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The effects of teaching set size on learning with special and regular education children

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The effects of teaching set size on learning with special and regular education children
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Mishkin, Michael L., 1951-
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viii, 126 leaves : ill. ; 28 cm.

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Developmental disabilities ( jstor )
Educational environment ( jstor )
Educational research ( jstor )
Learning ( jstor )
Learning disabilities ( jstor )
Learning rate ( jstor )
Mastery learning ( jstor )
Special education ( jstor )
Special needs students ( jstor )
Students ( jstor )
Counselor Education thesis Ph. D
Dissertations, Academic -- Counselor Education -- UF
Learning ability -- Psychological aspects ( lcsh )
Learning ability -- Testing ( lcsh )
Marion County ( local )
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bibliography ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (Ph. D.)--University of Florida, 1987.
Bibliography:
Bibliography: leaves 119-125.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Michael L. Mishkin.

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THE EFFECTS OF TEACHING SET SIZE ON LEARNING WITH SPECIAL AND REGULAR EDUCATION CHILDREN






By

MICHAEL L. MISHKIN


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


UNIVERSITY OF FLORIDA


1987

















ACKNOWLEDGEMENTS

I wish to acknowledge those people who contributed to the successful completion of this study.

Thanks go to Dr. William Wolking provided much

support, guidance, and patience as chairman of my doctoral committee. He helped me to blend my knowledge of education and psychology. Thanks also go to the other members of my committee: Dr. Janet Larsen, for her unflagging interest in and enthusiasm with my educational pursuits, and Dr. Robert Jester, for his humanistic approach to teaching me research design.

A special thanks go to my family. My parents, Arthur and Arlene Mishkin, have always encouraged me in my educational and professional endeavors. My twin sister, Marilyn, sought similar educational pursuits and lent me support and encouragement during all of my school years. My older sister, Francine, provided a model for high educational pursuits in my family.

Thanks go to Ms. Lisa Hurewitz, for her diligence and professional expertise in the preparation of this research manuscript.










I could not have conducted this research without the teacher assistants who collected the data. A special thanks also go to those six subjects in my study, Dorothy, Jesse, Keesha, Marketa, Matthew, and Mikki, whose involvement in this research may improve the learning experience for their peers.


iii
















TABLE OF CONTENTS


ACKNOWLEDGEMENTS ................................ ii
ABSTRACT ............................. *............. vii

CHAPTERS
I INTRODUCTION ......................... *........1

Overview of the Study ........................ 1
Significance of the Problem .................. 4
Statement of the Problem ..................... 6
Limitations and Delimitations of the Study... 7 Definition of Terms .......................... 7
Overview of Remainder of Dissertation ........ 9

II REVIEW OF THE LITERATURE ..................... 10

"Watered Down" Curriculum Approach ........... 11
Easy Task Learning Environments .............. 15
Within-Task Variables ........................... 18
Across-Task Variables ...................... 22
Summary .................................... 23
Precision Teaching ........................... 24
Studies on Hard-to-do Task Learning
and Leap Ups in Curriculum ............... 25
Summary .......29...................... 29
Recapitulation. ...... .. .. .. .. .. . ... .. .. . .... 30
III METHODOLOGY .................... .............. 32

Overview of the Study ........................ 32
Variables Under Investigation ................ 32
Independent Variable ....................... 32
Dependent Variables ........................ 33
Setting .............. ....................... 37
Subjects ..................................... 38












Experimental Design .......................... 39
Procedure ................................... 42
Pre-experimental Phase .................... 42
Experimental Phase ......................... 43
Material ..................................... 44
Curricular Materials ....................... 44
Data Recording Form ........................ 46
Data Recording and Analyses .................. 46
Data Recording ............................. 46
Data Analyses .............................. 47

IV ANALYSES AND RESULTS ......................... 49
Celeration ................................... 50
Total Learning Rate .......................... 60
Mastery ...................................... 61
Across Category Summary ...................... 62
Accuracy ..................................... 64
Recapitulation ......................... 68

V DISCUSSION AND CONCLUSIONS ....................... 70

Discussion ................................... 70
Uncontrolled Sources of Variance ........... 70
Significance of Set Size .................. 72
Significance of Initial Level of
Difficulty .................. 73
Limitations of the Sample.................. 74
Limitations by Set Size .................... 74
Limitations by Treatment Design ............ 75
Implications for Teachers .................. 75
Implications for School Psychologists ...... 76 Recommendations for Future Research ........ 78
Conclusions ........................ 80


APPENDICES

A EXCEPTIONAL STUDENT EDUCATION PROGRAM
ELIGIBILITY REQUIREMENTS ......................... 81

B WORD LISTS ..................................... 84

C DATA RECORDING FORM .......................... 108












Page

D FREQUENCY MULTIPLIERS FOR CELERATIONS,
MASTERIES, AND ACCURACIES .................... 100

REFERENCES ......................... o ****......... 118

BIOGRAPHICAL SKETCH.............................. 125














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

THE EFFECTS OF TEACHING SET SIZE ON LEARNING
WITH SPECIAL AND REGULAR EDUCATION CHILDREN By

Michael L. Mishkin

December 1987

Chairman: Dr. William D. Wolking Major Department: Counselor Education

This study was designed to assess the effects of large task size versus small task size on the learning of special and regular education children.

A single subject design with one replication per

subject was used with six subjects. Two subjects each were learning disabled, educable mentally handicapped, and regular education. Each pair of subject types was randomly selected from a pool of subjects of the respective educational classification.

Each subject was given a pretest to identify 30 words

the subject could not spell correctly. Each word chosen was randomly assigned to either a 10-word list or a 20-word list. Each subject's performance was measured once a day with each word list. Upon mastery of the spelling words,


vii











a new pretest was given and an identical procedure was followed in the replications involving the new words.

The study involved four dimensions of students' spelling performance. Three of these dimensions were measures of learning or change in spelling performance over time. The last dimension was the degree of mastery of the spelling material. Initial accuracy of spelling on the first day of data collection was also examined. Differences between these dependent variables were obtained, and an arbitrary standard of a 5% difference between these variables for different task sizes was the criterion of comparison used to suggest a practical difference.

Mixed results were found within and across subjects and exceptionalities. Set size did not systematically or exclusively affect learning outcomes. Initial level of difficulty also did not systematically control learning. These findings support the conclusion that the easy task curriculum approach may not always be best. Some students, on some occasions, can improve faster with larger than traditional set sizes. Greater understanding of larger than traditional teaching set size curriculum strategies is needed to maximize students' learning.


viii
















CHAPTER I

INTRODUCTION

Overview of the Study

Special education placement of academically

disadvantaged students has been a major issue since passage of Public Law 94-142. This federal law requires every handicapped child and youth to be provided special education and related services at public expense. Special education involves use of specially designed instruction to meet the unique needs of handicapped children. Public Law 94-142 also requires these children to be placed in the least restrictive educational environments, with as much time spent in regular education classes as possible.

Research findings related to educating exceptional children in regular education settings, as reviewed by Corman and Gottlieb (1978), suggested that instructional techniques are more important to improved academic achievement than the setting in which children learn. However, in light of available evidence which has pointed toward the lack of academic achievement, questions have been raised about the superiority of the social environment provided by the special class (Siegel, 1969; Sparks & Blackman, 1965).











Precision teaching, a rapidly expanding technology of teaching and learning, has facilitated accurate accumulation of data on students' learning rates. Until recently, precision teachers employed an "easy task" or simplified approach to teaching exceptional students. In this approach teachers selected tasks with few or no errors and worked on improving the speed of responding. Typically the instruction was boring and rates of learning frequently were low.

Since 1978, precision teaching research has been done (e.g., McGreevy, 1980) that suggested greater learning could be accomplished when learning environments included initially hard-to-do tasks. McGreevy's early work in this area (McGreevy, 1978) led him to believe that children did not need easy-to-do tasks to stay motivated and could learn more with initially high error rates. Johnson (1961, cited in Johnson, 1962) had earlier concluded that little learning could take place when much of the motivation or drive to achieve had been removed from the learning environment, as was the case with exceptional student education classes whose main objective was to reduce academic frustration.

Bijou (1970) indicated that the school psychologist should work to prevent academic retardation. However, school psychologists have usually not been involved with direct teaching processes except as consultants. In the










context of school psychology, consultation can be defined as

a process of interaction between two
professional persons--the consultant, who is a specialist, and the consultee, who invokes the consultant's help in regard to a current work
problem with which he is having some difficulty
and which he has decided is within the other's
area of specialized competence. (Caplan, 1970,
p. 19)



Consultation with both regular and exceptional

student education teachers can help create intervention techniques that improve the academic performance of students in the classroom. Such consultative work conducted prior to a full-fledged psychological evaluation could be advantageous. Observation and evaluation of the teaching-learning process itself could provide the classroom teacher with more immediate feedback than would feedback from a child's participation in an exceptional student education program for several weeks. Communications between the teacher and school psychologist in a consultation situation also would be easier to carry out than the communications among the individual education plan committee members responsible for the child's special program placement. This consultation could also serve to reduce caseload demands on special education teachers, allowing them to provide more attention to needier students.










Significance of the Problem

There has been little research on the learning of

special education students who are given academic tasks of different teaching set sizes. Set size refers to the number of unique items to be learned. The basic premise of traditional teaching methods is that a larger teaching set size is more difficult to learn than a smaller teaching set size. Should curricular environments with a larger teaching set size prove to provide learning rates comparable to curriculum environments with a smaller teaching set size, then questions may be raised about the traditional teaching methods of special education students that involve easy to learn tasks and low error rates. Moreover, it was believed that study of this variable should provide more useful information about generalizability of findings if regular education students were included in this study. Certain results could affect existing teaching approaches toward children of all ability levels.

School psychologists, in their evaluation of children for special education classes, assist educators in placing children in a curriculum in which error rates are low. For those children who do not thrive in such a curricular environment further consultation may be needed. It is therefore important for school psychologists, who must consult with special education teachers, to develop











techniques to enhance the learning rates of students. Development of these techniques will not only allow the school psychologist to break from the traditional role of diagnostic evaluations, but will also provide school psychologists with more data about the teaching process with which to improve their role as consultants.

Standardized instruments for assessment of academic progress may not be sensitive enough measures of academic performance, nor are they easily interpretable by teachers. It would be helpful to the school psychologist if appropriate curriculum-based and criterion-referenced assessment tools were available. Significant results, relating the size of the teaching set to change in learning and improvement in accuracy for special and regular education students, would provide valuable information for both the practitioner and the researcher in the areas of assessment and applied learning tactics.

Having more accurate assessment information, as well as a greater understanding of larger than traditional teaching set size curriculum strategies, also would enable consultants to help teachers and administrators to design teaching strategies tailored to the child's best advantage. Placement of the learning disabled or educable mentally handicapped student in an exceptional student education program would then become a more selective process. Those students who could excel with a larger











than traditional set size could be differentiated from those who still needed the traditionally small set-small step (easy task) approach to instruction. Progress in the special class also may be faster if a larger set size is used, and the learner may gain increased confidence in his or her abilities.

Researchers interested in curriculum strategy issues may find results from this study to be useful in furthering the understanding of learning rates under curriculum environments using a small teaching set size versus a large teaching set size. Although this issue has recently been examined in the precision teaching literature (Bower & Orgel, 1981; McGreevy, 1978), relatively less is known about this approach in the context of traditional (i.e., nonprecision teaching) strategies of teaching. More research is clearly needed.



Statement of the Problem

The focus of this study was the effects of large teaching set size versus small teaching set size on students' learning rates. The following question was investigated: What are the effects of two set sizes (small set size comprised 10 spelling words, large set size comprised 20 spelling words) on several measures of learning and performance with educable mentally











handicapped, learning disabled, and regular education students?



Limitations and Delimitations of the Study

Interpretations of the results of this study need to be made in light of certain delimitations. The subjects lived in Marion County, Florida and had been referred for psychological evaluation to assess possible learning difficulties. This group was a special population whose characteristics may have influenced the results. The ages of the subjects were between eight and nine. The academic task chosen to be measured was spelling from dictation. The findings were further limited by such difficult to control factors as test anxiety and fine motor difficulties that may have been present in some of the subjects. The people used as teacher assistants were a bigger limitation. The children used were probably representative.



Definition of Terms

Many technical terms from precision teaching and behavior analysis are used in reporting this investigation. These terms are introduced throughout the first three chapters in their appropriate context and are defined below:

Accuracy - percentage of correct responses.











Celeration - change in frequency per unit of time;
measured by the ratio of two frequencies one week
apart drawn on a learning line.

Day line - vertical line on the standard behavior chart.

Fluency - final performance for rate correct and rate
incorrect (see mastery).
Frequency - basic unit of behavioral measurement; the
number of movements per unit of time (minute).
Frequency multiplier - value by which one frequency is
multiplied or divided to obtain a second; X assigned
when the second number is greater than the first;
/ assigned when the second number is less than the
first.

Learning - a change in performance per unit of time; also
called celeration.

Leap up - an upward curriculum change in scope and
sequence to a point where the student is making many
errors and few correct responses.

Mastery - percentage of performance standard achieved.

Mastery change - ratio obtained by dividing the ending
mastery by the beginning mastery.
Performance standard - criterion of minimum proficiency.

Precision teaching - comprehensive instructional system
for accelerating learning and maintaining high
proficiency, based on direct and continuous
measurement procedures.

Standard behavior chart - standard, six-cycle
semi-logarithmic chart that displays frequency as
movements per minute and learning as movements per
minute per minute.

Teaching set size - task size reported in terms of the
number of unique items to be taught.

Total learning measure - multiplier of the celerations
for correct responding and the celerations for error
responding combined.











Overview of Remainder of Dissertation

A review of the literature and a discussion of the theoretical frameworks underlying the various aspects of this study can be found in Chapter II. Implications for assessment tactics and applied learning are explored. Support for the instrumentation and assessment procedures are also presented.

The variables under study are listed in Chapter III. The population is described and sampling procedures are listed. Descriptions of the research design, research procedures, psychometric characteristics of participants, and data analysis procedures are provided. Methological limitations of the study are discussed.

Chapter IV contains the experimental findings. A discussion of the research questions in light of the results is also presented.

Chapter V contains a discussion of the results and conclusions. Uncontrolled sources of variance are explored first, followed by the significance of the findings of this study. Generalizability and limitations of the study are discussed next. The implications of these results and recommendations for future research complete the discussion.

















CHAPTER II

REVIEW OF THE LITERATURE



The literature review is divided into three sections. The focus of the first section is the historical perspective for the research in its description of the traditionally "watered-down" or easy to do curriculum approach used with the mildly and moderately retarded learners. More recent labels for such individuals include "learning disabled" and "educable mentally handicapped." Based primarily on an informal review of popular textbooks on teaching the mentally retarded and mildly handicapped, as well as a review of articles in journals dealing with special education, a history of teaching these types of students in easy task curriculum environments is provided. Some research implications of this curriculum approach are also discussed.

The second section includes an examination of some of the difficulties with operational definitions and research findings on easy to do tasks and low error learning environments. Presentation of the current practices on educating the mildly handicapped with easy task curricula provides a research context for the study.











The third section contains a review of the precision teaching literature on difficult task learning: large sets and curriculum leap ups. This section is based on a review of all articles from the Journal of Precision Teaching as well as Eshleman's (1983) compilation of all known precision teaching references. Many of the references in Eshleman's compilation were in the form of unpublished work (e.g., papers presented at conferences), thereby limiting the availability of some of the precision teaching research.



"Watered Down" Curriculum Approach

Those children classified as mildly handicapped have traditionally been served in special education classes. The term mildly handicapped refers to students who have been labeled as educable mentally retarded (more recently referred to as educable mentally handicapped), behavior disordered (now termed emotionally handicapped), and learning disabled (Miller & Davis, 1982). However, educable mentally handicapped students have been recognized and educated for a considerably longer period of time than have children who have more recently been classified as emotionally handicapped or learning disabled (Kauffman & Payne, 1975). The first topic of this section is the findings associated with educating educable mentally handicapped (EMH) students in special education











classes which have emphasized a watered down curriculum approach.

The most pervasive practice in the area of curriculum for the retarded youngster has been the use of a watered down general education curriculum (Klein, Pasch, & Frew, 1979). This approach appeared to have been established without any guiding philosophy. Rather, it was fostered by leaders in the field, such as Kirk and Johnson (1951), who suggested that two principles should guide the presentation of subject matter to retarded learners: "concrete level" and "gradual rate." Kirk, along with others, further expressed a somewhat paternalistic attitude toward retarded learners, implying that the development of specific content and objectives be avoided when teaching them because of the uncertainty of their achievement. For example, the opinion that retarded learners should be taught to read to the best of their ability was accepted as policy and offered a ready excuse for teachers who made little attempt to systematically teach these students to read (Klein et al., 1979).

Although a few special education programs for the retarded were established as early as 1915, special classes for EMH students only began to flourish in the early 1950s (Robinson & Robinson, 1976). The initial basis for these classes was the homogeneous grouping that narrowed differences in mental ability. A specialized











curriculum was then developed, thereby allowing teachers to be able to work with a group of students who had similar interests and academic needs (Robinson & Robinson, 1976). In reality, the range of educationally relevant behaviors in these exceptional student education classes was at least as great as the range in regular classes (Bruininks, Rynders, & Gross, 1974; MacMillan, 1971).

This heterogeneity came about because educational skills are imperfectly correlated with mental age or intelligence quotient, which formed the basis for grouping in these special classes, and because the chronological age range was typically wider than the range in regular classes (Robinson & Robinson, 1976). This wide range of skills and the absence of a readily available, specialized curriculum prompted EMH program teachers to water down the regular curriculum by lowering the level of difficulty of material and the amount of work to be completed. This approach was especially common in such skill areas as reading and arithmetic. It also was practiced by simply following the pattern of the general curriculum, but at a slower pace (Gallagher, 1967; Rothstein, 1962).

Research findings from EMH classes that use a watered down curriculum approach indicated that little learning may have actually taken place. Since progress was not judged in terms of the full range of curriculum aims for the nonretarded student, it was tempting to let matters









slide along at a comfortable pace, thereby minimizing frustration (Robinson & Robinson, 1976). Teachers often assigned a higher priority to personal adjustment and tended to demand less achievement than their pupils could deliver (Fine, 1967; Schmidt & Nelson, 1969). Johnson (1961, cited in Johnson, 1962) emphasized that despite the instruction provided, little learning could take place when much of the motivation or drive to achieve had been removed from the learning environment, as in exceptional student education classes whose primary objective was to remove pressures and to make the child happy. Teacher expectations about student performance also were powerful influences (Guskin & Spicker, 1968).

This watered down curriculum approach seemed to have been applied more recently to all classes for the mildly handicapped. Alley and Deshler (1979) noted it to be one of the most common approaches used with secondary school-aged, learning disabled students. Miller and Davis (1982) recommended a modified regular curriculum approach in noncategorical (i.e., regular education) classrooms.

In summary, special education has had a history of educating mentally retarded students in learning environments where errors are kept to a minimum by employing a watered down curriculum approach. The net result of this placement has been diminished learning for several reasons. Teachers have come to expect too little











of mentally retarded students. Programming involved the wrong curriculum objectives or no clear objectives. Attitudes and expectations also played a crucial role in motivating students to learn and the teachers to teach. Exceptional student education teachers often fostered the idea of slowness in their students by rationalizing that such a perception would protect them from failure and frustration. In actuality, this approach may have promoted a lack of effort on the part of these students, who were initially placed into special programs because their earlier efforts did not pay off.



Easy Task Learning Environments

Examination of the general learning environment can be made across the continuum of task difficulty level. There is a dichotomy between difficult task and easy task learning environments. In a difficult task learning environment students are presented tasks that are initially difficult to do, and instruction is designed to produce rapid reduction of errors. An integral part of an easy task learning environment involves assignment of tasks that are initially easy to do. Since there are few errors to reduce, the teacher's role is often reduced to providing a supervised practice. This approach is intended to provide students with positive learning experiences; if the task is easy enough, there will be











little chance of failure or of practicing wrong answers. A common approach is to present curriculum steps that are small and carefully sequenced from easiest to hardest.

Determination of the degree of difficulty of the task and the means of increasing the level of difficulty has not been clearly documented. A review of the literature on curriculum and instructional strategies provided indications that the terms used to describe this topic are inconsistent. Wehman and McLaughlin (1981) have tried to give useful definitions. The term "instructional strategies" was a label that reflected how to teach and included the various methods, materials, and time allocations used in teaching. A "domain" was a set of content and behavior elements which potentially could be taught. It was synonymous with curriculum area, such as arithmetic, language, motor, etc. A teacher was expected to have a very clear understanding of what the domains included. This understanding was to be in the form of a sequence of skills for each domain. This information was referred to as scope and sequence information. Scope referred to what was taught, both the broad and specific skills, and sequence referred to the order in which the skills were taught. Sequence usually followed a graduated continuum from easy to difficult.

