.
children Slosson




Book 425 kin- MRT.
(1974) dergarten Bender
children Slosson


2 years


Gray Oral
Gates
Reading


9 months I.evel
achieved
on Scott
Foresman
Reading
Series
2 years Level
achieved
on Scott
Foresman
Reading
Series


71 91 29 10 3 9 97 90 91




93 48 7 3 31 52 69 97 75






55 94 45 13 1 6 99 87 88


Eaves. 50 kinder- Predictive Concurrent Medical
Kendall. & garden Index. Draw Immediale diagnosis
C- chton children A-Person. & of MBD
(1972) Name Print-
ing


Eaves. 42 chll- MPI End of
Kendall. & dren Neuropedia- grade
Crichlon follow-up tric Exam 2 years
(1974) Psychologi-
cal Exam


2nd Recom-
mended
grade
placement


88 96 12 4 4 11 96 89 92


65 81 35 27 14 19 86 73 76


163 kin- MPI
dergarten
children


2 years Recom-
mended grade
placement


Feshbach, 572 kin- de lllrsch 15 months G;ltes-
Adelman, dergarten Predictive MacGin!ile
& Fuller children Index Reading
(1974) Test


59 63 41 10 8 37 92 90 85



61 26 39 74 25 7 75 93 73


473 kin- Satz
dergarten Battery
white
mates


End of 1st Teacher
grade rating of
2 years reading using
a scale


New chil- Abbreviated 9 months Teacher
dren; 12R Satz Sept. to rallng of
ktlhrl Iinely .1iii' a,!livel ment

ihlltl,'n
children
(male,
female.
black.
white)


16 100 84 21 0




10 100 81 45 0


Eaves.
et al.
(1974)


Satz &
Friel
(1974)

Salz &
Friel
11')7(1)


0 100 79




0 100 55












Table 4 continued


Study Sample Predlctlon Length of Performance Valid False False Valid
Instrument Prediction Test Poaltlvea Poaltlves Negatives Negatives
H .V H V H V H V


Overall
Hita


Satz, New chil- Abbreviated End of 2nd Classroom


Friel, & dren; 175 Satz


Rudegealr kinder-
(1976) garten
white
males
Reported 458/473
In Satz. kinder-
Taylor, garten


Frel, &
lietcher
(1977)
Reported
In Satz
et al.
(1977)

Reported
In Satz
et al.
(1977)


Satz
et al.
(1977)


grade reading
ry 3 years level


Salz
Battery


End of 2nd CInssioom
grade reading
3 years level


29 89 71 25 2 11 98 75






28 89 72 31 2 11 98 69


males


419/473
kinder-
garten
white
males
442/473
kinder-
garten
white
males
114 kin-
dergarten
children
(male,
female,
black,
white)
follow-up


Salz
Battery




Satz
Battery




Abbreviated
Satz
Battery


End of 2nd
grade
3 years



End of 5th
giade
6 years



End of 1st
grade
2 years


Classroom
reading
level



Classroom
reading
level



Classroom
reading
level


34 91 66 34 3 9 97 66





63 58 37 9 11 42 89 91





60 71 40 11 7 29 93 89


Same as Language End of 1st
above Battery grade
2 years


Classroom
reading
level


55 71 45 13 7 29 93 87 84


Note. From "Early Identification An Analysis of the
Research". By C.D. Mercer, B. Algozzine, and J. Trifiletti,
Learning Disability Quarterly, 1979, 2, 12-24.


aThe median overall hit rate is 79.


Satz
et al.
(1977)


__ ~_____I___









Satz, Taylor, Friel, and Fletcher (1977) utilized

linear discriminant function analyses to arrive at an

optimal predictor score for a set of 22 variables. The

criterion variable was teacher ratings of classroom

reading level. In a series of studies (see Table 4),

the Satz battery was longitudinally evaluated with a

group of 473 boys. Some of the major findings of

these studies include the following:

1. The overall hit rate for the Satz battery was

considered adequate as was the valid negative rate.

2. False negatives (i.e., children in need of treatment

but not identified) tended to be overrepresented.

3. False positives (i.e., those identified but not in

need of treatment) tended to be overrepresented.

4. The battery seemed adequate in identifying low-risk

children, but problems were apparent with regard to

selecting those children needing intervention.


Teacher Ratings as Predictors

By asking teachers to identify children needing

extra intervention, a fairly simple identification

procedure is utilized. Haring and Ridgway (1967)

analyzed the results of screening for 1200 kindergarten

children. They noted that teacher perceptions are

accurate predictors of future school-related problems.

Similar results are reported by Benger (1968), Ferinden









and Jacobson (1970), and Cowgill, Friedland, and

Shapiro (1973).

Teachers' ratings tend to be most effective in

identifying those children in need of intervention

and those not likely to need special programming.

An analysis of errors within a study by Keogh and

Smith (1970) indicates that only false positive

mistakes were made. This would result in children

being placed in programs when they really did not

need them. The magnitude of such errors would depend

upon the negative effects of labeling as balanced by

the positive effects of educational programming.


Areas of Assessment for Prediction

Language, intelligence, motor, social-emotional,

and preacademic are the primary areas which have been

included in early identification assessment. To date,

the preacademic area appears to identify high risk

learners more accurately than any of the others (Badian,

1976; Keogh & Becker, 1973; Magliocca, Rinaldi, Crew, &

Kunzelmann, 1977). These investigators suggest that

areas of assessment have direct relevance to criterion-

performance measures. These skills may include

recognition of letters, letter sounds, numbers, shapes,

colors, body parts, and basic concepts.

In summary, with full consideration for cost, time,

and effort involved in early identification and prediction,









teacher perception seems to offer more advantages than

batteries and single instruments. Numerous investiga-

tors (Badian, 1976; Benger, 1968; Glazzard, 1977;

Haring & Ridgway, 1967; Keogh & Becker, 1973; and

Kottmeyer, 1947) report that teacher perceptions are

good predictors of school problems, especially if

teachers are provided checklists which include items

that are related to academic learning. Only two

studies (Feshbach, Adelman, & Fuller, 1974; Keogh &

Smith, 1970) were located which provided full matrix

data. Their overall hit rates were impressive, i.e.,

90 percent and 77 percent, respectively.









Frequency Measurement of Academic Performance

The choice of an appropriate datum to describe

academic performance has been given careful and

deliberate attention by many experts in the applied

sciences of behavior change (Haughton, 1971a; Johnston

g Pennypacker, 1980; Koenig, 1972; Lindsley, 1971;

Lovitt, 1968; Skinner, 1953; and White & Haring, 1976).

Skinner (1953) in a landmark theoretical

discussion o tihe imipor'llnce of frequency as a datumr

discussed its advantages for a technology of special

teaching. The major considerations are outlined below:

1. Frequency of a response is an orderly datum. The

curves which represent its relation to many types of

independent variables are encouragingly simple and smooth.

2. The results of frequency measurement are easily

reproduced. It is seldom necessary to use groups of

subjects and associated statistical control to demonstrate

results. This method permits a direct view of behavioral

processes, whereas previously behavioral processes have

been inferred.

3. Concepts and laws which are emerging from studies of

frequency have an immediate reference to the behavior of

the individual.

4. Frequency of response provides a continuous record

of many basic processes. A learning curve can be









followed across many days of instruction and the condition

of the response at every moment is apparent in the record.

5. Frequency of response lends itself well to automatic

data recording and collection.

6. Frequency of response is a valuable datum because

it is a physical referent for the concept of probability.

As such it is a simple and direct datum which will

generally serve as a more deliberate description of

behavior than will inferences and hypothetical constructs

such as "learned," "mastered," "skilled," and "knowledgeable."

Such language becomes more useful when one can say that

a learner can solve two-digit addition problems at a

frequency of 50 correct digits per minute with two or

less error digits per minute.

Skinner's central point is that the element which is

used to describe academic performance must be a function

of the behavior of the learner.

White and Haring (1976) have described academic

performance in terms of movements. The smallest change

in learning that can be measured is an increase or

decrease of one whole movement. A movement is the

equivalent of a discrete observable response. Movements

have both physical and temporal features. Prominent

among the physical properties are topography, force, and

locus. Topography is the muscular or skeletal "shape"

of the behavior or behavior sequence. For example,









a movement may be either written or oral, involving

different muscles. A hand may be raised or lowered,

involving a different sequence of the same muscles.

Force is the magnitude of a movement. An individual

may whisper or shout. A child may push another

child playfully or shove with enough force to

physically damage another. Locus is the direction or

target of a movement. A child may talk to a peer or

to the teacher. Answers may be written in the proper

positions or not.

In addition to the physical properties of topography,

force, and locus, a movement also possesses temporal

dimensions. These include duration, latency, and

frequency. Duration is the amount of time a movement

lasts. A child may take a minute or several minutes

to respond to a question. A child may take a long time

to get dressed in the morning, or may dress quickly.

In these examples, the physical elements of the

movement may remain essentially the same, but they

take more or less time to complete. Latency is an

important temporal dimension of behavior. It is the time

between an event in the environment, usually an

instruction, and the onset of the movement. A child may

take a long time to begin to answer a question. He

may take a long time to begin dressing in the morning.

Frequency is the number of times a movement occurs

during an observation period. By convention, frequency








for academic skills is expressed in terms of one minute

of observation (Lindsley, 1971).

The importance of frequency can be examined through

an example of reading behavior in which one student reads

at a frequency of 100 words per minute, while another

student reads at 10 words per minute. They each form the

words in the same way (i.e., the physical properties of

the behavior are the same). They each begin reading at

the same time (i.e., they demonstrate similar latency).

Both students read in the same amount of time (i.e.,

their duration is the same). Interestingly, these

students read differently. One student is much more

fluent with the skill than the other, as evidenced

by reading more words in the same amount of time.

Traditionally, experiments in learning have been

concerned with changes in the character or topography of

behavior (Bijou, 1972). The student learns how to do

something new, acquiring new behavior. But the conditions

which produce the topography of new behavior may continue

to have an effect when the topography dimension no longer

changes appreciably. After behavior has been acquired,

further reinforcement maintains it as part of the current

repertoire of the individual (Ferster & Skinner, 1957).


Frequency versus Percentage Statements

Many of the studies reviewed contrasted frequency

measurement of academic performance with percentage

statements (Haughton, 1969; White, 1972a; White & Haring,








1976). Accuracy percentage is defined as the number of

correct responses divided by the number of items presented

or attempted. Traditionally, educators have emphasized

accuracy in the initial development of academic skills.

It is becoming increasingly apparent that frequency

of academic performance is at least as important as

accuracy, and perhaps even more important when advanced

material is presented (Gaasholt, 1970; Haughton, 1971a;

Starlin, 1971). Frequency seems to be a better

indicator of the individual's ability to maintain,

generalize, and apply academic skills outside the

classroom (Thomas, 1972; White 9 Haring, 1976).

White and Haring (1976) have identified three

difficulties that can arise with use of percentage

statements. First, there must be adequate time to attempt

each item. If performance is based on all the items ,

presented, when the student does not have adequate time

to attempt all of them, then the student is penalized for

being slow. If the percentage is based on only the

attempted items, the student learns to attempt only those

items he is sure of. Secondly, percentage statements do

not address the actual number of movements the student

has made. For example, a basketball game in which six

out of tem baskets are made yields a percentage of

60 percent. The same student in another game could make

three out of four baskets for a superior percentage









of 75 percent. But realistically, fewer baskets were

made on a per-game basis. The final and most

serious deficiency of percentage statements is that they

can only measure learning up to the point where the

student stops making errors. In fact, learning can improve

beyond this point. Accuracy is only one way in which

academic performance can improve. An upper limit on

the value which a measurement can take is called a

record ceiling. Record ceilings represent artificial

limits on the measurement strategy. They ignore the

fact that one or more aspects of a student's performance

can be further developed.

In general, professionals tend to use percentage

statements when they want to describe an individual's

accuracy, and they use frequency when they wish to

describe an individual's fluency or speed. It is

important to realize that there is no need to support

a dual system of educational measurement. Frequency

statements can be converted to percentage statements

through a simple calculation:

PERCENT CORRECT FREQUENCY CORRECT
FREQUENCY ERRORS


Considerations for Measurement of Frequency

The primary concern of measurement is that the data

accurately represent the specific properties of the

behavior which is being measured (Johnston 9 Pennypacker,









1980). Three problems can be identified which influence

the measurement of frequency of academic performance.

These are the record floor, record ceiling, and

performance ceiling.


Record Floor

A record floor is the lowest possible non-zero

value that can be calculated or recorded in any

given measurement situation (White, 1972a). In many

situations, the record floor is determined by the accuracy

of the timing device. For instance, if timings are made

with a stopwatch with a second hand that jumps in 0.25

second intervals, events which take less than 0.25

seconds will "fall through the floor" and will be

recorded as "zero." Because data points falling below

the record floor are disjointed from the remainder of

the data by the distance from the record floor to zero,

they will tend to pull any estimates of progress down

toward the record floor. For this reason, data which

falls below the record floor should be avoided. As a

rule of thumb, White (1972a) suggests that prediction

based on data where more than 10 percent of the points

fall below the record floor will generally not be

accurate. In fact, data collection procedures should

be designed to place the majority of data at least ten

times above the record floor. For example, a stopwatch









with a 0.25 second capacity should not be used for

movements which are likely to be less than 2.5

seconds in duration.

Record floors are easily calculated for forms of

data which constitute a ratio (e.g., frequency = count/

time; percentage = count correct/total count). In cases

such as these, a "1" is placed in the numerator of the

ratio and the result is calculated (e.g., frequency record

floor = 1/time; percentage record floor = l/total count).

One can lower the record floor and increase the

sensitivity of measurement in many cases by increasing

the value of the denominator. In the case of frequency,

the observation time should be increased. There will

be situations in which modification of the data collection

procedure is impossible or not practical. It may then be

necessary to alter the unit of behavior. For example, if

"answers" to math problems are being counted, perhaps

counting "digits written" will increase the magnitude of

the data points sufficiently above the record floor. The

increase in sensitivity gained by selection of smaller and

smaller units of behavior must be weighed against the

increasing difficulty of counting and recording such movements.


Record Ceiling

There is a limit to how high data values can go.

Unlike toe record floor, the record ceiling is usually









not a function of the timing device or measurement

instrument per se. It is usually a function of the

measurement situation or the conditions of measurement.

If the behavior being counted is answers to math facts,

and there are exactly 50 problems on a sheet for a

one minute timing, then the highest possible recordable

frequency is 50 answers per minute. Rates of behavior

will be restricted by any artificial record ceiling

above which the rate is undefined (White g Haring, 1976).

There are several ways in which record ceilings

appear to affect academic performance in addition to the

simple limits they impose on rates. In many cases, a

learner's frequency will begin to slow down as the record

ceiling is approached, and before it is actually

reached. In other cases, there may be a "jump" to the

record ceiling as it is approached. Many learners

decelerate their frequency after reaching a record

ceiling. Because a record ceiling can affect academic

performance in unpredictable ways, it is advisable to

adjust the measurement condition so that the ceiling

is roughly ten times greater than the highest expected

value of the data.


Performance Ceiling

In addition to record ceilings and floors imposed

by data collection procedures, there is undoubtedly some

physiological limit to any human behavior (White & Haring,









1976). Performance ceilings can sometimes be estimated

by measurement of the learner's ability to perform a

"tool" movement which is prerequisite or a physical

component of the task behavior. For example, the tool

movement for writing answers to math facts is writing

digits 0 through 9. By measuring the learner's

frequency of writing digits 0 through 9, one can estimate

the maximum possible frequency for solving math facts.

In theory, if the learner could solve the math facts

instantaneously, then the frequency for math facts

would have an upper limit or performance ceiling

imposed by the time necessary to write the digits.

In practice, tool movements as estimators of

performance ceilings seem to have a fairly stable

relationship to task behaviors. White (1972b)

reports findings from a study with 18 elementary

children in which almost all children wrote digits 1.6

times faster than they were able to solve math facts.

White and Haring (1976) suggest targeting tool

movements for instruction in situations where the

frequency of the tool movement is less than one-half

to two-thirds of the desired task performance. The

rationale for increasing the tool rate is that the

performance ceiling will be proportionally increased,

thereby removing the possibility of a physiological

limit to the frequency of the instructional movement.









In summary, the recent application of operant

technology to learning has introduced frequency as an

important measure of academic performance. Lindsley

(1971), Starlin (1971) and other learning technologists

have used dual measures of frequency correct and

frequency errors to describe academic performance.

The advantages of using frequency units include increased

sensitivity of measurement for small changes in learning,

the potential for more direct observation of learning,

and the possibility of a universal scale of measurement

for both within and between learner performance. Similar

measures in the physical sciences have had great success

and have contributed to the advancement of knowledge

through more precise control of phenomenon. A popular

example is kilometers per hour as a measure of velocity.

The choice of frequency as the preferred unit for

measuring academic behavior is not without problems.

The sensitivity and utility of frequency measurement is

subject to problems of measurement design including

record floor, record ceiling, and performance ceiling.

However, these problems are not insolvable and may be

viewed as elements of instructional design. They do not

outweigh the advantages of frequency units over

percentage statements with respect to describing academic

performance.









Studies of Frequency Performance Standards

Considerable attention has been recently directed

to the performance of learners in the basic skill areas

of reading, writing, spelling, and math computation.

These skills are seen as important prerequisites for

later, more complex academic learning in content areas

such as social studies and science. Since basic skills

are of importance, various attempts have been made to

specify performance criteria for them. Despite the

critical role that mastery of these skills is assumed

to have on learning outcomes, percentage accuracy

statements continue to be chosen for performance standards

despite little or no evidence that optimal learning

will result (Block, 1974).

White and Haring (1976) define criterion performance

as the minimum level of performance which facilitates

learning in the next step of a sequential task hierarchy

and/or is required for maintenance in, or improvement of

the environment of the learner. In practice, performance

standards are derived from empirical observation of learners

who are considered proficient at the skill.

In reading programs, the assumption is usually made

that the frequency of reading words will of necessity be

very slow in early stages (Jenkinson, 1973). However,

Speer and Lamb (1976) have demonstrated a strong relationship

between high frequencies of first grade students' visual









processing of letters, and subsequent reading achievement

as measured by the Gates-McGinite Reading Test. The

implication is that if frequency of academic performance

is important in terms of learning outcomes, educators may

be setting the stage for failure by exclusive attention

to percentage accuracy statements as the criterion for

academic performance. Studies of academic performance

standards for math, reading, spelling, and writing will

now be presented.


Math Frequency Standards

Haughton (1971a) has reported a strong relationship

between the frequency of writing digits and math

computation (r = .9 to .99). Learners were instructed

to write digits one through ten for one minute. It was

observed that children who wrote digits at frequencies

of 20 to 30 digits per minute or less were also poor

performers in math computation. Haughton also reported

that learners performing at frequencies of 30 to 40

digits per minute on basic math facts were able to

accelerate while progressing to more complex tasks. Those

learners performing below 30 digits per minute decelerated

their frequencies as they progressed to more complex tasks.

This finding has been replicated in Marie Gaasholt's

(1970) research. Gaasholt found the frequency of 80 digits

per minute when writing digits one through ten, and the

frequency of 40 to 50 digits per minute on basic math facts









to be appropriate performance criteria for movements in

addition, subtraction, multiplication, and division.

Tomaras (1974b) reported normative frequency data

for tracing digits sampled from seven first grade class-

rooms in the Tacoma Public Schools S.S.T. Learning

Disability Project. Three distinct stimulus sheets were

used with digits one through four, five through seven,

and eight through zero. Median frequencies from the seven

classrooms were 29, 31, 23, 37, 37, and 43 digits per minute.

In a separate study, Tomaras (1974a) reported the

results of using a timed measurement format for mathematics

instruction in the first grade. A performance criteria of

30 digits per minute was set for fluency using probes

from the Tacoma Publis Schools S.S.T. Learning Disability

Project and addition and subtraction sheets adapted from

the Addison-Wesley Math Series. The control group

followed the traditional classroom format of the Addison-

Wesley workbook supplemented by other teacher worksheets.

No frequency performance standards were required in the

control group. The results indicate that the mean grade

equivalent score measured by the California Achievement

Test in Mathematics for the experimental group was grade

1.6. This can be compared to a mean grade equivalent score

of 1.3 for the control group. Findings were significant

at the .10 level. The timed measurement format also

affected the spread on the grade equivalent scale,









placing more children higher on the scale than at

the bottom of the scale. Tomaras reports a median writing

digits frequency of 32 digits per minute based on screening

thousands of children in first grade classrooms. The

frequencies varied from 0 to 60 digits per minute.

Wolking and Schwartz (1973) gathered normative

frequency data on a number of academic skills across

grades. Data from low achievers (LO) and high achievers

(HI) are presented in Table 5. The frequency of high

achievers for writing digits to addition problems varied

from an average 12 correct digits per minute with 1 error

per minute in first grade to an average of 86 correct

digits per minute with 0 errors per minute in sixth grade.

Low achievers varied from an average of 1 correct digit

per minute with 4 errors per minute in first grade to

54 correct digits per minute with 0 errors in sixth grade.

Thomas Lovitt has supervised a large number of

precision teaching projects at the Experimental Education

Unit at the University of Washington. Lovitt (1976)

reports that 50 digits per minute is considered an adequate

frequency standard for most mathematics skills.


Reading Frequency Standards

A large number of research efforts have been directed

toward identifying the frequency of oral reading necessary

to generate proficient readers. Eric Haughton (1971a)








Table 5


Rate of Growth Toward Adult Proficiency:
Differences Between High and Low Achievement Children, Grades 1 6


Grade One Two Three Four Five Six Adult
Number Skills C E C E C E C E C E CE C E


Hear Instructions
Write Numbers, Seq.

Hear Numbers, Dictated
at 32/minute
Write Numbers

See Numbers, Random
Say Number Names


22 2
6 3


14 1
6 8

76 0
28 3


See Addition Problems 12 1
Write Numbers 1 4

Reading Skills


38 0
26 3


32 0
13 1

94 0
62 0

23 0
9 2


62 0
36 0


32 0
32 0

112 0
80 0


34 0
14 3


81 0
63 0


32 0
32 0


88 0 116 9
87 0 94 0


32 0
32 0


32 0
32 0


120 0 124 0 150 0
98 0 102 0 124 0


48 0
34 0


58 0
33 1


86 0
54 0


156 0



32 0


204 0


132 0


Hear Instructions
Say Words

See Letters d,b,p,q
Mark d's


120 0 132 0 132 0 156 0 174 0 180 0
108 0 108 0 132 0 144 0 156 0 156 12


20 0
14 4


28 0
18 0


31 0
44 0


36 0
33 0


38 0
36 0


49 0
41 0


252 0


76 0









Table 5 continued


Grade One Two Three Four Five Six Adult
Reading Skills C E C E C E C E C E C E C E


Hear Letters Dictated
at 30/minute
Write Letters

See Small Letters
Say Letter Names

See Small Letters
Say Letter Sounds

See Regular Words
Say Words

See Irregular Words
Say Words


19 11 28 0 30 0
4 26 14 15 21 9


68 4 84 0
24 22 48 6


36 4
1 8


52 0
16 4


104 0
64 4

44 0
24 4


50 8 100 0 108 0
1/2 38 6 11 28 8


50 9
0 -


30 0
24 2


30 0
28 2


30 0
28 2


124 0 122 0 142 0
76 0 88 3 104 0


50 0
36 3


126 0
54 8


52 0
30 3


64 0
34 6


138 0 148 0
74 4 104 2


90 0 104 0 128 0 134 0
6 17 16 12 48 12 74 8


150 0
90 6


30 0


196 0


108 0


198 0


198 0


Writing Skills


See Squares
Write X's


20 0
12 0


See 0's
Put Dot in O's

See Numbers, Random
Write Numbers

See Letters, Random
Write Letters


22 0
18 0


38 2 43 2
24 11 39 9


25 0
11 0

25 0
11 0


30 0
29 0

27 0
30 0


28 0
28 0

58 1
44 8

44 0
39 0

40 0
41 0


38 0
28 0

66 5
56 4

66 0
52 0

61 0
48 0


50 0
30 0

79 0
65 0

79 0
61 0

74 0
61 0


45 0
41 0


85 0
81 0

100 0
80 0

88 0
72 0


78 1


110 0


145 0


127 0










Table 5


- continued


Grade One Two Three Four Five Six Adult
Writing Skills C E C E C E C E C E C E C E

Hear Regular Words 4 0 14 2 24 0 32 0 32 0 36 0 48 0 HI
Say Letters 0 1 6 4 6 10 6 20 4 22 4 LO

Hear Irregular Words 2 6 12 4 18 2 28 0 32 0 32 0 48 0 HI
Say Letters 0 2 5 5 6 8 6 14 4 16 5 LO









found that children reading above 100 words per minute

in third and fourth grade did not decelerate their

performances when the reading curriculum became more

advanced. It was concluded that a minimum rate of

100 words per minute is a useful performance standard

for oral reading.

Johnson (1971) found that 90 percent of students

reading below 50 correct words per minute had

relatively high error raten betweenn 2 and 20

errors per minute). Only 30 to 40 percent of students

reading between 50 and 100 correct words per minute

has errors in oral reading. Of the students reading

above 100 words per minute, only 10 percent made

errors.

Starlin (1970) reported that children whose frequency

of oral reading was 5 to 10 words per minute had severe

difficulty with reading and had not mastered prerequisite

reading skills such as saying sounds. Haughton (1971a)

reported that some of these children needed speech

acceleration because they talked too slowly. The

conclusion was that oral reading ability is a function

of the frequency of certain prerequisite skills such as

saying sounds, saying phonetically irregular words

(also called basic sight words), and speech production.









Camp (1973) studied the relationship between

frequency of reading texted words and long term

retention in 46 children with severe reading disability.

The majority of the children had learning curves

qualitatively similar to normal children. Rank order

correlations between reading frequencies and three

measures of retention ranged between r = .54 and r = .94.

The data suggests that individual differences in frequency

may account for a large share of individual differences

in retention.

Thomas (1972) studied instruction in reading rate

acceleration and the effects upon comprehension. Three

experimental classes were randomly selected in each of

grades two, four, and six in Montana schools. Standardized

protests and posttests of comprehension were administered

to nine classes including 407 learners. The experimental

classes were trained to increase frequencies of reading

texted words over a six week period at the beginning of

the school year. Results of the study indicate that the

learners in second grade made significant gains in reading

comprehension. The first grade experimental group made

significant gains in both reading rate and comprehension.

When the groups were equated on the basis of intelligence

quotients, the differences maintained. The differences

did not decline when measured again at the end of the


school year.









Alper, Nowlin, Lemoine, Perine, and Bettencourt

(1974) reported that 100 words per minute with two or

less errors per minute is considered mastery for oral

reading. Th author reported several other academic

performance criteria in current use (see Table 6).

These frequencies may be contrasted with Lovitt's

(1976) recommendations of 100 words per minute for oral

reading and 65 per minute frequencies for see to say

word parts. Suggested performance standards from the

Great Falls Montana Precision Teaching Project are a

more recent guide (see Table 7). These standards

suggest frequencies of 200+ for oral reading of texted

words and 60 to 80 sounds per minute for isolated

phonics sounds.

Summarizing the studies in reading, two salient

factors emerge: (1) there is a frequency standard for

oral reading above which children make few errors and

are able to progress to more difficult reading without

decelerating, and (2) there appears to be important

prerequisite skills to oral reading. By developing

each prerequisite skill to an appropriate proficiency

level before introducing new materials, acquisition

moves smoothly and rapidly (IIaughton, 1969). Holding

a skill at proficiency level is simplified because all

the precursors have been thoroughly learned.









Table 6

Tentative Mastery Levels in Reading


Rate Correct Rate Incorrect


Sounds:

Consonants

Vowels

Alphabet Names

Phonetically Predictable
3, 4, and 5 Letter Words

Dolch Sight Words

Reading in Books at
All Grade Levels


80/min.

80/min

80/min.


80/min.

60-80/min.


100-120/min.


1-2/min.

1-2/min.

1-2/min.


1-2/min.

1-2/min.


1-2/min.









Spelling Frequency Standards

Starlin (1971) presented academic standards for

spelling performance. For learners in kindergarten

through second grade, a frequency of 30 to 50 correct

letters spelled per minute with 2 or less errors per

minute was considered adequate. For third grade

through adult levels, 50 to 70 correct letters spelled

per minute with 2 or less errors per minute was

considered adequate. These standards can be contrasted

with suggested performance standards from the Great

Falls Montana Precision Teaching Project. The Project

recommends 80 to 100 letters per minute for hear to

write dictated spelling words, and 15 to 25 words per

minute for hear to write dictated words.

The Starlin (1971) study was the only experimental

study which could be identified on the subject of spelling

frequency standards. Researchers have been reluctant

to study this area because the frequencies seemed to

be dependent on the rate of presentation of the stimulus

words. Recently, new techniques have been used whereby

the stimulus words are presented at a much faster

rate than the child can spell. In the typical application,

a stimulus word is presented every 3 seconds. Some words

are not spelled, but a stimulus word is always present

shortly after completion of a previous word, regardless

of how long it takes to spell the previous word.









Writing Frequency Standards

Kunzelman (1970) and Haughton (1971a) have demonstrated

that children and adults have a higher frequency of writing

letters in words than writing letters in isolation.

Wolking and Schwartz (1973) report normative data on

writing random letters. High achievers averaged from 25

letters per minute with no errors per minute in first

grade, to 88 letters per minute with no errors per minute

in sixth grade. Low achievers averaged from 11 letters

per minute with no errors per minute in first grade to 72

letters per minute with no errors per minute in sixth

grade (see Table 5). This data should be evaluated in

a developmental sense rather than as performance standards

per se. Wolking (1980) recommends the use of 120 letters

per minute with 2 or less errors per minute as a general

performance standard for writing skills. Lovitt (1976)

has used 125 symbols per minute as the desired frequency

standard, but cautions that research has not been

conducted which could justify that value.

Suggested performance standards from the Great Falls

Montana Precision Teaching Project (1979) are presented

in Table 7. It can be observed that the performance

criteria listed are generally higher than other

recommendations. Performance standards change periodically.

The trend is toward higher frequencies.









Table 7

Suggested Performance Standards
Great Falls Montana Precision Teaching Project


Skill Standard

Reading

See/Say Isolated Sounds 60-80 sounds/min.

See/Say Phonetic Words 60-80 words/min.

Think/Say Alphabet (fowards) 400+ letters/min.

See/Say Letter Names 60-100 letters/min.

See/Say Sight Words 80-100 words/min.

See/Say Words in Context (oral read) 200+ words/min.

See/Think Words in Context (silent read) 400+ words/min.

Think/Say Ideas or Facts 15-30 ideas/min.


Handwriting

See/Write Slashes

See/Write Circles

Think/Write Alphabet

See/Write Letters (count 3 for each
letter: slant, form, and ending)

See/Write Cursive Letters Connected
(count 3 for each letter)


Spelling

Hear/Write Dictated Words

Hear/Write Dictated Words


200-400 slashes/min.

100-150 circles/min.

80-100 letters/min.


75 correct/min.


125 correct/min.




80-100 letters/min.

15-25 words/min.









Table 7 continued


Skill

Mathematics

See/Write Numbers Random

Think/Write Numbers (0-9) Serial

See/Say Numbers

Think/Say Numbers in Sequence
(count-bys)

See/Write Math Facts


Standard


100-120 digits/min.

120-160 digits/min.

80-100 numbers/min.


150-200+ numbers/min.

70-90 digits/min.









A Frequency Model of Learning

White and Haring (1976) define fluency in relative

terms. In their opinion, the question of fluency should

be judged in terms of what will make the skill useful

for the child. Reading at a frequency of 50 words per

minute may well serve the needs of a second grade child,

but will not suffice for the college freshman. White

and Haring have proposed a five-stage learning model

through which a child acquires each discrete academic skill.

In their model, the learner can move through stages of

acquisition, fluency building, maintenance, application,

and adaptation. Identification of the first three stages

of the model is based on the frequency of correct and error

performance. Closely related skills can be in several

different stages of the model, dependent upon the

frequencies of performance for each skill. In the White

and Haring learning model, differential instruction is

programmed depending on the learning stage which in turn

is based on the frequencies of academic performance.

Although there is little research to support the

White and Haring learning model, it has stimulated efforts

to identify academic performance standards to use as goals

in the fluency-building stage. The model is primarily of

practical value in that the stages of learning have specific

and concrete teaching procedures. The White and Haring

work has organized and directed the efforts of many learning

technologists.









In summary, the majority of studies included for

examination of frequency measurement criteria are an

outgrowth of the precision teaching model developed

by 0. R. Lindsley (1971). Central to this model is the

use of frequency measurement. The studies of frequency

performance criteria for academic skills have followed

two schools of thought. One belief is that the criteria

should be set at the median frequency for a group of

similar peers. The followers of this belief have

identified normative frequencies for various grade levels

and types of learners. The problem with this type of

data is that populations operating under a precision

teaching model will have much higher normative frequency

values than populations operating in a traditional

instructional framework.

Other researchers have attempted to identify critical

frequencies above which subsequent learning will be

facilitated and below which learning is hindered. The

problem with this approach is that it is dependent on an

identified sequenced curriculum. Furthermore, once the

critical frequency is identified, a higher frequency must

be specified as the desired criterion frequency in order

to avoid the problems associated with the performance

ceiling.

Despite the many problems of identifying frequency

performance criteria, it remains a fertile area for





58



research. The objective is to identify frequency

performance standards which will produce maintaining or

rising initial frequencies and celebrations as new

curriculum material is presented. The central issue

appears to be whether critical frequencies can

be identified which will facilitate academic performance

for basic skills in reading, spelling, writing, and math

computation.









Predictive Studies Using Frequency Measurement

Prediction using any method is a tenuous endeavor.

In essence, one is implying that the conditions which

produced the prediction data will remain in effect and

produce similar progress in the future (White, 1972a).

In reality, many new variables can be introduced at any

time, or the existing values can diminish or be enhanced

(i.e., through boredom, maturation, etc.). The problem

is further complicated by the complex role of the

teacher in arranging the instructional environment to

maximize learning. Almost by definition, conditions

will not remain the same in a learning situation.

Implied in the use of data for instructional

decision-making under the precision teaching model is

prediction of academic performance. One predicts, on

the basis of available academic performance information,

whether or not the learner will meet established performance

standards within an acceptable time limit. If the

prediction indicates failure to attain the standard, then

the instructional procedures are changed. If the pre-

diction indicates attainment of the standard, than a change

should not be necessary. Thus prediction of academic

performance serves a primary role in the timing and

selection of instructional methods and procedures.

In predicting academic performance, one is concerned

with the trend of the frequency values. There are a









number of methods for quantifying the trend, among

which the most popular are celebration and slope.

The use of data from academic performance to

predict subsequent performance requires resolution of

two basic considerations: the type of data collected,

and the amount of data needed for prediction. White

(1972a) maintains that the type of data used for prediction

should have the capacity to vary over a wide range of

values. In addition, the data should remain comparable

from day to day. White identifies three types of data

which meet these criteria: counts of the number of times

a behavior occurs where the time in which the counts are

taken remains constant from day to day; frequency, in which

the behavior count for each day is divided by the time over

which the counts were collected; and time or temporal values

such as latency, the time necessary to begin responding once

an instruction is given. Frequency is the most commonly

employed of these acceptable data types.

The ability to accurately predict subsequent academic

performance depends on the quantity and quality of data

used for prediction. Theoretically, the more data used

for prediction, the better the chances for accurate prediction.

White (1972b) analyzed the predictive utility of the

median slope for predicting academic performance within

instructional phases (i.e., within periods of instruction

in which the conditions of instruction were held constant).









The criteria for success in prediction was the deviation

of data values from the median slope predicted line of

progress. White found that 9 and 11 data points had

optimal predictive ability over a wide range of days

into prediction. Interestingly, a reduction of

predictive utility occurred after 13 predictive data

points. This was attributed to reduction in the

number of projects to sample which contained many

data points. In general, the prediction had greater

accuracy as the number of data points for prediction

increased.


Predictive Studies

White (1972a) analyzed the results of 116 classroom

precision teaching projects. The projects included tasks

such as writing answers to addition and subtraction

problems, saying digits, and reading sight words. Four

different methods were compared for using initial

frequency data to predict subsequent academic performances

of single individuals. All four methods were slope

calculations. The methods were compared using 3 initial

data points, then gradually increasing the number of

days into prediction until 11 or 12 data points were

included in the calculations. The slope methods used

included the least-squares regression solution, median

slope method, corrected slope method, and split-middle

technique.









The findings indicate that median estimates of

trend, and in particular the median slope method, were

more consistently accurate than the least-squares

regression solution. The probability of acceptable

prediction over one week or more into the future was

not within reasonable limits until at least seven

data points were used for prediction. The split-middle

technique performed well enough to be considered an

alternative to the median slope method for use by

teachers and other educational practitioners.

Critical analysis of the White study reveals that

there was much variety in which method was better in

individual cases. Over a large number of cases, the

median estimates predicted better than other methods.

Another problem with the study was the method of ranking

used to judge the "closeness" of prediction. Exact

quantification of the accuracy of prediction was not

reported.

A significant finding not mentioned in the conclusions

of the White (1972a) study was the influence of variability

of the frequency values. The median slope method was

drastically affected by trends in deviations or variance

in the data, to the exclusion of trends in frequency. A

correction factor was applied to the median slope calcula-

tions to minimize the effects of variability in the data.









Consequently, the utility of variability for predicting

future academic performance of single individuals was

not explored.

In a landmark dissertation study, Koenig (1972)

studied the utility of least squares straight line

projections on semilogarithmic charts to predict future

frequencies. In this research, the first 10 to 14

frequencies of each phase of instruction was used to pre-

dict to the next 10 to 14 frequencies within phase. The

percentage of future frequencies contained in the envelope

formed by bounce lines was used to assess the accuracy of

the projection technique. A total of 14,452 phases across

a variety of academic and behavioral tasks were analyzed.

The major findings of this study were:

1. Variability about straight line celebrations and quarter-

intersect celebration lines was found to be relatively constant

in proportion and symmetrical above and below the line.

2. The least-squares celebration line was slightly better

at bisecting future data than the quarter-intersect method.

Both methods performed adequately.

3. The bounce envelope projection technique did not

perform well for predicting future frequencies. The

least-squares projection envelope contained 70 percent

or more of the projected frequencies only 42 percent of

the time. About 21 percent of the time, 90 percent or

more of the frequencies were contained.









4. Projecting only to the next quarter containing five

to seven of the frequencies improved the projection.

The overall conclusion from the Koenig study was

that least-squares and quarter-intersect straight lines

usually represent human frequencies accurately. It

should be noted that straight line methods represented

the data well despite the fact that about one-third of

the human frequency phases were changing more than 10

percent weekly. The other two-thirds of the phases

changed less than 10 percent weekly.

Koenig (1980) analyzing data from over 8,000

children reports that prediction within phases of

precision teaching episodes requires at least six data

points for math and spelling, and eight data points for

reading to attain significant correlation values for

prediction. The dependent measure was the frequency of

correct movements. Data which contains large amounts

of variability require additional data points to obtain

significant prediction correlations. Koenig recommends

exclusion of the first data point, and at least ten

daily observations for prediction studies using frequency

correct measures. The data in Table 8 summarize and

organize Koenig's prediction results for math, spelling,

and reading movements. It can be observed that the t

values for correlation become acceptably small and








Table 8


The Predictive Strength of Learning Indicesa
Based on Nine Performances (Excluding First)
Compared to Learning Indices Based on Fewer Performances


Learning Index Learning Index Based on Days 2 through 10
Based On Days MATH SPELLING READING
mean comparison mean comparison mean comparison
r t p r t p r t p

2 through 3 .18 11.9 .0005 .09 10.3 .0005 .40 8.7 .0005

2 through 4 .51 7.4 .0005 .44 5.9 .0005 .37 7.3 .0005

2 through 5 .69 5.4 .0005 .19 5.1 .0005 .34 5.7 .0005

2 through 6 .77 1.7 .08 .68 2.4 .02 .80 5.7 .0005

2 through 7 .85 1.7 .08 .97 1.9 .06 .88 2.6 .01

2 through 8 .93 1.9 .06 .99 1.4 .17 .94 0.2 .85 *

2 through 9 .98 2.2 .03 .99 1.4 .17 .97 -1.2 .25


Note. Personal


communication with Carl Koenig 1980
communication with Carl Koenig, 1980


aData represents over 8000 children' movements in math, spelling, and reading.

b681 third grades with all 10 performances reported.

*Indicates points at which error probability passes through p = .05. For math and
spelling this occurs on days 2 through 6. For reading days 2 through 8.









significant at six days for math and spelling (t = 1.7

and 2.4, respectively), and eight days for reading (t = .2).

Pace (1980) explored the use of celebration and

frequency for predicting children referred for special

education services. Using the International Management

System Learning Screening Procedure (Koenig & Kunzelmann,

1980), an overall hit rate of 64 percent was achieved

across grades one through six. The sum of celebration

ranks in the lower quartile was used for prediction.

This procedure yielded a 25 percent referral rate

composed of a high percentage of false positives and

false negatives.

The same screening procedure using frequency

rather than celebration increased the overall hit rate

from 83 percent to 100 percent across grades. These

values compare favorably with the best of the early

identification studies using traditional measurement

techniques. The significant finding of this study was

that celebration ranks lessen the accuracy of prediction,

while frequency ranks demonstrated superior predictive

utility. This must be viewed as a tentative finding due

to limitations in the design of the study which did not

include mentally retarded children and an overall three

percent minority population in the school district under

investigation. It should be noted that under the Learning

Screening Procedure, the content of the screening items

is taken from skills in the existing curriculum.









Stiles (1973) studied the utility of using

frequency measures from individual learners to predict

their scores on the Short Form Tests of Academic Aptitude/

Comprehension Tests of Basic Skills (SFTAA/CTBS) of the

California Test Bureau. Data from 348 third grade

students' performances on the SST stimulus sheets were

used for prediction. One minute samples from each day over

a ten day period were collected on such skills as

writing random digits, addition problems, subtraction

problems, hear to write letters, writing random letters,

saying sounds, and saying words. The celebrations and mid-

point frequencies were used to predict SFTAA/CTBS performance.

Results of the Stiles study indicate that 36 percent

of the variation or differences in language intelligence

scores can be accounted for by differences in rates of

performance on the SST skills. The variables which

explained the greatest amount of the variance (i.e., the

variables which entered the regression formula first) were

the frequency of saying words and writing random numbers.

The addition of other variables to the equation increased

the variance accounted for by 6 to 12 percent.

Hanby (1975) described the use of frequency of oral

language performance to identify children with language

deficiencies. A non-tested preschool class was used to

select a picture from the Ginn Pre-Reading Picture









Series which had the highest number of verbal responses.

In the testing procedure, children were asked to tell

what they saw happening in the picture. The frequency

of words responding during a 15 or 30 second timing each

day was recorded. A class summary of frequencies was

plotted on polar logarithmic charts and language

deficient students were identified by a criterion of

one-half of the class median frequency value. An

alternative criteria discussed was the median frequency

by age in months.

An advantage of using the frequency procedure described

in the Hanby study is that the class median celebration

value could be used as a criterion for instruction.

The class median celebration value reported was X1.3

(30 percent growth in frequency values per week).

In summary, predictive studies using frequency

measurement can be classified into two groups: those

which attempted to predict academic performance within

phases of instruction (White, 1972b; Koenig, 1972; Koenig,

1980); and those which attempted to predict to some

external criteria (Pace, 1980; Stiles, 1973; Hanby, 1975).

The latter studies are similar to the early identification

studies reviewed earlier in that the emphasis is on

prediction of children at risk for academic failure.

They differed in that frequency measurement was the dependent

measure used for prediction.









All of the investigations in this section were

concerned with frequency correct measures, while a few

studies also considered celebration and variability

for prediction (White, 1972a; Koenig, 1972; Pace, 1980;

Hanby, 1975).

Important findings from the frequency measurement

studies include the number of data points into prediction

(Koenig, 1980); the relationship of variability to both

celebration and frequency correct measurements (White,

1972a; Koenig, 1980); and the utility of frequency correct

measures over celebration measures for prediction of

problem learners (Stiles, 1973; Pace, 1980).

None of the frequency measurement prediction studies

attempted to combine frequency, celebration, and variability

measures for prediction of subsequent academic performance.

Additionally, no studies attempted to predict across

phases from baseline to instruction.

The present study extends and builds upon the previous

research findings to include multiple dimensions of

frequency, celebration, and variability measures for

prediction of academic performance. It also breaks new

ground in attempting to predict from baseline to

instructional phases.













CHAPTER III

METHOD


Sixty learners were assessed over a five-day period

by fourteen teachers using the Sequential Precision

Assessment Resource Kit II (Trifiletti, Rainey, &

Trifiletti, 1979). This assessment procedure was

followed by twenty days of academic instruction on the

skills identified as deficient during assessment. During

instruction the teachers used precision teaching methods

to maximize academic performance. Following instruction

the data from the study were analyzed to determine the

predictive utility of frequency, celebration, and variability

dimensions of academic performance. The content of instruc-

tional tasks was coded for further analyses of relationships

between frequency, celebration, and variability of academic

performance during assessment and instruction.


Subjects

The subjects were students enrolled in the Summer

Learning Disabilities Program sponsored by the Department

of Special Education of the University of Florida. They

ranged in age from seven years two months to fifteen years

five months.