Task analysis is the breaking down of specific skills into smaller steps which may be easier for the child to











learn. This process involves a logical sequencing of steps from simple to complex or beginning to end. Skill sequencing may be considered a functional progression of instructional objectives within a given domain. It can "provide a framework of tasks or objectives within which many types of instructional programs may be organized" (Williams & Gotts, 1977, p. 221, cited in Wehman & McLaughlin, 1981).

These definitions have not been helpful to those who want to design and experimentally control easy and difficult tasks. Mercer (1979) also pointed out that reviews of studies on the sequencing of skills or skill hierarchies provide no conclusive evidence regarding the validity of hierarchical orderings of specific skills. Since no systematic definitions of easy and difficult seemed to exist, a framework can be proposed that refers to potentially manipulable variables that seem likely to make a task easy or difficult.

Task difficulty level has been derived from the

concept of curriculum step size. Frequently, steps were defined as logical breakdowns of skills, and small steps were defined as a further breakdown of these skills (Wehman & McLaughlin, 1981). Step size was defined in terms of the variables which made a task easy to do or difficult to do. These variables have been viewed on two levels: within task and across tasks. Three within-task











variables seemed to be important: (a) the number of steps within the teaching sequence, (b) the number of units in the teaching set, and (c) the procedures which control prompting and fading. Across-tasks variables included

(a) time spent on curriculum, (b) number of steps in the curriculum, and (c) how many steps are skipped in moving up a vertical curriculum sequence. The following sections are organized around the way these six variables have been addressed in the traditional literature and how easy task learning environments have been used in educating mildly handicapped students.

Within-Task Variables

Number of steps. This variable refers to the number of steps needed to teach a task. The small step approach within task involves breaking down a task into smaller subskills. This can be accomplished by breaking existing steps down further or by adding steps. Many educators have advocated this small step approach with mildly handicapped students to enable them to receive reinforcement after each small step and to experience much success with few errors (Adamson & Adamson, 1979; Haring & Bateman, 1977; Lowenbraum & Affleck, 1976).

Smith (1974) strongly advocated such an approach with mildly handicapped students. In comparing the curriculum goals for the educably mentally handicapped and the intellectually normal, he stated that:











the goals to be achieved by both groups are
quite similar during the early stages. To be
sure, though, it may be essential that the
special education teacher be quite exacting in
"fractioning-down" each skill into very small
skill components so that the youngsters are not placed in a pedagogical situation in which they
are expected to make inordinately large leaps
from one set of skills to another without having
first demonstrated competence in those smaller
areas that lie between. For intellectually
normal children one does not have to be as
careful to delineate all the precise intervening
skills (as well as teach for each) since these
youngsters seem to have greater facility for filling in gaps and making larger conceptual
leaps. (p. 83)



Myers and Hammill (1976) suggested that scope and sequence charts have not been notably successful with mildly handicapped. They argued that their ineffectiveness was partially due to the tasks' not being broken down into small enough steps to enable the teacher to teach only one element of a task at a time. They suggested that students with learning disabilities need specific, discrete, and sequential teaching. These students need to know the one thing they are attempting to learn. Smead (1977) argued that small, carefully guided steps were insufficient by themselves without being coupled with massive general experience.

Task size. Task size, or amount or material, refers to the length of the task, the number of items to be learned (Blake, 1976). Reduction in the number of items in the teaching set for mildly handicapped learners has











been part of the small step approach to teaching them. The fewer the items presented to a student at one time the smaller the step. The assumption behind this was that the smaller step would have provided the student with more success by having allowed him or her to learn items more quickly (Howell, 1979).

Early work dealing with the concept of task size was provided in the field of psychology. Examination of the length of material to be memorized and to consequent retention was conducted by Kjersted (1919), Robinson and Heron (1922), and Robinson and Darrow (1924) who found that task difficulty increased disproportionately with task length for adults. The topic has not been studied extensively since their work (Blake, 1975).

Blake (1975) believed that the task size strongly

influences learning. She described it: "When material is added, the task gets disproportionately harder. That is, there is not a unit change in difficulty for every unit change in length. Instead, as material is added, the task becomes very much harder" (p. 369). She studied the effect of task length on learning sentences, concepts, sight vocabulary, synonyms, and homonyms in the performances of retarded and normal pupils. Some of her findings supported the contention that learning was affected by task size and that increments made the task











disproportionately more difficult, especially for the retarded learners.

Prompting and fading. Two important and frequently used instructional strategies with mildly handicapped students have been prompting and the fading of prompts (Salvia & Sindelar, 1982). Two questions were essential in examination of these strategies: When should fading of prompts begin? How rapidly should it proceed so as not to disrupt the child's performance? A comparison of data collected during the original phase and after the first step in fading procedure could be made. Similarity in the rate of improvement during the two phases may have indicated that the first step had been successful; i.e., the child had maintained growth even though a less pronounced prompt had been used. If the rate of improvement decreased, this may have meant that too large a step had been taken and that an intermediate step was required.

Extensive work with prompting and fading was

conducted by Sidman and Stoddard (Sidman & Stoddard, 1966; Sidman & Stoddard, 1967; Stoddard & Sidman, 1967). The researchers developed a program to teach nonverbal autistic children a difficult circle-ellipse discrimination. Judicious timing of cue presentation and fading as well as the insertion of a few intermediate steps in lieu of many smaller steps accelerated learning.











Across-Task Variables

Time spent. The amount of time spent on a particular task refers to how slowly or quickly a teacher moves through the curricular sequence. The basic idea underlying literature of this nature with the mildly handicapped was to teach more slowly those students who could not learn as fast (Howell, 1979). The same objectives taught in the regular classroom setting were taught to the mildly handicapped student, but with more time allowed for each step. This approach did not permit the exceptional student exposure to subsequent parts of the curriculum as early as the normal student, because it was based on a calendar-based criterion for teaching rather than a performance-based criterion. It further ensured that the exceptional student would continually fall further behind academically.

Number of steps. The number of steps in a curriculum sequence refers to the number of objectives into which a total curriculum is divided. This number can vary according to the curriculum guide used or how the teacher decided to break down the objectives into smaller steps. Miller and Davis (1982) cautioned teachers of the mildly handicapped when curriculum guides were used for reading, math, social studies, and language arts, because the objective may have been stated in broad, global terms that needed to be broken down for handicapped learners.











Step up a vertical curriculum. The size of the step up in a vertical curriculum refers to the number of levels in a curriculum sequence that are "jumped up" or "leaped up" at one time (Eaton & Wittman, 1982). The term "jump up" refers to a moderately daring movement, whereas the term "leap up" refers to a very daring movement. An example of a jump up is moving a student from one-place subtraction with regrouping to three-place subtraction with regrouping. The concept is discussed further in the section on precision teaching literature. Summary

Six variables have been identified that seemed to help logically to define the level of difficulty of a task. These variables have been derived from the generic concept of step size.

The small step approach to learning has been most frequently used with mildly handicapped children. More specifically, the modifications involved addition of more steps to skill learning, presentation of a smaller set size, spending more time on a particular step, and breakdown of curriculum sequences into smaller steps. Little empirical evidence has supported the use of easy-to-do tasks to educate mildly handicapped students. Attention to the details of when to prompt and how to fade prompts has shown potential for improving learning.











Precision Teaching

For many years precision teachers charted students' performances, while continuing to implement traditional public school curriculum strategies (McGreevy, Thomas, Lacy, Krantz, & Salisbury, 1982). Congruent with the rest of special education, precision teachers were "caught up" in the small step, easy task approach to instruction. Within the precision teaching population a great deal of attention has been focused on the attainment of functional fluency and mastery levels of performance (Bower & Orgel, 1981). There has been little evidence to suggest that students who show low performance frequencies in simpler skills would also show low performance levels in more demanding tasks (Barrett, 1979).

The primary focus of precision teachers has been "the provision of curricular and other environmental arrangements which accelerate acquisition of fluency and mastery attainment" (Bower & Orgel 1981, p. 3). The potential contributory effects of difficult tasks on learning had been overlooked until Neely's 1978 study (cited in Bower & Orgel, 1981), because errors were to be avoided. All (1977) described the positive effect of high error rate from difficult tasks on learning appropriately: "The two-line learning picture dramatically and graphically represented the possible honeymoon











relationship of initial high rates of errors and correct learning" (cited in Bower & Orgel, 1981, p. 3).

Bower and Orgel (1981) reported that Lindsley began to question the effectiveness of curricular strategies involving hard to do tasks that emphasized high initial performance and few errors in 1978. He felt that this approach may have provided less opportunity for learning. Therefore, strategies to generate initially high error rates through hard-to-do tasks were suggested as a means of providing a more efficient and effective learning environment. Empirical evidence showing that errors could serve as opportunities to accelerate learning was provided in Neely's 1978 6-year study involving his supervision of a special education program. His data indicated that accelerated learning took place when students were encouraged to work on skills that produced initially high error rates.

Studies on Hard to do Task Learning and Leap Ups in
Curriculum

A review of the precision teaching literature in the Journal of Precision Teaching, carried by this researcher, located six studies that addressed the issue of hard to do task learning and leap-ups in curriculum (McGreevy, 1978; McGreevy, 1980; Stromberg & Chappel, 1980; Bower & Orgel, 1981; Eaton & Wittman, 1982; McGreevy et al., 1982). A











seventh relevant study was a doctoral dissertation on curriculum leap-ups (Gerent, 1985).

McGreevy in 1978 conducted the first of such studies to explore the possibility that initially hard to do tasks may have been easy to learn (cited in McGreevy, 1980). He compared the initial correct performance and learning of a group of mildly handicapped elementary school children on similar screening and remediation tasks. He found that screening tasks administered daily for 10 days without instruction produced lower initial correct frequencies and higher correct celerations. On the other hand, he determined that "see-say words" remediation tasks were 4 times easier to do but 1.3 times harder to learn than the similar, previously administered screening tasks. Even though the students learned these tasks at the rate of X1.2 per week (the preceding X indicates accelerating rate), McGreevy concluded that the remediation efforts had been relatively ineffective. He further concluded that children did not need easy to do tasks to remain motivated, they could have learned more than originally thought possible, and a lower initial performance provided a greater opportunity for learning.

In his second project, McGreevy (1980) once again demonstrated low initial performance followed by rapid learning in an 18-year-old moderately retarded young man. The subject was given a see-say task on the first 29 words











of Wilson's Essential Vocabulary. The initial accuracy ratio of /19 (the preceding / indicates decelerating rate) attested to the difficulty of the task; errors vastly exceeded corrects. However, subsequent celerations of X2.6 for corrects and /2.6 for incorrects suggested that the low initial performance provided a greater opportunity for learning. McGreevy (1980) also suggested that hard to do (i.e., low initial performance) did not necessarily mean hard to learn (i.e., subsequently slow learning).

Stromberg and Chappel in 1980 attempted to teach a

math curriculum to an entire second grade class at a pace suggested by the adopted text (cited in McGreevy et al. 1982). This text was provided with precision teaching for four months and four phases of instruction, resulting initial accuracy ratios ranging from Xl to X65, most of which included no errors. The median correct celeration was X1.4, while the error celerations were almost all X1.0. After four months the entire class was leaped up to a new task involving all math operations introduced in the second grade text. The outcomes were lower initial performances and more rapid learning. Initial accuracy ratios ranged from X6 to /1.6 and included many errors. Correct celerations ranged from X1.5 to X2.7, with a median celeration of X2.0. Error celerations ranged from /1.6 to /8, with a median celeration of /2.4. The










implication here was that the new task was hard to do but easy to learn.

Bower and Orgel (1981) attempted to generate

initially high error rates, steep error learning, and rapidly accelerating correct learning with undergraduate college students. They set very high aims for the students to meet in learning psychology facts relevant to the curriculum. All groups produced more errors than corrects when starting each set of flash cards. In all cases, terminal performance levels produced dramatic division of errors and multiplication of correct frequencies.

Another encouraging investigation of leap ups

involved the work of Eaton and Wittman (1982) with three learning disabled children, whose accurate performance (few to no errors) of the multiplication and division tables or identification of simple fractions precluded meeting their fluency aims (not completing problems quickly enough). Upon implementation of the leap up procedure, all three children were completing the math problems quickly enough in 9 to 10 days. That is, their learning accelerated dramatically when they moved ahead to curriculum that was new to them.

A related investigation was conducted by McGreevy et al. (1982). Twenty-four severely handicapped students were given "hard-to-do" and "extremely hard-to-do" tasks,











in which the degree of difficulty was determined by the initial performance data. Correlations were made between three measures of initial performance (initial number correct, initial number of incorrect, and initial accuracy ratio) and each of two measures of learning (correct and incorrect celerations) and of variability (bounces around correct and incorrect celerations). The correlations clearly indicated no relationship between initial performance and subsequent learning or variability. Another correlation made between initial performance (initial number correct) and learning (gain score) also indicated no relationship.

Gerent (1985) completed her doctoral research on the effects of curriculum leap ups on short-term learning rates. A curriculum leap up was defined as an upward curriculum change that resulted in a student's making at least 10% more errors than correct responses. Two single subject designs were used. In the "Leap and Keep" design, the preleap-up skill was continued when the leap-up skill was introduced. In the "Leap and Leave" design, the preleap-up skill was dropped when the leap-up skill began. Twenty-four of 29 experiments showed enhanced learning during the leap up condition. Summary

Until about 1980, precision teachers had emphasized the traditionally small step, easy task approach to










instruction. The leap-up tactics, on the other hand, have shown greater potential for enhanced learning. Studies on high error learning have shown that leap ups in curriculum may provide a means for increasing the learning of some students, with errors serving as learning opportunities. Curriculum leap ups may prove useful for exceptional, average, and accelerated students, a potential worthy of further study.



Recapitulation

The traditional approach to teaching educably

mentally handicapped students has involved simplified subject matter and a slower pace than that employed with regular education students. Its purpose has been to reduce academic frustration by diminishing chance for errors. The watered down and small step curricula are most commonly used, in spite of a lack of empirical evidence validating their effectiveness. Opponents of this approach have felt that several factors have had negative consequences on the step curriculum. These factors include little motivation on the students' part, low learning rate, and an ever increasing gap between special education students and their chronological age peers.

A review of the literature on curriculum strategies resulted in confusion regarding the distinction between easy and difficult tasks. A framework has been proposed











to help clarify the variables involved. Six variables have been identified which evolve from the generic concept of step size. Five have been used in educating the mildly handicapped in easy task, low error environments. They include addition of more steps to skill learning, reduction of set size, increased amount of time spent on a particular step, breakdown of curriculum sequences into smaller steps, and prompts.

The sixth variable, step up in a vertical curriculum, has come under closer scrutiny in recent precision teaching literature. This approach employs a difficult task, higher error learning environment to educate students. Research evidence has begun to accumulate suggesting that regular as well as special education students may experience enhanced learning when they are placed in situations that involve initially hard to do tasks. Jump ups, leap ups, and hard-to-do tasks have been the common techniques employed by precision teachers. However, little formal attention has been given to the set size.


















CHAPTER III

METHODOLOGY

Overview of the Study

The purpose of the study was to assess the effects of difficult task learning environments, using a larger than traditional teaching set size on the academic performance of children of varying levels of achievement in the area of spelling. Questions have been raised about the effectiveness of a simplified (easy to do) curriculum with exceptional children. Precision teaching techniques have recently been used to explore the use of initially hard to do tasks in exceptional student education programs.



Variables Under Investigation Independent Variable

The independent variable for this study was teaching set size, or the number of unique problems or units in the teaching set. In the context of this study, each student was exposed to two conditions. In the small set size condition, 10 spelling words were administered. Ten-word spelling tests are commonly used by teachers because they are easy to score. In the large set size condition, 20 spelling words were administered, providing a 100%











increase in set size. Research has demonstrated that a two-fold increase in set size resulted in a disproportionately greater increase in difficulty of material to be learned (Blake, 1975). Dependent Variables

Frequency, or movements per minute, was selected as the basic unit of measurement in this investigation. For many academic tasks, frequency has yielded more information than other standard educational measurements (Haring, Lovitt, Eaton, & Hansen, 1978). Frequencies of correct and incorrect responding provide measures of the amount of learning achieved.

Celeration for correct and error responding, the first two of four dependent variables measured in this investigation, was the rate of change over time, as measured by the ratio of two frequencies one week apart drawn on a learning line. Celeration has been found to be a sensitive dimension that is likely to detect changes in the independent variable being manipulated (Koenig, 1972).

The third dependent variable measured was the total learning measure, which was a combination of the celerations for correct and error responding. This measure conveniently consolidated improvement in correct and incorrect responding into one number.












Figure 1 is a sample graph of these dependent variables and Table 1 has the raw data that are graphically presented in Figure 1. The figure illustrates both a small set size and a large set size condition. The name of the behavior being measured, the formula for calculating it, and the value or the behavior being measured under small and large set size conditions have been given. A multiplication sign (X) preceding the value indicated that the frequency of the behavior was accelerating. A division sign (/) preceding the value indicated that the frequency of the behavior was decelerating.

In Figure 1, A and B represent the initial

frequencies for correct and incorrect responding in both phases. The initial frequency is the point where the learning lines (one each for correct and incorrect) crossed the first day line in a phase. The letters C and D represent the final frequencies for correct and incorrect responding on the learning lines. The letters E and F mark the celerations for correct and error responding. The letter G represents the total learning measure. Graphically, it can be visualized as the size of the angle between the celeration for correct responding and the celeration for incorrect responding.

The last dependent variable was mastery change. Mastery change was represented by the ratio between


















1-4







0
Uo


WEEKS


0 7 14 21 28 35 42 49


WEEKS


0 7 14 21 28 35 42 49


Figure 1


Graphic Examples of Dependent Variable Measures







Table 1

Dependent Variable Measures and Their Formulae


Value
Small Large
Symbol Name Formula Set Size Set Size A Initial Performance Frequency for Correct 45 45 B Initial Performance Frequency for Errors 5 35 C Final Performance Frequency for Correct 50 80 D Final Performance Frequency for Errors 0 0 E Celerations Correct mov/min/wk for Correct X1.20 X1.62 F Celerations Error mov/min/wk for Errors /1.41 /7.80 G Total Learning Cel for Corrects X Cel Rate for Errors X1.69 X12.64 H Mastery Change Ending Percentage of (not shown in Minimum Performance
Figure 1) Achieved - Beginning Percentage of Minimum
Performance Achieved











initial and final masteries, where mastery refers to the percentage of minimum performance standard achieved. An arbitrary standard of 80 spelling transitions per minute was used because that proficiency rate has been associated with a well established skill (Evans, 1981; Evans, Mercer, & Evans, 1983; Evans & Evans, 1985).



Setting

This study was conducted in the Marion County Public School System, a northcentral Florida school district of over 24,000 students (School, 1986). At the elementary school level, exceptional student education program services were provided to eligible students in a varying exceptionalities setting. Such classes were comprised of students of more than one exceptionality, although each student received a curriculum individualized to his or her specific educational needs, as described by an individual education plan. The data were collected by this investigator, selected teachers aides, and secretaries (hereinafter referred to as teacher assistants). Because spelling was the academic task for the study, only those exceptional student education students whose individual education plan included remediation in spelling were included in this study. Spelling was part of the basic curriculum for regular education students; therefore, no distinction was made among these students.











Subjects

There were six subjects in this investigation. Two subjects were identified as learning disabled (SLD) (with remediation in spelling specified in their individual education plan), two were educable mentally handicapped (EMH), and two were normal, i.e., enrolled in regular education (RE). All six were chosen from the elementary school level and were matched on the basis of intelligence quotients with their counterpart in the same exceptionality. Using a random numbers table, each subject was randomly selected from a pool of subjects in all three exceptionalities. The learning disabled and educable mentally handicapped students had met the Florida Department of Education and the Marion County School System guidelines for their respective exceptional student education program placements (See Appendix A). The regular education students were chosen from a pool of students who had been evaluated and subsequently deemed ineligible for an exceptional student education program because of average or above intelligence and no identified academic deficiencies. These evaluation criteria provided the identifying psychometric data on all six subjects. All subjects were within one year of each other chronologically, their ages ranging from 8-1 to 9-0. Table 2 provides the biographical and psychometric characteristics of all six subjects.