In May, 1979, a packet of information was mailed to

teachers of exceptional student education in Alachua County,

70









Florida. The teachers were asked for referrals of

exceptional learners who might benefit from summer

instruction. Children were selected from the referrals

on a first-come, first-served basis for a total of

sixty children. The entire population of sixty children,

fourteen teachers, and two teacher-managers of the Summer

Learning Disabilities Program were used for the study.

The students in the study were exceptional students

from public and private schools in Alachua County, Florida.

The majority of the students were children with mild to

moderate specific learning disabilities.

The teachers employed in the study were enrolled

as a practicum teaching experience for partial fulfillment

of the requirements for the Master of Education in Special

Education. The teacher-managers elected the experience

as part of the requirements for the Doctor of Philosophy

in Special Education.


Equipment

Apparatus

The assessment instrument used for the study was

the Sequential Precision Assessment Resource Kit II

(Trifiletti et al., 1979). This instrument is based

upon White and Haring (1976) procedures for precision

assessment. A description of the Sequential Precision

Assessment Resource Kit II (SPARK II) instrument is

provided in Appendix B. Probes from the SPARK II were









used to gather data from which frequency, celebration

and variability measurements were derived.

Tool skill probes, single skill probes, and mixed

skill probes from the SPARK II were administered. Teachers

scored the performance of learners on the probes and this

information was recorded on assessment summary sheets.

A computer program was used to generate weekly

frequency charts for each teacher-learner-task (triad)

combination. The charts displayed both frequency and

accuracy of performance on each skill, and were cumulative

from the onset of instruction. A listing of the computer

program written in Fortran language is provided in Appendix

C. Appendix D contains a sample frequency chart and

directions for interpretation.


Setting

The study was conducted at the P.K. Yonge Laboratory

School of the College of Education, University of Florida.

Assessment and instruction of learners was carried out in

ordinary elementary classrooms during a special summer

program. The dates of the assessment and instruction

phases of the study were from June 25, 1979, to August 7, 1979.


Procedure

The study consisted of three phases. The first was

an orientation and training period for the teachers and

managers of the study. The second phase was a five-day









assessment period during which each learner was

administered probes from the SPARK II. The final

phase consisted of 20 teaching days of individualized

instruction for each learner. The instruction employed

precision teaching methodology in order to maximize

academic performance. Each of these phases of the

study will now be described in detail.


Training Procedures

All of the teachers and teacher-managers attended

a college course and an intensive workshop on precision

teaching procedures prior to onset of the study. These

procedures were reviewed during a two-hour training session.

A syllabus of the training session is included in Appendix E.

The teachers were trained in interpretation of the

computer charts during individual sessions with their

teacher-manager.


Initial Precision Assessment

During the assessment phase of the study, the

teachers administered three types of probes from the

SPARK II; tool skill probes, mixed skill probes, and

single skill probes. The mixed skill probes were used

to identify possible deficient skills in reading,

mathematics, and language arts. Mixed skill probes were

administered to each learner on the first and second days

of assessment. Teachers then examined the results of









the mixed skill probes to select single skill probes

for further assessment. The frequency, celebration,

and variability derived from learner's performance

on mixed skill probes were used to predict subsequent

academic performance.

The single skill probes administered to each

learner were selected on the basis of information

gained from the mixed skill probes. Single skill

probes were administered on days three, four, and

five of the initial assessment period. Data from the

single skill probes were used to select skills for

instruction. The frequency, celebration, and varia-

bility measures derived from the single skill probes

were used to predict subsequent academic performance.

Tool skill probes were used to assess performance

on important prerequisite skills such as saying letters,

writing letters, saying digits, and writing digits. The

tool skill probes were repeatedly administered to each

learner on each day of initial assessment.

Frequency, celebration, and variability measures of

each learner's performance on the tool skills were

computed. These data were later used to predict

subsequent academic performance.

The order of administration of probes for initial

assessment is presented in Table 9. Upon completion of

the initial assessment, teachers selected six to ten









Table 9

Administration Schedule of
Probes During Initial Assessment


Day 1 Day 2 Day 3 Day 4 Day 5


Tool Tool Tool Tool Tool
Skill Skill Skill Skill Skill
Probes Probes Probes Probes Probes



Mixed Mixed Single Single Single
Skill Skill Skill Skill Skill
Probes Probes Probes Probes Probes









skills for instruction with each learner. Selection was

based upon teacher's clinical judgement and the information

obtained during assessment.

Instruction

The third part of the study involved instruction

using precision teaching methods. Teachers administered

daily timed probes from the SPARK II and other sources

for instructional targets. Performance data were charted

daily by each teacher. These charts were collected

each weekend and the data were keypunched by the

experimenter to produce weekly computerized charts of

each learner's performance. The computerized charts

flagged celebration values which were less than 25 percent

weekly improvement. Teachers were required to change

their instruction for these skills in order to optimize

learning.

Experimental Design

The experimental design for this experiment follows

a predictive model. The predictor variables were median

frequency correct, weekly celebration, and variability

of performance on academic skills during assessment.

This information was obtained by measuring performance on

mixed skill probes, single skill probes, and tool skill

probes from the SPARK II. The criterion variables were

weekly celebration during the first instructional phase and

second instructional phase.









Frequency was defined as the median value of the

correct movements per minute of observation. Since the

computer generated charts used an equal interval scale,

celebration was defined as the ratio of two points seven

days apart on a least squares regression line plotted

through the frequency correct points. Variability of

academic performance was defined as the sum of squares

of error about a regression line plotted through the

frequency correct points.

Data Collection

Data describing the baseline initial assessment were

collected and recorded by teachers on summary forms

provided by the experimenter. Data from daily instruction

were collected by teachers and recorded on ratio charts.

Data from initial baseline assessment and instruction were

keypunched by the experimenter. This effort produced

the computerized charts as well as formed the data for

statistical analyses.

Data Analysis

The data for this study were statistically analyzed

using multiple regression procedures and the stepwise

solution (Nie, Hull, Jenkins, Steinbrenner, S Brent, 1975).

In this procedure, the computer enters independent variables

into the regression equation in single steps from best to

worst. The independent variable that explains the greatest

amount of variance in the dependent variable will enter








first; the independent variable that explains the greatest

amount of variance in conjunction with the first will

enter second, and so on. In other words, the independent

variable that explains the greatest amount of variance

unexplained by the variables already in the equation enters

the equation at each step. Minimum default values of

F ratio (F = .01) and tolerance (T = .001) were used to

control inclusion of independent variables at each step.

The computer facilities of the Northeast Regional

Data Center (NERDC) and the Statistical Package for the

Social Sciences (SPSS) were employed to obtain the data

analyses. The data were organized into an SPSS data set

on punched cards by the addition of a control card to

each set of teacher-learner-task data. The control card

contained codes which categorized the triad into nine

categories of stimulus content, nine categories of input/

output modality, and three categories of skill. These

categories and their codes are presented in Table 10.

Although not all of the categories are utilized in this

study, they were designed to be of utility for subsequent

programmatic research. Also present on the control card

were codes for the teacher, learner, and number of data

points obtained during assessment. Triads with less than

three data points during assessment or instruction were

omitted from the statistical analyses since variability

values could not be meaningfully computed for them.









Table 10

Categories for Coding of Each
Teacher-Learner-Task Triad


STIMULUS MOVEMENT ASSESSMENT
CONTENT MODALITY PROBE


1. Letters 1. See-say 1. Tool skill probe

2. Numbers 2. See-write 2. Single skill probe

3. Phonics sounds 3. See-do 3. Mixed skill probe

4. Sight words 4. Think-say

5. Texted words 5. Think-write

6. Number problem 6. Think-do

7. Phonics words 7. Hear-say

8. Shapes/symbols 8. Hear-write

9. Spelling words 9. Hear-do













CHAPTER IV

RESULTS


The measurements used for prediction were the median

frequency correct value from baseline assessment phase,

the weekly celebration value from baseline phase, and

the variability value (i.e., the value for the sum of

squared deviations from the line of best fit through

the frequency correct points) of baseline phase. Each

case was composed of a separate teacher-learner-task

triad. The predicted variables were the weekly celebration

value for the first instructional phase (i.e., phase two)

and the weekly celebration value for the second instructional

phase (i.e., phase three). Triads were selected for analyses

if the number of data points in predictor and predicted phases

was three or more.


Reliability

Table 11 provides percentage agreement between the

experimenter and the observer (teacher) for each week of

the study. Agreement information is shown for the

frequency correct values collected daily by the teachers.

A small samole of each teacher's recording during

one day of each week was rescored by the experimenter.









Table 11

Percentage of Interobserver Agreement for Recording
of Predictor Variable across Weeks of the Study


Baseline

Week 1

98

99

100

85

100

87

100

100

98

100

100

94

100

100


Week

100

100

100

100

100

89

100

100

100

100

98

100

100

100


Teacher

Teacher

Teacher

Teacher

Teacher

Teacher

Teacher

Teacher

Teacher

Teacher

Teacher

Teacher

Teacher

Teacher

Teacher


Instruction

2 Week 3 Week 4

100 100

100 100

97 100

100 100

98 100

100 100

100 100

100 100

100 100

100 100

100 100

100 98

100 100

94 100


Week 5

100

99

100

100

100

100

100

100

99

100

95

100

100

100









The minimum acceptable total agreement percentage for

recording of frequency correct values was 80 percent.

Percentage values were generally lower during

baseline than during instruction. The lower reliability

during baseline can be attributed to the unfamiliarity

of the teachers with the recording procedures used to

collect the data.


Analyses of Prediction Results


The results of prediction are displayed in Table 12,

Table 13, and Table 14. The first column contains the

number of separate teacher-learner-task triads which

produced the correlation values. The second column on

the tables contains the type of skill probe, type of

stimulus content, or type of input/output modality

represented by the triads. Columns 3, 4, 5, and 6 contain

product moment correlation values for frequency correct

measures. Column 7 contains the amount of variance R2 ex-

plained by prediction variables predicting to celebration for

the first instructional phase. Column 8 contains the amount

of variance R2 explained by predictor variables predicting

to celebration for the second instructional phase.

The questions of interest to this study will now

be examined with respect to the statistical results.

(1) Can frequency, celebration, and variability of

baseline performance on tool skill probes be used to

predict the rate of learning during instruction?









Only 2 percent of the phase two celebration was

explained by frequency, celebration, and variability of

tool skill performance during assessment (see Table 12).

The prediction to phase three explained 4 percent of the

variance in celebration. There were 93 triads in the

prediction to phase two celebration, and 46 triads in the

prediction to phase three celebration. It appears that

frequency, celebration, and variability of tool skill

performance are not useful for prediction of celebration

during instruction.

(2) Can frequency, celebration, and variability of

baseline performance on single skill probes be used to

predict the rate of learning during instruction?

Only 1 percent of the phase two celebration was

explained by frequency, celebration, and variability of

single skill performance during assessment (see Table 12).

The prediction to phase three also explained 1 percent of

the variation in celebration. There were 177 triads in

the prediction to phase two celebration, and 66 triads in

the prediction to phase three celebration. Frequency,

celebration, and variability of single skill performance

are not useful for prediction of celebration during

instruction.

(3) Can frequency, celebration, and variability of

baseline performance on mixed skill probes be used to

predict the rate of learning during instruction?








Table 12


Analyses of Triads Categorized
by Type of Skill Probe


Amount of Variance R2
Explained by Baseline
Predictor Variablesa
Correlation r


Mean
Frequency
Phase 1
with
Mean
Frequency
Phase 2


Median
Frequency
Phase 1
with
Median
Frequency
Phase 2


Celeration Variability
Phase 1 Phase 1
with with
Celeration Variability
Phase 2 Phase 2


Predicting
To
Celeration
Phase 2


Predicting
To
Celeration
Phase 3


100 Tool .94* .91" -.03 .43* .02 .04
Skill (N=93) (N=45)

182 Single .85* .81" .07 -.01 .01 .01
Skill (N=177) (N=66)

16 Mixed .90* .90* -.01 .16 .11 ---
Skill (N=16) (N=2)



a Predictor variables were baseline median frequency, baseline celebration, and
baseline variability


Correlation value r was significant at the .05 level


Number
Of
Triads
for
r


Type
Of
Skill
Probe









Eleven percent of the variation in phase two

celebration was explained by frequency, celebration, and

variability of performance on mixed skill probes (see

Table 12). There were 16 triads in this prediction.

The first variable to enter the regression equation

was variability, followed by median frequency.

The prediction to the second instructional phase (phase

3) contained only two triads, therefore the R2 value

was not meaningful.

(4) Is there a differential predictive relationship

by academic task stimuli from baseline performance to

performance during instruction? The different task

stimuli include letters, digits, phonics sounds, sight

words, texted words, number problems, phonics words,

and spelling words. These task stimuli will be discussed

individually in the following text.


Tasks with Letters

There were 60 triads in the prediction to phase two,

and 23 triads in the prediction to phase three celebration.

Seventeen percent of the variation in phase two celebration

was explained by frequency, celebration, and variability

of baseline performance on tasks with letters. Six percent

of the variation in phase three celebration was explained by

the prediction. Celeration entered the regression pre-

diction equation first, followed by variability and median

frequency for predicting to phase two.







Table 13

Analyses of Triads Categorized
by Type of Stimulus Content


Correlation r


Amount of Variance R2
Explained by Baseline
Predictor Variablesa


Stimulus
Content


Mean
Frequency
Phase 1
with
Mean
Frequency
Phase 2


Median
Frequency
Phase 1
with
Median
Frequency
Phase 2


Celeration Variability
Phase 1 Phase 1
with with
Celeration Variability
Phase 2 Phase 2


Predicting
To
Celeration
Phase 2


Predicting
To
Celeration
Phase 3


64 Letters


.93*


44 Digits .98*
19 Phonics Sounds .76*


3 Sight Words

5 Texted Words


.68

.91*


129 Number Problem .75*

26 Phonics Words .54*

8 Spelling Words .91*


.90*
.96*
.68
.70

.90*

.71*


.88*


.30*
-.28
.50
-.98

-.34

-.08

.12

-.35


.03
.75*
.02


.17 (N=60)
.07 (N=41)
.53 (N=17)


.06 (N=23)
.07 (N=24)
.22 (N=9)


.72

.31


-.03

-.06

.64


.02 (N=126) .02 (N=39)

.08 (N=26) **

* A **


*Correlation value r was significant

**Insufficient data for computation.


at the .05 level.


Number
Of
Triads
for
r









Tasks with Digits

There were 41 triads in the prediction to phase two

celebration, and 24 triads in the prediction to phase three.

Seven percent of the variation in phase two and phase

three celebration could be explained by baseline predictor

variables on tasks with digits (see Table 13).


Tasks with Phonics Sounds

There were 17 triads in the prediction to phase two

celebration, and 9 triads in the prediction to phase three

celebration using frequency, celebration, and variability

of baseline performance as predictors (see Table 13).

Fifty-three percent of the variation in performance during

phase two could be explained by baseline performance.

Twenty-two percent of the variation in performance during

phase three could be explained by baseline performance;

however this figure should be viewed with caution due to

the small number of triads for computation.


Tasks with Sight Words

The R2 values on Table 13 for prediction of performance

with sight words have been omitted since the number of

triads for computation of these values was less than 10.


Tasks with Texted Words

The R2 values on Table 13 for prediction of performance

with texted words have been omitted since the number of

triads for computation of these values was less than 10.









Tasks with Number Problems

There were 126 triads in the prediction of phase

two celebration using frequency, celebration, and variability

of tasks with number problems. Only 2 percent of the phase

two celebration was explained by baseline variables.

Likewise, only 2 percent of the phase three variation in

celebration was due to variation in baseline variables of

frequency, celebration, and variability on number problem

tasks (see Table 13).


Tasks with Phonics Words

There were 26 triads in the prediction of

phase two celebration using frequency, celebration,

and variability of tasks with phonics words. Eight

percent of the variance in phase two celebration could be

explained by performance characteristics during baseline

(see Table 13). The prediction to phase three celebration

had only 8 triads, and thus the R2 value has been

omitted.


Tasks with Spelling Words

There were only 8 triads each in the predictions

of phase two celebration and phase three celebration.

As such, the R2 values have been omitted (see Table 13).

When the number of cases for multiple regression is less

than 10, the R2 values are artificially inflated.









The amount of variance R2 in phase two celebration

explained by baseline predictor variables ranged from

2 percent for number problems to 53 percent for phonics

sounds. Predicting to phase three celebrations generally

yielded lower R2 values. Two of the five academic task

stimuli appeared to have a differential predictive

relationship and were higher in amount of variance

explained by predictor variables. In general, the

predictive ability of frequency, celebration, and

variability during assessment were characterized by

low positive values.

(5) Is there a differential predictive relationship

by input and output modality of learners from baseline

academic performance to performance during instruction?

The different input and output modalities of interest

include see to say, see to write, see to do, hear to say,

hear to write, hear to do, think to say, think to write,

think to do.

Since the teachers in this study were free to decide

instructional targets, not all of the input and output

modality combinations were present in the data. Sixty-five

triads were see to say, 133 were see to write, 24 were

think to say, and 74 were think to write. These will

now be discussed individually.









See To Say Tasks

Sixty-two triads were included in the prediction of

celebration during phase two from baseline performance on

see to say tasks. Twenty-six percent of the variation in

phase two celebration could be explained by frequency,

celebration, and variability of baseline performance on see

to say tasks. There were 29 triads in the prediction of

celebration during phase three from baseline performance on

see to say tasks. Only 3 percent of the variation in phase

three celebration could be explained by baseline performance

measures (see Table 14).


See To Write Tasks

See to write tasks included 130 triads for prediction.

Two percent of the variation in phase two celebration was

explained by baseline performance measures. There were 39

triads in the prediction of phase three celebration from

baseline performance on see to write tasks. Again, only 2

percent of the variation was explained (see Table 14).

Think To Say Tasks

There were 20 triads in the prediction of phase two

celebration from baseline performance on think to say tasks.

Five percent of the variation in phase two celebration

was explained by baseline performance measures. There were

12 triads in the prediction of phase three celebration. Nine-

teen percent of the variation in celebration was explained

b bageline po@dic t V'iable (bI' Tddll 1 U







Table 14


Analyses of Triads Categorized
by Type of Input/Output Modality


Correlation r


Amount of Variance R2
Explained by Baseline
Predictor Variablesa


Input
Output
Modality


Mean
Frequency
Phase 1
with
Mean
Frequency
Phase 2


Median
Frequency
Phase 1
with
Median
Frequency
Phase 2


Celeration
Phase 1
with
Celeration
Phase 2


Variability
Phase 1
with
Variability
Phase 2


Predicting
To
Celeration
Phase 2


Predicting
To
Celeration
Phase 3


65 See/Say .83* .79* .42* .08 .26 (N=62) .03 (N=29)

133 See/Write .76* .72* -.09 -.03 .02 (N=130) .02 (N=39)

24 Think/Say .88* .85* -.25 .33 .05 (N=20) .19 (N=12)

74 Think/Write .87* .79* .07 .20 .16 (N=72) .09 (N=31)




a Predictor variables were baseline median frequency, baseline celebration, and
baseline variability


Correlation value r was significant at the .05 level


Number
Of
Triads
for
r


_ __ __









Think To Write Tasks

There were 72 triads in the prediction of phase two

celebration from baseline performance on think to write

tasks. Sixteen percent of the variation in phase two

celebration could be explained by baseline predictor

variables. There were 31 triads in the prediction .of

phase three celebration from baseline performance on

think to write tasks. Nine percent of the variation

in celebration was explained by frequency, celebration,

and variability of baseline performance on think to

write tasks (see Table 14).

In summary of the analyses of triads categorized

by type of input/output modality, the amount of variance

R2 in phase two celebration explained by baseline predictor

variables ranged from 2 percent for see to write tasks,

to 26 percent for see to say tasks. Predicting to phase

three celebrations generally yielded lower predictive

values except for think to say tasks where the R2 value

increased.

It appears that there is a small differential pre-

dictive relationship by input/output modality of the task,

however the amount of variance R2 explained by predictor

variables is generally small. The predictive ability of

frequency, celebration, and variability of baseline

performance ranged from low positive to moderate positive.













CHAPTER V

DISCUSSION


There has been a great deal of interest in the

prediction of learning performance. The extent to which

this is possible depends upon the type of data and the

amount of data for prediction (White, 1972a). Previous

studies have examined the degree to which performance can

be predicted within instructional phases (White, 1972a;

Koenig, 1972; Koenig, 1980).

The present study employed operant learning techniques

to further clarify the relationship of variables that may

be useful for prediction of academic performance. Of

interest was the utility of prediction from baseline

assessment to instructional phases. Students' frequencies

of performance on a great number of tasks were measured

during a week of baseline data collection. Each separate

triad was categorized into eight different types of

academic task stimuli, four different types of input/output

madality, and three different types of skill probe.

Following baseline data collection, teachers selected

skills for instruction and delivered instruction over a

five week period. Daily frequency measures were recorded by

teachers. The data were analyzed by computer to produce









frequency, celebration, and variability values for each

phase of instruction


Findings

The findings of this study are discussed relative to

the experimental questions. Prediction from baseline

performance to performance under instruction was generally

low when skills were categorized by tool skill, single

skill, or mixed skill probes. The amount of variation in

instructional celebration which could be explained by base-

line performance measures ranged from 1 percent with single

skills to 11 percent with mixed skills. The important

finding is that a student's baseline academic performance

is not a controlling or predicting factor for performance

during instruction.

Prediction categorized by type of stimulus content

produced differential predictive strengths. Unfortunately,

R2 values for sight words, texted words, and spelling

words had to be omitted due to small numbers of triads

available for their calculation. Of the remaining

stimulus categories, strength of prediction (amount of

variation in instructional celebrations) ranged from

R2=.02 for number problems to R2=.53 for phonics sounds.

Letters stimuli (R2=.17) predictions were slightly stronger

than digits stimuli (R2=.02) predictions. In general, there

appeared to be a trend for language stimuli to predict better

than math stimuli. This trend is tentative and will require




Full Text

PAGE 1

FREQUENCY, CELERATION, AND VARIABILITY OF ACADEMIC PERFORMANCE AS PREDICTORS OT LEARNING By John J. Trifiletti A DISSERTATION PRESENTED TO • THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1980

PAGE 2

To Diane, my wife and best friend, and to the expression of our love, John Cristopher, III.

PAGE 3

ACKNOWLEDGMENTS I wish to express my sincere appreciation to all my committee members for their support, encouragement, and for their constructive suggestions, with special thanks to Dr. William Wolking for his encouragement, guidance, and intellectual stimulation throughout my program of studies. Deserving of special acknowledgment is Dr. Cecil Mercer for advice, support, and writing skills . I would also like to extend my appreciation to Dr. Thorn Hodgson for his guidance in the systems engineering area and programming skills. Finally, I wish to acknowledge my wife, Diane, who has given me the emotional and intellectual support I've needed throughout my program.