Table 2

Psychometric Descriptors of Subjects


Chronological Age
Exceptionality Name Per First Data Day IQ1


EMH Dorothy 9-0 69 EMH Marketa 8-5 67 RE Keesha 9-0 89 RE Mikki 8-4 103 SLD Jesse 8-1 93 SLD Matthew 9-0 96 1 based on Full Scale Intelligence Quotient of Wechsler
Intelligence Scale for Children-Revised, given within
the past three years.



Experimental Design

The experimental design in this study was single subject with alternating treatments. A single subject design was selected to provide for analysis of individual level and to demonstrate within subject control (Tawney & Gast, 1984). This strategy for conducting research has been documented in the literature (e.g., Baer, Wolf, & Risley, 1968; Bailey, 1977; Johnston & Pennypacker, 1980; Sidman, 1960). This strategy has promoted an interactive approach between the experimenter and the independent variable because it allowed for the identification of experimental sources of both intraindividual and interindividual variability while the data are being











generated by the subject. Also, this strategy permitted the use of ratio comparisons within and across experimental conditions (Tenenbaum, 1983).

The alternating treatments design compared the

effectiveness of two or more interventions by introducing them over the same time period. The interventions were then counterbalanced across sessions and time of day (Tawney & Gast, 1984). An experimental effect can be demonstrated when one intervention is consistently associated with a different level of responding than other interventions. The rapid alternation of two interventions can not only control for maturational and historical threats that may have occurred in a multitreatment design, but can also reduce sequencing problems because no single intervention was consistently introduced first and maintained for an extended period of time (Barlow & Hayes, 1979; Sulzer-Azaroff & Mayer, 1977). Replication of the differential effects of the interventions across different behaviors and/or across different conditions demonstrates external validity (Tawney & Gast, 1984).

The specific design in this investigation is

illustrated in Figure 2. There was no baseline, only an intervention comparison phase. Optimal guidelines included

1. Operational definition of all intervention
procedures.







41



35 Intervention Comparison

30
U
25
25 o o A corrects 1 U o ----- o B correct
a4 KEY * * A errors
-r- W V) 20
V 2 *-------* B errors
. O

0 -, - 15
rA
z 0
) 10 4
z aic



0

1 2 3 4 5 6 7 8 9 10





Figure 2


Alternating Treatments Design












2. Determination of a schedule for counterbalancing
the presentation of the interventions across time
(i.e., within sessions, across days).

3. Determination of how intervention procedures were
to be counterbalanced across teachers, settings,
activities, etc.

4. Introduction of interventions (A and B) in a
rapidly alternating fashion in accordance with the counterbalancing schedule. Alternation of
conditions continued until the experimental
effect was demonstrated favoring the
effectiveness of one intervention over the other.

5. Continuation of the most effective intervention
(B or C) in the final phase of the study (Tawney
& Gast, 1984).


Certain limitations to the alternating treatments

design have been documented. This design has required a high level of consistency across individuals administering the different interventions; therefore, high procedural reliability was of critical importance when evaluating the data (Tawney & Gast, 1984).



Procedure

Pre-experimental Phase

During this phase a sufficient number of spelling

words from an original pool of words (see Appendix B, List One) was administered to each student to identify 30 words the student did not know how to spell. Each of the 30 words chosen from the original pool of words contained at least one transition correct and two transition errors (see section on curricular materials for explanation).











Each word was then randomly assigned to either the 10-word list or the 20-word list. Upon completion of this activity, the teacher assistants were given the two spelling lists and were familiarized with the test/teach procedure explained below. Since each tester worked at one particular school, they worked solely with the student subject(s) in attendance at their school of employment. All teacher assistants were employed by the Marion County School System as either a teacher, an aide, or a secretary.

Experimental Phase

Each student assessed during the pre-experimental

phase was then exposed to the 30 spelling words selected from the original pool of words. Two daily spelling timings were given to each student from this selection of words. The small set size condition exposed the students to 10 spelling words, whereas the large set size condition exposed the students to 20 spelling words. There was no duplication of words in the two conditions. For each word to be spelled, the teacher assistant read the word aloud, read a sentence with the word in it, then reread the word.





1 A spelling timing is a brief measure of a monitored spelling activity and is not the same as a spelling test, which is a measurement of spelling performance.











Daily timings from both lists of spelling words were taken for each student. This procedure continued until 100% mastery of the words had been obtained or time constraints provided a necessary stopping point (e.g., Christmas vacation or Easter break). The additional calendar days that had not provided opportunities for daily assessments may have confounded the test results by allowing the subject to forget already learned words.

Upon completion of each daily timing, a brief,

intense teaching episode occurred. The student wrote those words misspelled. The teacher assistant then copied the misspelled word, then wrote the correct spelling. The student then copied the correctly spelled word.

Intrasubject replication followed the completions of the first experiment. Each student was exposed to a new list of 30 words taken from a different selection of words (see Appendix B, List Two) containing at least one transition correct and two transition errors. The above sequence of events involving daily timings was carried out during this replication.



Material

Curricular Materials

The pool of spelling words used in this study was obtained from Classroom Reading Inventory (Silvaroli, 1965) and The Riverside Spelling Program (Wallace, 1984).











The lists of words chosen for each student have been provided in Appendix B. Upon administration of these words to each student, a reduced list of words was obtained, each word of which contained at least one transition correct and two transition errors.

A transition is defined as any two consecutive spaces in a word. When two consecutive letters of a word are correctly placed, this is a transition correct. For example, in the word cloud, a transition correct would be
A
cloud. The caret sign above the adjacent letters, "c" and "l" indicated a transition correct. A transition error is defined as any two consecutive letters in a word not correctly juxtapositioned. For example, in the word cloud, if it were spelled clowd, then a transition error would be clwd. The "w" is an incorrect letter for the word cloud. Another example of a transition error might be caused by a letter omitted, as in the case of the word cld, where the "u" has been omitted. The caret sign below the adjacent letters "o" and "d" indicates a transition error.

In recapitulation, three spelling variations of the word cloud are further exemplified. In the spelling
A^AAAA
cloud, there are six transition corrects and zero transition errors. The no letter to "c" transition is counted as a transition correct because it is not preceded by any letter. The final letter "d" also is counted as a











transition correct because it is not followed by any
AAA A
letter. In the spelling clowed, there are four transition
VVV
corrects and three transition errors. In the spelling
AAA A
clod, there are four transition corrects and one
V
transition error.

Data Recording Form

For each student the daily numbers of transition corrects and transition errors were recorded for each condition (small set size and large set size). A sample form is provided in Appendix C. Each daily recording included the rate correct (to the left of the slash mark) and the rate incorrect (to the right of the slash mark). The standard behavior chart was used to display and analyze all the data from this investigation. A sample graphic representation of these data is provided in Appendix D.



Data Recording and Analyses Data Recording

Daily data were recorded on the data recording form

provided in Appendix C. Small set size and large set size frequency correct and frequency incorrect were listed adjacently for comparative purposes.

These same frequency data were plotted on the

standard behavior chart and can be found in Chapter IV. This graphic representation allowed visual analysis of the











small set size and large set size conditions. As well, a series of frequency plots over time shows linear change, thus allowing easier predictability than the more common curvilinear plots across time. Data Analyses

Visual inspection of all data and frequency

multipliers, summarized in Appendix D, was used for data analyses. Frequency multipliers, the ratio between two frequencies, were used because they quantify the distance visualized between two frequencies on the standard behavior chart (Pennypacker, Koenig, & Lindsley, 1972). These ratios were obtained by dividing the smaller frequency into the larger frequency. When 1.00 is subtracted from the obtained ratio value and then is multiplied by 100, the percent change is derived. Differences between large and small set sizes were examined to determine if the measures of learning for the large set size were equal to or greater than the measures of learning for the small set size. If the large set size measures were within 5% of the small set size measures, they were described as equal. A finding was therefore interpreted as significant (i.e., the large set size was favored) if the large set size measures were at least 95% of the small set size measures. Replication also served part of the function of statistical tests of significance.








48


Therefore, the obtained results have been evaluated in the context of expert judgment of their practical importance.
















CHAPTER IV

ANALYSES AND RESULTS



The purpose of this study was to investigate the effects of teaching set size on several measures of learning for both special and regular education students. The study was based on a single subject design with the alternating treatments of 10 and 20 spelling words as independent conditions. Differences in celeration, total learning rate and fluency, between the 10- and 20-word set size were examined for each subject. Frequency correct responding and error responding on a spelling dictation test were the dependent measures.

Primary interest has been given to results large

enough to make a practical difference to psychologists and teachers. Therefore, an experimental finding was deemed significant if the measures of learning for the large set size were greater than or equal to the measures of learning for the small set size. If the large set size measures were within 5% of the small set size measures, the measures were described as equal. The interpretation given to this equality was that children could learn as well with a large set size as with a small set size. The











strict criterion of 5% was chosen because a lot more learning could be obtained with the large set size if the measures of learning for both set sizes were equal (i.e., within 5% of each other). The frequency multipliers are summarized in table form in Appendix D.



Celeration

The first variables examined in this chapter are celerations for correct and error responding. Mixed results were obtained as demonstrated in Table 3. The standard behavior charts are provided in Figures 3-8. As shown in Table 3, Dorothy and Marketa were the EMH subjects. Learning for correct responses with 20 words was faster than or equal to learning for correct responses with 10 words in Dorothy's first experiment. Dorothy's second experiment showed faster learning for correct responses with 10 words than with 20 words. In both experiments Dorothy reduced her error responses more quickly with 20 words than with 10 words. For Marketa results from experiment one showed faster learning for correct responses and faster reduction of error responses with 10 words. Sufficient experiment two results could not be obtained with Marketa, because his high rate of absenteeism made it difficult for him to learn consistently the words within a reasonable amount of time.






Table 3

Differences in Small and Large Set Size



Celerations Celerations Total Exceptionality Name Experiment Correct Error Learning Mastery


EMH Dorothy 1 >a > >

2 > EMIl Marketa 1 < < < >
2 insufficient data RE Keesha 1 < > > <
2 > > > > RE Mikki 1 > < < >
2 < < > SLD Jesse 1< > < < 2 > > > > SLD Matthew 1 < < < >
2 > < > >


Note: EMH = Educable Mentally Handicapped; RE = Regular Education; SLD = Specific
Learning Disabled

a > represents a learning measure of the large set size that is greater than or equal
to the same learning measure of the small set size.

b < represents a learning measure of the large set size which is less than the same
learning measure of the small set size.











Calendar Weeks


1/25 2/1 2/8


2/15


2/22 3/1


3/8


3/15 19/


*1


1


Successive Calendar Days Figure 3

Standard Behavior Chart for Dorothy (EMH)


I19C


-)u


Large Set Size




0
o


Small Set Size


Cf% - . . . I I . I . . I I . I I I . . . . . . . . . . . . . .


-- - - - - - -...... . . B


MMMI ,


tilimmitm ..........


449-F 1 i- - --f- f H f t7 rat T
till I lift Al


:.r:


1:











Calendar Weeks 1/18 1/25 2/1 2/8 2/15 3/
50




Large i0 Set ILItl Size 5



50 11i




10
Small i Set + Size 5
;iiii



Successive Calendar Days

Figure 4

Standard Behavior Chart for Marketa (EMH)


- +n
-tw











Calendar Weeks


11/16 11/23 11/30 12/7 12/14 1/11 1/18 1/25 2/1


Successive Calendar Days


Figure 5


Standard Behavior Chart for Keesha (RE)


Large Set Size




0



Small Set Size









Calendar Weeks


1/11 1/18 1/25 2/1 2/8 2/15 3/8 3/15


Large 10-Set
Size 5




w
r- 100":: : II19





Small 10 Set I Size 1 H l





Successive Calendar Days Figure 6

Standard Behavior Chart for Mikki (RE) on












Calendar Weeks


Large 10 t Set 5 Size

4-J

0 0 HIM



Small 10
Set
Size 5





Successive Calendar Days
Figure 7
Standard Behavior Chart for Jesse (SLD)












Calendar Weeks


l :.7 . . .! .: .: .. . .I1 ~ .1-.1- ..I ..

1 i 1 14A I',,




.T. . . . .. . ..; : lI I I l.. .. . . . . . .
I ;; ; I1111 M ill 1 1 1
I.I..M. I.IlllHllll ill Miii i I I Iii I l ft( I 1 11 11" Il



I : I1! 1 I I A % : l[ I I L I1I I l I :.: IT- - 1 I I III I HI - H ill :
_ il]|! ~~2/ 2/151II II[ ~ !11l!I :l !,ilS ccessiv C"aIIil~ll l enda : Days_


Figure 8

Standard Behavior Chart for Matthew (SLD)


Large Set Size


Small Set Size


1/4


L/11


1/18 1/25


2/8 2/15


3/15











In summary, for the EMH group the 10-word list was associated with faster learning for correct responses in two of three experiments and faster reduction of error responses in one of three experiments. The 20-word list was associated with faster learning for correct responses in one of three experiment and faster reduction of error responses in two of three experiments.

The RE subjects showed similarly mixed results during both experiments. Keesha demonstrated faster learning for correct responses with 10 words in experiment one; in contrast, the 20-word list showed learning for correct responses equal to or faster than the 10-word list in experiment two. Reduction of Keesha's error responses with 20 words in both experiments was equal to or faster than her reduction of error responses with 10 words. In experiment one, Mikki demonstrated learning for correct responses with 20 words faster than or equal to learning for correct responses with 10 words. In experiment two, she demonstrated faster learning for correct responses with 10 words. Mikki's reduction of error responses was consistently faster with 10 words across both experiments.

In summary, for the RE subjects the 10-word list was associated with faster learning for correct responses in two of four experiments, and the 20-word list was associated with equal or faster learning for correct responses in two of four experiments. Intrasubject











replication provided a consistent reduction of error responses. Keesha consistently demonstrated equal or faster reduction of error responses with 20 words; whereas, Mikki consistently demonstrated faster reduction of error responses with 10 words.

Mixed results were also obtained for the SLD

subjects. Jesse learned the correct responses of the 10-word list more quickly in experiment one, but he learned the correct responses of the 20-word list at least as quickly as the 10-word list in experiment two. He reduced error responses of the 20-word list at least as quickly as the 10-word list during both experiments. Matthew followed a pattern of learning correct responses similar to Jesse. He learned the correct responses of the 10-word list more quickly in experiment one, but he learned the correct responses of the 20-word list at least as quickly in experiment two. His reduction of error responses of the 10-word list was quicker than his reduction of error responses of the 20-word list in both experiments.

In summary, for the SLD group half of the four

experiments had faster learning for correct responses as well as faster reduction of error responses with 10 words. Both Jesse and Matthew provided a consistent intrasubject replication with reduction of error responses; however,











Jesse performed equally well or better with the 20-word list, and Matthew performed better with the 10-word list.



Total Learning Rate

An analysis was made of the total learning measure (celerations for correct and error responding combined). These findings have been summarized in Table 3. Dorothy learned her 20-word list at least as quickly as her 10-word list in both experiments. Marketa learned his 10-word list faster than his 20-word list in experiment one. As mentioned previously, Marketa's experiment two did not produce sufficient data. In summary, Dorothy learned her 20-word list more quickly and Marketa learned his 10-word list more quickly.

The RE subjects were evenly split with their total learning rates for both word lists. Keesha learned her 20-word list more quickly across both experiments; whereas Mikki learned her 10-word list more quickly across both experiments. In summary, the intrasubject replication established on the total learning measure for each subject provided opposite results.

The SLD subjects provided mixed results for their total learning measures. In experiment one, Jesse and Matthew both learned their 10-word list more quickly, but they both learned their 20-word lists equally quickly if not faster in experiment two.












Mastery

The findings for mastery of the minimum performance

standard are also summarized in Table 3. Dorothy showed a mastery on her 20-word list than was equal to or greater than the mastery on her 10-word list in experiment one. Mastery on her 10-word list was greater than mastery on her 20-word list in experiment two. Marketa displayed a mastery on his 20-word list that equalled or exceeded the mastery on his 10-word list in experiment one. Experiment-two results, as previously mentioned, were insufficient. In summary, two of three experiments were associated with mastery of the minimum performance standard on 20 words that equalled or exceeded mastery on 10 words. One experiment was associated with greater mastery on 10 words.

The RE subjects also showed a generally equal or

greater mastery on the 20-word list. Specifically, Keesha showed a greater mastery on her 10-word list in experiment one, but she showed a mastery on her 20-word list that equalled or exceeded the mastery on her 10-word list in experiment two. Mikki showed a mastery on her 20-word list that consistently equalled or exceeded the mastery on her 10-word list in both experiments. In summary, for the RE subjects three of four experiments were associated with











equal or greater mastery of the minimum performance standard on the 20-word list.

The SLD students also demonstrated an equal or better established mastery on the 20-word list than on the 10-word list. Jesse showed a greater mastery on his 10-word list in experiment one, but he showed a mastery on his 20-word list that equalled or exceeded the mastery on his 10-word list in experiment two. Matthew showed a mastery on his 20-word list that consistently equalled or exceeded the mastery on his 10-word list in both experiments. In summary, for the SLD subjects three of four experiments were associated with equal or greater mastery of the minimum performance standard on the 20-word list.



Across Category Summary

The overall findings for celerations for correct responding, celerations for error responding, total learning, and mastery of the minimum performance standard across all three groups of subjects are summarized in Table 4. Equal or faster learning for correct responses with 20 words was demonstrated in five experiments and faster learning for correct responses with 10 words was demonstrated in six experiments. Reduction of errors was equal or faster with 20 words in six experiments and faster with 10 words in five experiments. Equal or











Table 4

Number of Experiments Favored Across Categories


>a


Celerations Correct 5 6 Celerations Error 6 5 Total Learning 6 5 Mastery 8 3




a > represents a learning measure of the large set size
that is greater than or equal to the same learning
measure of the small set size.

b < represents a learning measure of the large set size
which is less than the same learning measure of the
small set size.



superior learning with 20 words was found in six experiments, in contrast to superior learning with 10 words in five experiments. Mastery of the minimum performance standard was equal or greater with 20 words in eight trials, as opposed to three trials in which mastery for 10 words was greater. Intrasubject replication with celerations for error responding, total learning, and mastery of the minimum performance standard was demonstrated only for some of the subjects. The learning











measures were equal or superior with the large set size in 25 of the 44 experiments.



Accuracy

Each of the 30 words obtained from the spelling

pre-test was randomly assigned to either the 10-word list or the 20-word list. A post hoc analysis was made of the measure of initial accuracy, an estimate of the initial level of difficulty of each pair of word lists. Initial accuracy was obtained for each subject on the first day of data collection. It can be seen from Table 5 that the difference in level of difficulty between any pair of word lists ranged from 4% to 49%. Closer examination has been given to beginning accuracies as measures of task difficulty because of the possible effect of initial difficulty on measures of learning. For example, if a particular 20-word list was more difficult than the 10-word list paired with it, celeration, total learning, and mastery may have been affected by this difference.

The 10-word list in experiment one for Dorothy was 9% easier on the first day of data collection than the 20-word list. However, all four measures of learning on her 20-word list were equal to or greater than the four measures of learning on the 10-word list. The group of words in her second experiment included a 10-word list that was 25% easier than the 20-word list; however, the











Table 5

Differences in Initial Accuracies Between Small and Large Set Size



Difference
in Initial Easier
Exceptionality Name Experiment Accuracies Set Sizea


EMH Dorothy 1 9a 10 2 25 10

EMH Marketa 1 28 10
2 insufficient data

RE Keesha 1 8 10 2 12 20

RE Mikki 1 15 10 2 19 10

SLD Jesse 1 49 20 2 8 10

SLD Matthew 1 4 10 2 8 20

a based on higher initial accuracy



10-word list was associated with faster learning for correct responses and a greater mastery, and the 20-word list was associated with a faster reduction of error responses and a greater total learning.

Experiment one for Marketa included a 10-word list that was 28% easier on the first day than the 20-word list. Celerations for correct and error responding were faster with the 10-word list, and greater learning of the











10-word list was obtained. Mastery of the minimum performance standard on the 20-word list was equal to or greater than the mastery on the 10-word list. There were, as reported, insufficient data for experiment two.

For Keesha, experiment one included a 10-word list that was initially 8% easier than the 20-word list. Faster reduction of error responses and greater total learning were found with the 10-word list, in contrast to faster learning of correct responses and greater mastery on the 20-word list. In experiment two, for which the 20-word list was 12% easier for Keesha, all four measures of learning on her 20-word list were equal to or greater than the same four measures on her 10-word list.