PAGE 4

TABLE OF CONTENTS ACKNOWLEDGMENTS iii ABSTRACT vi CHAPTER I INTRODUCTION 1 Importance of the Study 1 Rationale Statement of the Problem 8 CHAPTER II REVIEW OF RELATED LITERATURE .... 12 Early Identification Research 1*+ Prediction-Performance Comparison Matrix ... 15 Single Instruments as Predictors 19 Multiple Instrument Batteries as Predictors . . 23 Teacher Ratings as Predictors 2 7 Areas of Assessment for Prediction 28 Frequency Measurement of Academic Performance . . 3 Frequency versus Percentage Statements ... 33 Considerations for Measurement of Frequency . . 35 Record Floor 36 Record Ceiling 37 Performance Ceiling 38 Studies of Frequency Performance Standards . . 41 Math Frequency Standards 42 Reading Frequency Standards 44 Spelling Frequency Standards 52 Writing Frequency Standards 53 A Frequency Model of Learning 56 Predictive Studies Using Frequency Measurement . . 59 Predictive Studies 61 CHAPTER III METHOD 70 Subjects 70 Equipment 71 Setting 72 Procedure ;f Training Procedures 7 3 Initial Precision Assessment 7 3 Instruction 7 ^ Experimental Design 76 Data Collection 77 Data Analysis 77

PAGE 5

CHAPTER IV RESULTS 80 Reliability 80 Analyses of Prediction Results 82 CHAPTER V DISCUSSION 93 Findings 94 Interpretation of the Findings 9 5 Problems and Limitations of the Study 97 Practical Implications 97 Suggestions for Further Research 9 8 REFERENCES 10 ° APPENDICES A. DEFINITIONS 108 B. DESCRIPTION OF SPARK II INSTRUMENT . . . HI C. FORTRAN PROGRAM FOR COMPUTERIZED CHARTS AND SUMMARY STATISTICS 114 D. SAMPLE FREQUENCY CHART 12 5 E. SYLLABUS OF TEACHER TRAINING SESSION ... 128 BIOGRAPHICAL SKETCH . 129

PAGE 6

Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy FREQUENCY, CELERATION, AND VARIABILITY OF ACADEMIC PERFORMANCE AS PREDICTORS OF LEARNING By John J. Trifiletti December, 1980 Chairman: William D. Wolking Major Department: Special Education This study examined the predictive ability of frequency, celeration, and variability measures of academic performance during assessment for predicting celerations during instruction. Data from 360 separate teacher-learner-task triads in reading, spelling, writing, and mathematics were evaluated. Learners were assessed over a five day period, then received twenty days of instruction during which daily timed samples of their academic performance were recorded. The amount of variance in celerations explained by baseline predictor variables was generally small. Moderate amounts of variance were explained by predictor variables for phonics sounds tasks and see to say tasks .

PAGE 7

CHAPTER I INTRODUCTION There are multiple dimensions to the academic performance of learners in the classroom. Accuracy of performance, expressed in terms of percentage statements, has traditionally been used as the primary measure of academic performance. Recently, other dimensions of academic performance have received attention (Haughton, 1971a; White, 1972a; White £ Haring, 1976). These include frequency, the speed of performance; celeration, the rate of change in performance over days; and variability, the variation in frequency about a trend line. The problem of interest to this study is the use of frequency, celeration, and variability measures of performance during assessment to predict subsequent academic performance during instruction. Importance of the Study Schools are designed to change the behavior of children. Ideally, learners progress from little or no knowledge or skill to a desired level of academic performance. This change occurs as a direct or indirect result of instruction. The general purpose of assessment is to determine whether a learner's performance is changing appropriately. Assessment for instruction or teaching refers to the process 1

PAGE 8

of obtaining information about a student's instructional needs (Wiederholt, Hammill, 8 Brown, 1978). To facilitate instructional programming the assessment must provide information in two areas. First, it must help the teacher select what to teach the individual student. Second, it must help the teacher determine how to teach the student for optimal progress (Mercer £ Mercer, 1980). Of equal importance is the use of assessment to predict and prevent failure. Such prediction depends upon the sensitivity of educational measurement and the examination of multiple dimensions of performance. This study is aimed at determination of the utility of frequency, celeration, and variability of academic performance during assessment for predicting subsequent performance during instruction. As such, it builds and extends upon previous research which has explored the use of multiple dimensions of academic performance to predict subsequent learning (White, 1972a). Rationale Traditionally, educational assessment has been of limited success and has progressed little beyond assumtions and concepts from the 19th century. The ideas of Galton, Simon, Binet , Terman , and others with respect to global variables and group measurement techniques remain relatively unchanged except for the development of new statistical procedures for the evaluation of group performance data. Statistical evaluation has not

PAGE 9

compensated for the inaccurate and incomplete measurement of academic performance fostered by reliance on accuracy as a single dimension of academic performance. Traditional educational measurement is based upon norm-referenced comparison. . An individual's performance is converted to a norm-referenced variable such as grade level, age level, or percentile. Sensitivity is thus limited by the dimensions and units used in measureing. An additional problem with traditional educational measurement is the reliance on percentage accuracy statements to describe a single dimension of performance. Percentage statements are subject to a number of measurement problems (Haughton, 1969; White £ Haring, 1976). These include an arbitrary ceiling effect and inadequate description of performance. When percentage accuracy statements alone are used to describe academic performance, changes beyond 100 percent cannot be reflected by the measurement. Yet there are many ways in which learners can increase performance beyond 100 percent accuracy. For instance, the latency (time to onset) of the performance can decrease, or the speed of performance can increase. Furthermore, accuracy statements inadequately describe academic performance when there are multiple ways to obtain the same unit of measurement. For instance, a student who correctly answers three out of four questions during a class period

PAGE 10

might be compared with a student who correctly answers 30 out of 40 questions. The latter student's performance far exceeds the former, yet using percentage accuracy statements alone, both students will be equated at 75 percent correct. Lindsley (1971) has developed alternative measurement procedures within an instructional system of precision teaching. In this model, frequency measurement is employed to describe multiple dimensions of academic performance. Frequency measures have been found to be more sensitive for description of individual behavior than evaluation using percentage criteria (Pennypacker , 1972). With frequency measurement, both speed and accuracy dimensions of performance are considered. As such, frequency is a better measure of the fluency of performance. It is believed that high frequencies of performance facilitate acquisition and retention of academic behavior (Starlin, 1971; Haughton, 1971a). The rationale for high rates of accurate responding during instruction is that they insure against practicing errors and rapid loss of skills due to inadequate learning. Key differences between precision teaching and traditional educational measurement include emphasis on frequency as a standard measurement unit, emphasis on multiple dimensions of performance, the use of

PAGE 11

criterion-referenced as opposed to norm-referenced comparison, and frequent direct measurement (see Table 1). Lindsley's (1971) precision teaching begins with measurement of the frequency of performance prior to instruction. This baseline measurement serves as a reference point for comparison with subsequent measurements during instruction. Following baseline measurement, specific skills are identified as targets for instruction, and instruction begins. During the course of instruction, daily measurements of the performance of each skill are obtained and graphically displayed on standard behavior Charts. Integral to precision teaching is a system of instructional decision-making and optimization based on observation of the daily measurements. White and Haring (1976) have recently expanded upon the baseline aspects of precision teaching with their procedures for precision assessment. Precision assessment provides for examination of a wide range of skills in the learner's repertoire through the use of mixed skill probes. A mixed skill probe is similar to a traditional achievement test in that the items from many skills are presented. The difference is that frequency of performance is measured, and the assessment does not end at this point. Next, single skill probes are used to obtain speed and accuracy measures of skills in need of instruction. A single skill probe differs from a mixed skill probe in that it contains

PAGE 12

Table 1 A Comparison of Traditional Measurement and Precision Teaching Traditional PsychoEducational Measurement Precision Teaching BehaviorAnalytic Measurement Norm-referenced Criterion-referenced Measurement before and after instruction, infrequent Measurement direct or indirect Daily or frequent measurement Measurement always direct Individuals are compared to a group Individuals are compared with themselves Considers accuracy dimension of academic performance No standard unit of measurement Considers multiple dimensions of performance Frequency used as standard unit of measurement

PAGE 13

items from only one skill domain. Additionally, single skill probes contain many items representing a single skill, and thus constitute a better sample of the movement than the mixed skill probe or an achievement test. A third type of skill, the tool skill probe, is used to assess skills such as saying digits, writing digits, saying letters, writing letters, and saying letter sounds. These skills are considered prerequisite to more advanced skills which build upon them (see Table 2). An additional dimension of academic performance is celeration, the rate of change in frequency across days. Celeration has been used as a criterion measure to evaluate performance during instruction. White and Haring (1976) recommend a number of possible procedures for determining acceptable performance during instruction, one of which is the standard celeration. The standard celeration procedure is based on research by Liberty (1975). In a working paper from the University of Washington, Liberty analyzed several hundred programs dealing with all types of skills and children of all ages. Liberty observed that, of the children whose programs showed some progress, about 53 percent accelerated at a rate of XI. 25 (25 percent improvement in frequency per week). About 66 percent of the children achieved a -rl.25 for deceleration targets (25 percent improvement in frequency per week). In the absence of other criteria, White and Haring recommend

PAGE 14

minimum celeration values of XI. 25 for acceleration targets and-j-1.2 5 for deceleration targets. In summary, the sensitivity of measurement provided by precision teaching and precision assessment is seen by many educators as an improvement over traditional educational measurement. The use of multiple measures of performance, criterion-referenced evaluation, and continuous daily measurement holds great promise for increased instructional control and subsequent increased academic performance. The use of frequency and multiple dimensions of academic performance to predict learning is a relatively new area for research. This study explores the use of frequency and multiple dimensions of initial academic performance to predict performance during instruction. Statement of the Problem The problem of interest to this study is the use of frequency, celeration, and variability dimensions of performance during baseline assessment to predict academic performance during instruction. The specific questions this study will address are: (1) Can frequency, celeration, and variability of baseline performance on tool skill probes be used to predict the rate of learning during instruction? (2) Can frequency, celeration, and variability of baseline performance on single skill probes be used to

PAGE 15

Table 2 The Relationship of Tool Skills To Complex Academic Skills Prerequisite Tool Skills Complex Academic Skills Write Digits 0-9 Write digits for addition Write digits for subtraction Write digits for multiplication Write digits for division Write digits for fractions Write digits to record time Write Letters A Z Write letters for basic sight words Write letters for texted words Write letters for name Write letters for spelling words

PAGE 16

10 predict the rate of learning during instruction? (3) Can frequency, celeration, and variability of baseline performance on mixed skill probes be used to predict the rate of learning during instruction? (4) Is there a differential predictive relationship by academic task stimuli from baseline performance to performance during instruction? The different academic task stimuli of interest include letters, digits, phonics sounds, sight words, texted words, number problems, phonics words, and spelling words. (5) Is there a differential predictive relationship by input and output modality of learners from baseline performance to performance during instruction? The different input and output modalities of interest include see to say, see to write, see to do, hear to say, hear to write, hear to do, think to say, think to write, think to do For each of the above questions, the rate of learning will be measured by celeration. Celeration is defined as the percent of change in frequency per week. The answers to these questions increase our knowledge of how academic skills are learned. This study also extends our knowledge of measurement procedures. History makes clear that the development of accurate observation and measurement procedures inevitably leads to an explosion of technology and knowledge. The telescope in astronomy, the microscope in biology, x-rays and blood counts in medicine, the Geiger counter in physics, Neilson ratings

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11 in television advertising, and the cumulative recorder in psychology are illustrative. Following each of these technological achievements in measurement was a rapid upgrading of the discipline involved. The consequence of refined and sensitive educational measurement may be a technology of education in which the effects of a given instructional procedure on a given individual are predictable and replicable. The questions under investigation in this study are a small step toward the development of such a technology of educational measurement .

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CHAPTER II REVIEW OF RELATED LITERATURE The review of literature is presented in three parts. The related area of early identification research is reviewed in the first section. The focus here is on early identification studies concerned with the prediction of learning failure. The second section contains the theoretical and research basis for the use of frequency as a measurement datum for academic performance. Consideration was given to major theoretical landmarks in the literature, as well as experimental works. Studies of frequency performance criteria for academic behaviors in reading, writing, computational math, and spelling are reviewed in this section. The final section of the literature review contains predictive studies using frequency measurement. These studies are similar in nature to the present research and are the foundation from which this research extends. In order to survey the related literature, an ERIC document search was made using key words "frequency," "rate," and "learning." In addition, the following journals were searched from their initial publications to date, with the exception of Review of Educational 12

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13 Research which was searched from 1960 to present. 1 . Academic Therapy 2 . Exceptional Children 3 . Educational Technology 4. Journal of Applied Behavior Analysis 5 . Journal of Applied Psychology 6 . Journal of Educational Measurement 7 . Journal of Educational Psychology 8 . Journal of Educational Research 9 . Journal of Experimental Analysis of Behavior 10 . Journal of Experimental Psychology 11 . Journal of Learning Disabilities 12 . Journal of Measurement and Evaluation 13 . Journal of Personalized Instruction 14. Journal of Research and Development in Education 15. Journal of School Health 16. Journal of School Psychology In order to locate important theoretical discussion, the reference lists of selected journal articles were searched for relevant texts. Personal communication with experimenters added to the literature review.

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14 Early Identification Research There is currently a great interest in screening infants and preschool children to predict which ones are at risk for experiencing difficulty with subsequent learning. This interest is based on the assumption that treatment initiated prior to schooling will alleviate school-related problems. The studies of Kirk (1958) and Skeels (1966) and the reviews by Tjossem (1976) and Mercer, Algozzine, and Trifiletti (1979) have formed a basis for continued research in early identification and prediction. Proponents of prediction procedures to identify preschoolers at risk of school problems suggest several advantages of early identification. First, they believe early identification efforts are more likely to be successful due to the belief that the behavior of young children is more suceptable to change than that of older children (Hayden, 1974; Stimbert, 1971). Secondly, early identification enables preventive interventions ' during optimal developmental periods when personality characteristics are forming (Hayden, 1974; Stimbert, 1971). Finally, early identification enables earlier family adjustments and acceptance, providing additional support for intervention strategies (Hayden, 1974). Disadvantages of early identification are primarily concerned with the effect of misdiagnosis and labeling (Keogh 8 Smith, 1970).

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15 Prediction-Performance Comparison Matrix Mercer, Algozzine, and Trifiletti (1979) have presented a model for interpreting the predictive utility of standardized assessment instruments and batteries in which both vertical and horizontal percentages are analyzed. Integral to this model is construction of a prediction-performance comparison matrix which allows observation of predictions and outcomes (see Figure 1). Levels of prediction in terms of poor performance or good performance are compared with poor or good levels of criterion performance. Quadrant A of Figure 1 represents those students who performed poorly and who were predicted to perform poorly. Quadrant B refers to those students who performed well on the criterion measure, but were predicted to perform poorly. These are referred to as false positives. Quadrant C refers to students who were predicted to perform well, but in fact performed poorly. These are referred to as false negatives. Quadrant D refers to students predicted to perform well, who in fact did perform well. There are a number of ways of comparing prediction with performance on the matrix. Mercer (1975) reported that most prediction studies utilize the horizontal method of comparison. In the horizontal method observed values in each quadrant are compared with prediction

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16 PERFORMANCE Poor Prediction Good Poor Good Predicted Poor

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17 levels. Figure 2 is an example of a predictionperformance comparison from a hypothetical prediction study. Percentage of correct and incorrect outcomes can be obtained by applying the horizontal analysis method. In this case, 80 of 100 children predicted to perform poorly actually did so (80 percent), while 20 of 100 children predicted to perform poorly did well (20 percent). Similarly, 270 of 300 children predicted to perform well did so (90 percent), while 30 of 300 predicted to perform well actually performed poorly (10 percent). The overall hit rate describes the number of children who were correctly identified. It can be figured by adding the poor predicted poor in quadrant A with the good predicted good in quadrant D and dividing by the sum of all quadrants. The overall hit rate for the example in Figure 2 is 87.5 percent . Although the horizontal method serves as a way of organizing and evaluating prediction-performance information, it neglects consideration of the relationship between the observed values within the quadrants and the actual performance levels. This can be accomplished by vertically analyzing the matrix Figure 2 includes vertically computed percentages. For example, 72.7 percent (80 of 110) of the poorly performing students were predicted poor, and 14.5

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PERFORMANCE

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19 percent (20 of 290) of the good performing students were predicted to do poorly. Percentages generated by the vertical method will obviously differ from those figured by the horizontal method. Gallagher and Bradley (1972) advocated using the horizontal method for establishing false positives and the vertical method for computing false negatives. They also favored evaluating the overall hit rate and visually inspecting the entire matrix. Single Instruments as Predictors The majority of prediction studies use single instruments as predictive measures. General readiness tests (Ferinden £ Jacobson, 1970; Lessler £ Bridges, 1973), intelligence tests (Lessler S Bridges, 1973), language tests (Lyons £ Bangs, 1972), perceptual-motor tests (Keogh £ Smith, 1970), and general physical factors such as unusual birth history (Galante, Flye , £ Stephens, 1972) have been used as single predictors. An analysis of these studies using horizontal and vertical percentages is presented in Table 3. As illustrated in Table 3, the Metropolitan Reading Readiness Test (MRRT) yielded favorable percentages in both short-term and long-term analyses. In comparing this instrument to the Lee-Clark Readiness Test (LC) and the California Test of Mental Maturity (CTMM) , Lessler and BFidp§ (1973) soneludsd that the HPT ii ths felit

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20 Table 3 An Analysis of Single Instruments as Predictors Using Horizontal (H) and Vertical (V) Percentages Study Sample Prediction Length ol Performance Valid False FaUe Valid Instrument Prediction Test Positives Po<lves Negatives Negatives II V II V II V II V Overall Mil" Ferlnden ft 67 kinder .lacobson garlcn (1970) children Fcrinden & Jacubson (1970) Fcrind. n & Jarob c on (1970) Keoyh & Smith (1970) KfCHjIl & Smith (19701 Galante, Flue. & Stephens 11972; Galante Rye. & Stephens (1972) Lyons & Bangs (1072) Lynns Rt Knn.li (1972) 64 kindergarten children C7 kindergarten children 2') kinder garten children 2d kindergarten children 71 kindergarten children 71 kinder garten children 35 1st grader? 23 1st ...mien Evanston 8 months WHAT 56 50 44 17 20 50 80 83 Early Heading Identification Scale WHAT 8 months WRAT 63 100 37 27 100 73 Reading Lyons & 35 I si Bang* graders (1972) Lyons & 23 1st Bangs graders (1972) l.essler & 293 lsl Bridges graders (1973) Lcssler& 196 lsl Bridges graders (107.3) foJtovviip Reading MRRT 8 months WRAT 57 85 43 28 8 15 92 72 Reading Bender 6 v. ais CAT Reading Bender 6 years CAT Arllhmellc 47 El 53 44 9 13 91 56 40 100 60 4. r > 100 Unusual 7 years Stanford 56 41 44 14 24 59 76 S6 birth Achievement history & Horn Expectancy Birth 7 years Sunford 25 27 75 37 34 73 06 63 order Achievement & Horn Expectancy LLAT I \/t years SRA 67 35 33 33 65 65 35 67 with special Arithmetic Intervention HAT I '/J years SRA 91 71 9 11 33 29 67 89 without Arllhmellc special intervention LLAT V/i years SRA with Reading special intervention LLAT 1 '.'2 years SRA without Reading special Intervention MRIH 9 months CAT & «6 87 14 M 13 13 87 86 Teacher Rating MRRT End of 2nd CAT & 91 62 9 10 39 38 61 90 grade Teacher 21 months K.tliny 30 70 70 64 25 30 75 3< 82 75 18 18 25 25 75 82

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21 Table 3 continued Study Sample Prediction Length of Performance Valid Falae False Valid Instrument Prediction Teat Positive* Positives Negatives Negatives Overall HVH VHVH V Hit 8 Lessler &

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22 predictor of the three. Badian (1976) reported a median correlation of .58 between the MRRT and subsequent reading achievement and concluded that group-administered readiness tests yield better prediction results than group-administered or individually administered intelligence tests. In evaluating Badian' s conclusion, it is important to remember that the relationship between predictive and criterion instruments is crucial to the outcome of predictive studies, i.e., the nature of the items on each test will greatly influence the relationships between them. In support of this qualification, Dykstra (1967) noted that letter naming is one of the best predictors of reading achievement. Analysis of studies using language tests as single predictors indicates that educational intervention can greatly influence achievement. Lyons and Bangs (197 2) used the Language and Learning Assessment for Training Test (LLAT) to predict reading and mathematics achievement with and without intervention. The overall hit rate of the LLAT declined when children received intervention. In other words, the predictive outcomes were influenced by subsequent educational programming. In a study using the Bender Visual-Motor Gestalt Test (Bender) as a predictive instrument, Keogh and Smith (1970) obtained good false negative percentages but found a large percentage of false positives. Keogh

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23 and Smith (1961) and Ferinden and Jacobson (1970) suggested that a good score on the Bender is usually followed by satisfactory achievement; however, low scores tend not to be predictive. While only one study of the predictive nature of physical factors contained enough information to obtain a horizontal and vertical analysis, many investigations have been reported within this area. Physical anomalies (Waldrop £ Goering, 1971; Waldrop, Pedersen, £ Bell, 1968), developmental history (Denhoff, Hainsworth, £ Hainsworth, 1972; Hoffman, 1971; Pasamanick, Rogers, £ Lilienfeld, 1965; Wilborn £ Smith, 1974), and dental enamel defects (Cohen £ Diner, 1970) have been studied in attempts to establish their utility as predictive measures. Mercer and Trifiletti (1977) have examined the studies involving the predictive nature of physical factors. Multiple-Instrument Batteries as Predictors A well-known multiple-instrument prediction study was conducted by de Hirsch, Jansky, and Langford (1966). A sample of 53 middle-class kindergarten children was used The battery consisted of 37 variables which were used to predict reading performance. The authors concluded that while background information is not useful as a predictor, chronological age is a significant predictor.

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24 Also, it was reported that predictions for girls are more accurate than those for boys. An analysis of the horizontal and vertical percentages obtained for the de Hirsch et al. study and other multiple-battery prediction studies is presented in Table 4. An overall hit rate of 91 percent is indicated as are good percentages in other categories, with the exception of false positives. Gallagher and Bradley (1972) are critical of this study and indicate that the results were obtained by applying the index to the same group on whom it was developed. Cross validation has not been as successful. Feshbach, Adelman, and Fuller (1974) used the de Hirsch Index to predict reading achievement in second grade. As indicated in Table 4, the overall hit rate was 73 percent and the number of false positives was high. Likewise, Eaves, Kendall, and Critchton (1972) administered the de Hirsch Predictive Index in a prediction study and obtained positive results for prediction of concurrent medical diagnosis of Minimal Brain Damage (MBD). Eaves, Kendall, and Critchton (1974) used the de Hirsch Modified Predictive Index (MPI) to predict teacherrecommended grade placement. Their results were similar to those of Feshbach et al . The overall hit rate was 76 percent and a high percentage of false positives was found. The de Hirsch indices do not seem to have strong empirical support.

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25 Table 4 An Analysis of Multiple-Instrument Batterise as Predictors Using Horizontal (H) and Vertical (V) Percentages Study

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26 Table 4 continued Study

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27 Satz, Taylor, Friel, and Fletcher (1977) utilized linear discriminant function analyses to arrive at an optimal predictor score for a set of 22 variables. The criterion variable was teacher ratings of classroom reading level. In a series of studies (see Table 4), the Satz battery was longitudinally evaluated with a group of 473 boys. Some of the major findings of these studies include the following: 1. The overall hit rate for the Satz battery was considered adequate as was the valid negative rate. 2. False negatives (i.e., children in need of treatment but not identified) tended to be overrepresented . 3. False positives (i.e., those identified but not in need of treatment) tended to be overrepresented. 4. The battery seemed adequate in identifying low-risk children, but problems were apparent with regard to selecting those children needing intervention. Teacher Ratings as Predictors By asking teachers to identify children needing extra intervention, a fairly simple identification procedure is utilized. Haring and Ridgway (1967) analyzed the results of screening for 1200 kindergarten children. They noted that teacher perceptions are accurate predictors of future school-related problems. Similar results are reported by Benger (1968), Ferinden

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28 and Jacobson (1970), and Cowgill, Friedland, and Shapiro (1973). Teachers' ratings tend to be most effective in identifying those children in need of intervention and those not likely to need special programming. An analysis of errors within a study by Keogh and Smith (1970) indicates that only false positive mistakes were made. This would result in children being placed in programs when they really did not need them. The magnitude of such errors would depend upon the negative effects of labeling as balanced by the positive effects of educational programming. Areas of Assessment for Prediction Language, intelligence, motor, social-emotional, and preacademic are the primary areas which have been included in early identification assessment. To date, the preacademic area appears to identify high risk learners more accurately than any of the others (Badian, 1976; Keogh £ Becker, 1973; Magliocca, Rinaldi, Crew, £ Kunzelmann, 1977). These investigators suggest that areas of assessment have direct relevance to criterionperformance measures. These skills may include recognition of letters, letter sounds, numbers, shapes, colors, body parts, and basic concepts. In summary, with full consideration for cost, time, and effort involved in early identification and prediction,

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29 teacher perception seems to offer more advantages than batteries and single instruments. Numerous investigators (Badian, 1976; Benger, 1968; Glazzard, 1977; Haring £ Ridgway, 1967; Keogh £ Becker, 1973; and Kottmeyer, 1947) report that teacher perceptions are good predictors of school problems, especially if teachers are provided checklists which include items that are related to academic learning. Only two studies (Feshbach, Adelman, £ Fuller, 1974; Keogh £ Smith, 1970) were located which provided full matrix data. Their overall hit rates were impressive, i.e., 90 percent and 77 percent, respectively.

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30 Frequency Measurement of Academic Performance The choice of an appropriate datum to describe academic performance has been given careful and deliberate attention by many experts in the applied sciences of behavior change (Haughton, 1971a; Johnston S Pennypacker, 1980; Koenig, 1972; Lindsley, 1971; Lovitt, 1968; Skinner, 1953; and White S Haring, 1976). Skinner (1953) in a landmark theoretical discussion of the Importance of frequency as a datum discussed its advantages for a technology of special teaching. The major considerations are outlined below: 1. Frequency of a response is an orderly datum. The curves which represent its relation to many types of independent variables are encouragingly simple and smooth. 2. The results of frequency measurement are easily reproduced. It is seldom necessary to use groups of subjects and associated statistical control to demonstrate results. This method permits a direct view of behavioral processes, whereas previously behavioral processes have been inferred. 3. Concepts and laws which are emerging from studies of frequency have an immediate reference to the behavior of the individual. 4. Frequency of response provides a continuous record of many basic processes. A learning curve can be

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31 followed across many days of instruction and the condition of the response at every moment is apparent in the record. 5. Frequency of response lends itself well to automatic data recording and collection. 6. Frequency of response is a valuable datum because it is a physical referent for the concept of probability. As such it is a simple and direct datum which will generally serve as a more deliberate description of behavior than will inferences and hypothetical constructs such as "learned," "mastered," "skilled," and "knowledgeable." Such language becomes more useful when one can say that a learner can solve two-digit addition problems at a frequency of 50 correct digits per minute with two or less error digits per minute. Skinner's central point is that the element which is used to describe academic performance must be a function of the behavior of the learner. White and Haring (1976) have described academic performance in terms of movements. The smallest change in learning that can be measured is an increase or decrease of one whole movement. A movement is the equivalent of a discrete observable response. Movements have both physical and temporal features. Prominent among the physical properties are topography, force, and locus. Topography is the muscular or skeletal "shape" of the behavior or behavior sequence. For example,

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32 a movement may be either written or oral, involving different muscles. A hand may be raised or lowered, involving a different sequence of the same muscles. Force is the magnitude of a movement. An individual may whisper or shout. A child may push another child playfully or shove with enough force to physically damage another. Locus is the direction or target of a movement. A child may talk to a peer or to the teacher. Answers may be written in the proper positions or not. In addition to the physical properties of topography, force, and locus, a movement also possesses temporal dimensions. These include duration, latency, and frequency. Duration is the amount of time a movement lasts. A child may take a minute or several minutes to respond to a question. A child may take a long time to get dressed in the morning, or may dress quickly. In these examples, the physical elements of the movement may remain essentially the same, but they take more or less time to complete. Latency is an important temporal dimension of behavior. It is the time between an event in the environment, usually an instruction, and the onset of the movement. A child may take a long time to begin to answer a question. He may take a long time to begin dressing in the morning. Frequency is the number of times a movement occurs during an observation period. By convention, frequency

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33 for academic skills is expressed in terms of one minute of observation (Lindsley, 1971). The importance of frequency can be examined through an example of reading behavior in which one student reads at a frequency of 100 words per minute, while another student reads at 10 words per minute. They each form the words in the same way (i.e., the physical properties of the behavior are the same). They each begin reading at the same time (i.e., they demonstrate similar latency). Both students read in the same amount of time (i.e., their duration is the same). Interestingly, these students read differently. One student is much more fluent with the skill than the other, as evidenced by reading more words in the same amount of time. Traditionally, experiments in learning have been concerned with changes in the character or topography of behavior (Bijou, 1972). The student learns how to do something new, acquiring new behavior. But the conditions which produce the topography of new behavior may continue to have an effect when the topography dimension no longer changes appreciably. After behavior has been acquired, further reinforcement maintains it as part of the current repertoire of the individual (Ferster 8 Skinner, 1957). Frequency versus Percentage Statements Many of the studies reviewed contrasted frequency measurement of academic performance with percentage statements (Haughton, 19G9; White, 1972a; White £ Haring,

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34 1976). Accuracy percentage is defined as the number of correct responses divided by the number of items presented or attempted. Traditionally, educators have emphasized accuracy in the initial development of academic skills. It is becoming increasingly apparent that frequency of academic performance is at least as important as accuracy, and perhaps even more important when advanced material is presented (Gaasholt, 1970; Haughton, 1971a; Starlin, 1971). Frequency seems to be a better indicator of the individual's ability to maintain, generalize, and apply academic skills outside the classroom (Thomas, 1972; White S Haring, 1976). White and Haring (1976) have identified three difficulties that can arise with use of percentage statements. First, there must be adequate time to attempt each item. If performance is based on all the items , presented, when the student does not have adequate time to attempt all of them, then the student is penalized for being slow. If the percentage is based on only the attempted items, the student learns to attempt only those items he is sure of. Secondly, percentage statements do not address the actual number of movements the student has made. For example, a basketball game in which six out of tern baskets are made yields a percentage of 60 percent. The same student in another game could make three out of four baskets for a superior percentage

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35 of 75 percent. But realistically, fewer baskets were made on a per-game basis. The final and most serious deficiency of percentage statements is that they can only measure learning up to the point where the student stops making errors. In fact, learning can improve beyond this point. Accuracy is only one way in which academic performance can improve. An upper limit on the value which a measurement can take is called a record ceiling. Record ceilings represent artificial limits on the measurement strategy. They ignore the fact that one or more aspects of a student's performance can be further developed. In general, professionals tend to use percentage statements when they want to describe an individual's accuracy, and they use frequency when they wish to describe an individual's fluency or speed. It is important to realize that there is no need to support a dual system of educational measurement. Frequency statements can be converted to percentage statements through a simple calculation: mRRFPT FREQUENCY CORRECT rtKUiUNi ^ukkjlui FREQUENCY ERRORS Considerations for Measurement of Frequency The primary concern of measurement is that the data accurately represent the specific properties of the behavior which is being measured (Johnston S Pennypacker,

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36 1980). Three problems can be identified which influence the measurement of frequency of academic performance. These are the record floor, record ceiling, and performance ceiling. Record Floor A record floor is the lowest possible non-zero value that can be calculated or recorded in any given measurement situation (White, 1972a). In many situations, the record floor is determined by the accuracy of the timing device. For instance, if timings are made with a stopwatch with a second hand that jumps in 0.25 second intervals, events which take less than 0.25 seconds will "fall through the floor" and will be recorded as "zero." Because data points falling below the record floor are disjointed from the remainder of the data by the distance from the record floor to zero, they will tend to pull any estimates of progress down toward the record floor. For this reason, data which falls below the record floor should be avoided. As a rule of thumb, White (1972a) suggests that prediction based on data where more than 10 percent of the points fall below the record floor will generally not be accurate. In fact, data collection procedures should be designed to place the majority of data at least ten times above the record floor. For example, a stopwatch

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37 with a 0.25 second capacity should not be used for movements which are likely to be less than 2.5 seconds in duration. Record floors are easily calculated for forms of data which constitute a ratio (e.g., frequency = count/ time; percentage = count correct/total count). In cases such as these, a "1" is placed in the numerator of the ratio and the result is calculated (e.g., frequency record floor = 1/time; percentage record floor = 1/total count). One can lower the record floor and increase the sensitivity of measurement in many cases by increasing the value of the denominator. In the case of frequency, the observation time should be increased. There will be situations in which modification of the data collection procedure is impossible or not practical. It may then be necessary to alter the unit of behavior. For example, if "answers" to math problems are being counted, perhaps counting "digits written" will increase the magnitude of the data points sufficiently above the record floor. The increase in sensitivity gained by selection of smaller and smaller units of behavior must be weighed against the increasing difficulty of counting and recording such movements Record Ceiling There is a limit to how high data values can go. Unlike toe record floor, the record ceiling is usually

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38 not a function of the timing device or measurement instrument per se. It is usually a function of the measurement situation or the conditions of measurement. If the behavior being counted is answers to math facts, and there are exactly 50 problems on a sheet for a one minute timing, then the highest possible recordable frequency is 50 answers per minute. Rates of behavior will be restricted by any artificial record ceiling above which the rate is undefined (White S Haring, 1976). There are several ways in which record ceilings appear to affect academic performance in addition to the simple limits they impose on rates. In many cases, a learner's frequency will begin to slow down as the record ceiling is approached, and before it is actually reached. In other cases, there may be a "jump" to the record ceiling as it is approached. Many learners decelerate their frequency after reaching a record ceiling. Because a record ceiling can affect academic performance in unpredictable ways, it is advisable to adjust the measurement condition so that the ceiling is roughly ten times greater than the highest expected value of the data. Performance Ceilings In addition to record ceilings and floors imposed by data collection procedures, there is undoubtedly some physiological limit to any human behavior (White £ Haring,

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39 1976). Performance ceilings can sometimes be estimated by measurement of the learner's ability to perform a "tool" movement which is prerequisite or a physical component of the task behavior. For example, the tool movement for writing answers to math facts is writing digits through 9. By measuring the learner's frequency of writing digits through 9, one can estimate the maximum possible frequency for solving math facts. In theory, if the learner could solve the math facts instantaneously, then the frequency for math facts would have an upper limit or performance ceiling imposed by the time necessary to write the digits. In practice, tool movements as estimators of performance ceilings seem to have a fairly stable relationship to task behaviors. White (1972b) reports findings from a study with 18 elementary children in which almost all children wrote digits 1.6 times faster than they were able to solve math facts. White and Haring (1976) suggest targeting tool movements for instruction in situations where the frequency of the tool movement is less than one-half to two-thirds of the desired task performance. The rationale for increasing the tool rate is that the performance ceiling will be proportionally increased, thereby removing the possibility of a physiological limit to the frequency of the instructional movement.

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40 In summary, the recent application of operant technology to learning has introduced frequency as an important measure of academic performance. Lindsley (1971), Starlin (1971) and other learning technologists have used dual measures of frequency correct and frequency errors to describe academic performance. The advantages of using frequency units include increased sensitivity of measurement for small changes in learning, the potential for more direct observation of learning, and the possibility of a universal scale of measurement for both within and between learner performance. Similar measures in the physical sciences have had great success and have contributed to the advancement of knowledge through more precise control of phenomenon. A popular example is kilometers per hour as a measure of velocity. The choice of frequency as the preferred unit for measuring academic behavior is not without problems. The sensitivity and utility of frequency measurement is subject to problems of measurement design including record floor, record ceiling, and performance ceiling. However, these problems are not insolvable and may be viewed as elements of instructional design. They do not outweigh the advantages of frequency units over percentage statements with respect to describing academic performance .

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41 Studies of Frequency Performance Standards Considerable attention has been recently directed to the performance of learners in the basic skill areas of reading, writing, spelling, and math computation. These skills are seen as important prerequisites for later, more complex academic learning in content areas such as social studies and science. Since basic skills are of importance, various attempts have been made to specify performance criteria for them. Despite the critical role that mastery of these skills is assumed to have on learning outcomes, percentage accuracy statements continue to be chosen for performance standards despite little or no evidence that optimal learning will result (Block, 1974). White and Haring (1976) define criterion performance as the minimum level of performance which facilitates learning in the next step of a sequential task hierarchy and/or is required for maintenance in, or improvement of the environment of the learner. In practice, performance standards are derived from empirical observation of learners who are considered proficient at the skill. In reading programs, the assumption is usually made that the frequency of reading words will of necessity be very slow in early stages (Jenkinson, 1973). However, Speer and Lamb (1976) have demonstrated a strong relationship between high frequencies of first grade students' visual

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42 processing of letters, and subsequent reading achievement as measured by the Gates-McGinite Reading Test. The implication is that if frequency of academic performance is important in terms of learning outcomes , educators may be setting the stage for failure by exclusive attention to percentage accuracy statements as the criterion for academic performance. Studies of academic performance standards for math, reading, spelling, and writing will now be presented. Math Frequency Standards Haughton (1971a) has reported a strong relationship between the frequency of writing digits and math computation (r = .9 to .99). Learners were instructed to write digits one through ten for one minute. It was observed that children who wrote digits at frequencies of 20 to 30 digits per minute or less were also poor performers in math computation. Haughton also reported that learners performing at frequencies of 30 to 40 digits per minute on basic math facts were able to accelerate while progressing to more complex tasks. Those learners performing below 30 digits per minute decelerated their frequencies as they progressed to more complex tasks. This finding has been replicated in Marie Gaasholt's (1970) research. Gaasholt found the frequency of 80 digits per minute when writing digits one through ten, and the frequency of 40 to 50 digits per minute on basic math facts

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43 to be appropriate performance criteria for movements in addition, subtraction, multiplication, and division. Tomaras (1974b) reported normative frequency data for tracing digits sampled from seven first grade classrooms in the Tacoma Public Schools S.S.T. Learning Disability Project. Three distinct stimulus sheets were used with digits one through four, five through seven, and eight through zero. Median frequencies from the seven classrooms were 29, 31, 23, 37, 37, and 43 digits per minute. In a seperate study, Tomaras (1974a) reported the results of using a timed measurement format for mathematics instruction in the first grade. A performance criteria of 30 digits per minute was set for fluency using probes from the Tacoma Publis Schools S.S.T. Learning Disability Project and addition and subtraction sheets adapted from the Addison-Wesley Math Series. The control group followed the traditional classroom format of the AddisonWesley workbook supplemented by other teacher worksheets. No frequency performance standards were required in the control group. The results indicate that the mean grade equivalent score measured by the California Achievement Test in Mathematics for the experimental group was grade 1.6. This can be compared to a mean grade equivalent score of 1.3 for the control group. Findings were significant at the .10 level. The timed measurement format also affected the spread on the grade equivalent scale,

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44 placing more children higher on the scale than at the bottom of the scale. Tomaras reports a median writing digits frequency of 32 digits per minute based on screening thousands of children in first grade classrooms. The frequencies varied from to 60 digits per minute. Wolking and Schwartz (197 3) gathered normative frequency data on a number of academic skills across grades. Data from low achievers (LO) and high achievers (HI) are presented in Table 5. The frequency of high achievers for writing digits to addition problems varied from an average 12 correct digits per minute with 1 error per minute in first grade to an average of 86 correct digits per minute with errors per minute in sixth grade. Low achievers varied from an average of 1 correct digit per minute with 4 errors per minute in first grade to 54 correct digits per minute with errors in sixth grade. Thomas Lovitt has supervised a large number of precision teaching projects at the Experimental Education Unit at the University of Washington. Lovitt (1976) reports that 50 digits per minute is considered an adequate frequency standard for most mathematics skills. Reading Frequency Standards A large number of research efforts have been directed toward identifying the frequency of oral reading necessary to generate proficient readers. Eric Haughton (1971a)

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45

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48 found that children reading above 100 words per minute in third and fourth grade did not decelerate their performances when the reading curriculum became more advanced. It was concluded that a minimum rate of 100 words per minute is a useful performance standard for oral reading. Johnson (1971) found that 90 percent of students reading below 50 correct words per minute had relatively high error rates (botwnon ? and ?0 errors per minute). Only 30 to 40 percent of students reading between 50 and 100 correct words per minute has errors in oral reading. Of the students reading above 100 words per minute, only 10 percent made errors . Starlin (1970) reported that children whose frequency of oral reading was 5 to 10 words per minute had severe difficulty with reading and had not mastered prerequisite reading skills such as saying sounds. Haughton (1971a) reported that some of these children needed speech acceleration because they talked too slowly. The conclusion was that oral reading ability is a function of the frequency of certain prerequisite skills such as saying sounds, saying phonetically irregular words (also called basic sight words), and speech production.

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49 Camp (1973) studied the relationship between frequency of reading texted words and long term retention in 46 children with severe reading disability. The majority of the children had learning curves qualitatively similar to normal children. Rank order correlations between reading frequencies and three measures of retention ranged between r = .54 and r = .94. The data suggests that individual differences in frequency may account for a large share of individual differences in retention. Thomas (1972) studied instruction in reading rate acceleration and the effects upon comprehension. Three experimental classes were randomly selected in each of grades two, four, and six in Montana schools. Standardized pretests and posttests of comprehension were administered to nine classes including 407 learners. The experimental classes were trained to increase frequencies of reading texted words over a six week period at the beginning of the school year. Results of the study indicate that the learners in second grade made significant gains in reading comprehension. The first grade experimental group made significant gains in both reading rate and comprehension. When the groups were equated on the basis of intelligence quotients, the differences maintained. The differences did not decline when measured again at the end of the school year.

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50 Alper, Nowlin, Lemoine, Perine , and Bettencourt (1974) reported that 100 words per minute with two or less errors per minute is considered mastery for oral reading. Th author reported several other academic performance criteria in current use (see Table 6). These frequencies may be contrasted with Lovitt's (1976) recommendations of 100 words per minute for oral reading and 65 per minute frequencies for see to say word parts. Suggested performance standards from the Great Falls Montana Precision Teaching Project are a more recent guide (see Table 7). These standards suggest frequencies of 200+ for oral reading of texted words and 60 to 80 sounds per minute for isolated phonics sounds. Summarizing the studies in reading, two salient factors emerge: (1) there is a frequency standard for oral reading above which children make few errors and are able to progress to more difficult reading without decelerating, and (2) there appears to be important prerequisite skills to oral reading. By developing each prerequisite skill to an appropriate proficiency level before introducing new materials, acquisition moves smoothly and rapidly (Ilaughton, 1969). Holding a skill at proficiency level is simplified because all the precursors have been thoroughly learned.

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51 Table 6 Tentative Mastery Levels in Reading Rate Correct Rate Incorrect Sounds : Consonants 80/min. 1-2/min. Vowels 80/min 1-2/min. Alphabet Names 80/min. 1-2/min. Phonetically Predictable 3, 4, and 5 Letter Words 80/min. 1-2/min. Dolch Sight Words 60-80/min. 1-2/min. Reading in Books at All Grade Levels 100-120/min. 1-2/mm,

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52 Spelling Frequency Standards Starlin (1971) presented academic standards for spelling performance. For learners in kindergarten through second grade, a frequency of 30 to 50 correct letters spelled per minute with 2 or less errors per minute was considered adequate. For third grade through adult levels, 50 to 70 correct letters spelled per minute with 2 or less errors per minute was considered adequate. These standards can be contrasted with suggested performance standards from the Great Falls Montana Precision Teaching Project. The Project recommends 80 to 100 letters per minute for hear to write dictated spelling words, and 15 to 25 words per minute for hear to write dictated words. The Starlin (1971) study was the only experimental study which could be identified on the subject of spelling frequency standards. Researchers have been reluctant to study this area because the frequencies seemed to be dependent on the rate of presentation of the stimulus words. Recently, new techniques have been used whereby the stimulus words are presented at a much faster rate than the child can spell. In the typical application, a stimulus word is presented every 3 seconds. Some words are not spelled, but a stimulus word is always present shortly after completion of a previous word, regardless of how long it takes to spell the previous word.

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53 Writing Frequency Standards Kunzelman (1970) and Haughton (1971a) have demonstrated that children and adults have a higher frequency of writing letters in words than writing letters in isolation. Wolking and Schwartz (197 3) report normative data on writing random letters. High achievers averaged from 25 letters per minute with no errors per minute in first grade, to 88 letters per minute with no errors per minute in sixth grade. Low achievers averaged from 11 letters per minute with no errors per minute in first grade to 7 2 letters per minute with no errors per minute in sixth grade (see Table 5). This data should be evaluated in a developmental sense rather than as performance standards per se. Wolking (1980) recommends the use of 120 letters per minute with 2 or less errors per minute as a general performance standard for writing skills. Lovitt (1976) has used 125 symbols per minute as the desired frequency standard, but cautions that research has not been conducted which could justify that value. Suggested performance standards from the Great Falls Montana Precision Teaching Project (1979) are presented in Table 7. It can be observed that the performance criteria listed are generally higher than other recommendations. Performance standards change periodically. The trend is toward higher frequencies.