For Mikki, a 15% easier 10-word list was found in

experiment one. A faster reduction of error responses, as well as greater total learning, were observed with 10-word list, but faster learning of correct responses and greater mastery were found with the 20-word list. For Mikki's experiment two, the 10-word list was once again easier, this time by 19%. Faster celerations for correct and error responding as well as greater total learning were seen with the 10-word list; whereas mastery of the 20-word list equalled or exceeded mastery of the 10-word list.

Jesse's experiment one was associated with a 49% easier 20-word list, but faster learning for correct responses, a better learning rate, and greater mastery











with the 10-word list. Reduction of error responses was equal or faster for the 20-word list. The 10-word list in Jesse's second experiment was 8% easier, but all four measures of learning on his 20-word list were equal to or greater than the same four measures on his 10-word list. In Matthew's first experiment, his 10-word list was 4% easier and was associated with faster celerations for correct and error responding as well as a greater total learning. Mastery for his 20-word list was equal to or greater than mastery for the 10-word list. In Matthew's second experiment, his 20-word list was 8% easier and was associated with equal or faster learning of correct responses and equal or greater total learning and mastery. His 10-word list was associated with a faster reduction of his error responses.

In summary, mixed results did not show a consistent relationship between initial level of difficulty of the 10-word lists and the celerations for correct responding, celerations for error responding, total learning, and mastery. Table 6 contains the superior measures of learning when the 20-word list was easier as well as when the 10-word list was easier. It can be seen from this table, for example, that when the 10-word list was initially easier, the four measures of learning were not always equal or superior for the 10-word list.












Table 6

Number of Superior Measures of Learning for Each Initially Easier Word List



Initially Easier Word List


10-Word List 20-Word List >a


Celerations correct 3 5 2 1 Celerations Error 4 4 2 1 Total Learning 4 4 2 1 Mastery 6 2 2 1



a > represents a learning measure of the large set size
that is greater than or equal to the same learning
measure of the small set size.

b < represents a learning measure of the large set size
which is less than the same learning measure of the
small set size.



Recapitulation

Traditional teaching techniques have been based on

the premise that a larger teaching set size would provide more difficult work than a smaller teaching set size. The average student was expected to find 20 spelling words harder to do than 10 spelling words. Faster learning for correct responses and faster reduction of error responses, as well as superior learning overall and mastery of the








69


minimum performance standard were not consistently found with either the large or the small set size. Teaching set size did not appear to be a variable that provided a consistent effect on learning spelling words. Despite the fact that initial accuracy varied by as much as 49% from one 10-word list to its matching 20-word list, no consistent influence on the above mentioned learning variables was noted.

















CHAPTER V

DISCUSSION AND CONCLUSIONS



At the beginning of this chapter, examination is given to uncontrolled sources of variance. The significance of teaching set size and initial level of difficulty on the four learning measures used in this study is the next topic discussed. Although the effects of set size and initial level of difficulty were mixed, certain implications can be made about their influence. Also discussed are the limitations of this study because of the teacher assistants used, sample, set size, and treatment design. Implications for teachers and school psychologists are then explored. Recommendations for future research and concluding remarks follow.



Discussion

Uncontrolled Sources of Variance

Traditional teaching methods in special education have been based on the easy task learning approach. Teachers have been taught that the smaller the number of items in the teaching set the lower the academic frustration. The underlying assumption of the increase in











teaching set size was that the 20-word list would be more difficult than the 10-word list, especially for special education children.

Several of the teacher assistants were skeptical that their subjects could learn 30 new spelling words. They felt that their pessimistic expectations about the larger set size would be communicated to the students, causing the students to do more poorly with the 20-word list than with the 10-word list. The one teacher assistant who was most vocal about task difficulty did work with a student who occasionally hid from her when it was time for the spelling session. Another teacher assistant worked with two students, one who responded very enthusiastically to the one-to-one attention being received and the other who was indifferent toward the spelling task. This latter teacher assistant, who was a secretary by profession, displayed unflagging enthusiasm toward both students.

These differences in the behavior of teacher

assistants and subjects were not controlled during this study and may have had some measurable influence on the outcomes. Such influence has been well documented in the literature (Rosenthal, 1966; Rosenthal & Jacobsen, 1966; Rosenthal & Jacobsen, 1968). One might logically expect experienced teachers to have more confidence and skills when teaching difficult tasks. Aides and secretaries have less experience with educational expectations of students











than certified teachers. The effect of their expectations may be exaggerated since they may be more intimidated by hard to do tasks.

Significance of Set Size

A comparison of these results was made within and

among subjects across word lists. Inconsistent findings between experiments for each subject were noted. Inconsistent results across exceptionality were also noted. There was wide variation across exceptionalities in celerations for correct responding, celerations for error responding, total learning, and mastery change from one experiment to the next. For example, all four of Dorothy's measures of learning for the 20-word list in experiment one were equal or superior to the same four measures for the 10-word list, whereas, only an equal or greater reduction of error responses and an equal or greater total learning in experiment two were associated with the 20-word list.

Set size did not seem to be controlling learning

outcomes systematically or exclusively. These findings are not consistent with Blake's (1975) conclusions that learning was affected by task size and that increments in set size made the task disproportionately more difficult, especially for the retarded learner. The common practice with EMH students of watering down the regular curriculum by reducing the amount of work completed (Gallagher, 1967;











Rothstein, 1962) should probably be revisited. Some students may benefit equally well from larger teaching set size as from a smaller teaching set size. More work needs to be done to determine which students, under what conditions, can profit from larger teaching set sizes. Significance of Initial Level of Difficulty

Examination of these results across initial level of difficulty also revealed inconsistencies. Celerations for correct responding, celerations for error responding, total learning, and mastery change varied widely from one level of initial difficulty to another. For example, the 10-word list in Dorothy's first experiment was 9% easier than the 20-word list. Equal or faster learning for correct responses as well as reduction of error responses were associated with the 20-word list.

A methodological point can be made about the measure of initial accuracy. Initial accuracy provides a way of gauging the success of randomization procedures. In this study words were randomly assigned to both set size conditions to ensure that initial accuracies of each paired word list would be equal. The variable of initial accuracy provided a sensitive measurement system that permitted one to see how the randomization actually affected level of difficulty. In this study, initial accuracies ranged from less 4% to 49%, indicating that some paired word lists were not of comparable levels of











difficulty. The randomization procedure used in this study was not as effective as originally desired, providing a caveat to future researchers. Initial levels of difficulty may provide an easy and useful measure of the effectiveness of the randomization procedure. Limitations of the Sample

One limitation of this study involved the

characteristics of the research sample. Each student involved in this study had been referred to the psychological services section of the Marion County, Florida, School System due to suspected learning problems. Generalizing these results to a wider population should be made with appropriate caution in light of the restriction which this limitation imposes. An increase in set size may have a completely different effect on the academic performance of students who are not suspected of having learning difficulties. Unreferred students generally tend to have greater academic success in school and may respond differently to interventions tried. Limitations by Set Size

Another limitation of this study was the size of the teaching sets used. The size of the large teaching set was double the size of the small teaching set. Blake (1975) suggested that increments in task size make the task disproportionately more difficult in that there is not a unit of change in difficulty for every unit change











in length. Doubling the set size from 10 words to 20 words in this study may not have made the spelling task disproportionately harder. W.D. Wolking (personal communication, June 19, 1987) found that a threefold increment in set size provided equal or better learning in vocabulary and math content areas with some students. Other set sizes and other academic subjects may produce different results.

Limitations by Treatment Design

Tawney and Gast (1984) have discussed alternating

treatment designs and their limitations. The alternating treatment design used in this study required a high level of consistency across teacher assistants administering the different spelling tasks. High procedural reliability is of critical importance when evaluating the data. Each teacher assistant was given the same set of instructions for administering the spelling timings. Any differences in the actual administration across teacher assistants may have caused subtle and uncontrolled differences in the way in which the independent variable was applied. Implications for Teachers

The implication of this study is that in slightly more than half the cases regular and special education subjects may learn at least as well with a larger teaching set size as with a smaller teaching set size. Therefore, teachers should begin to explore this issue further,











knowing that some students may benefit from a larger teaching set size, whereas other may not. In many of the experiments of this study there was little difference in how quickly a student learned new words or reduced error responses when the teaching set size was increased. Teachers may need to be trained to work with students under hard-to-do task curricula because some students may show enhanced learning from such a curricular approach.

The mixed results of this study also indicate that teaching set size and initial level of task difficulty were not systematically controlling variables. Such uncontrolled influences as teacher assistant expectations, the one-to-one attention each student received from the teacher assistant, and the varied professional backgrounds of the teacher assistants (some of whom had no teaching experience) may have been significant factors. Implications for School Psychologists

The main thrust of a psychological evaluation of children for special education classes today is the identification of those students who would benefit from an easy task curricular environment. School psychologists traditionally recommend placement in easy to do curricular environments for those students who are academically below grade level. The standardized test instruments currently being used by school psychologists may not be sensitive enough to differentiate those students who could benefit










from difficult task curricular environments from those students who require easy task curricular environments to thrive. The four special education students in this study showed greater learning of some of the larger set size words. Therefore, curriculum-based and criterionreferenced assessment tools may need to be developed to supplement the repertoire of standardized test instruments already being used by school psychologists. Such assessment tools may not only be more easily interpreted by teachers, but they may also be more sensitive in identifying those students who may benefit from the larger than traditional teaching set size.

The school psychologist's role as a consultant often precedes the school psychologist's involvement in the full fledged evaluation process for special education placement. Greater understanding of larger than traditional teaching set size curriculum strategies could enable school psycholgists as consultants to help teachers and administrators to design teaching strategies to the child's best advantage. The mixed results of this study indicate that some special education students may do well with hard to do tasks. Introduction of hard to do tasks in the regular classroom setting may be an appropriate prereferral intervention to carry out. Should this intervention prove ineffective, the particular student could then be referred for a psychological evaluation to











assess the need for an easy task curricular environment offered in many special education classes. Placement of the learning disabled or educable mentally handicapped student in an exceptional student education program would then become a more selective process. Differentiation could then be made between those students who may excel more in a larger than traditional teaching set size from those who may still need the traditionally easy task approach to instruction.

Consultation between the school psychologist and the special education teacher may also involve the introduction of hard to do tasks in the special education classroom setting. Since some enhanced learning with the larger set size was observed in this study, progress in the special education class may be faster if a larger set size is used while the learner may gain increased confidence in his/her abilities. These same arguments can be made for trying higher grade level tasks than is typically done.

Recommendations for Future Research

The mixed results of this study suggest that variables in addition to teaching set size were influencing the outcomes. Identification of these other variables should be carried out to gain better understanding of ways to enhance learning. One such unexamined variable was teacher/student resistance to hard











to do tasks. Following Gerent's (1985) recommended examination of this issue, its effect on the learning measures of one student in this study who hid from the teacher assistant remains unknown. There is a need to explore this issue more carefully.

The effect of a larger teaching set size on

self-concept enhancement may be a correlative issue that merits examination. The larger set size might also enable special education students to cover more areas of the curriculum, thereby allowing them to be compared more favorably to the regular education peers in terms of number of curriculum objectives mastered.

Longer range data collection is warranted to

determine if the student could adjust to and/or the teacher could support the student in a hard to do task curricular environment for an extended period of time. Each experiment conducted in this study lasted only a few weeks, and there was a brief intermission of one to two weeks followed by one replication.

Future researchers examining teaching set size should extend the range of increment from double the set size to triple the set size. This increase should provide information about a ceiling increment, beyond which effective learning can no longer take place.

A more homogeneous group of subjects should provide a larger within category sample from which conclusions can











be drawn. A group of strictly EMH subjects, for example, would provide results with greater generalizability to the EMH population.



Conclusions

The mixed findings of this study provided

inconclusive results. The enhanced learning with the large set size in some of the experiments, as well as the comparable learning (i.e., differences of less than 5%) between large and small teaching set size, provide sufficient challenge to the traditional, watered down curriculum approach to merit further research in this area. Other variables may influence learning more systematically. Identification of these variables is imperative if special and regular education programs are to provide the best services to meet the individual child's needs.











APPENDIX A


EXCEPTIONAL STUDENT EDUCATION PROGRAM ELIGIBILITY REQUIREMENTS

Programs for Educable Mentally Handicapped


Definition: One who is mildly impaired in intellectual and adaptive behavior and whose development reflects a reduced rate of learning. The measured intelligence of an educable mentally handicapped student generally falls between two (2) and three (3) standard deviations below the mean and the assessed adaptive behavior falls below age and cultural expectations.

Eligibility Criteria: Criteria for eligibility for a special program for the mentally handicapped as required by Rule 6A-6.3011(2)(a)-(c), FAC, are as follows:

A. the measured level of intellectual functioning, as
determined by performance on an individual test of
intelligence, is two (2) or more standard deviations
below the mean. The standard error of measurement may
be considered in individual cases. The profile on
intellectual functioning shows consistent sub-average
performance in a majority of the areas evaluated;

B. the assessed level of adaptive behavior falls below
age and cultural expectations; and

C. sub-average performance on an individually
administered standardized test of academic achievement
for the appropriate age level is demonstrated. A
behavioral observation or criterion referenced test
for a student whose level of functioning is not
appropriately measured by an academic test may be
substituted.

D. age of student











Programs for Specific Learning Disabilities


Definition: A specific learning disability is defined as a disorder in one (1) or more of the basic psychological processes involved in understanding or in using spoken or written language. Disorders may be manifested in listening, thinking, reading, talking, writing, spelling, or arithmetic. Such disorders do not include learning problems which are due primarily to visual, hearing, or motor handicaps, to mental retardation, to emotional disturbance, or to an environmental deprivation.

Eligibility Criteria: A student is eligible for special programs for specific learning disabilities if the student meets all of the following criteria:

A. Evidence of a disorder in one (1) or more of the basic
psychological processes. Basic psychological process
areas include visual, auditory, motor, and language
processes.

1. Documentation of process disorder must include one
(1) standardized instrument in addition to the
instrument used to determine the student's level
of intellectual functioning.

2. In addition, a district may establish criteria for
the use of more than one (1) instrument to
determine a process disorder and other criteria
which will assist in determining a process
disorder.

B. Evidence of academic achievement which is
significantly below the student's level of
intellectual functioning.

1. For students below age seven (7), evidence must be
presented that the student exhibits a significant
discrepancy between levels of intellectual
functioning and achievement on tasks required for
listening, thinking, reading, talking, writing,
spelling or arithmetic.

2. For students below age seven (7), evidence must be
presented that the student exhibits a discrepancy
of one (1) standard deviation or more between an intellectual standard score and academic standard
score in reading, writing, arithmetic, or
spelling.








83


3. For students ages eleven (11) and above, evidence
must be presented that the student exhibits a
discrepancy of one and one-half (1-1/2) standard
deviations or more between an intellectual
standard score and academic standard score in
reading, writing, arithmetic, or spelling.

4. A district may establish criteria for the use of
more than one (1) instrument to determine a
deficit area, and other criteria which will assist
in determining an academic deficit.











APPENDIX B

Twenty-Word List 1 for Dorothy



1. food - What kind of food do you want?
2. she - She will like it.
3. into - He got into the car.
4. barn - The cow is in the barn.
5. feet - His feet were bare.
6. went - He went with his father.
7. now - I want it now.
8. work - Do you work today?
9. little - That is a little box. 10. play - Can I go out and play? 11. green - My eyes are green. 12. was - Was she there? 13. said - She said it to me. 14. can - I can do that. 15. stop - Please stop doing that. 16. blue - The book is blue. 17. look - Look at the dog. 18. day - This is her third day here. 19. read - Read me a story. 20. brown - My dog has brown hair.







85


Ten-Word List 1 for Dorothy



1. them - Give them to me.
2. bus - I took a bus to town.
3. saw - I saw the moon.
4. funny - The clown was very funny.
5. good - You are good to me. 6. car - My car drives fast. 7. big - How big is the box?
8. see - See what I have.
9. black - It was black inside. 10. three - Three pieces were left.











Twenty-Word List 2 for Dorothy



1. ring - That is a pretty ring on your finger.
2. ship - We saw a big ship sail by.
3. lamp - Turn on the lamp so you can see.
4. clap - Clap your hands twice.
5. bag - The food is in the bag.
6. tail - I tied a bow on my dog's tail.
7. joke - That was a funny joke.
8. desk - Do your work at your desk.
9. bank - All my money is in the bank. 10. wet - I fell in the mud puddle and got wet. 11. farm - I grew up on a farm. 12. well - Are you feeling well? 13. tub - He took a bath in the tub. 14. chop - Don't chop down that tree. 15. let - Let me help you with that. 16. game - I want to play a game with you. 17. hard - That is a hard question to answer. 18. dot - Don't forget to dot your is. 19. jar - Pour the water into this jar. 20. pail - Put the sand in this pail.







87


Ten-Word List 2 for Dorothy



1. fish - I like to fish on the weekends.
2. pen - Please put you name down in pen, not pencil.
3. hay - My horse likes to eat hay.
4. fast - Boy, can you run fast.
5. bird - There is a pretty bird in the cage.
6. wig - She wore a wig on her head. 7. doll - Can I play with your doll?
8. tent - You can use my tent to go camping.
9. heat - Heat this pot of water on the stove. 10. wind - The strong wind blew my hat off.










Twenty-Word List 1 for Keesha


1. knights
2. examined 3. instinct 4. rumored 5. delicious 6. octave

7. hearth

8. terrific
9. salmon 10. briskly 11. billows

12. strutted 13. dragon 14. customers

15. whether 16. amount 17. musical 18. pacing 19. oars 20. knowledge


The knights in shining armor arrived. My physician examined me. He worked solely on instinct. He was rumored to be missing. The pie was delicious. The third octave was what I wanted to
play.
It was warm by the hearth of the
fireplace.
They are terrific at their work. I like to eat smoked salmon. The wind blew briskly. Billows of smoke poured from the burning
house.
The chicken strutted across the yard. The dragon blew out flame. There were no customers in the store
tonight.
Whether or not to do it is the question. What is the amount I owe you? The musical play was enjoyed by all. The dog kept pacing up and down the yard. There were no oars in the rowboat. He seems to have a lot of knowledge.











Ten-Word List 1 for Keesha


1. sentinel
2. hymn
3. nostrils

4. sharpness

5. sensitive
6. calmly 7. freedom
8. wreath
9. scientists 10. considerable


The sentinel stood guard at the fort. We sang a Christmas hymn. His nostrils widened when he smelled
smoke.
The sharpness of the knife made it
dangerous.
She is sensitive to that perfume. He calmly left the room. All they wanted was their freedom. She made the Christmas wreath. Scientists do important research.
- He took a considerable amount of time to
complete the test.











Twenty-Word List 2 for Keesha


1.
2.

3.
4.

5.
6.
7.
8.
9.
10.


arrangement transferred

clipped appointment

prehistoric suitcase windmill weightless disappear injured -


11. imperfect

12. imitation 13. reflection 14. wadded

15. quicken

16. remove 17. uneasy 18. everywhere 19. earthquake 20. eyesight -


The flower arrangement looked pretty. I was transferred to a different
classroom.
She clipped her fingernails last night. Your appointment is for two o'clock
today.
This dinosaur was a prehistoric animal. I packed my suitcase for a long trip. We saw a windmill in Holland. The astronaut was weightless in space. The magician made the rabbit disappear. The football player was injured in last
night's game.
This diamond is imperfect because of a
crack.
That actor did a good imitation of me. I saw my reflection in the pond. He wadded up his paper and threw it in
the trash can.
We must quicken our pace to catch up
with them.
Please remove your shoes. He was uneasy being in that room. They were everywhere around us. The earthquake destroyed many buildings. My doctor helped me get my eyesight
back.











Ten-Word List 2 for Keesha


1. puncture -


giraffe parachute

tongue bugle lizard plumber quiver tomorrow autumn -


Be careful not to puncture yourself with
that nail.
A giraffe can be up to thirty feel tall. He used a parachute after he jumped out
of the plane.
Don't stick your tongue out at me. He blew the bugle to wake everyone up. That is an ugly lizard you have for a pet. Call the plumber to fix our kitchen sink. There were six arrows left in his quiver. You can finish your work tomorrow. Autumn is one of the four seasons of the
year.


2.
3.

4.
5.
6.
7.
8.
9.
10.











Twenty-Word List 1 for Jesse


her them food tell please peanut stopping frog street

birthday climb beautiful waiting cowboy high people mice corn room gray -


That belongs to her. Give them to me. What kind of food do you want? Tell me what you like. Please stop by again. Peanut butter tastes good. Why are you stopping the car? A frog jumped in front of me. Look both ways before you cross the
street.
Happy birthday to you. I will climb up the ladder. That is a beautiful dress. I am waiting for a cab. The cowboy rode a white horse. How high can you jump? They were nice people. Mice are afraid of cats. He likes corn on the cob. This room is mine. The old man had gray hair.


1 .
2.
3.
4.
5.
6.
7.
8.
9.

10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.




Full Text

PAGE 1

THE EFFECTS OF TEACHING SET SIZE ON LEARNING WITH SPECIAL AND REGULAR EDUCATION CHILDREN By MICHAEL L. MISHKIN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1 987

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ACKNOWLEDGEMENTS I wish to acknowledge those people who contributed to the successful completion of this study. Thanks go to Dr. William Wolking provided much support, guidance, and patience as chairman of my doctoral committee. He helped me to blend my knowledge of * education and psychology. Thanks also go to the other members of my committee: Dr. Janet Larsen, for her unflagging interest in and enthusiasm with my educational pursuits, and Dr. Robert Jester, for his humanistic approach to teaching me research design. A special thanks go to my family. My parents, Arthur and Arlene Mishkin, have always encouraged me in my educational and professional endeavors. My twin sister, Marilyn, sought similar educational pursuits and lent me support and encouragement during all of my school years. My older sister, Francine, provided a model for high educational pursuits in my family. Thanks go to Ms. Lisa Hurewitz, for her diligence and professional expertise in the preparation of this research manuscript. ii

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I could not have conducted this research without the teacher assistants who collected the data. A special thanks also go to those six subjects in my study, Dorothy, Jesse, Keesha, Marketa, Matthew, and Mikki, whose involvement in this research may improve the learning experience for their peers. iii

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TABLE OF CONTENTS Page ACKNOWLEDGEMENTS i i ABSTRACT vii CHAPTERS I INTRODUCTION 1 Overview of the Study 1 Significance of the Problem 4 Statement of the Problem 6 Limitations and Delimitations of the Study... 7 Definition of Terms 7 Overview of Remainder of Dissertation 9 II REVIEW OF THE LITERATURE 10 "Watered Down" Curriculum Approach 11 Easy Task Learning Environments 15 Within-Task Variables 18 Across-Task Variables 22 Summary 23 Precision Teaching 24 . Studies on Hard-to-do Task Learning and Leap Ups in Curriculum 25 Summary 29 , Recapitulation * 30 III METHODOLOGY !!!!!!! 32 , Overview of the Study 32 p., ' Variables Under Investigation 32 Independent Variable [ 32 Dependent Variables ] 33 Setting | Subjects !!!!!!!! 38 iv

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Page Experimental Design 39 Procedure 42 Pre-experimental Phase 42 Experimental Phase 43 Material 44 Curricular Materials 44 Data Recording Form 46 Data Recording and Analyses 46 Data Recording 46 Data Analyses 47 IV ANALYSES AND RESULTS 49 Celeration 50 Total Learning Rate 60 Mastery 61 Across Category Summary 62 Accuracy 64 Recapitulation 68 V DISCUSSION AND CONCLUSIONS 70 Discussion 70 Uncontrolled Sources of Variance 70 Significance of Set Size 72 Significance of Initial Level of Difficulty 73 Limitations of the Sample 74 •r Limitations by Set Size 74 Limitations by Treatment Design 75 Implications for Teachers 75 Implications for School Psychologists 76 Recommendations for Future Research 78 Conclusions gg APPENDICES A EXCEPTIONAL STUDENT EDUCATION PROGRAM ELIGIBILITY REQUIREMENTS gi B WORD LISTS 84 C DATA RECORDING FORM 108 V

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Page D FREQUENCY MULTIPLIERS FOR CELERATIONS , MASTERIES, AND ACCURACIES 100 REFERENCES 118 BIOGRAPHICAL SKETCH 125 vi

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy THE EFFECTS OF TEACHING SET SIZE ON LEARNING WITH SPECIAL AND REGULAR EDUCATION CHILDREN By Michael L. Mishkin December 1987 Chairman: Dr. William D. Wolking Major Department: Counselor Education This study was designed to assess the effects of large task size versus small task size on the learning of special and regular education children. A single subject design with one replication per subject was used with six subjects. Two subjects each were learning disabled, educable mentally handicapped, and regular education. Each pair of subject types was randomly selected from a pool of subjects of the respective educational classification. Each subject was given a pretest to identify 30 words the subject could not spell correctly. Each word chosen was randomly assigned to either a 1 0-word list or a 20-word list. Each subject's performance was measured once a day with each word list. Upon mastery of the spelling words. vii

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a new pretest was given and an identical procedure was followed in the replications involving the new words. The study involved four dimensions of students' spelling performance. Three of these dimensions were measures of learning or change in spelling performance over time. The last dimension was the degree of mastery of the spelling material. Initial accuracy of spelling on the first day of data collection was also examined. Differences between these dependent variables were obtained, and an arbitrary standard of a 5% difference between these variables for different task sizes was the criterion of comparison used to suggest a practical difference. Mixed results were found within and across subjects and exceptionalities. Set size did not systematically or exclusively affect learning outcomes. Initial level of difficulty also did not systematically control learning. These findings support the conclusion that the easy task curriculum approach may not always be best. Some students, on some occasions, can improve faster with larger than traditional set sizes. Greater understanding of larger than traditional teaching set size curriculum strategies is needed to maximize students' learning. viii

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CHAPTER I INTRODUCTION Overview of the Study Special education placement of academically disadvantaged students has been a major issue since passage of Public Law 94-142. This federal law requires every handicapped child and youth to be provided special education and related services at public expense. Special education involves use of specially designed instruction to meet the unique needs of handicapped children. Public Law 94-142 also requires these children to be placed in the least restrictive educational environments, with as much time spent in regular education classes as possible. Research findings related to educating exceptional children in regular education settings, as reviewed by Corman and Gottlieb (1978), suggested that instructional techniques are more important to improved academic achievement than the setting in which children learn. However, in light of available evidence which has pointed toward the lack of academic achievement, questions have been raised about the superiority of the social environment provided by the special class (Siegel, 1969; Sparks & Blackman, 1965). 1

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2 Precision teaching, a rapidly expanding technology of teaching and learning, has facilitated accurate accumulation of data on students' learning rates. Until recently, precision teachers employed an "easy task" or simplified approach to teaching exceptional students. In this approach teachers selected tasks with few or no errors and worked on improving the speed of responding. Typically the instruction was boring and rates of learning frequently were low. Since 1978, precision teaching research has been done (e.g., McGreevy, 1980) that suggested greater learning could be accomplished when learning environments included initially hard-to-do tasks. McGreevy 's early work in this area (McGreevy, 1978) led him to believe that children did not need easy-to-do tasks to stay motivated and could learn more with initially high error rates. Johnson (1961, cited in Johnson, 1962) had earlier concluded that little learning could take place when much of the motivation or drive to achieve had been removed from the learning environment, as was the case with exceptional student education classes whose main objective was to reduce academic frustration. Bijou (1970) indicated that the school psychologist should work to prevent academic retardation. However, school psychologists have usually not been involved with direct teaching processes except as consultants. In the

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context of school psychology, consultation can be defined a process of interaction between two professional persons — the consultant, who is a specialist, and the consultee, who invokes the consultant ' s help in regard to a current work problem with which he is having some difficulty and which he has decided is within the other's area of specialized competence. (Caplan, 1970, p. 19) Consultation with both regular and exceptional student education teachers can help create intervention techniques that improve the academic performance of students in the classroom. Such consultative work conducted prior to a full-fledged psychological evaluation could be advantageous. Observation and evaluation of the teaching-learning process itself could provide the classroom teacher with more immediate feedback than would feedback from a child's participation in an exceptional student education program for several weeks. Communications between the teacher and school psychologist in a consultation situation also would be easier to carry out than the communications among the individual education plan committee members responsible for the child's special program placement. This consultation could also serve to reduce caseload demands on special education teachers, allowing them to provide more attention to needier students.

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4 Significance of the Problem There has been little research on the learning of special education students who are given academic tasks of different teaching set sizes. Set size refers to the number of unique items to be learned. The basic premise of traditional teaching methods is that a larger teaching set size is more difficult to learn than a smaller teaching set size. Should curricular environments with a larger teaching set size prove to provide learning rates comparable to curriculum environments with a smaller teaching set size, then questions may be raised about the traditional teaching methods of special education students that involve easy to learn tasks and low error rates. Moreover, it was believed that study of this variable should provide more useful information about generalizability of findings if regular education students were included in this study. Certain results could affect existing teaching approaches toward children of all ability levels. School psychologists, in their evaluation of children for special education classes, assist educators in placing children in a curriculum in which error rates are low. For those children who do not thrive in such a curricular environment further consultation may be needed. it is therefore important for school psychologists, who must consult with special education teachers, to develop

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5 techniques to enhance the learning rates of students. Development of these techniques will not only allow the school psychologist to break from the traditional role of diagnostic evaluations, but will also provide school psychologists with more data about the teaching process with which to improve their role as consultants. Standardized instruments for assessment of academic progress may not be sensitive enough measures of academic performance, nor are they easily interpretable by teachers, it would be helpful to the school psychologist if appropriate curriculum-based and criterion-referenced assessment tools were available. Significant results, relating the size of the teaching set to change in learning and improvement in accuracy for special and regular education students, would provide valuable information for both the practitioner and the researcher in the areas of assessment and applied learning tactics. Having more accurate assessment information, as well as a greater understanding of larger than traditional teaching set size curriculum strategies, also would enable consultants to help teachers and administrators to design teaching strategies tailored to the child's best advantage. Placement of the learning disabled or educable mentally handicapped student in an exceptional student education program would then become a more selective process. Those students who could excel with a larger

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6 than traditional set size could be differentiated from those who still needed the traditionally small set-small step (easy task) approach to instruction. Progress in the special class also may be faster if a larger set size is used, and the learner may gain increased confidence in his or her abilities. Researchers interested in curriculum strategy issues may find results from this study to be useful in furthering the understanding of learning rates under curriculum environments using a small teaching set size versus a large teaching set size. Although this issue has recently been examined in the precision teaching literature (Bower & Orgel, 1981; McGreevy, 1978), relatively less is known about this approach in the context of traditional (i.e., nonprecision teaching) strategies of teaching. More research is clearly needed. Statement of the Problem The focus of this study was the effects of large teaching set size versus small teaching set size on students' learning rates. The following question was investigated: What are the effects of two set sizes (small set size comprised 10 spelling words, large set size comprised 20 spelling words) on several measures of learning and performance with educable mentally

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7 handicapped, learning disabled, and regular education students? Limitations and Delimitations of the Study Interpretations of the results of this study need to be made in light of certain delimitations. The subjects lived in Marion County, Florida and had been referred for psychological evaluation to assess possible learning difficulties. This group was a special population whose characteristics may have influenced the results. The ages of the subjects were between eight and nine. The academic task chosen to be measured was spelling from dictation. The findings were further limited by such difficult to control factors as test anxiety and fine motor difficulties that may have been present in some of the subjects. The people used as teacher assistants were a bigger limitation. The children used were probably representative. Definition of Terms Many technical terms from precision teaching and behavior analysis are used in reporting this investigation. These terms are introduced throughout the first three chapters in their appropriate context and are defined below: Accuracy percentage of correct responses.

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Celeration change in frequency per unit of time; measured by the ratio of two frequencies one week apart drawn on a learning line. Day line vertical line on the standard behavior chart. Fluency final performance for rate correct and rate incorrect (see mastery). Frequency basic unit of behavioral measurement; the number of movements per unit of time (minute). Frequency multiplier value by which one frequency is multiplied or divided to obtain a second; X assigned when the second number is greater than the first; / assigned when the second number is less than the first. Learning a change in performance per unit of time; also called celeration. Leap up an upward curriculum change in scope and sequence to a point where the student is making many errors and few correct responses. Mastery percentage of performance standard achieved. Mastery change ratio obtained by dividing the ending mastery by the beginning mastery. Performance standard criterion of minimum proficiency. Precision teaching comprehensive instructional system for accelerating learning and maintaining high proficiency, based on direct and continuous measurement procedures. Standard behavior chart standard, six-cycle semi-logarithmic chart that displays frequency as movements per minute and learning as movements per minute per minute. Teaching set size task size reported in terms of the number of unique items to be taught. Total learning measure multiplier of the celerations for correct responding and the celerations for error responding combined.

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Overview of Remainder of Dissertation A review of the literature and a discussion of the theoretical frameworks underlying the various aspects of this study can be found in Chapter II. Implications for assessment tactics and applied learning are explored. Support for the instrumentation and assessment procedures are also presented. The variables under study are listed in Chapter III. The population is described and sampling procedures are listed. Descriptions of the research design, research procedures, psychometric characteristics of participants, and data analysis procedures are provided. Methological limitations of the study are discussed. Chapter IV contains the experimental findings. A discussion of the research questions in light of the results is also presented. Chapter V contains a discussion of the results and conclusions. Uncontrolled sources of variance are explored first, followed by the significance of the findings of this study. Generalizability and limitations of the study are discussed next. The implications of these results and recommendations for future research complete the discussion.

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CHAPTER II REVIEW OF THE LITERATURE The literature review is divided into three sections. The focus of the first section is the historical perspective for the research in its description of the traditionally "watered-down" or easy to do curriculum approach used with the mildly and moderately retarded learners. More recent labels for such individuals include "learning disabled" and "educable mentally handicapped." Based primarily on an informal review of popular textbooks on teaching the mentally retarded and mildly handicapped, as well as a review of articles in journals dealing with special education, a history of teaching these types of students in easy task curriculxira environments is provided. Some research implications of this curriculum approach are also discussed. The second section includes an examination of some of the difficulties with operational definitions and research findings on easy to do tasks and low error learning environments. Presentation of the current practices on educating the mildly handicapped with easy task curricula provides a research context for the study. 10

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1 1 The third section contains a review of the precision teaching literature on difficult task learning: large sets and curriculiim leap ups. This section is based on a review of all articles from the Journal of Precision Teaching as well as Eshleman's (1983) compilation of all known precision teaching references. Many of the references in Eshleman's compilation were in the form of unpublished work (e.g., papers presented at conferences), thereby limiting the availability of some of the precision teaching research. "Watered Down" Curriculum Approach Those children classified as mildly handicapped have traditionally been served in special education classes. The term mildly handicapped refers to students who have been labeled as educable mentally retarded (more recently referred to as educable mentally handicapped), behavior disordered (now termed emotionally handicapped), and learning disabled (Miller & Davis, 1982). However, educable mentally handicapped students have been recognized and educated for a considerably longer period of time than have children who have more recently been classified as emotionally handicapped or learning disabled (Kauffman & Payne, 1975). The first topic of this section is the findings associated with educating educable mentally handicapped (EMH) students in special education

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12 classes which have emphasized a watered down curriculum approach. The most pervasive practice in the area of curriculum for the retarded youngster has been the use of a watered down general education curriculum (Klein, Pasch, & Frew, 1979). This approach appeared to have been established without any guiding philosophy. Rather, it was fostered by leaders in the field, such as Kirk and Johnson (1951), who suggested that two principles should guide the presentation of subject matter to retarded learners: "concrete level" and "gradual rate." Kirk, along with , others, further expressed a somewhat paternalistic attitude toward retarded learners, implying that the development of specific content and objectives be avoided when teaching them because of the uncertainty of their achievement. For example, the opinion that retarded learners should be taught to read to the best of their ability was accepted as policy and offered a ready excuse for teachers who made little attempt to systematically teach these students to read (Klein et al., 1979). Although a few special education programs for the retarded were established as early as 1915, special classes for EMH students only began to flourish in the early 1950s (Robinson & Robinson, 1976). The initial basis for these classes was the homogeneous grouping that narrowed differences in mental ability. A specialized

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1 3 curriculum was then developed, thereby allowing teachers to be able to work with a group of students who had similar interests and academic needs (Robinson & Robinson, 1976). In reality, the range of educationally relevant behaviors in these exceptional student education classes was at least as great as the range in regular classes (Bruininks, Rynders, & Gross, 1974; MacMillan, 1971). This heterogeneity came about because educational skills are imperfectly correlated with mental age or intelligence quotient, which formed the basis for grouping in these special classes, and because the chronological age range was typically wider than the range in regular classes (Robinson & Robinson, 1976). This wide range of skills and the absence of a readily available, specialized curriculum prompted EMH program teachers to water down the regular curriculum by lowering the level of difficulty of material and the amount of work to be completed. This approach was especially common in such skill areas as reading and arithmetic. it also was practiced by simply following the pattern of the general curriculum, but at a slower pace (Gallagher, 1967; Rothstein, 1962). Research findings from EMH classes that use a watered down curriculum approach indicated that little learning may have actually taken place. Since progress was not judged in terms of the full range of curriculum aims for the nonretarded student, it was tempting to let matters

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1 4 slide along at a comfortable pace, thereby minimizing frustration (Robinson & Robinson, 1976). Teachers often assigned a higher priority to personal adjustment and tended to demand less achievement than their pupils could deliver (Fine, 1967; Schmidt & Nelson, 1969). Johnson (1961, cited in Johnson, 1962) emphasized that despite the instruction provided, little learning could take place when much of the motivation or drive to achieve had been removed from the learning environment, as in exceptional student education classes whose primary objective was to remove pressures and to make the child happy. Teacher expectations about student performance also were powerful influences (Guskin & Spicker, 1968). This watered down curriculum approach seemed to have been applied more recently to all classes for the mildly handicapped. Alley and Deshler (1979) noted it to be one of the most common approaches used with secondary school-aged, learning disabled students. Miller and Davis (1982) recommended a modified regular curriculum approach in noncategorical (i.e., regular education) classrooms. In summary, special education has had a history of educating mentally retarded students in learning environments where errors are kept to a minimum by employing a watered down curriculum approach. The net result of this placement has been diminished learning for several reasons. Teachers have come to expect too little

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15 of mentally retarded students. Programming involved the wrong curriculum objectives or no clear objectives. Attitudes and expectations also played a crucial role in motivating students to learn and the teachers to teach. Exceptional student education teachers often fostered the idea of slowness in their students by rationalizing that such a perception would protect them from failure and frustration. In actuality, this approach may have promoted a lack of effort on the part of these students, who were initially placed into special programs because their earlier efforts did not pay off. Easy Task Learning Environments Examination of the general learning environment can be made across the continuum of task difficulty level. There is a dichotomy between difficult task and easy task learning environments. In a difficult task learning environment students are presented tasks that are initially difficult to do, and instruction is designed to produce rapid reduction of errors. An integral part of an easy task learning environment involves assignment of tasks that are initially easy to do. Since there are few errors to reduce, the teacher's role is often reduced to providing a supervised practice. This approach is intended to provide students with positive learning experiences; if the task is easy enough, there will be

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16 little chance of failure or of practicing wrong answers, A common approach is to present curriculum steps that are small and carefully sequenced from easiest to hardest. Determination of the degree of difficulty of the task and the means of increasing the level of difficulty has not been clearly documented. A review of the literature on curriculum and instructional strategies provided indications that the terms used to describe this topic are inconsistent. Wehman and McLaughlin (1981) have tried to give useful definitions. The term "instructional strategies" was a label that reflected how to teach and included the various methods, materials, and time allocations used in teaching. A "domain" was a set of content and behavior elements which potentially could be taught. It was synonymous with curriculum area, such as arithmetic, language, motor, etc. A teacher was expected to have a very clear understanding of what the domains included. This understanding was to be in the form of a sequence of skills for each domain. This information was referred to as scope and sequence information. Scope referred to what was taught, both the broad and specific skills, and sequence referred to the order in which the skills were taught. Sequence usually followed a graduated continuum from easy to difficult. : Task analysis is the breaking down of specific skills into smaller steps which may be easier for the child to

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1 7 learn. This process involves a logical sequencing of steps from simple to complex or beginning to end. Skill sequencing may be considered a functional progression of instructional objectives within a given domain. It can "provide a framework of tasks or objectives within which many types of instructional programs may be organized" (Williams & Gotts, 1977, p. 221, cited in Wehman & McLaughlin, 1 981 ) . These definitions have not been helpful to those who want to design and experimentally control easy and difficult tasks. Mercer (1979) also pointed out that reviews of studies on the sequencing of skills or skill hierarchies provide no conclusive evidence regarding the validity of hierarchical orderings of specific skills. Since no systematic definitions of easy and difficult seemed to exist, a framework can be proposed that refers to potentially manipulable variables that seem likely to make a task easy or difficult. Task difficulty level has been derived from the concept of curriculum step size. Frequently, steps were defined as logical breakdowns of skills, and small steps were defined as a further breakdown of these skills (Wehman & McLaughlin, 1981). Step size was defined in terms of the variables which made a task easy to do or difficult to do. These variables have been viewed on two levels: within task and across tasks. Three within-task