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54 Table 7 Suggested Performance Standards Great Falls Montana Precision Teaching Project Skill Standard Reading See/Say Isolated Sounds See/Say Phonetic Words Think/Say Alphabet (towards) See/Say Letter Names See/Say Sight Words 60-80 sounds/min. 60-80 words/min. 400+ letters/min. 60-100 letters/min. 80-100 words/min. See/Say Words in Context (oral read) 200+ words/min. See/Think Words in Context (silent read) 400+ words/min. Think/Say Ideas or Facts 15-30 ideas/min. Handwriting See/Write Slashes See/Write Circles Think/Write Alphabet See/Write Letters (count 3 for each letter: slant, form, and ending) See/Write Cursive Letters Connected (count 3 for each letter) 200-400 slashes/min. 100-150 circles/min. 80-100 letters/min. 7 5 correct /min. 125 correct/min. Spelling Hear/Write Dictated Words Hear/Write Dictated Words 80-100 letters/min. 15-25 words/min.

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55 Table 7 continued Mathematics Skill Standard See/Write Numbers Random 100-120 digits/min. Think/Write Numbers (0-9) Serial 120-160 digits/min. See/Say Numbers 80-100 numbers/min. Think/ Say Numbers in Sequence (count-bys) 150-200+ numbers/min. See/Write Math Facts 70-90 digits/min.

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56 A Frequency Model of Learning White and Haring (1976) define fluency in relative terms. In their opinion, the question of fluency should be judged in terms of what will make the skill useful for the child. Reading at a frequency of 50 words per minute may well serve the needs of a second grade child, but will not suffice for the college freshman. White and Haring have proposed a five-stage learning model through which a child acquires each discrete academic skill. In their model, the learner can move through stages of acquisition, fluency building, maintenance, application, and adaptation. Identification of the first three stages of the model is based on the frequency of correct and error performance. Closely related skills can be in several different stages of the model, dependent upon the frequencies of performance for each skill. In the White and Haring learning model, differential instruction is programmed depending on the learning stage which in turn is based on the frequencies of academic performance. Although there is little research to support the White and Haring learning model, it has stimulated efforts to identify academic performance standards to use as goals in the fluency-building stage. The model is primarily of practical value in that the stages of learning have specific and concrete teaching procedures. The White and Haring work has organized and directed the efforts of many learning technologists .

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57 In summary, the majority of studies included for examination of frequency measurement criteria are an outgrowth of the precision teaching model developed by 0. R. Lindsley (1971). Central to this model is the use of frequency measurement. The studies of frequency performance criteria for academic skills have followed two schools of thought. One belief is that the criteria should be set at the median frequency for a group of similar peers. The followers of this belief have identified normative frequencies for various grade levels and types of learners. The problem with this type of data is that populations operating under a precision teaching model will have much higher normative frequency values than populations operating in a traditional instructional framework. Other researchers have attempted to identify critical frequencies above which subsequent learning will be facilitated and below which learning is hindered. The problem with this approach is that it is dependent on an identified sequenced curriculum. Furthermore, once the critical frequency is identified, a higher frequency must be specified as the desired criterion frequency in order to avoid the problems associated with the performance ceiling. Despite the many problems of identifying frequency performance criteria, it remains a fertile area for

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58 research. The objective is to identify frequency performance standards which will produce maintaining or rising initial frequencies and celerations as new curriculum material is presented. The central issue appears to be whether critical frequencies can be identified which will facilitate academic performance for basic skills in reading, spelling, writing, and math computation.

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59 Predictive Studies Using Frequency Measurement Prediction using any method is a tenuous endeavor. In essence, one is implying that the conditions which produced the prediction data will remain in effect and produce similar progress in the future (White, 1972a). In reality, many new variables can be introduced at any time, or the existing values can diminish or be enhanced (i.e., through boredom, maturation, etc.). The problem is further complicated by the complex role of the teacher in arranging the instructional environment to maximize learning. Almost by definition, conditions will not remain the same in a learning situation. Implied in the use of data for instructional decision-making under the precision teaching model is prediction of academic performance. One predicts, on the basis of available academic performance information, whether or not the learner will meet established performance standards within an acceptable time limit. If the prediction indicates failure to attain the standard, then the instructional procedures are changed. If the prediction indicates attainment of the standard, than a change should not be necessary. Thus prediction of academic performance serves a primary role in the timing and selection of instructional methods and procedures. In predicting academic performance, one is concerned with the trend of the frequency values. There are a

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60 number of methods for quantifying the trend, among which the most popular are celeration and slope. The use of data from academic performance to predict subsequent performance requires resolution of two basic considerations: the type of data collected, and the amount of data needed for prediction. White (1972a) maintains that the type of data used for prediction should have the capacity to vary over a wide range of values. In addition, the data should remain comparable from day to day. White identifies three types of data which meet these criteria: counts of the number of times a behavior occurs where the time in which the counts are taken remains constant from day to day; frequency, in which the behavior count for each day is divided by the time over which the counts were collected", and time or temporal values such as latency, the time necessary to begin responding once an instruction is given. Frequency is the most commonly employed of these acceptable data types. The ability to accurately predict subsequent academic performance depends on the quantity and quality of data used for prediction. Theoretically, the more data used for prediction, the better the chances for accurate prediction. White (1972b) analyzed the predictive utility of the median slope for predicting academic performance within instructional phases (i.e., within periods of instruction in which the conditions of instruction were held constant).

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61 The criteria for success in prediction was the deviation of data values from the median slope predicted line of progress. White found that 9 and 11 data points had optimal predictive ability over a wide range of days into prediction. Interestingly, a reduction of predictive utility occured after 13 predictive data points. This was attributed to reduction in the number of projects to sample which contained many data points. In general, the prediction had greater accuracy as the number of data points for prediction increased . Predictive Studies White (1972a) analyzed the results of 116 classroom precision teaching projects. The projects included tasks such as writing answers to addition and subtraction problems, saying digits, and reading sight words. Four different methods were compared for using initial frequency data to predict subsequent academic performances of single individuals. All four methods were slope calculations. The methods were compared using 3 initial data points, then gradually increasing the number of days into prediction until 11 or 12 data points were included in the calculations. The slope methods used included the least-squares regression solution, median slope method, corrected slope method, and split-middle t§ehfliqu@i

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62 The findings indicate that median estimates of trend, and in particular the median slope method, were more consistently accurate than the least-squares regression solution. The probability of acceptable prediction over one week or more into the future was not within reasonable limits until at least seven data points were used for prediction. The split-middle technique performed well enough to be considered an alternative to the median slope method for use by teachers and other educational practitioners. Critical analysis of the White study reveals that there was much variety in which method was better in individual cases. Over a large number of cases, the median estimates predicted better than other methods . Another problem with the study was the method of ranking used to judge the "closeness" of prediction. Exact quantification of the accuracy of prediction was not reported. A significant finding not mentioned in the conclusions of the White (1972a) study was the influence of variability of the frequency values. The median slope method was drastically affected by trends in deviations or variance in the data, to the exclusion of trends in frequency. A correction factor was applied to the median slope calculations to minimize the effects of variability in the data.

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63 Consequently, the utility of variability for predicting future academic performance of single individuals was not explored. In a landmark dissertation study, Koenig (1972) studied the utility of least squares straight line projections on semilogarithmic charts to predict future frequencies. In this research, the first 10 to 14 frequencies of each phase of instruction was used to predict to the next 10 to 14 frequencies within phase. The percentage of future frequencies contained in the envelope formed by bounce lines was used to assess the accuracy of the projection technique. A total of 14,452 phases across a variety of academic and behavioral tasks were analyzed. The major findings of this study were: 1. Variability about straight line celerations and quarterintersect celeration lines was found to be relatively constant in proportion and symmetrical above and below the line. 2. The least-squares celeration line was slightly better at bisecting future data than the quarter-intersect method. Both methods performed adequately. 3. The bounce envelope projection technique did not perform well for predicting future frequencies. The least-squares projection envelope contained 70 percent or more of the projected frequencies only 42 percent of the time. About 21 percent of the time, 90 percent or more of the frequencies were contained.

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64 4-. Projecting only to the next quarter containing five to seven of the frequencies improved the projection. The overall conclusion from the Koenig study was that least-squares and quarter-intersect straight lines usually represent human frequencies accurately. It should be noted that straight line methods represented the data well despite the fact that about one-third of the human frequency phases were changing more than 10 percent weekly. The other two-thirds of the phases changed less than 10 percent weekly. Koenig (1980) analyzing data from over 8,000 children reports that prediction within phases of precision teaching episodes requires at least six data points for math and spelling, and eight data points for reading to attain significant correlation values for prediction. The dependent measure was the frequency of correct movements. Data which contains large amounts of variability require additional data points to obtain significant prediction correlations. Koenig recommends exclusion of the first data point, and at least ten daily observations for prediction studies using frequency correct measures. The data in Table 8 summarize and organize Koenig' s prediction results for math, spelling, and reading movements. It can be observed that the t values for correlation become acceptably small and

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66 significant at six days for math and spelling (t = 1.7 and 2.4, respectively), and eight days for reading (t = .2) Pace (1980) explored the use of celeration and frequency for predicting children referred for special education services. Using the International Management System Learning Screening Procedure (Koenig S Kunzelmann, 1980), an overall hit rate of 64 percent was achieved across grades one through six. The sum of celeration ranks in the lower quartile was used for prediction. This procedure yielded a 2 5 percent referral rate composed of a high percentage of false positives and false negatives. The same screening procedure using frequency rather than celeration increased the overall hit rate from 83 percent to 100 percent across grades. These values compare favorably with the best of the early identification studies using traditional measurement techniques. The significant finding of this study was that celeration ranks lessen the accuracy of prediction, while frequency ranks demonstrated superior predictive utility. This must be viewed as a tenative finding due to limitations in the design of the study which did not include mentally retarded children and an overall three percent minority population in the school district under investigation. It should be noted that under the Learning Screening Procedure, the content of the screening items is taken from skills in the existing curriculum.

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67 Stiles (1973) studied the utility of using frequency measures from individual learners to predict their scores on the Short Form Tests of Academic Aptitude/ Comprehension Tests of Basic Skills (SFTAA/CTBS) of the California Test Bureau. Data from 348 third grade students' performances on the SST stimulus sheets were used for prediction. One minute samples from each day over a ten day period were collected on such skills as writing random digits, addition problems, subtraction problems, hear to write letters, writing random letters, saying sounds, and saying words. The celerations and midpoint frequencies were used to predict SFTAA/CTBS performance Results of the Stiles study indicate that 36 percent of the variation or differences in language intelligence scores can be accounted for by differences in rates of performance on the SST skills. The variables which explained the greatest amount of the variance (i.e., the variables which entered the regression formula first) were the frequency of saying words and writing random numbers. The addition of other variables to the equation increased the variance accounted for by 6 to 12 percent. Hanby (1975) described the use of frequency of oral language performance to identify children with language deficiencies. A non-tested preschool class was used to select a picture from the Ginn Pre-Reading Picture

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68 Series which had the highest number of verbal responses. In the testing procedure, children were asked to tell what they saw happening in the picture. The frequency of words responding during a 15 or 30 second timing each day was recorded. A class summary of frequencies was plotted on polar logarithmic charts and language deficient students were identified by a criterion of one-half of the class median frequency value. An alternative criteria discussed was the median frequency by age in months . An advantage of using the frequency procedure described in the Hanby study is that the class median celeration value could be used as a criterion for instruction. The class median celeration value reported was XI. 3 (30 percent growth in frequency values per week). In summary, predictive studies using frequency measurement can be classified into two groups: those which attempted to predict academic performance within phases of instruction (White, 1972b; Koenig, 1972; Koenig, 1980); and those which attempted to predict to some external criteria (Pace, 1980; Stiles, 1973; Hanby, 1975). The latter studies are similar to the early identification studies reviewed earlier in that the emphasis is on prediction of children at risk for academic failure. They differed in that frequency measurement was the dependent measure used for prediction.

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69 All of the investigations in this section were concerned with frequency correct measures , while a few studies also considered celeration and variability for prediction (White, 1972a; Koenig, 1972; Pace, 1980; Hanby, 1975). Important findings from the frequency measurement studies include the number of data points into prediction (Koenig, 1980); the relationship of variability to both celeration and frequency correct measurements (White, 1972a; Koenig, 1980); and the utility of frequency correct measures over celeration measures for prediction of problem learners (Stiles, 1973; Pace, 1980). None of the frequency measurement prediction studies attempted to combine frequency, celeration, and variability measures for prediction of subsequent academic performance. Additionally, no studies attempted to predict across phases from baseline to instruction. The present study extends and builds upon the previous research findings to include multiple dimensions of frequency, celeration, and variability measures for prediction of academic performance. It also breaks new ground in attempting to predict from baseline to instructional phases.

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CHAPTER III METHOD Sixty learners were assessed over a five-day period by fourteen teachers using the Sequential Precision Assessment Resource Kit II (Trifiletti, Rainey, g Trifiletti, 1979). This assessment procedure was followed by twenty days of academic instruction on the skills identified as deficient during assessment. During instruction the teachers used precision teaching methods to maximize academic performance. Following instruction the data from the study were analyzed to determine the predictive utility of frequency, celeration, and variability dimensions of academic performance. The content of instructional tasks was coded for further analyses of relationships between frequency, celeration, and variability of academic performance during assessment and instruction. Subjects The subjects were students enrolled in the Summer Learning Disabilities Program sponsored by the Department of Special Education of the University of Florida. They ranged in age from seven years two months to fifteen years five months. In May, 1979, a packet of information was mailed to teachers of exceptional student education in Alachua County, 70

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71 Florida. The teachers were asked for referrals of exceptional learners who might benefit from summer instruction. Children were selected from the referrals on a first-come, first-served basis for a total of sixty children. The entire population of sixty children, fourteen teachers , and two teacher-managers of the Summer Learning Disabilities Program were used for the study. The students in the study were exceptional students from public and private schools in Alachua County, Florida, The majority of the students were children with mild to moderate specific learning disabilities. The teachers employed in the study were enrolled as a practicum teaching experience for partial fulfillment of the requirements for the Master of Education in Special Education. The teacher-managers elected the experience as part of the requirements for the Doctor of Philosophy in Special Education. Equipment Apparatus The assessment instrument used for the study was the Sequential Precision Assessment Resource Kit II (Trifiletti et al., 1979). This instrument is based upon White and Haring (1976) procedures for precision assessment. A description of the Sequential Precision Assessment Resource Kit II (SPARK II) instrument is provided in Appendix B. Probes from the SPARK II were

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72 used to gather data from which frequency, celeration and variability measurements were derived. Tool skill probes, single skill probes, and mixed skill probes from the SPARK II were administered. Teachers scored the performance of learners on the probes and this information was recorded on assessment summary sheets. A computer program was used to generate weekly frequency charts for each teacher-learner-task (triad) combination. The charts displayed both frequency and accuracy of performance on each skill, and were cumulative from the onset of instruction. A listing of the computer program written in Fortran language is provided in Appendix C. Appendix D contains a sample frequency chart and directions for interpretation. Setting The study was conducted at the P.K. Yonge Laboratory School of the College of Education, University of Florida. Assessment and instruction of learners was carried out in ordinary elementary classrooms during a special summer program. The dates of the assessment and instruction phases of the study were from June 25, 1979, to August 7, 1979 Procedure The study consisted of three phases. The first was an orientation and training period for the teachers and managers of the study. The second phase was a five-day

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73 assessment period during which each learner was administered probes from the SPARK II. The final phase consisted of 20 teaching days of individualized instruction for each learner. The instruction employed precision teaching methodology in order to maximize academic performance. Each of these phases of the study will now be described in detail. Training Procedures All of the teachers and teacher-managers attended a college course and an intensive workshop on precision teaching procedures prior to onset of the study. These procedures were reviewed during a two-hour training session. A syllabus of the training session is included in Appendix E. The teachers were trained in interpretation of the computer charts during individual sessions with their teacher-manager . Initial Precision Assessment During the assessment phase of the study, the teachers administered three types of probes from the SPARK II; tool skill probes, mixed skill probes, and single skill probes. The mixed skill probes were used to identify possible deficient skills in reading, mathematics, and language arts. Mixed skill probes were administered to each learner on the first and second days of assessment. Teachers then examined the results of

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74 the mixed skill probes to select single skill probes for further assessment. The frequency, celeration, and variability derived from learner's performance on mixed skill probes were used to predict subsequent academic performance. The single skill probes administered to each learner were selected on the basis of information gained from the mixed skill probes. Single skill probes were administered on days three, four, and five of the initial assessment period. Data from the single skill probes were used to select skills for instruction. The frequency, celeration, and variability measures derived from the single skill probes were used to predict subsequent academic performance. Tool skill probes were used to assess performance on important prerequisite skills such as saying letters, writing letters, saying digits, and writing digits. The tool skill probes were repeatedly administered to each learner on each day of initial assessment. Frequency, celeration, and variability measures of each learner's performance on the tool skills were computed. These data were later used to predict subsequent academic performance. The order of administration of probes for initial assessment is presented in Table 9. Upon completion of the initial assessment, teachers selected six to ten

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Table 9 Administration Schedule of Probes During Initial Assessment 75 Day 1

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76 skills for instruction with each learner. Selection was based upon teacher's clinical judgement and the information obtained during assessment. Instruction The third part of the study involved instruction using precision teaching methods. Teachers administered daily timed probes from the SPARK II and other sources for instructional targets. Performance data were charted daily by each teacher. These charts were collected each weekend and the data were keypunched by the experimenter to produce weekly computerized charts of each learner's performance. The computerized charts flagged celeration values which were less than 25 percent weekly improvement. Teachers were required to change their instruction for these skills in order to optimize learning . Experimental Design The experimental design for this experiment follows a predictive model. The predictor variables were median frequency correct, weekly celeration, and variability of performance on academic skills during assessment. This information was obtained by measuring performance on mixed skill probes, single skill probes, and tool skill probes from the SPARK II. The criterion variables were weekly celeration during the first instructional phase and second instructional phase.

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77 Frequency was defined as the median value of the correct movements per minute of observation. Since the computer generated charts used an equal interval scale, celeration was defined as the ratio of two points seven days apart on a least squares regression line plotted through the frequency correct points. Variability of academic performance was defined as the sum of squares of error about a regression line plotted through the frequency correct points. Data Collection Data describing the baseline initial assessment were collected and recorded by teachers on summary forms provided by the experimenter. Data from daily instruction were collected by teachers and recorded on ratio charts. Data from initial baseline assessment and instruction were keypunched by the experimenter. This effort produced the computerized charts as well as formed the data for statistical analyses. Data Analysis The data for this study were statistically analyzed using multiple regression procedures and the stepwise solution (Nie, Hull, Jenkins, Steinbrenner , & Brent, 1975). In this procedure, the computer enters independent variables into the regression equation in single steps from best to worst. The independent variable that explains the greatest amount of variance in the dependent variable will enter

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first; the independent variable that explains the greatest amount of variance in conjunction with the first will enter second, and so on. In other words, the independent variable that explains the greatest amount of variance unexplained by the variables already in the equation enters the equation at each step. Minimum default values of F ratio (F = .01) and tolerance (T = .001) were used to control inclusion of independent variables at each step. The computer facilities of the Northeast Regional Data Center (NERDC) and the Statistical Package for the Social Sciences (SPSS) were employed to obtain the data analyses. The data were organized into an SPSS data set on punched cards by the addition of a control card to each set of teacher-learner-task data. The control card contained codes which categorized the triad into nine categories of stimulus content, nine categories of input/ output modality, and three categories of skill. These categories and their codes are presented in Table 10. Although not all of the categories are utilized in this study, they were designed to be of utility for subsequent programmatic research. Also present on the control card were codes for the teacher, learner, and number of data points obtained during assessment. Triads with less than three data points during assessment or instruction were omitted from the statistical analyses since variability values could not be meaningfully computed for them.

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79 Table 10 Categories for Coding of Each Teacher-Learner-Task Triad

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CHAPTER IV RESULTS The measurements used for prediction were the median frequency correct value from baseline assessment phase, the weekly celeration value from baseline phase, and the variability value (i.e., the value for the sum of squared deviations from the line of best fit through the frequency correct points) of baseline phase. Each case was composed of a separate teacher-learner-task triad. The predicted variables were the weekly celeration value for the first instructional phase (i.e., phase two) and the weekly celeration value for the second instructional phase (i.e., phase three). Triads were selected for analyses if the number of data points in predictor and predicted phases was three or more . Reliability Table 11 provides percentage agreement between the experimenter and the observer (teacher) for each week of the study. Agreement information is shown for the frequency correct values collected daily by the teachers. A small samole of each teacher's recording during one day of each week was rescored by the experimenter. 80

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Table 11 Percentage of Interobserver Agreement for Recording of Predictor Variable across Weeks of the Study

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82 The minimum acceptable total agreement percentage for recording of frequency correct values was 80 percent. Percentage values were generally lower during baseline than during instruction. The lower reliability during baseline can be attributed to the unfamiliarity of the teachers with the recording procedures used to collect the data. Analyses of Prediction Results The results of prediction are displayed in Table 12, Table 13, and Table 14. The first column contains the number of separate teacher-learner-task triads which produced the correlation values. The second column on the tables contains the type of skill probe, type of stimulus content, or type of input/output modality represented by the triads. Columns 3, 4, 5, and 6 contain product moment correlation values for frequency correct 2 measures. Column 7 contains the amount of variance R explained by prediction variables predicting to celeration for the first instructional phase. Column 8 contains the amount of variance R 2 explained by predictor variables predicting to celeration for the second instructional phase. The questions of interest to this study will now be examined with respect to the statistical results. (1) Can frequency, celeration, and variability of baseline performance on tool skill probes be used to predict the rate of learning during instruction?

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83 Only 2 percent of the phase two celeration was explained by frequency, celeration, and variability of tool skill performance during assessment (see Table 12). The prediction to phase three explained 4 percent of the variance in celeration. There were 9 3 triads in the prediction to phase two celeration, and 46 triads in the prediction to phase three celeration. It appears that frequency, celeration, and variability of tool skill performance are not useful for prediction of celeration during instruction. (2) Can frequency, celeration, and variability of baseline performance on single skill probes be used to predict the rate of learning during instruction? Only 1 percent of the phase two celeration was explained by frequency, celeration, and variability of single skill performance during assessment (see Table 12). The prediction to phase three also explained 1 percent of the variation in celeration. There were 177 triads in the prediction to phase two celeration, and 66 triads in the prediction to phase three celeration. Frequency, celeration, and variability of single skill performance are not useful for prediction of celeration during instruction. (3) Can frequency, celeration, and variability of baseline performance on mixed skill probes be used to predict the rate of learning during instruction?