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18 variables seemed to be important: (a) the number of steps within the teaching sequence, (b) the number of units in the teaching set, and (c) the procedures which control prompting and fading. Across-tasks variables included (a) time spent on curriculum, (b) number of steps in the curriculum, and (c) how many steps are skipped in moving up a vertical curriculum sequence. The following sections are organized around the way these six variables have been addressed in the traditional literature and how easy task learning environments have been used in educating mildly handicapped students. Within-Task Variables Number o f steps . This variable refers to the number of steps needed to teach a task. The small step approach within task involves breaking down a task into smaller subskills. This can be accomplished by breaking existing steps down further or by adding steps. Many educators have advocated this small step approach with mildly handicapped students to enable them to receive reinforcement after each small step and to experience much success with few errors (Adamson & Adamson, 1979; Haring & Bateman, 1977; Lowenbraum & Affleck, 1976). Smith (1974) strongly advocated such an approach with mildly handicapped students. In comparing the curriculum goals for the educably mentally handicapped and the intellectually normal, he stated that:

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1 9 the goals to be achieved by both groups are quite similar during the early stages. To be sure, though, it may be essential that the special education teacher be quite exacting in "fractioning-down" each skill into very small skill components so that the youngsters are not placed in a pedagogical situation in which they are expected to make inordinately large leaps from one set of skills to another without having first demonstrated competence in those smaller areas that lie between. For intellectually normal children one does not have to be as careful to delineate all the precise intervening skills (as well as teach for each) since these youngsters seem to have greater facility for filling in gaps and making larger conceptual leaps. (p. 83) Myers and Hammill (1976) suggested that scope and sequence charts have not been notably successful with mildly handicapped. They argued that their ineffectiveness was partially due to the tasks' not being broken down into small enough steps to enable the teacher to teach only one element of a task at a time. They suggested that students with learning disabilities need specific, discrete, and sequential teaching. These students need to know the one thing they are attempting to learn. Smead (1977) argued that small, carefully guided steps were insufficient by themselves without being coupled with massive general experience. Task size . Task size, or amount or material, refers to the length of the task, the number of items to be learned (Blake, 1976). Reduction in the number of items in the teaching set for mildly handicapped learners has

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20 been part of the small step approach to teaching them. The fewer the items presented to a student at one time the smaller the step. The assumption behind this was that the smaller step would have provided the student with more success by having allowed him or her to learn items more quickly (Howell, 1979). Early work dealing with the concept of task size was provided in the field of psychology. Examination of the length of material to be memorized and to consequent retention was conducted by Kjersted (1919), Robinson and Heron (1922), and Robinson and Darrow (1924) who found that task difficulty increased disproportionately with task length for adults. The topic has not been studied extensively since their work (Blake, 1975). Blake (1975) believed that the task size strongly influences learning. She described it: "When material is added, the task gets disproportionately harder. That is, there is not a unit change in difficulty for every unit change in length. Instead, as material is added, the task becomes very much harder" (p. 369). She studied the effect of task length on learning sentences, concepts, sight vocabulary, synonyms, and homonyms in the performances of retarded and normal pupils. Some of her findings supported the contention that learning was affected by task size and that increments made the task

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disproportionately more difficult, especially for the retarded learners. Prompting and fading . Two important and frequently used instructional strategies with mildly handicapped students have been prompting and the fading of prompts (Salvia & Sindelar, 1982). Two questions were essential in examination of these strategies: When should fading of prompts begin? How rapidly should it proceed so as not to disrupt the child's performance? A comparison of data collected during the original phase and after the first step in fading procedure could be made. Similarity in the rate of improvement during the two phases may have indicated that the first step had been successful; i.e., the child had maintained growth even though a less pronounced prompt had been used. If the rate of improvement decreased, this may have meant that too large a step had been taken and that an intermediate step was required. Extensive work with prompting and fading was conducted by Sidman and Stoddard (Sidman & Stoddard, 1966; Sidman & Stoddard, 1967; Stoddard & Sidman, 1967). The researchers developed a program to teach nonverbal autistic children a difficult circle-ellipse discrimination. Judicious timing of cue presentation and fading as well as the insertion of a few intermediate steps in lieu of many smaller steps accelerated learning.

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22 Across-Task Variables Time spent. The amount of time spent on a particular task refers to how slowly or quickly a teacher moves through the curricular sequence. The basic idea underlying literature of this nature with the mildly handicapped was to teach more slowly those students who could not learn as fast (Howell, 1979). The same objectives taught in the regular classroom setting were taught to the mildly handicapped student, but with more time allowed for each step. This approach did not permit the exceptional student exposure to subsequent parts of the curriculum as early as the normal student, because it was based on a calendar-based criterion for teaching rather than a performance-based criterion. It further ensured that the exceptional student would continually fall further behind academically. Number of steps . The number of steps in a curriculum sequence refers to the number of objectives into which a total curriculum is divided. This number can vary according to the curriculum guide used or how the teacher decided to break down the objectives into smaller steps. Miller and Davis (1982) cautioned teachers of the mildly handicapped when curriculum guides were used for reading, math, social studies, and language arts, because the objective may have been stated in broad, global terms that needed to be broken down for handicapped learners.

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23 Step up a vertical curriculum . The size of the step up in a vertical curriculum refers to the number of levels in a curriculum sequence that are "jumped up" or "leaped up" at one time (Eaton & Wittman, 1982). The term "jump up" refers to a moderately daring movement, whereas the term "leap up" refers to a very daring movement. An example of a jump up is moving a student from one-place subtraction with regrouping to three-place subtraction with regrouping. The concept is discussed further in the section on precision teaching literature. Summary Six variables have been identified that seemed to help logically to define the level of difficulty of a task. These variables have been derived from the generic concept of step size. The small step approach to learning has been most frequently used with mildly handicapped children. More specifically, the modifications involved addition of more steps to skill learning, presentation of a smaller set size, spending more time on a particular step, and breakdown of curriculum sequences into smaller steps. Little empirical evidence has supported the use of easy-to-do tasks to educate mildly handicapped students. Attention to the details of when to prompt and how to fade prompts has shown potential for improving learning.

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24 Precision Teaching For many years precision teachers charted students' performances, while continuing to implement traditional public school curriculum strategies (McGreevy, Thomas, Lacy, Krantz, & Salisbury, 1982). Congruent with the rest of special education, precision teachers were "caught up" in the small step, easy task approach to instruction. Within the precision teaching population a great deal of attention has been focused on the attainment of functional fluency and mastery levels of performance (Bower & Orgel, 1981). There has been little evidence to suggest that students who show low performance frequencies in simpler skills would also show low performance levels in more demanding tasks (Barrett, 1979). The primary focus of precision teachers has been "the provision of curricular and other environmental arrangements which accelerate acquisition of fluency and mastery attainment" (Bower & Orgel 1981, p. 3). The potential contributory effects of difficult tasks on learning had been overlooked until Neely's 1978 study (cited in Bower & Orgel, 1981), because errors were to be avoided. All (1977) described the positive effect of high error rate from difficult tasks on learning appropriately: "The two-line learning picture dramatically and graphically represented the possible honeymoon

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25 relationship of initial high rates of errors and correct learning" (cited in Bower & Orgel, 1981, p. 3). Bower and Orgel (1981) reported that Lindsley began to question the effectiveness of curricular strategies involving hard to do tasks that emphasized high initial performance and few errors in 1978. He felt that this approach may have provided less opportunity for learning. Therefore, strategies to generate initially high error rates through hard-to-do tasks were suggested as a means of providing a more efficient and effective learning environment. Empirical evidence showing that errors could serve as opportunities to accelerate learning was provided in Neely's 1978 6-year study involving his supervision of a special education program. His data indicated that accelerated learning took place when students were encouraged to work on skills that produced initially high error rates. Studies on Hard to do Task Learning and Leap Ups in Curriculum ~ ~ A review of the precision teaching literature in the Journal of Precis ion Teaching , carried by this researcher, located six studies that addressed the issue of hard to do task learning and leap-ups in curriculum (McGreevy, 1978; McGreevy, 1980; Stromberg & Chappel, 1980; Bower & Orgel, 1981; Eaton & Wittman, 1982; McGreevy et al. , 1982). A

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26 seventh relevant study was a doctoral dissertation on curriculum leap-ups (Gerent, 1985). McGreevy in 1978 conducted the first of such studies to explore the possibility that initially hard to do tasks may have been easy to learn (cited in McGreevy, 1980). He compared the initial correct performance and learning of a group of mildly handicapped elementary school children on similar screening and remediation tasks. He found that screening tasks administered daily for 10 days without instruction produced lower initial correct frequencies and higher correct celerations. On the other hand, he determined that "see-say words" remediation tasks were 4 times easier to do but 1.3 times harder to learn than the similar, previously administered screening tasks. Even though the students learned these tasks at the rate of XI. 2 per week (the preceding X indicates accelerating rate), McGreevy concluded that the remediation efforts had been relatively ineffective. He further concluded that children did not need easy to do tasks to remain motivated, they could have learned more than originally thought possible, and a lower initial performance provided a greater opportunity for learning. In his second project, McGreevy (1980) once again demonstrated low initial performance followed by rapid learning in an 18-year-old moderately retarded young man. The subject was given a see-say task on the first 29 words

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27 of Wilson's Essential Vocabulary. The initial accuracy ratio of /1 9 (the preceding / indicates decelerating rate) attested to the difficulty of the task; errors vastly exceeded corrects. However, subsequent celerations of X2.5 for corrects and /2.6 for incorrects suggested that the low initial performance provided a greater opportunity for learning. McGreevy (1980) also suggested that hard to do (i.e., low initial performance) did not necessarily mean hard to learn (i.e., subsequently slow learning). Stromberg and Chappel in 1980 attempted to teach a math curriculum to an entire second grade class at a pace suggested by the adopted text (cited in McGreevy et al. 1982). This text was provided with precision teaching for four months and four phases of instruction, resulting initial accuracy ratios ranging from XI to X65, most of which included no errors. The median correct celeration was XI. 4, while the error celerations were almost all M.r^ XI. 0. After four months the entire class was leaped up to a new task involving all math operations introduced in the second grade text. The outcomes were lower initial performances and more rapid learning. Initial accuracy ratios ranged from X6 to /I. 6 and included many errors. Correct celerations ranged from XI . 5 to X2.7, with a median celeration of X2.0. Error celerations ranged from /I. 6 to /8, with a median celeration of /2.4. The

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28 implication here was that the new task was hard to do but easy to learn. Bower and Orgel (1981) attempted to generate initially high error rates, steep error learning, and rapidly accelerating correct learning with undergraduate college students. They set very high aims for the students to meet in learning psychology facts relevant to the curriculum. All groups produced more errors than corrects when starting each set of flash cards. In all cases, terminal performance levels produced dramatic division of errors and multiplication of correct frequencies . Another encouraging investigation of leap ups involved the work of Eaton and Wittman (1982) with three learning disabled children, whose accurate performance (few to no errors) of the multiplication and division tables or identification of simple fractions precluded meeting their fluency aims (not completing problems quickly enough). Upon implementation of the leap up procedure, all three children were completing the math problems quickly enough in 9 to 1 0 days. That is, their learning accelerated dramatically when they moved ahead to curriculum that was new to them. A related investigation was conducted by McGreevy et al. (1982). Twenty-four severely handicapped students were given "hard-to-do" and "extremely hard-to-do" tasks.

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29 in which the degree of difficulty was determined by the initial performance data. Correlations were made between three measures of initial performance (initial number correct, initial number of incorrect, and initial accuracy ratio) and each of two measures of learning (correct and incorrect celerations) and of variability (bounces around correct and incorrect celerations). The correlations clearly indicated no relationship between initial performance and subsequent learning or variability. Another correlation made between initial performance (initial number correct) and learning (gain score) also indicated no relationship. Gerent (1985) completed her doctoral research on the effects of curriculum leap ups on short-term learning rates. A curriculum leap up was defined as an upward curriculum change that resulted in a student's making at least 10% more errors than correct responses. Two single subject designs were used. In the "Leap and Keep" design, the preleap-up skill was continued when the leap-up skill was introduced. In the "Leap and Leave" design, the preleap-up skill was dropped when the leap-up skill began. Twenty-four of 29 experiments showed enhanced learning during the leap up condition. Summary Until about 1980, precision teachers had emphasized the traditionally small step, easy task approach to

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• 30 instruction. The leap-up tactics, on the other hand, have shown greater potential for enhanced learning. Studies on high error learning have shovm that leap ups in curriculum may provide a means for increasing the learning of some students, with errors serving as learning opportunities. Curriculum leap ups may prove useful for exceptional, average, and accelerated students, a potential worthy of further study. Recapitulation The traditional approach to teaching educably mentally handicapped students has involved simplified subject matter and a slower pace than that employed with regular education students. Its purpose has been to reduce academic frustration by diminishing chance for errors. The watered down and small step curricula are most commonly used, in spite of a lack of empirical evidence validating their effectiveness. Opponents of this approach have felt that several factors have had negative consequences on the step curriculum. These factors include little motivation on the students' part, low learning rate, and an ever increasing gap between special education students and their chronological age peers. A review of the literature on curriculum strategies resulted in confusion regarding the distinction between easy and difficult tasks. A framework has been proposed

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31 to help clarify the variables involved. Six variables have been identified which evolve from the generic concept of step size. Five have been used in educating the mildly handicapped in easy task, low error environments. They include addition of more steps to skill learning, reduction of set size, increased amount of time spent on a particular step, breakdown of curriculum sequences into smaller steps, and prompts. The sixth variable, step up in a vertical curriculum, has come under closer scrutiny in recent precision teaching literature. This approach employs a difficult task, higher error learning environment to educate students. Research evidence has begun to accumulate suggesting that regular as well as special education students may experience enhanced learning when they are placed in situations that involve initially hard to do tasks. Jump ups, leap ups, and hard-to-do tasks have been the common techniques employed by precision teachers. However, little formal attention has been given to the set size.

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CHAPTER III METHODOLOGY Overview of the Study The purpose of the study was to assess the effects of difficult task learning environments, using a larger than traditional teaching set size on the academic performance of children of varying levels of achievement in the area of spelling. Questions have been raised about the effectiveness of a simplified (easy to do) curriculum with exceptional children. Precision teaching techniques have recently been used to explore the use of initially hard to do tasks in exceptional student education programs. Variables Under Investigation Independent Variable The independent variable for this study was teaching set size, or the number of unique problems or units in the teaching set. In the context of this study, each student was exposed to two conditions. In the small set size condition, 10 spelling words were administered. Ten-word spelling tests are commonly used by teachers because they are easy to score. In the large set size condition, 20 spelling words were administered, providing a 100% 32

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33 increase in set size. Research has demonstrated that a two-fold increase in set size resulted in a disproportionately greater increase in difficulty of material to be learned (Blake, 1975). Dependent Variables Frequency, or movements per minute, was selected as the basic unit of measurement in this investigation. For many academic tasks, frequency has yielded more information than other standard educational measurements (Haring, Lovitt, Eaton, & Hansen, 1978). Frequencies of correct and incorrect responding provide measures of the amount of learning achieved. Celeration for correct and error responding, the first two of four dependent variables measured in this investigation, was the rate of change over time, as measured by the ratio of two frequencies one week apart drawn on a learning line. Celeration has been found to be a sensitive dimension that is likely to detect changes in the independent variable being manipulated (Koenig, 1972). The third dependent variable measured was the total learning measure, which was a combination of the celerations for correct and error responding. This measure conveniently consolidated improvement in correct and incorrect responding into one number.

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34 Figure 1 is a sample graph of these dependent variables and Table 1 has the raw data that are graphically presented in Figure 1 . The figure illustrates both a small set size and a large set size condition. The name of the behavior being measured, the formula for calculating it, and the value or the behavior being measured under small and large set size conditions have been given. A multiplication sign (X) preceding the value indicated that the frequency of the behavior was accelerating. A division sign {/) preceding the value . indicated that the frequency of the behavior was decelerating. In Figure 1 , A and B represent the initial frequencies for correct and incorrect responding in both phases. The initial frequency is the point where the learning lines (one each for correct and incorrect) crossed the first day line in a phase. The letters C and D represent the final frequencies for correct and incorrect responding on the learning lines. The letters E and F mark the celerations for correct and error responding. The letter G represents the total learning measure. Graphically, it can be visualized as the size of the angle between the celeration for correct responding and the celeration for incorrect responding. The last dependent variable was mastery change. Mastery change was represented by the ratio between

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Figure 1 Graphic Examples of Dependent Variable Measures

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0) 0) N o in in o o oo u to m oo • • • (0 CN !-» >< (1) x; 3 H (0 > rH N o T— rH -H in in o o (N (0 CO in • • • E r— cn 4J X CO 4J rH 4-1 O (U E CO 0 m 0) )H U iw 0> 3 TJ u V4 0 u 0) n c fi 0) 0 Sh 0 U u H tn U w u w 4J (0 s -H s x: M U rH Sh u !h M 0 0 0) C 0 0) HH < 3 0 0 0 0 MH m (1) 14H CQ 0 e MH IW MH <4H M >H O 0) 0 0 M 0) 1 OJ u 0 >i >1 >1 >1 s u u Q) CTi C O 0 o o u ft ICJ (0 C c c C c c u w E 0) -P E <3) 0) a) 0) •H -H 0 Cn 3 > C !h 3 3 3 3 E E MH >H C E 0) 0) 0 ty cr CP cr 0 •H -H -H O HH 0) Q) 0) > > rH MH T3 C X! ^^ ^1 u M 0 0 ix: Sh cn (U 0) Sh -M -U 3 m O tji m c -H S ^fa fa o

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37 initial and final masteries, where mastery refers to the percentage of minimum performance standard achieved. An arbitrary standard of 80 spelling transitions per minute was used because that proficiency rate has been associated with a well established skill (Evans, 1981; Evans, Mercer, & Evans, 1983; Evans & Evans, 1985). Setting This study was conducted in the Marion County Public School System, a northcentral Florida school district of over 24,000 students (School, 1986). At the elementary school level, exceptional student education program services were provided to eligible students in a varying exceptionalities setting. Such classes were comprised of students of more than one exceptionality, although each student received a curriculum individualized to his or her specific educational needs, as described by an individual education plan. The data were collected by this investigator, selected teachers aides, and secretaries (hereinafter referred to as teacher assistants). Because spelling was the academic task for the study, only those exceptional student education students whose individual education plan included remediation in spelling were included in this study. Spelling was part of the basic curriculum for regular education students; therefore, no distinction was made among these students.

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38 Subjects There were six subjects in this investigation. Two subjects were identified as learning disabled (SLD) (with remediation in spelling specified in their individual education plan), two were educable mentally handicapped (EMH), and two were normal, i.e., enrolled in regular education (RE). All six were chosen from the elementary school level and were matched on the basis of intelligence quotients with their counterpart in the same exceptionality. Using a random numbers table, each subject was randomly selected from a pool of subjects in all three exceptionalities. The learning disabled and educable mentally handicapped students had met the Florida Department of Education and the Marion County School System guidelines for their respective exceptional student education program placements (See Appendix A). The regular education students were chosen from a pool of students who had been evaluated and subsequently deemed ineligible for an exceptional student education program because of average or above intelligence and no identified academic deficiencies. These evaluation criteria provided the identifying psychometric data on all six subjects. All subjects were within one year of each other chronologically, their ages ranging from 8-1 to 9-0. Table 2 provides the biographical and psychometric characteristics of all six subjects.

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39 Table 2 Psychometric Descriptors of Subjects Exceptionality Name Chronological Age Per First Data Day EMH Dorothy 9-0 69 EMH Marketa 8-5 67 RE Keesha 9-0 89 RE Mikki 8-4 103 SLD Jesse 8-1 93 SLD Matthew 9-0 96 ^ based on Full Scale Intelligence Quotient of Wechsler Intelligence Scale for Children-Revised, given within the past three years. Experimental Design The experimental design in this study was single subject with alternating treatments. A single subject design was selected to provide for analysis of individual level and to demonstrate within subject control (Tawney & Cast, 1984). This strategy for conducting research has been documented in the literature (e.g., Baer, Wolf, & Risley, 1968; Bailey, 1977; Johnston & Pennypacker, 1980; Sidman, 1960). This strategy has promoted an interactive approach between the experimenter and the independent variable because it allowed for the identification of experimental sources of both intraindividual and interindividual variability while the data are being

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40 generated by the subject. Also, this strategy permitted the use of ratio comparisons within and across experimental conditions (Tenenbaum, 1983). The alternating treatments design compared the effectiveness of two or more interventions by introducing them over the same time period. The interventions were then counterbalanced across sessions and time of day (Tawney & Cast, 1984). An experimental effect can be demonstrated when one intervention is consistently associated with a different level of responding than other interventions. The rapid alternation of two interventions can not only control for maturational and historical threats that may have occurred in a multitreatment design, but can also reduce sequencing problems because no single intervention was consistently introduced first and maintained for an extended period of time (Barlow & Hayes, 1979; Sulzer-Azaroff & Mayer, 1977). Replication of the differential effects of the interventions across different behaviors and/or across different conditions demonstrates external validity (Tawney & Gast, 1984). The specific design in this investigation is illustrated in Figure 2. There was no baseline, only an intervention comparison phase. Optimal guidelines included 1 . Operational definition of all intervention procedures .