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84 3 3 O £) W3 O CO 3 P Oh rt) C_> rH rH CO -H TJ .* Ifl 00 •H 3 4u H O Mh 0) o a CO E-i cu CO >i >>.3 H 3 3 < K

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85 Eleven percent of the variation in phase two celeration was explained by frequency, celeration, and variability of performance on mixed skill probes (see Table 12). There were 16 triads in this prediction. The first variable to enter the regression equation was variability, followed by median frequency. The prediction to the second instructional phase (phase 2 3) contained only two triads, therefore the R value was not meaningful. (4) Is there a differential predictive relationship by academic task stimuli from baseline performance to performance during instruction? The different task stimuli include letters, digits, phonics sounds, sight words, texted words, number problems, phonics words, and spelling words. These task stimuli will be discussed individually in the following text. Tasks with Letters There were 60 triads in the prediction to phase two, and 23 triads in the prediction to phase three celeration. Seventeen percent of the variation in phase two celeration was explained by frequency, celeration, and variability of baseline performance on tasks with letters. Six percent of the variation in phase three celeration was explained by the prediction. Celeration entered the regression prediction equation first, followed by variability and median frequency for predicting to phase two.

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86

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87 Tasks with Digits There were 41 triads in the prediction to phase two celeration, and 24 triads in the prediction to phase three. Seven percent of the variation in phase two and phase three celeration could be explained by baseline predictor variables on tasks with digits (see Table 13). Tasks with Phonics Sounds There were 17 triads in the prediction to phase two celeration, and 9 triads in the prediction to phase three celeration using frequency, celeration, and variability of baseline performance as predictors (see Table 13). Fifty-three percent of the variation in performance during phase two could be explained by baseline performance. Twenty-two percent of the variation in performance during phase three could be explained by baseline performance; however this figure should be viewed with caution due to the small number of triads for computation. Tasks with Sight Words The R 2 values on Table 13 for prediction of performance with sight words have been omitted since the number of triads for computation of these values was less than 10. Tasks with Texted Words The R 2 values on Table 13 for prediction of performance with texted words have been omitted since the number of triads for computation of these values was less than 10.

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Tasks with Number Problems There were 126 triads in the prediction of phase two celeration using frequency, celeration, and variability of tasks with number problems. Only 2 percent of the phase two celeration was explained by baseline variables. Likewise, only 2 percent of the phase three variation in celeration was due to variation in baseline variables of frequency, celeration, and variability on number problem tasks (see Table 13). Tasks with Phonics Words There were 26 triads in the prediction of phase two celeration using frequency, celeration, and variability of tasks with phonics words. Eight percent of the variance in phase two celeration could be explained by performance characteristics during baseline (see Table 13). The prediction to phase three celeration had only 8 triads, and thus the R 2 value has been omitted . Tasks with Spelling Words There were only 8 triads each in the predictions of phase two celeration and phase three celeration. As such, the R 2 values have been omitted (see Table 13). When the number of cases for multiple regression is less than 10, the R values are artificially inflated.

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3° The amount of variance R z in phase two celeration explained by baseline predictor variables ranged from 2 percent for number problems to 5 3 percent for phonics sounds. Predicting to phase three celerations generally yielded lower R 2 values. Two of the five academic task stimuli appeared to have a differential predictive relationship and were higher in amount of variance explained by predictor variables. In general, the predictive ability of frequency, celeration, and variability during assessment were characterized by low positive values. (5) Is there a differential predictive relationship by input and output modality of learners from baseline academic performance to performance during instruction? The different input and output modalities of interest include see to say, see to write, see to do, hear to say, hear to write, hear to do, think to say, think to write, think to do . Since the teachers in this study were free to decide instructional targets , not all of the input and output modality combinations were present in the data. Sixty-five triads were see to say, 13 3 were see to write, 24 were think to say, and 74 were think to write. These will now be discussed individually.

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90 See To Say Tasks Sixty-two triads were included in the prediction of celeration during phase two from baseline performance on see to say tasks. Twenty-six percent of the variation in phase two celeration could be explained by frequency, celeration, and variability of baseline performance on see to say tasks. There were 29 triads in the prediction of celeration during phase three from baseline performance on see to say tasks. Only 3 percent of the variation in phase three celeration could be explained by baseline performance measures (see Table 14). See To Write Tasks See to write tasks included 130 triads for prediction. Two percent of the variation in phase two celeration was explained by baseline performance measures. There were 39 triads in the prediction of phase three celeration from baseline performance on see to write tasks. Again, only 2 percent of the variation was explained (see Table 14). Think To Say Tasks There were 20 triads in the prediction of phase two celeration from baseline performance on think to say tasks. Five percent of the variation in phase two celeration was explained by baseline performance measures. There were 12 triads in the prediction of phase three celeration. Nineteen percent of the variation in celeration was explained by baseline predictor' VafiaDies (§SS Tlfil§ IhJi

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91

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92 Think To Write Tasks There were 72 triads in the prediction of phase two celeration from baseline performance on think to write tasks. Sixteen percent of the variation in phase two celeration could be explained by baseline predictor variables. There were 31 triads in the prediction .of phase three celeration from baseline performance on think to write tasks. Nine percent of the variation in celeration was explained by frequency, celeration, and variability of baseline performance on think to write tasks (see Table 14). In summary of the analyses of triads categorized by type of input/output modality, the amount of variance R 2 in phase two celeration explained by baseline predictor variables ranged from 2 percent for see to write tasks, to 26 percent for see to say tasks. Predicting to phase three celerations generally yielded lower predictive 2 values except for think to say tasks where the R value increased . It appears that there is a small differential predictive relationship by input/output modality of the task, o however the amount of variance R explained by predictor variables is generally small. The predictive ability of frequency, celeration, and variability of baseline performance ranged from low positive to moderate positive.

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CHAPTER V DISCUSSION There has been a great deal of interest in the prediction of learning performance. The extent to which this is possible depends upon the type of data and the amount of data for prediction (White, 1972a). Previous studies have examined the degree to which performance can be predicted within instructional phases (White, 1972a; Koenig, 1972; Koenig, 1980). The present study employed operant learning techniques to further clarify the relationship of variables that may be useful for prediction of academic performance. Of interest was the utility of prediction from baseline assessment to instructional phases. Students' frequencies of performance on a great number of tasks were measured during a week of baseline data collection. Each seperate triad was categorized into eight different types of academic task stimuli, four different types of input/output madality, and three different types of skill probe. Following baseline data collection, teachers selected skills for instruction and delivered instruction over a five week period. Daily frequency measures were recorded by teachers. The data were analyzed by computer to produce 93

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94 frequency, celeration, and variability values for each phase of instruction Findings The findings of this study are discussed relative to the experimental questions. Prediction from baseline performance to performance under instruction was generally low when skills were categorized by tool skill, single skill, or mixed skill probes. The amount of variation in instructional celeration which could be explained by baseline performance measures ranged from 1 percent with single skills to 11 percent with mixed skills. The important finding is that a student's baseline academic performance is not a controlling or predicting factor for performance during instruction. Prediction categorized by type of stimulus content produced differential predictive strengths. Unfortunately, R 2 values for sight words, texted words, and spelling words had to be omitted due to small numbers of triads available for their calculation. Of the remaining stimulus categories, strength of prediction (amount of variation in instructional celerations) ranged from R 2 =.02 for number problems to R 2 =.53 for phonics sounds. Letters stimuli (R 2 =.17) predictions were slightly stronger than digits stimuli (R 2 =.02) predictions. In general, there appeared to be a trend for language stimuli to predict better than math stimuli. This trend is tentative and will require

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95 further research for confirmation. The relatively strong predictive value for phonics sounds (R 2 =.63) may be an artifact of the population sample employed in the study. The majority of the children had specific learning disabilities which are often associated with reading skills. Phonics sounds are a critical reading skill. It can be argued that children with deficiencies in this skill might show a more predictable relationship from baseline to instruction if the skill generally did not respond to instruction . When the skills were categorized by input/output madality, prediction strengths were again low with the exception of see to say movements (R 2 =.26). It should be noted that phonics sounds which showed high predictive strength were see to say movements. Phonics sounds were 17 of the 62 triads in the see to say category. Prediction strengths for see to write movements (R 2 =.02) and think to say movements (R 2 =.05) were generally low. Think to write movements demonstrated slightly stronger predictive strength (R 2 =.16) for phase two celeration. Interpretation of the Findings It is clear that the prediction of academic performance from baseline to instructional phases is weaker than prediction within instructional phases. At a molar level, interpretation of the predictive findings relative to White's (1972a) findings are illustrative of the advantage

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96 of instructional control for prediction. Instructional control is a function of the fact that environmental conditions are more stable within phases than across phases. The generally low predictive findings for baseline predictor variables predicting to instruction are largely due to the reduced group variability during instruction. The high degree of instructional control attained by precision teaching methods washes out any predictive ability which might be found in baseline academic performance measures. At a molecular level of interpretation, some of the analyses explained fair to moderate amounts of variation in academic performance. Of particular interest are phonics sounds skills and see to say skills. The interpretation here is that the source of control for a learner's academic performance is partly a function of the state of performance prior to instruction. Key variables for measurement of initial states of performance may be frequency, celeration, and variability. It should be noted that in the majority of cases, the frequency value entered the stepwise regression procedure first, followed by celeration and variability, respectively. The frequency of initial performance is of greater predictive utility than celeration or variability when predicting to celeration under instruction.

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97 Problems and Limitations of the Study The foremost limitation of any study of prediction of academic performance is the quantity and quality of the data used for prediction. The second problem is the choice of variables for prediction. In this study relatively few days were available for collection of the baseline assessment data. The teachers were charged with assessing a wide range of skills over a small number of days. Many of the skills assessed were not chosen for instruction, further limiting the quantity of data available for prediction. The choice of baseline median frequency, celeration, and variability measures to predict instructional celeration may limit generalization of the findings. Other variables could have been chosen, but would not work in stepwise multiple regression due to the suppression effect when variables are highly correlated. Practical Implications The major implication of this study is that academic performance under instruction is largely not a function of baseline academic performance characteristics. The conditions which control and determine academic performance are a function of events and conditions during instruction rather than during assessment.

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98 There were two exceptions to this finding. Tasks with phonics sounds and see to say tasks were partially determined or explained by baseline academic performance characteristics. The usefulness of baseline academic performance measures for selecting instructional targets was confirmed. Suggestions for Further Research The foregoing research stimulates an unlimited variety of questions related to the prediction of academic behavior, Much research is needed to fully understand temporal dimensions of academic performance. First, it appears that with respect to some types of tasks, academic performance is slightly more predictable than others. The type of task may interact with the input/output modality. This question could be addressed in subsequent research by holding the task constant while varying the input /output modality. Second, it is assumed in predictive studies that observations of a similar "type" contribute equally to prediction. In fact, there may be differential effects due to the level of complexity of an academic skill. Addition, subtraction, multiplication and division tasks in this study were combined under the global variable "number problems." There may be differential effects due to the varying levels of complexity among these skills. Even within addition problems, there may be differential

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99 effects for basic addition fact problems, and advanced problems requiring renameing. It may be of value to investigate prediction within a single subject. The median frequency value employed for prediction in this study should be evaluated against other possible predictors including the mean frequency. The median frequency has proven predictive utility in other studies but has not been compared against mean frequency for prediction purposes. An additional research possibility is the use of slope values rather than celeration values for predictor and predicted variables. Finally, the first requirement of any science is that of replication, for it is the soundest test of reliability (Sidman, 1960). Replication of the present study with careful control over the selection of tasks, the number of data points for prediction, and the number of observations into prediction should further refine and expand the present knowledge base.

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REFERENCES Alper, T. , Nowlin, L., Lemoine , K. , Ferine, M. , S Bettencourt, B. The rated assessment of academic skills. Academic Therapy , 1974, 9_( 3 ) , 151-164. Badian, N.W. Early prediction of academic underachievement . Paper presented at the meeting of the 54th Annual International Convention of the Council for Exceptional Children, Chicago, April 1976. (ERIC Document Reproduction Service No. ED 122 500). Benger, K. The relationships of perception, personality, intelligence, and grade one reading achievement. Perception and reading . Newark, Delaware: International Reading Association, 1968. Bijou, S.W. The technology of teaching young handicapped children. In S.W. Bijou and E. Ribes-Inesta (Eds.), Behavior modification: Issues and extensions . Hew York : Academic Press, 1972 . Block, J.H. (Ed.). Mastery learning . Mew York: Holt, Rinehart and Winston, Inc., 1974. Book, R.M. Predicting reading failure: A screening battery for kindergarten children. Journal of Learning Disabilities , 1974, ]_, 43-56. Camp, 3. Learning rate and retention in retarded readers. Journal of Learning Disabilities , 1973, 6_( 2 ) , 65-71. Cohen, H.J., 6 Diner, H. The significance of developmental enamel defects in neurological diagnosis. Pediatrics , 1970, 46_ , 737-747. Cowgill, M.L., Friedland, S., S Shapiro, R. Predicting learning disabilities from kindergarten reports. Journal of Learning Disabilities , 1973, 6_, 577-582. de Kirsch, K. , Jansky, J., S Langford, W.S. Predicting reading failure . New York: Harper £ Row, 19 56. Denhoff, E., Hainsworth, P.K., S Hainsworth, M.L. The child at risk for learning disorder. Clinical Pediatrics, 1972, 11, 164-170. 100

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101 Dykstra, R. The use of reading readiness tests for diagnosis and prediction: A critique. In T.C. Barrett (Ed.) / The evaluation of children's reading achievement . Newark, Delaware: International Reading Association, 1967. Eaves, L.C., Kendall, D.C., S Crichton, J.U. The early detection of minimal brain dysfunction. Journal of Learning Disabilities , 1972, 5_, 454-462. Eaves, L.C., Kendall, D.C., £ Crichton, J.U. The early identification of learning disabilities: A followup report. Journal of Learning Disabilities , 1974, 7, 632-638. Ferinden, W.E., Jr., 5 Jacobson, S. Early identification of learning disabilities. Journal of Learning Disabilities , 1970, 3, 589-593. Ferster, C.B., S Skinner, B.F. Schedules of reinforcement . New York: Appleton-Century-Crof ts , 1957. Feshbach, S., Adelman, H. , & Fuller, W.W. Early identification of children with high risk of reading failure. Journal of Learning Disabilities , 1974, 10, 639-644. Gaasholt, M. Precision techniques in the management of teacher and child behaviors. Exceptional Children , 1970, 37_(2) , 129-135. Galante, M.C., Flye , M.E., & Stephens, L.S. Cumulative minor defects: A longitudinal study of the relation of physical factors to school achievement. Journal of Learning Disabilities , 1972, 5_, 75-80^. Gallagher, J.J., & Bradley, R.H. Early identification of developmental difficulties. In I.J. Gordon (Ed.), Early childhood education: The seventyfirst yearbook of the National Society for the Study of Education (Part II). Chicago, Illinois: Distributed by the University of Chicago Press, 1972. Glazzard, M. The effectiveness of three kindergarten predictors for first-grade achievement. Journal of Learning Disabilities , 1977, 10, 95-99. Great Falls Montana precision teaching project training manual, 197 y. Great Falls, Montana: Distributee by the Sacajawea Plan National Diffusion Network, Great Falls Public Schools, 1979.

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102 Hanby, V.L. Measuring oral language performance of preschool children . Unpublished working paper. Experimental Education Unit, Child Development and Mental Retardation Center, University of Washington, 1975. Haring, N.G., £ Ridgway , R.W. Early identification of children with learning disabilities. Exceptional Children , 1967, 33_, 387-395. Haughton, E. Counting together: Precision teaching rationale69 . Eugene, Oregon: College of Education, University of Oregon, 1969. Haughton, E. AimsGrowing and sharing. In S.W. Bijou, O.R. Lindsley, S E. Haughton (Eds.), Lets < try doing something else kind of thingBehavioral principles and the exceptional child . Arlington, Virginia : Council for Exceptional Children , 1971. (a) Haughton, E. Correlation of say sounds to say words . Behaviorgrams , Article 061 , 1971 . (b) Hayden, A.H. Perspectives of early childhood education in special education. In N.G. Haring (Ed.), Behavior of exceptional children: An introduction to special education . Columbus, Ohio: Charles E." Merrill, 1 9 7 M. Hayden, A.H., S Haring, N.G. Early intervention for high risk infants and young children: Programs for Down's Syndrome children. In T.D. Tjossem (Ed.), Intervention strategies for high risk infants and young children . Baltimore: University Park Press, 1976. Hoffman, M.W. Early indications of learning problems. Academic Therapy , 1971, 7, 23-35. Jenkinson, M. Ways of teaching. In R.C. Staiger (Ed.), The teaching of reading . Lexington, Massachusetts: Ginn, 1973. Johnson, N . Data published in the Behavior Bank . Kansas City, Kansas: Behavior Bank, 1971. Johnston, J.M., £ Pennypacker, H.S. Strategies and tactics of human behavioral research . Boston: Houghton-Mifflin, 1980.

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103 Keogh, B.K., 8 Becker, L.D. Early detection of learning problems: Questions, cautions, and guidelines. Exceptional Children , 1973, 40_, 5-12. Keogh, B.K., 8 Smith, C.E. Group techniques and proposed scoring system for the Bender Gestalt Test with children. Journal of Clinical Psychology , 1961, 17, 17 2-17 5. Keogh, B.K., 8 Smith, C.E. Early identification of educationally high potential and high risk children. Journal of School Psychology , 1970, 8, 285-290. Kirk, S.A. Early education of the mentally retarded: An experimental study . Urbana , 111.: University of Illinois Press, 1958. Koenig, C.H. Charting the future course of behavior (Doctoral dissertation, University of Kansas, 1972). Dissertation Abstracts International , 1972, 33 , 3071A-4586A. (University Microfilms No. 73-1850,70) Koenig, C.H. Personal comminication with author, 1980. Koenig, C.H. Precision teaching with emotionally disturbed pupils . Unpublished master's thesis , University of Kansas, 1967. Kottmeyer, W. Readiness for reading. Elementary English , 1947, 2_4, 3 5 5-36 6. Kunzelman, H.P. (Ed.), Precision Teaching . Seattle, Washington: Special Child Publications, 1970. Lessler, K. , £ Bridges, J.S. The prediction of learning problems in a rural setting: Can we improve on ^ readiness tests? Journal of Learning Disabilities , 1973, 6_, 90-94. Liberty, K.A. Data decision rules . Unpublished working paper. Experimental Education Unit, Child Development and Mental Retardation Center, University of Washington, 1975. Lindsley, O.R. Direct measurement and prosthesis of retarded children. Journal of Education , 1964, 147 , 62-81. Lindsley, O.R. Precision teaching in perspective: An interview with Ogden R. Lindsley. Teaching Exceptional Children , 1971, 3(3), 114-120.

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104 Lovitt, T. Personal communication with author, 197 6. Lovitt, T., Kunzelmann, H. , Nolen, P., £ Hulten, W. The dimensions of classroom data. Journal of Learning Disabilities , 1968, 1(12), 710-781. Lyons, J.S., £ Bangs, T. Effects of preschool language training on later academic achievement of children with language and learning disabilities: A descriptive analysis. Journal of Learning Disabilities , 1972, 5, 585-592. Magliocca, L.A., Rinaldi , R.T., Crew, J.L., £ Kunzelmann, H.P. Early identification of handicapped children through a frequency sampling technique. Exceptional Children , 1977, 43, 414-420. Mercer, CD. Preliminary review of early identification indices for learning disabled children . Paper presented at the meeting of the Conderence of the State of Florida Association for Children with Learning Disabilities, Tampa, Florida, 1975. Mercer, CD., Algozzine, B., £ Trifiletti, J. Early identificationAn analysis of the research. Learning Disability Quarterly , 1979, 2_, 12-24. Mercer, CD., S Mercer, A.R. Teaching students with learning problems . Columbus: Charles E. Merrill, 1980. Mercer, CD., £ Trifiletti, J.J. The development of screening procedures for the early detection of children with learning problems. The Journal of School Health , 1977, 47_, 526-532. Nie, N.H., Hull, C.H., Jenkins, J.C, Steinbrenner , K. , £ Brent, D.H. Statistical package for the social sciences New York: McGraw-Hill , 1975 . Pace, R.C An evaluation of learning screening as a child find procedure (Doctoral dissertation, University of Utah, 1979). Dissertation Abstracts International , 1979, 40, 1121A-2306A. (University Microfilms No. 7922389, 124) Pasamanick, B., Rogers, M.E., £ Lilienfeld, A.M. Pregnancy experience and the development of behavior disorder in children. American Journal of Psychiatry , 1965, 112 , 613-618.

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105 Pennypacker , H.S. Handbook of the standard behavior chart . Kansas City, Kansas: Precision Media, 1972. Satz, P., £ Priel, J. Some predictive antecedents of specific reading disability: A preliminary two year follow-up. Journal of Learning Disabilities , 1974^, 7, 437-444. Satz, P., £ Friel, J. The predictive validity of an abbreviated screening battery: A preliminary cross validation study . Manuscript submitted for publication, 1976. Satz, P., Friel, J., £ Rudegeair, F. Some predictive antecedents of specific reading disability: A two-, threeand four year follow-up. In J.T. Guthrie (Ed.), Aspects of reading acquisition . Baltimore: Johns Hopkins Press, 1976. Satz, P., Taylor, H.G., Friel, J., £ Fletcher, J.M. Some developmental and predictive precursors of reading disabilities: A six year follow-up . Manuscript submitted for publication, 1977. Sidman, M. Tactics of scientific research . New York: Basic Books, 1960. Skeels, H.M. Adult status of children with contrasting early life experiences. Monographs of the Society for Research in Child Development , 1966, 31 ( 3 ) , T7-121 Skinner, 3.F. Some contributions of an experimental analysis of behavior to psychology as a whole. American Psychologist , 1953, 8_, 69-73. Skinner, B.F. Contingencies of reinforcement: A theoretical analysis . New York: AppletonCentury-Crofts, 1967. Speer, 0., £ Lamb, G. First grade reading ability and fluency in naming verbal symbols. The Reading Teacher , 1976, 2_6, 572. Starlin, C. Evaluating progress in reading. In S. Bateman, (Ed.), Learning Disorders IV . Seattle: Special Child Publications, 1970. Starlin, C. Peers and precision. Teaching Exceptional Children, 1971, 3(3), 129-133.