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41 35 30 o -1-1 O 3 r-4 a sac CO o (U (X. CO u Li C C 0) CO 3 ^ Li O e H O 3 Z XI o 3 25 20 °-::! 15 10 Intervention Comparison oKEY * 5.0 A corrects •o B correct -> A errors B errors Figure 2 Alternating Treatments Design

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42 2. Determination of a schedule for counterbalancing the presentation of the interventions across time (i.e., within sessions, across days). 3. Determination of how intervention procedures were to be counterbalanced across teachers, settings, activities, etc. 4. Introduction of interventions (A and B) in a rapidly alternating fashion in accordance with the counterbalancing schedule. Alternation of conditions continued until the experimental effect was demonstrated favoring the effectiveness of one intervention over the other. 5. Continuation of the most effective intervention (B or C) in the final phase of the study (Tawney & Gast, 1984). Certain limitations to the alternating treatments design have been documented. This design has required a high level of consistency across individuals administering the different interventions; therefore, high procedural reliability was of critical importance when evaluating the data (Tawney & Gast, 1984). Procedure Pre-experimental Phase During this phase a sufficient number of spelling words from an original pool of words (see Appendix B, List One) was administered to each student to identify 30 words the student did not know how to spell. Each of the 30 words chosen from the original pool of words contained at least one transition correct and two transition errors (see section on curricular materials for explanation).

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Each word was then randomly assigned to either the 1 0-word list or the 20-word list. Upon completion of this activity, the teacher assistants were given the two spelling lists and were familiarized with the test/teach procedure explained below. Since each tester worked at one particular school, they worked solely with the student subject (s) in attendance at their school of employment. All teacher assistants were employed by the Marion County School System as either a teacher, an aide, or a secretary. Experimental Phase Each student assessed during the pre-experimental phase was then exposed to the 30 spelling words selected from the original pool of words. Two daily spelling timings^ were given to each student from this selection of words. The small set size condition exposed the students to 10 spelling words, whereas the large set size condition exposed the students to 20 spelling words. There was no duplication of words in the two conditions. For each word to be spelled, the teacher assistant read the word aloud, read a sentence with the word in it, then reread the word. 1 A spelling timing is a brief measure of a monitored spelling activity and is not the same as a spelling test, which is a measurement of spelling performance.

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44 Daily timings from both lists of spelling words were taken for each student. This procedure continued until 100% mastery of the words had been obtained or time constraints provided a necessary stopping point (e.g., Christmas vacation or Easter break). The additional calendar days that had not provided opportunities for daily assessments may have confounded the test results by allowing the subject to forget already learned words. Upon completion of each daily timing, a brief, intense teaching episode occurred. The student wrote those words misspelled. The teacher assistant then copied the misspelled word, then wrote the correct spelling. The student then copied the correctly spelled word. Intrasubject replication followed the completions of the first experiment. Each student was exposed to a new list of 30 words taken from a different selection of words (see Appendix B, List Two) containing at least one transition correct and two transition errors. The above sequence of events involving daily timings was carried out during this replication. Material Curricular Materials The pool of spelling words used in this study was obtained from Classroom Reading Inventory (Silvaroli, 1965) and The Riverside Spelling Program (Wallace, 1984).

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The lists of words chosen for each student have been provided in Appendix B. Upon administration of these words to each student, a reduced list of words was obtained, each word of which contained at least one transition correct and two transition errors. A transition is defined as any two consecutive spaces in a word. When two consecutive letters of a word are correctly placed, this is a transition correct. For example, in the word cloud, a transition correct would be A cloud. The caret sign above the adjacent letters, "c" and "1" indicated a transition correct. A transition error is defined as any two consecutive letters in a word not correctly juxtapositioned. For example, in the word cloud, if it were spelled clowd, then a transition error would be clc^d. The "w" is an incorrect letter for the word cloud. Another example of a transition error might be caused by a letter omitted, as in the case of the word clc^d, where the "u" has been omitted. The caret sign below the adjacent letters "o" and "d" indicates a transition error. In recapitulation, three spelling variations of the word cloud are further exemplified. in the spelling AAA AAA cloud, there are six transition corrects and zero transition errors. The no letter to "c" transition is counted as a transition correct because it is not preceded by any letter. The final letter "d" also is counted as a

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46 transition correct because it is not followed by any letter. In the spelling clowed, there are four transition V vv corrects and three transition errors. In the spelling AA A A clod, there are four transition corrects and one transition error. Data Recording Form For each student the daily numbers of transition *' corrects and transition errors were recorded for each condition (small set size and large set size). A sample form is provided in Appendix C. Each daily recording included the rate correct (to the left of the slash mark) and the rate incorrect (to the right of the slash mark). The standard behavior chart was used to display and analyze all the data from this investigation. A sample graphic representation of these data is provided in Appendix D. Data Recording and Analyses Data Recording Daily data were recorded on the data recording form provided in Appendix C. Small set size and large set size frequency correct and frequency incorrect were listed adjacently for comparative purposes. These same frequency data were plotted on the standard behavior chart and can be found in Chapter IV. This graphic representation allowed visual analysis of the

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47 small set size and large set size conditions. As well, a series of frequency plots over time shows linear change, thus allowing easier predictability than the more common curvilinear plots across time. Data Analyses Visual inspection of all data and frequency multipliers, summarized in Appendix D, was used for data analyses. Frequency multipliers, the ratio between two frequencies, were used because they quantify the distance visualized between two frequencies on the standard behavior chart (Pennypacker , Koenig, & Lindsley, 1972). These ratios were obtained by dividing the smaller frequency into the larger frequency. When 1.00 is subtracted from the obtained ratio value and then is multiplied by 100, the percent change is derived. Differences between large and small set sizes were examined to determine if the measures of learning for the large set size were equal to or greater than the measures of learning for the small set size. If the large set size measures were within 5% of the small set size measures, they were described as equal. A finding was therefore interpreted as significant (i.e., the large set size was favored) if the large set size measures were at least 95% of the small set size measures. Replication also served part of the function of statistical tests of significance. t. , ; ^ • ^

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48 Therefore, the obtained results have been evaluated in the context of expert judgment of their practical importance.

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CHAPTER IV ANALYSES AND RESULTS The purpose of this study was to investigate the effects of teaching set size on several measures of learning for both special and regular education students. The study was based on a single subject design with the alternating treatments of 10 and 20 spelling words as independent conditions. Differences in celeration, total learning rate and fluency, between the 10and 20-word set size were examined for each subject. Frequency correct responding and error responding on a spelling dictation test were the dependent measures. Primary interest has been given to results large enough to make a practical difference to psychologists and teachers. Therefore, an experimental finding was deemed significant if the measures of learning for the large set size were greater than or equal to the measures of learning for the small set size. If the large set size measures were within 5% of the small set size measures, the measures were described as equal. The interpretation given to this equality was that children could learn as well with a large set size as with a small set size. The 49

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50 strict criterion of 5% was chosen because a lot more learning could be obtained with the large set size if the measures of learning for both set sizes were equal (i.e., within 5% of each other). The frequency multipliers are summarized in table form in Appendix D. Celeration The first variables examined in this chapter are celerations for correct and error responding. Mixed results were obtained as demonstrated in Table 3. The standard behavior charts are provided in Figures 3-8. As shown in Table 3, Dorothy and Marketa were the EMH subjects. Learning for correct responses with 20 words was faster than or equal to learning for correct responses with 10 words in Dorothy's first experiment. Dorothy's second experiment showed faster learning for correct responses with 10 words than with 20 words. In both experiments Dorothy reduced her error responses more quickly with 20 words than with 10 words. For Marketa results from experiment one showed faster learning for correct responses and faster reduction of error responses with 10 words. Sufficient experiment two results could not be obtained with Marketa, because his high rate of absenteeism made it difficult for him to learn consistently the words within a reasonable amount of time.

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51 a) N •H CO 4J (1) CO 0) 0u ij T3 C n3 rH (0 e CO c •H cn 0) 0 c n 0) V4 0) 0) H J3 •H Q (0 -p 0 Eh U | /\| V CO c •H x: o o Q (0 4J 0) M U (0 s S S '1^1 /V I /\ I V ^1 x: cu to CO dj CO 0) ^^ (0 Q CO Q CO iH n> 3 d) o tr g •r-l w (0 CO •H 0 0 d) (D c to II Q CO 4J CD (C CO (U d) c rH 0 -H CD 4J CD H (C H o 3 4J 0 'O H 4J >^ (C 0 • (1) r— 1 N (U N 3 *H N Di CO -H CD CO Pi 4J d) II CO Q) CD CO pq -l >— 1 rH d) 3) CO N Qj d) d) -H Qj r; d) r* rn (0 o I 1 •r-l Q) 'd 0 M-l 0 CD c o nj (D d) >H K U H >, (0 CO ly uj ,—1 (1) (Tl rtl C 111 4J 1^ O* 4-J r* In ti_i e cj (11 J3 Li r* w r-f iD M (0 d) Q; (u d} ID -H "-H 3 t-H CD 3 (fl (13 T3 CP Q) d) W C CO e CD E •H 4J (0 4J II c C CD C CP a) d) c CD 0 CD -H
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54 Nl i-J CO siuno3 CiJ PS to >^ CO CO a j:: CO u (U CO CU c r-l o CO o u > CO •H CO u M (U u 0 o o •H 3 > CO CO x: (U CO t3 u
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57 u *j N s:iunoo « n CO 0) -H E
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58 In summary, for the EMH group the 10-word list was associated with faster learning for correct responses in two of three experiments and faster reduction of error responses in one of three experiments. The 20-word list was associated with faster learning for correct responses in one of three experiment and faster reduction of error responses in two of three experiments. The RE subjects showed similarly mixed results during both experiments. Keesha demonstrated faster learning for correct responses with 10 words in experiment one; in contrast, the 20-word list showed learning for correct responses equal to or faster than the 1 0-word list in experiment two. Reduction of Keesha 's error responses with 20 words in both experiments was equal to or faster than her reduction of error responses with 10 words. In experiment one, Mikki demonstrated learning for correct responses with 20 words faster than or equal to learning for correct responses with 10 words, in experiment two, she demonstrated faster learning for correct responses with 10 words. Mikki ' s reduction of error responses was consistently faster with 10 words across both experiments. In summary, for the RE subjects the 1 0-word list was associated with faster learning for correct responses in two of four experiments, and the 20-word list was associated with equal or faster learning for correct responses in two of four experiments. Intrasubject

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59 replication provided a consistent reduction of error responses. Keesha consistently demonstrated equal or faster reduction of error responses with 20 words; whereas, Mikki consistently demonstrated faster reduction of error responses with 10 words. Mixed results were also obtained for the SLD subjects. Jesse learned the correct responses of the 10-word list more quickly in experiment one, but he learned the correct responses of the 20-word list at least as quickly as the 10-word list in experiment two. He reduced error responses of the 20-word list at least as quickly as the 1 0-word list during both experiments. Matthew followed a pattern of learning correct responses similar to Jesse. He learned the correct responses of the 10-word list more quickly in experiment one, but he learned the correct responses of the 20-word list at least as quickly in experiment two. His reduction of error responses of the 1 0-word list was quicker than his reduction of error responses of the 20-word list in both experiments. In summary, for the SLD group half of the four experiments had faster learning for correct responses as well as faster reduction of error responses with 10 words. Both Jesse and Matthew provided a consistent intrasubject replication with reduction of error responses; however.

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60 Jesse performed equally well or better with the 20-word list/ and Matthew performed better with the 10-word list. Total Learning Rate An analysis was made of the total learning measure (celerations for correct and error responding combined). These findings have been summarized in Table 3. Dorothy learned her 20-word list at least as quickly as her 10-word list in both experiments. Marketa learned his 10-word list faster than his 20-word list in experiment one. As mentioned previously, Marketa ' s experiment two did not produce sufficient data. In summary, Dorothy learned her 20-word list more quickly and Marketa learned his 10-word list more quickly. The RE subjects were evenly split with their total learning rates for both word lists. Keesha learned her 20-word list more quickly across both experiments; whereas Mikki learned her 10-word list more quickly across both experiments. In summary, the intrasubject replication established on the total learning measure for each subject provided opposite results. The SLD subjects provided mixed results for their total learning measures. in experiment one, Jesse and Matthew both learned their 10-word list more quickly, but they both learned their 20-word lists equally quickly if not faster in experiment two.

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61 Mastery The findings for mastery of the minimum performance standard are also siimmarized in Table 3. Dorothy showed a mastery on her 20-word list than was equal to or greater than the mastery on her 10-word list in experiment one. Mastery on her 1 0-word list was greater than mastery on her 20-word list in experiment two. Marketa displayed a mastery on his 20-word list that equalled or exceeded the mastery on his 10-word list in experiment one. Experiment-two results, as previously mentioned, were insufficient. In summary, two of three experiments were associated with mastery of the minimum performance standard on 20 words that equalled or exceeded mastery on 10 words. One experiment was associated with greater mastery on 1 0 words. . The RE subjects also showed a generally equal or greater mastery on the 20-word list. Specifically, Keesha showed a greater mastery on her 10-word list in experiment one, but she showed a mastery on her 20-word list that equalled or exceeded the mastery on her 1 0-word list in experiment two. Mikki showed a mastery on her 20-word list that consistently equalled or exceeded the mastery on her 10-word list in both experiments. In summary, for the RE subjects three of four experiments were associated with

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62 equal or greater mastery of the minimum performance standard on the 20-word list. The SLD students also demonstrated an equal or better established mastery on the 20-word list than on the 10-word list. Jesse showed a greater mastery on his 10-word list in experiment one, but he showed a mastery on his 20-word list that equalled or exceeded the mastery on his 10-word list in experiment two. Matthew showed a mastery on his 20-word list that consistently equalled or exceeded the mastery on his 10-word list in both experiments. In summary, for the SLD subjects three of four experiments were associated with equal or greater mastery of the minimum performance standard on the 20-word list. Across Category Summary The overall findings for celerations for correct responding, celerations for error responding, total learning, and mastery of the minimum performance standard across all three groups of subjects are summarized in Table 4. Equal or faster learning for correct responses with 20 words was demonstrated in five experiments and faster learning for correct responses with 10 words was demonstrated in six experiments. Reduction of errors was equal or faster with 20 words in six experiments and faster with 10 words in five experiments. Equal or

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63 Table 4 Number of Experiments Favored Across Categories Celerations Correct 5 6 Celerations Error 6 5 Total Learning 6 5 Mastery 8 3 a 2. represents a learning measure of the large set size that is greater than or equal to the same learning measure of the small set size. b < represents a learning measure of the large set size which is less than the same learning measure of the small set size. superior learning with 20 words was found in six experiments, in contrast to superior learning with 10 words in five experiments. Mastery of the minimum performance standard was equal or greater with 20 words in eight trials, as opposed to three trials in which mastery for 10 words was greater. Intrasubject replication with celerations for error responding, total learning, and mastery of the minimum performance standard was demonstrated only for some of the subjects. The learning

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64 measures were equal or superior with the large set size in 25 of the 44 experiments. Accuracy Each of the 30 words obtained from the spelling pre-test was randomly assigned to either the 1 0-word list or the 20-word list. A post hoc analysis was made of the measure of initial accuracy, an estimate of the initial level of difficulty of each pair of word lists. Initial accuracy was obtained for each subject on the first day of data collection. It can be seen from Table 5 that the difference in level of difficulty between any pair of word lists ranged from 4% to 49%. Closer examination has been given to beginning accuracies as measures of task difficulty because of the possible effect of initial difficulty on measures of learning. For example, if a particular 20-word list was more difficult than the 10-word list paired with it, celeration, total learning, and mastery may have been affected by this difference. The 10-word list in experiment one for Dorothy was 9% easier on the first day of data collection than the 20-word list. However, all four measures of learning on her 20-word list were equal to or greater than the four measures of learning on the 10-word list. The group of words in her second experiment included a 10-word list that was 25% easier than the 20-word list; however, the

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65 Table 5 Differences in Initial Accuracies Between Small and Large Set Size Difference in Initial Easier Exceptionality Name ExDe r iine n t Accuracies Set Size^ EMH Dorothy 1 9^ 1 0 2 25 10 EMH Marketa 1 28 1 0 2 insufficient data RE Keesha 1 8 1 0 2 12 20 RE Mikki 1 1 5 1 0 2 19 10 SLD Jesse 1 49 20 2 8 10 SLD Matthew 1 4 1 0 2 8 20 based on higher initial accuracy 10-word list was associated with faster learning for correct responses and a greater mastery, and the 20-word list was associated with a faster reduction of error responses and a greater total learning. Experiment one for Marketa included a 10-word list that was 28% easier on the first day than the 20-word list. Celerations for correct and error responding were faster with the 10-word list, and greater learning of the

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66 10-word list was obtained. Mastery of the minimiam performance standard on the 20-word list was equal to or greater than the mastery on the 10-word list. There were, as reported, insufficient data for experiment two. For Keesha, experiment one included a 10-word list that was initially 8% easier than the 20-word list. Faster reduction of error responses and greater total learning were found with the 1 0-word list, in contrast to faster learning of correct responses and greater mastery on the 20-word list. In experiment two, for which the 20-word list was 12% easier for Keesha, all four measures of learning on her 20-word list were equal to or greater than the same four measures on her 10-word list. For Mikki, a 15% easier 1 0-word list was found in experiment one. A faster reduction of error responses, as well as greater total learning, were observed with 10-word list, but faster learning of correct responses and greater mastery were found with the 20-word list. For Mikki ' s experiment two, the 10-word list was once again easier, this time by 19%. Faster celerations for correct and error responding as well as greater total learning were seen with the 1 0-word list; whereas mastery of the 20-word list equalled or exceeded mastery of the 10-word list. Jesse's experiment one was associated with a 49% easier 20-word list, but faster learning for correct responses, a better learning rate, and greater mastery

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67 with the 10-word list. Reduction of error responses was equal or faster for the 20-word list. The 10-word list in Jesse's second experiment was 8% easier, but all four measures of learning on his 20-word list were equal to or greater than the same four measures on his 1 0-word list. In Matthew's first experiment, his 1 0-word list was 4% easier and was associated with faster celerations for correct and error responding as well as a greater total learning. Mastery for his 20-word list was equal to or greater than mastery for the 10-word list. In Matthew's second experiment, his 20-word list was 8% easier and was associated with equal or faster learning of correct responses and equal or greater total learning and mastery. His 10-word list was associated with a faster reduction of his error responses. In summary, mixed results did not show a consistent relationship between initial level of difficulty of the 10-word lists and the celerations for correct responding, celerations for error responding, total learning, and mastery. Table 6 contains the superior measures of learning when the 20-word list was easier as well as when the 10-word list was easier. It can be seen from this table, for example, that when the 10-word list was initially easier, the four measures of learning were not always equal or superior for the 1 0-word list.

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68 Table 6 Number of Superior Measures of Learning for Each Initially Easier Word List Initially Easier Word List 1 0-Word List 20-Word List > < Celerations correct 3 5 2 1 Celerations Error 4 4 2 1 Total Learning 4 4 2 1 Mastery 6 2 2 1 a >_ represents a learning measure of the large set size that is greater than or equal to the same learning measure of the small set size. b < represents a learning measure of the large set size which is less than the same learning measure of the small set size. Recapitulation Traditional teaching techniques have been based on the premise that a larger teaching set size would provide more difficult work than a smaller teaching set size. The average student was expected to find 20 spelling words harder to do than 10 spelling words. Faster learning for correct responses and faster reduction of error responses, as well as superior learning overall and mastery of the

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69 minimum performance standard were not consistently found with either the large or the small set size. Teaching set size did not appear to be a variable that provided a consistent effect on learning spelling words. Despite the fact that initial accuracy varied by as much as 49% from one 10-word list to its matching 20-word list, no consistent influence on the above mentioned learning variables was noted.