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106 Stiles, R.L. Stepwise multiple regression study of SST basic movement cycle data with SFTAA/CTBS results from 348 third grade pupils . Tacoma , Washington: Tacoma Public Schools, Pupil Personnel Services Research Department, 197 3. Stimbert , V.E. A technology of preschool education. Educational Technology , 19 71, 11(2), 9-13. Thomas, S.L. An analysis of reading rate improvement in grades two, four, and six (Doctoral dissertation, Montana State University, 1972). Dissertation Abstracts International , 1972, 3_3_, 3071A-4586A. (University iMicrofilms No. 73-2649, 135) Tjossem, T.D. Early intervention: Issues and approaches In T.D. Tjossem (Ed.), Intervention strategies for high risk infants and young children . Baltimore: University Park Press, 1976. Tomaras , S.N. Timed math in the first grade . Tacoma, Washington! SST Project, 1974. (a) Tomaras, S.N. Trace to write numbers in first grade . Tacoma, Washington: SST Project, 1974. (b) Trifiletti, J.J., Rainey, N.S., £ Trifiletti, D.T. Sequential Precision Assessment Resource Kit II . Archer, Florida: Precision People, 1979. Waldrop, M.F., £ Goering, J.D. Hyperactivity and minor physical anomalies in elementary school children. American Journal of Orthopsychiatry , 1971, 41, 602-607. Waldrop, M.F., Pedersen, F.A., £ Bell, R.A. Minor physical anomalies and behavior in preschool children. Child Development , 1958, ~3_9, 391-400. White, O.R. Working paper number 15. The prediction of human performance in the single case: An examination of four techniques . Eugene , Oregon : Regional Resource Center for Handicapped Children, 1972. (a) White, O.R. Working paper number 16. A namual for the calculation and use of the median slopeA technique of progress estimation and prediction in the single case . Eugene , Oregon : Regional Resource Center for Handicapped Children, 1972. (b)

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107 White, O.R., 8 Haring, N.G. Exceptional teaching multimedia training package . Columbus, Ohio: Charles E. Merrill, 1976/ Wiederholt, J.L., Hammill, D.D., £ Brown, V. The resource teacher: A guide to effective practices . Boston: Allyn £ Bacon, 1978. Wilborn, B.L., £ Smith, D.A. Early identification of children with learning problems. Academic Therapy , 1974, 9, 363-371. Wolking, W.D. Personal communication with author, 1980. Wolking, W.D., £ Schwartz, S. Rate of growth toward adult proficiency: Differences between high and low achievement children, grades 1-6 . Paper presented at the International Symposium of Learning Disabilities, Miami Beach, Florida, October 1973.

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APPENDIX A DEFINITIONS accuracy Accuracy is a measure of the correctness of academic performance. It is calculated as the ratio of correct items to total items on a test, expressed as a percent. celeration Celeration is the rate of change in frequency of behavior over time. Acceleration is an increase in frequency over time. Deceleration is a decrease in frequency over time. celeration value The celeration value is the rate of change in frequency of behavior over a period of one week. The unit of celeration is movements per minute per week. criterion A criterion is a specified value for a dimension of academic performance of concern in an instructional intervention. Another term used interchangeably with criterion is performance standard. fl uency Fluency represents the rate or speed of performance. frequency Frequency is defined as the number of movements per minute of observation time. 108

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109 initial assessment For this study initial assessment refers to the measurement of academic performance during the five days prior to the onset of specific instructional activities. minimum celeration The minimum celeration is the least amount of weekly change in frequency judged acceptable. mixed skill probe A mixed skill probe contains items from a number of different skills for purposes of assessment of academic performance. For example, the mixed skill probe for addition might contain items representing all of the basic addition facts. movement A movement is a discrete, observable, countable, and repeatable unit of behavior. Examples of academic movements include writing digits, saying words, and pointing to pictures on cards. operant conditioning Operant conditioning is a series of procedures and techniques whereby behavior is controlled by antecedents and consequents in the immediate environment. precision assessment Precision assessment is a procedure described by White and Haring (1976) which uses frequency measurement of academic performance to identify and describe deficient skills. precision teaching Precision teaching is an instructional system developed by Lindsley (1971) which uses frequency measurement of academic performance to optimize learning.

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110 prerequisite skill A prerequisite skill forms part of the movement of a more complex skill. A prerequisite skill is also called a tool skill, probe A probe is a device, instrument, or period of time used to sample a learner's performance of a skill, rate Rate is a term used in educational measurement to describe frequency, the number of movements divided by the observation time in minutes. single skill probe A single skill probe contains a number of assessment items representing a single skill. An example is a stimulus sheet containing times 3 multiplication problems. tool skill A tool skill is a skill considered prerequisite to a more complex skill. For example, writing digits is prerequisite to solving two-digit multiplication problems. tool skill probe A tool skill probe contains items representing a single prerequisite skill. variability For this study variability is defined as the sum of squared deviations from a least squares regression line plotted through frequency correct values of a learner's academic performance.

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APPENDIX B DESCRIPTION OF SPARK II INSTRUMENT Precision assessment is a procedure for targeting deficient skills in a learner's repertoire. Precision assessment is used for both initial assessment and continuous monitoring of academic performance. The SPARK II instrument allows measurement of correct and error frequencies of performance. This performance data is used for instructional decision making, as well as setting realistic goals and expectations for learning. The basic technique of SPARK II is the timed performance sample or probe. After giving directions, probe items are presented and the learner's performance is recorded over a short period of time, usually one minute. A probe consists of the directions and/or items presented to the learner, the learner's performance, and the timed format. Since every academic skill in the learner's repertoire need not be assessed in depth, SPARK II includes two types of probes: mixed skill probes and single skill probes. Mixed skill probes have many different academic skills and are used for quick assessment in order to narrow the range of possibly deficient skills. Ill

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112 Single skill probes contain items representing only one specific skill. For example, the single skill probe for addition facts 7's contains only simple addition problems with "7" as one of the addends in every item. Single skill probes are timed for one minute and scored for frequency correct and frequency errors. They form the baseline for continuous monitoring of academic performance as the learner moves toward mastery of the skill. For organizational purposes the skills assessed by SPARK II are arranged in strands. A strand is a list or a sequency of skills which build toward a complex academic behavior such as addition. SPARK II includes strands for math readiness, addition, subtraction, multiplication, division, fractions, money, time, reading readiness, reading sight words, phonetic reading, structural analysis reading, manuscript writing, and cursive writing. Following initial precision assessment with SPARK II instruction begins on the deficient skills that have been selected. The data from the single skill probes are charted and displayed to form a brief baseline of initial performance. During the instructional period, single skill probes will be administered daily, or as frequently as possible. Observation of the daily performance on single skill probes allows instructional decisions to optimize instruction. These instructional

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113 decisions generally include alterations in directions, instructional materials, and contingencies. SPARK II is a criterion referenced instrument capable of measureing academic performance for over 350 skills. It has been designed as a classroom assessment instrument which can function in a precision teaching environment .

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APPENDIX C FORTRAN PROGRAM FOR COMPUTERIZED CHARTS AND SUMMARY STATISTICS The following computer program is written in Fortran programming language. The program accepts data cards in which the first data card must be the number of data cards per case minus one. This must be followed by the data cards for each case. Each case begins with a triad card with the teacher's name in columns 1-19, learner's name in columns 20 38, and task name in columns 39 80. The data cards for each case which follow the triad card must contain three digit integer values seperated by single spaces for day, count of correct movements, and count of error movements, respectively. Blank cards must be added to each case to insure the same number of cards per case. The day value preceeding a phase change must have a negative sign. An example of the charts produced by this computer program has been included in Appendix D. A copy of the program in BASIC programming language designed for interactive use with the Radio Shack TRS-80 Model II computer is available by request from the experimenter • 114

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115 DIMENSION RD(oO),RF(bO),XA(bO),RA(60),AA(bO)»UA(bO),i*i>(bU), ! JF(bO) INTEGER D(bO), F(bO), A(o0), C(bO) INTEGER E,Q,M1,L9,LE INTEGER AP(bO)/' '/, AX(bO)/' '/, PP(60)/« '/, PX(bO)/' '/ INTEGER DT(bO), FT(bO), AT(bO) INTEGER T(19)/' '/, L(19)/' '/, TASKC42)/' •/ INTEGER l\, Id, 11, bLANK, X, EYE, AN, ERR DATA BLANK/' '/ DATA X/'O'/ DATA EYE/' I '/ DATA ERR/'X'/ DATA Zl/'M '/ DATA Z2/'K V DATA Z3/'F '/ ****************** GET ThL UATA READ ************************* READ (b,222) i'^DATA £22 FORMAT (II) NDATA = NDATA * 6 23 READ (5,21,END=99) ( T CJ ) , J = l , 19) , (L ( J) , J=l , 19) , (T ASK C J ) , J= 1#«2) 21 FORMAT (80A1) N = READ Cb,u5) (DTU), F T ( 1 ) , AT(I), 1 = 1, NDATA) 4b FORMAT(ie(I3#lX)) DU «7 I=l,bO IF (DT(I) .EU. 0) GO U) 47 NsN+1 D(N)sDTd) FCN)=FT(1) ACN)sAT(l) a7 CONTINUE DO 9a2 1=1, N QD(I)=FLUAT(f>(D) QF(I)=FLl)AT(F(I)) QA(I)=FLOAT(A(I))

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116 9«2 CONTINUE DO 683 1=1, N IF(QFd).NE.O) GO TO 657 QA(I)=0.0 GO TO 683 657 QA(I)=(QF(I)/(QF(I)+QA(I)))*10 0.0 683 CONTINUE C C *************** FIND THE LARGEST AND LUWEST FLUENCY VALUE C LOW = F(l) 20 LARGt=0 DO 24 1=1, N IF (F(I) .GT. LARGE) LARGE=F(I) IF (F(I) .LE. LOW) LOW = F(I) 24 CONTINUE C C *********** PRINT HEADER AND FIRST 5 LINES OF FLUENCY GRAPH C LI = LARGE + 5 L2 = LARGE t 4 L3 = LARGE t 3 La = LARGE t 2 L5 = LARGE + 1 WRITE (6,25) (T(J),Jsl,19),(L(J),Jsl,19), ( TASK ( J) , J = l , 42) , L 1 , L2, * L3,L4,L5 25 FORMAT (*1'.»//10X» 'TEACHER = ',19A1, 5X, 'LEARNER = ',19A1, 5X, *'TASK = ',42A1,//40X, 'GRAPH OF FREQ. CORRECT ' , 5 C/5X, 13, 1 X, • I • ) ) C C ********* LOAD DUMMY VECTORS WITH CHARTING MARKS ********** C LARGE = LARGE + 1 DO 28 Ksl, LARGE DO 2b 1=1,60 PP(I) = BLANK PX(I) = BLANK

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117 26 CONTINUE DO 27 J=1,N IF (F(J) .EU.(LARGE-K))PX(IABS(D(J))) = X IF (D(J) .LT. 1) PP(IABS(0(J))) = EYE 27 CONTINUE C **************** TRUNCATE LARGE CHARTS ******************** C PRINT THE FLUENCY CHART C NS = LARGE K WRITE (6,29) NS, (PP(J), J=l,60) 29 FORMAT (5X,I3,1X, • I ' ,2X,60(A1, IX)) WRITE (6,30) (PX(J), J=l,60) 30 FORMAT ( '• , 10X,60(A1, IX) ) IF ((LARbL-LUW) .GE. 05 .AND. NS .EO. (LOW-5)) GO TU 100 28 CONTINUE C C **************PK'INT THE BOTTOM OP THE FLUENCY GRAPH ********* C 100 WRITE (6,31) 31 FORMAT (' + •., 9X,120('-')) WRITE (to, 33) Z1,Z2,Z3,Z1,Z2,Z3,Z1,Z2,Z3,Z1,Z2,Z3,Z1,Z2,Z3,Z1,Z2, * Z3,Z1,Z2,Z3,Z1,Z2,Z3,Z1 33 FORMAT ( 1 1 X , 8 ( A4, A4, Aa, 2X ) , A4) C C *********** PRINT ACCURACY CHART ************************* C DO 109 1 = 1, N F(I)=F(I)+A(I) 109 CONTINUE WRITE (6,107) 107 FORMAT (////SIX, 'GRAPH OF ACCURACY (X CORRECT )',// ) DO 101 1=1 , N RF(I)=FLOAT(F (I)) RAUmLUAT(AUn G = RF(1) RA(I)

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11! IF (G .GT. 0.0) GO TO 302 RA(I) = 0.0 A(I) = GO TO 409 302 RA(I) = (G/RF(I))*100.0 A(I) = (G/RFU))* 100.0 A(I) = ACI) / 5 A(I) = A(I) * 5 «09 RD(I)=FLOAT(D(l)) 101 CONTINUE LARGL = 105 DO 102 1=5,105,5 NS = LARGE-I DO 103 K=l,60 AX(K) = HLANK PP(K) = BLANK 103 CONTINUE DO 104 J=1,N IF CACJ) .EQ. NS) AX(IAUS(D(J))) = ERR IF (D(J) .LT. 1) PPCIADS(DCJ))) = EYh 104 CONTINUE WRITE (6,105) NS, (AX(J),J=l,b0) 105 FORMAT (5X , 13, IX, ' I • , 1 X , 60 ( A 1, IX) ) WRITE (6,110) (PP(J), J=l,b0) 110 FORMAT (' + '., 11X, 60(A1,1X)) 102 CONTINUE WRITE (6,31) WRITE (6,33) Z1,Z2,Z3,Z1,Z2,Z3,Z1,Z2,Z3,Z1,Z2,Z3,Z1,Z2,Z3,Z1,Z2, * Z3,Z1,Z2,Z3,Z1,Z2,Z3,Z1 WRITE(6,13) 13 FORMAT (///15X,'N',5X,'FCEL',7X,'ACEL',6X,'FSL0PE',4X,' ASLOPE «,3X, •FMEAN'^X^AMEAN'^X.'FMAX'^X^AMAXSeX^FVARSHX, 'AVAK-, *2X,'FMLDIAN')

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119 ********************* CELERATIONS ************************* N IS THE TOTAL NUMBER UF DAYS IN THIS TRIAD J POINTS TO THE FIRST DAY OF THE NEW PHASE LL IS A PHASE COUNTER K COUNTS THE DAYS WITHIN A PARTICULAR PHASE JJ = 1 LL = 8 K = 9 DO 75 I=JJ,N J = I + 1 K = K + 1 IF (D(I) .LT. 0) GO TO 07 75 CONTINUE 67 JJ = J IF(K.LT.2.AND.J.GE.N) GO TO 23 LL = LL + 1 IF (K .LT. 2) GO TO 8 L2 = J-l LI = J-K QD(L2)=AbS(0D(L2)) DO 207 1K=L1,L2 II=IK-Lltl AA(II)=UF(IK) 207 CONTINUE HtAPSURT DATA FOR MEDIAN ************ c

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120 121 125 209 917 921 925 213 205 IFCJT.EU.M) GO TO 121 IF(AA(JT+1).GT.AA(JT)) JT=JT+1 IFCB.Gl.AA(JT)) GO TO 125 AA(IP)=AA(JT) IP = JT GO TO 117 AA(IP)=B CONTINUE. 11 = 1 MT=K-1 DO 213 MMsl,MT MsK-MM B=AA(M+1) AA(M+1)=AA(1) IP = II JT=IP*IP IF(JT.GT.M) GO TO 925 lF(JT.LU.M) GU TO 921 IF(AA(JT+1).GT.AA(JT)J JT=JT+1 IF(B.GE.AAUT)) GO TU 925 AA(IP)=AA(JT) IP = JT GO TO 917 AA(IP)=b CONTINUE XE=AA((K/2)*1) IF((K-(2*(K/2))).EQ.O) XE= ( ( AA (K/2) ) + ( AA ( (K/2) t 1 ) » /d SXY=0.0 SX = 0.0 SY = 0.0 SXS = 0.0 ASXY=0.0 ASX=0.0 ASY=0.0 ASXS=0.0 SA=0.0

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121 FC=O.G AC=0.0 DO 11 I=L1,L2 SA=SA+0A(1) IF(&F(I) .GE. FC) FC=UFCI) lFCUA(I) .&L. AC) AC=UA(I) SXY = SXY*(UD(I)*CJF (I)) SX=SX+QD(I) SY = SY + GIF(I) SXS=SXS+(OD(I)**2) ASXY = ASXY+(QD(I)*UA(JJ) ASX=ASX+QD(I) ASY = ASY-MJA(I) ASXS=ASXS+(GD(I)**2) 11 CONTINUE XK = K XD2=UD(Ll)+7.0 XD1=G)D(L1) Dl = XK*SXY 02 = SX*SY D3 = XK*SXS Da = SX**2 P1=D1-D2 IF(Pl.Nt.O) GU TU 303 B1=0.0 GO tu aio Bl = (Dl-D2)/CD3-Da) IF(SA.NE.O) GO TO 601 AM=0.0 GO TO 60S AM=SA/XK 605 IF(SX.NE.O) GO TU 611 XM=0.0 GO TO 612 611 XM=SX/XK 612 IF(SY.NE.O) GO TO 613 YM = 0.0 303 410 601

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122 613 614 91 411 304 616 617 618 619 * XD1) * XD2) 92 CU TO 614 YM=SY/XK B0=YM-(B1*XM) YF = BO + (Bl YS = BO + (Bl SE=0.0 DO 91 I=L1,L2 SEP=B0+(B1*QD(I)) SE=SE+((QF(I)-SEP)**2) CONTINUE D5=XK*ASXY 06=ASX*ASY D7=XK*ASXS D8=ASX**2 P1=D5-Db IF(Pl.NE.O) GO TO 411 AB1=0.0 GO TO 304 AB1=(D5-D6)/(D7-D6) IF(ASX.NE.O) GO TO 616 AXMbO.O GO 10 617 AXM=ASX/XK IF(ASY.NE.O) GU TO 616 AYM=0.0 GO TO 619 AYM=ASY/XK AB0=AYM-(AB1*AXM) AYF = ABO + (AB1 * XD1) AYS=AB0+(AB1*XD2) SLAsO.O DO 92 I=L1,L2 SEAT=AB0t(ABl*UD(D) SEA=SEA*((QA(I)-SLAT)**2) CONTINUE PlsYF-YS

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123 IFCPl.NE.O) GU TO 89 CELsl.O GO TO 63 69 IFCYF.fcU.O. AND. YS. GT.O) GO TG 958 GO TO 9«8 958 YF=YF+1.0 YS=YS+1 .0 9aB IF(YF. GT.O. AND. YS.LT.O) GO TO 955 IF(YF.LT.O.AUD.YS.GT.O) GU TO 956 IF(YF. GT.O. AND. YS. GT.O) GO TU 957 955 YF=YS-(AUS(YS)+YF) CLL=-1.0*(YF/YS) GO TO fa3 956 YF=(2*YS)+ABS(YF) CLL=YF/YS GO TO 63 957 IF(YF.GT.YS) CEL=-1 . 0* C YK/YG) IF(YS.GT.YF) CtL=YS/YF 63 P1=AYF-AY5 IF(Pl.fJt.O) GO TO 88 ACll=1.0 GO TO 80 68 IFUYF. EQ.O. AND. AYS. GT.O) GO TO 81 GO TO 82 81 AYF=AYFtl.O AYS=AYStl.O 82 IF (AYF .GT.O. AUO.AYS.LT. 0) GU TO 83 IFUYF. LT.O. AND. AYS. GT.O) GO TU 8a IFUYF. GT.O. AND. AYS. GT.O) GU TO 85 83 AYF=AYS-(ABS(AYS)+AYF) ACEl«-l.O*(AYF/AYS) GO TO 80 84 AYF=(2*AYS)tABSCAYF) ACEL=AYF/AYS GO TO 80 65 IFUYF. GT. AYS) ACtL=1 . 0* ( AYF /AYS)

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124 ec 65 99 IFUYS.GT.AYK ) ACtL = A Y5/ A YfHR1TE.C6#65) LLr K, CEL, ACLL, Ul , Abl , YM# AM,F-C, AC , SE» SLA, At FORMAT C///1X, 'PHASE • y 2(i3»3X)»8(F7.3»3X)»2CF10.i#iX) # F'O.^J IF(J .GL. fJ) Gu Tb ^3 GO TO 6 STOP END

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APPENDIX D SAMPLE FREQUENCY CHART The frequency charts contained on the following pages are an example of the computerized charts used in this study. The horizontal axes are the time in days. The vertical axes are the frequency in terms of movements per minute and accuracy in terms of percent correct movements. A vertical column of I ' s represents a phase change. The first phase represents baseline assessment phase. The following phases are instructional phases. At the bottom of the accuracy chart are a number of summary statistics listed by phase. The statistics are defined as follows : N Number of data points FCEL Frequency celeration value ACEL Accuracy celeration value FSLOPE Frequency slope value ASLOPE Accuracy slope value FMEAN Frequency mean value AMEAN Accuracy mean value FMAX Frequency maximum value AMAX Accuracy maximum value FVAR Frequency variability value AVAR Accuracy variability value FMEDIAN Median frequency value 125

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126

PAGE 133

127 j"t o I ^J oLnoi/*oj"»o j"»ou"»oj"» :

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APPENDIX E SYLLABUS OF TEACHER TRAINING SESSION I. Initial Precision Assessment II. How to Use SPARK II III. Types of Probes A. Tool Skill Probes B. Mixed Skill Probes C. Single Skill Probes IV. How to Administer Probes V. When to Administer Probes VI. Recording Assessment Data VII. Selecting Instructional Targets VIII. Recording Instructional Data IX. Phase Changes and Instructional Decision Making X. Setting Performance Standards 128

PAGE 135

BIOGRAPHICAL SKETCH John J. Trifiletti was born at Clearwater, Florida, on June 7, 1947. After attending elementary schools in Mammaroneck and Harrison, New York, he returned with his family to Clearwater at the age of seven. He graduated from Clearwater High School in 1965. After receiving the Bachelor of Arts in education from the University of Florida in 1970, he received a second Bachelor of Arts in psychology from the University of North Florida. In 1975 upon completion of a Master of Education degree in special education with an emphasis in learning disabilities, Mr. Trifiletti entered the doctoral program in special education in the area of learning disabilities at the University of Florida. Mr. Trifiletti has held teaching positions in regular education and special education. Experiences include education of prison inmates and secondary level varying exceptionalities. Administrative positions include Director of the Riverside Adult Group Living Home in Jacksonville, Florida, Diagnostic and Resource coordinator for the nine county Alachua, Florida region, and interim principal of the Secondary Center for Exceptional Student Education in Gainesville, Florida. 129

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130 Mr Trifiletti will complete requirements for the degree of Doctor of Philosophy in December, 1980. He has accepted a position as Coordinator of Education and Research for the Youth Study Unit of Hope Haven Childrens Hospital in Jacksonville, Florida.

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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 Fhilosophy . a dis: ertation for the degree of Doctor o uMiM William D. Wolking, Professor of Special 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 or Philosophy. , Charles Forgnone Professor of Special Pducation 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. & Cecil D. Mercer Professor of Special Education my op: t certify that I have read this study and that in )inion 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. . \ ,"' , T Bob Algozzine Professor of Special Education

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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 . Thorn Kodgsof Professor of Industrial and Systems Engineering This dissertation was submitted to the Graduate Faculty of the Department of Special Education in the College of Education and to the Graduate Council, and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. December, 1980 Dean for Graduate Studies and Research

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UNIVERSITY OF FLORIDA 3 1262 08552 9393


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UF00098073_00001.mets
METS:structMap STRUCT1 mixed
METS:div DMDID ORDER 0 main
D1 1 Main
P1 Page i
METS:fptr
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