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CHAPTER V DISCUSSION AND CONCLUSIONS At the beginning of this chapter, examination is given to uncontrolled sources of variance. The significance of teaching set size and initial level of difficulty on the four learning measures used in this study is the next topic discussed. Although the effects of set size and initial level of difficulty were mixed, certain implications can be made about their influence. Also discussed are the limitations of this study because of the teacher assistants used, sample, set size, and treatment design. Implications for teachers and school psychologists are then explored. Recommendations for future research and concluding remarks follow. Discussion Uncontrolled Sources of Variance Traditional teaching methods in special education have been based on the easy task learning approach. Teachers have been taught that the smaller the number of items in the teaching set the lower the academic frustration. The underlying assumption of the increase in 70

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71 teaching set size was that the 20-word list would be more difficult than the 10-word list, especially for special education children. Several of the teacher assistants were skeptical that their subjects could learn 30 new spelling words. They felt that their pessimistic expectations about the larger set size would be communicated to the students, causing the students to do more poorly with the 20-word list than with the 10-word list. The one teacher assistant who was most vocal about task difficulty did work with a student who occasionally hid from her when it was time for the spelling session. Another teacher assistant worked with two students, one who responded very enthusiastically to the one-to-one attention being received and the other who was indifferent toward the spelling task. This latter teacher assistant, who was a secretary by profession, displayed unflagging enthusiasm toward both students. These differences in the behavior of teacher assistants and subjects were not controlled during this study and may have had some measurable influence on the outcomes. Such influence has been well documented in the literature (Rosenthal, 1966; Rosenthal & Jacobsen, 1966; Rosenthal & Jacobsen, 1968). One might logically expect experienced teachers to have more confidence and skills when teaching difficult tasks. Aides and secretaries have less experience with educational expectations of students

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72 than certified teachers. The effect of their expectations may be exaggerated since they may be more intimidated by hard to do tasks. Significance of Set Size A comparison of these results was made within and among subjects across word lists. Inconsistent findings between experiments for each subject were noted. Inconsistent results across exceptionality were also noted. There was wide variation across exceptionalities in celerations for correct responding, celerations for error responding, total learning, and mastery change from one experiment to the next. For example, all four of Dorothy's measures of learning for the 20-word list in experiment one were equal or superior to the same four measures for the 10-word list, whereas, only an equal or greater reduction of error responses and an equal or greater total learning in experiment two were associated with the 20-word list. Set size did not seem to be controlling learning outcomes systematically or exclusively. These findings are not consistent with Blake's (1975) conclusions that learning was affected by task size and that increments in set size made the task disproportionately more difficult, especially for the retarded learner. The common practice with EMH students of watering down the regular curriculum by reducing the amount of work completed (Gallagher, 1967;

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73 Rothstein, 1962) should probably be revisited. Some students may benefit equally well from larger teaching set size as from a smaller teaching set size. More work needs to be done to determine which students, under what conditions, can profit from larger teaching set sizes. Significance of Initial Level of Difficulty Examination of these results across initial level of difficulty also revealed inconsistencies. Celerations for correct responding, celerations for error responding, total learning, and mastery change varied widely from one level of initial difficulty to another. For example, the 10-word list in Dorothy's first experiment was 9% easier than the 20-word list. Equal or faster learning for correct responses as well as reduction of error responses were associated with the 20-word list. A methodological point can be made about the measure of initial accuracy. Initial accuracy provides a way of gauging the success of randomization procedures. In this study words were randomly assigned to both set size conditions to ensure that initial accuracies of each paired word list would be equal. The variable of initial accuracy provided a sensitive measurement system that permitted one to see how the randomization actually affected level of difficulty. In this study, initial accuracies ranged from less 4% to 49%, indicating that some paired word lists were not of comparable levels of

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74 difficulty. The randomization procedure used in this study was not as effective as originally desired, providing a caveat to future researchers. Initial levels of difficulty may provide an easy and useful measure of the effectiveness of the randomization procedure. Limitations of the Sample One limitation of this study involved the characteristics of the research sample. Each student involved in this study had been referred to the psychological services section of the Marion County, Florida, School System due to suspected learning problems. Generalizing these results to a wider population should be made with appropriate caution in light of the restriction which this limitation imposes. An increase in set size may have a completely different effect on the academic performance of students who are not suspected of having learning difficulties. Unref erred students generally tend to have greater academic success in school and may respond differently to interventions tried. Limitations by Set Size Another limitation of this study was the size of the teaching sets used. The size of the large teaching set was double the size of the small teaching set. Blake (1975) suggested that increments in task size make the task disproportionately more difficult in that there is not a unit of change in difficulty for every unit change

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75 in length. Doubling the set size from 10 words to 20 words in this study may not have made the spelling task disproportionately harder. W.D. Wolking (personal communication, June 19, 1987) found that a threefold increment in set size provided equal or better learning in vocabulary and math content areas with some students. Other set sizes and other academic subjects may produce different results. Limitations by Treatment Design Tawney and Gast (1984) have discussed alternating treatment designs and their limitations. The alternating treatment design used in this study required a high level of consistency across teacher assistants administering the different spelling tasks. High procedural reliability is of critical importance when evaluating the data. Each teacher assistant was given the same set of instructions for administering the spelling timings. Any differences in the actual administration across teacher assistants may have caused subtle and uncontrolled differences in the way in which the independent variable was applied. Implications for Teachers The implication of this study is that in slightly more than half the cases regular and special education subjects may learn at least as well with a larger teaching set size as with a smaller teaching set size. Therefore, teachers should begin to explore this issue further.

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76 knowing that some students may benefit from a larger teaching set size, whereas other may not. In many of the experiments of this study there was little difference in how quickly a student learned new words or reduced error responses when the teaching set size was increased. Teachers may need to be trained to work with students under hard-to-do task curricula because some students may show enhanced learning from such a curricular approach. The mixed results of this study also indicate that teaching set size and initial level of task difficulty were not systematically controlling variables. Such uncontrolled influences as teacher assistant expectations, the one-to-one attention each student received from the teacher assistant, and the varied professional backgrounds of the teacher assistants (some of whom had no teaching experience) may have been significant factors. Implications for School Psychologists The main thrust of a psychological evaluation of children for special education classes today is the identification of those students who would benefit from an easy task curricular environment. School psychologists traditionally recommend placement in easy to do curricular environments for those students who are academically below grade level. The standardized test instruments currently being used by school psychologists may not be sensitive enough to differentiate those students who could benefit

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77 from difficult task curricular environments from those students who require easy task curricular environments to thrive. The four special education students in this study showed greater learning of some of the larger set size words. Therefore, curriculum-based and criterionreferenced assessment tools may need to be developed to supplement the repertoire of standardized test instruments already being used by school psychologists. Such assessment tools may not only be more easily interpreted by teachers, but they may also be more sensitive in identifying those students who may benefit from the larger than traditional teaching set size. The school psychologist's role as a consultant often precedes the school psychologist's involvement in the full fledged evaluation process for special education placement. Greater understanding of larger than traditional teaching set size curriculum strategies could enable school psycholgists as consultants to help teachers and administrators to design teaching strategies to the child's best advantage. The mixed results of this study indicate that some special education students may do well with hard to do tasks. Introduction of hard to do tasks in the regular classroom setting may be an appropriate prereferral intervention to carry out. Should this intervention prove ineffective, the particular student could then be referred for a psychological evaluation to

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78 assess the need for an easy task curricular environment offered in many special education classes. Placement of the learning disabled or educable mentally handicapped student in an exceptional student education program would then become a more selective process. Differentiation could then be made between those students who may excel more in a larger than traditional teaching set size from those who may still need the traditionally easy task approach to instruction. Consultation between the school psychologist and the special education teacher may also involve the introduction of hard to do tasks in the special education classroom setting. Since some enhanced learning with the larger set size was observed in this study, progress in the special education class may be faster if a larger set size is used while the learner may gain increased confidence in his/her abilities. These same arguments can be made for trying higher grade level tasks than is typically done. ' ' Recommendations for Future Research The mixed results of this study suggest that variables in addition to teaching set size were influencing the outcomes. Identification of these other variables should be carried out to gain better understanding of ways to enhance learning. One such unexamined variable was teacher/student resistance to hard

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79 to do tasks. Following Cerent's (1985) recommended examination of this issue, its effect on the learning measures of one student in this study who hid from the teacher assistant remains unknown. There is a need to explore this issue more carefully. The effect of a larger teaching set size on self-concept enhancement may be a correlative issue that merits examination. The larger set size might also enable special education students to cover more areas of the curriculum, thereby allowing them to be compared more favorably to the regular education peers in terms of number of curriculiom objectives mastered. ' * Longer range data collection is warranted to determine if the student could adjust to and/or the teacher could support the student in a hard to do task curricular environment for an extended period of time. Each experiment conducted in this study lasted only a few weeks, and there was a brief intermission of one to two weeks followed by one replication. Future researchers examining teaching set size should extend the range of increment from double the set size to triple the set size. This increase should provide information about a ceiling increment, beyond which effective learning can no longer take place. A more homogeneous group of subjects should provide a larger within category sample from which conclusions can

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80 be drawn. A group of strictly EMH subjects, for example, would provide results with greater generalizability to the EMH population. Conclusions The mixed findings of this study provided inconclusive results. The enhanced learning with the large set size in some of the experiments, as well as the comparable learning (i.e., differences of less than 5%) between large and small teaching set size, provide sufficient challenge to the traditional, watered down curriculum approach to merit further research in this area. Other variables may influence learning more systematically. Identification of these variables is imperative if special and regular education programs are to provide the best services to meet the individual child's needs.

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APPENDIX A EXCEPTIONAL STUDENT EDUCATION PROGRAM ELIGIBILITY REQUIREMENTS Programs for Educable Mentally Handicapped Definition ; One who is mildly impaired in intellectual and adaptive behavior and whose development reflects a reduced rate of learning. The measured intelligence of an educable mentally handicapped student generally falls between two (2) and three (3) standard deviations below the mean and the assessed adaptive behavior falls below age and cultural expectations. Eligibility Criteria ; Criteria for eligibility for a special program for the mentally handicapped as required by Rule 6A-6.301 1 (2) (a)-(c) , FAC, are as follows; A. the measured level of intellectual functioning, as determined by performance on an individual test of intelligence, is two (2) or more standard deviations below the mean. The standard error of measurement may be considered in individual cases. The profile on intellectual functioning shows consistent sub-average performance in a majority of the areas evaluated; B. the assessed level of adaptive behavior falls below age and cultural expectations; and C. sub-average performance on an individually administered standardized test of academic achievement for the appropriate age level is demonstrated. A behavioral observation or criterion referenced test for a student whose level of functioning is not appropriately measured by an academic test may be substituted. D. age of student 81

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82 Programs for Specific Learning Disabilities Definition ; A specific learning disability is defined as a disorder in one (1) or more of the basic psychological processes involved in understanding or in using spoken or written language. Disorders may be manifested in listening, thinking, reading, talking, writing, spelling, or arithmetic. Such disorders do not Include learning problems which are due primarily to visual, hearing, or motor handicaps, to mental retardation, to emotional disturbance, or to an environmental deprivation. Eligibility Criteria ; A student is eligible for special programs for specific learning disabilities if the student meets all of the following criteria; A. Evidence of a disorder in one (1) or more of the basic psychological processes. Basic psychological process areas include visual, auditory, motor, and language processes . 1 . Documentation of process disorder must Include one (1) standardized instrument in addition to the instrument used to determine the student's level of Intellectual functioning. 2. In addition, a district may establish criteria for the use of more than one (1) Instrument to determine a process disorder and other criteria which will assist in determining a process disorder. B. Evidence of academic achievement which is significantly below the student's level of Intellectual functioning. 1. For students below age seven (7), evidence must be presented that the student exhibits a significant discrepancy between levels of Intellectual functioning and achievement on tasks required for listening, thinking, reading, talking, writing, spelling or arithmetic. 2. For students below age seven (7), evidence must be presented that the student exhibits a discrepancy of one (1) standard deviation or more between an intellectual standard score and academic standard score m reading, writing, arithmetic, or spelling.

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For students ages eleven (11) and above, evidence must be presented that the student exhibits a discrepancy of one and one-half (1-1/2) standard deviations or more between an intellectual standard score and academic standard score in reading, writing, arithmetic, or spelling. A district may establish criteria for the use of more than one ( 1 ) instrument to determine a deficit area, and other criteria which will assist in determining an academic deficit.

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APPENDIX B Twenty-Word List 1 for Dorothy 1 . food What kind of food do you want? 2. she She will like it. 3. into He got into the car. 4. barn The cow is in the barn. 5. feet His feet were bare. 6. went He went with his father. 7. now I want it now. 8. work Do you work today? 9. little That is a little box. 10. play Can I go out and play? 1 1 . green My eyes are green. 12. was Was she there? 13. said She said it to me. 14. can I can do that. 15. stop Please stop doing that. 16. blue The book is blue. 17. look Look at the dog. 18. day This is her third day here. 19. read Read me a story. 20. brown My dog has brown hair. 84

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85 Ten-Word List 1 for Dorothy 1 . them Give them to me. 2. bus I took a bus to tovm. 3. saw I saw the moon. 4. funny The clown was very funny. 5. good You are good to me. 6. car My car drives fast. 7. big How big is the box? 8. see See what I have. 9. black It was black inside. 10. three Three pieces were left.

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86 Twenty-Word List 2 for Dorothy 1 . 2. 3. 4. 5. 6. 7. 8. 9. 10. 1 1 . 12. 13. 14. 15. 16. 17. 18. 19. 20. ring That is a pretty ring on your finger, ship We saw a big ship sail by. lamp Turn on the lamp so you can see. clap Clap your hands twice. bag The food is in the bag. tail I tied a bow on my dog's tail. joke That was a funny joke. desk Do your work at your desk. bank All my money is in the bank. wet I fell in the mud puddle and got wet. farm I grew up on a farm. well Are you feeling well? tub He took a bath in the tub. chop Don't chop down that tree. let Let me help you with that. game I want to play a game with you. hard That is a hard question to answer. dot Don't forget to dot your i's. jar Pour the water into this jar. pail Put the sand in this pail.

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87 Ten-Word List 2 for Dorothy 1 . fish I like to fish on the weekends. 2. pen Please put you name down in pen, not pencil, 3. hay My horse likes to eat hay. 4. fast Boy, can you run fast. 5. bird There is a pretty bird in the cage. 6. wig She wore a wig on her head. 7. doll Can I play with your doll? 8. tent You can use my tent to go camping. 9. heat Heat this pot of water on the stove. 10. wind The strong wind blew my hat off.

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88 Twenty-Word List 1 for Keesha 1 . knights The knights in shining armor arrived. 2. examined My physician examined me. 3. instinct He worked solely on instinct. 4. rumored He was rumored to be missing. 5. delicious The pie was delicious. 6. octave The third octave was what I wanted to play. 7. hearth It was warm by the hearth of the fireplace. 8. terrific They are terrific at their work. 9. salmon I like to eat smoked salmon. 10. briskly The wind blew briskly. 11 . billows Billows of smoke poured from the burning house. 12. strutted The chicken strutted across the yard. 13. dragon The dragon blew out flame. 14. customers There were no customers in the store tonight. 15. whether Whether or not to do it is the question. 16. amount What is the amount I owe you? 17. musical The musical play was enjoyed by all. 18. pacing The dog kept pacing up and down the yard. 19. oars There were no oars in the rowboat. 20. knowledge He seems to have a lot of knowledge.

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89 Ten-Word List 1 for Keesha 1 1 • sentinel — The sentinel stood guard at the fort. 2. hymn We sang a Christmas hymn. 3. nostrils His nostrils widened when he smelled smoke . 4. sharpness The sharpness of the knife made it dangerous . 5. sensitive She is sensitive to that perfume. 6. calmly He calmly left the room. 7. freedom All they wanted was their freedom. 8. wreath She made the Christmas wreath. 9. scientists Scientists do important research. 10. considerable He took a considerable amount of time complete the test. , >

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90 Twenty-Word List 2 for Keesha 1 . arrangement 2. transferred 3. clipped 4. appointment 5. prehistoric 6. suitcase 7. windmill 8. weightless 9. disappear 10. injured 1 1 . imperfect 12. imitation 13. reflection 1 4 . wadded 15. quicken 16. remove 17. uneasy 18. everywhere 19. earthquake 20. eyesight The flower arrangement looked pretty. I was transferred to a different classroom. She clipped her fingernails last night. Your appointment is for two o'clock today. This dinosaur was a prehistoric animal. I packed my suitcase for a long trip. We saw a windmill in Holland. The astronaut was weightless in space. The magician made the rabbit disappear. The football player was injured in last night's game. This diamond is imperfect because of a crack. That actor did a good imitation of me, I saw my reflection in the pond. He wadded up his paper and threw it in the trash can. We must quicken our pace to catch up with them. Please remove your shoes. He was uneasy being in that room. They were everywhere around us. The earthquake destroyed many buildings. My doctor helped me get my eyesight back.

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91 Ten-Word List 2 for Keesha 1 . puncture 2. giraffe 3. parachute 4. tongue 5. bugle 6. lizard 7. plumber 8. quiver 9. tomorrow 10. autumn Be careful not to puncture yourself with that nail. A giraffe can be up to thirty feel tall. He used a parachute after he jumped out of the plane. Don't stick your tongue out at me. He blew the bugle to wake everyone up. That is an ugly lizard you have for a pet, Call the plumber to fix our kitchen sink. There were six arrows left in his quiver. You can finish your work tomorrow. Autumn is one of the four seasons of the year.

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92 Tventy-Word List 1 for Jesse 1 . her That belongs to her. 2. them Give them to me. 3. food What kind of food do you want? 4. tell Tell me what you like. 5. please Please stop by again. 6. peanut Peanut butter tastes good. 7. stopping Why are you stopping the car? 8. frog A frog jumped in front of me. 9. street Look both ways before you cross the street. 10. birthday Happy birthday to you. 11 . climb I will climb up the ladder. 12. beautiful That is a beautiful dress. 13. waiting I am waiting for a cab. 14. cowboy The cowboy rode a white horse. 15. high How high can you jump? 16. people They were nice people. 1 7. mice Mice are afraid of cats. 18. corn He likes corn on the cob. 19. room This room is mine. 20. gray The old man had gray hair.

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93 Ten-Word List 1 for Jesse 1. many Many people can't swim. 2. painted I painted that picture myself. 3. eight Eight pieces are left. 4. trucks All the trucks were parked. 5. garden The garden had many flowers. 6. fireman The fireman wore a big, red hat. 7. stood She stood up and stretched. 8. head My head hurts this morning. 9. strong He is as strong as you are. 10. blows She blows bubbles often.

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94 Tventy-Word List 2 for Jesse 1 , 2, 3, 4, 5. 6, 7. 8. 9. 10. 11 . 12, 13. 14. 15. 16. 17. 18. 19. 20. trick glass drum swing whale pail broom tooth clay mouse shirt crown trap shake barn dinner butter father stove storm The magician did a neat trick on tv. Please pour me a glass of milk. He beat loudly on the dr\im. I like to play on the swing at the playground. A whale is a very big fish. You can use the shovel and pail at the beach. Use this broom and sweep the front room. She lost a tooth yesterday. I like to make things out of clay. The cat did not catch the mouse. That is a nice shirt you are wearing. The King wore a crown on his head. The animal was caught in the trap. Let me shake your hand. I have a cow in my barn. What did you eat for dinner last night? Do you like butter on your bread? My father came to school today. My mother cooked dinner on the stove. There is a bad storm outside.

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95 Ten-Word List 2 for Jesse 1 . sand 2. chain 3. skunk 4. hook 5. bean 6. class 7. church 8. j umped 9. river 10. burn Please don't bring sand inside my house. The dog was tied to a strong chain. A skunk is a pretty but smelly animal. I put a worm on my fishing hook. If you plant that bean, it will sprout and grow. My class was well behaved today. We go to church every Sunday. The dog jumped over the fence. Let us canoe across the river. Don't burn yourself on the hot stove.

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96 Twenty-Word List 1 for Marketa 1 . blue The book is blue. 2. and John and Mary like each other. 3. big How big is the box? 4. said She said it to me. 5. work Do your work today. 6. was Was she there? 7. day This is her third day here. 8. three Three pieces were left. 9. now I want it now. 10. read Read me a story. 1 1 . went He went with his father. 12. barn The cow is in the barn. 13. brown My dog has brown hair. 14. good You are good to me. 15. into He got into the car. 16. what What did he say? 17. saw I saw the moon. 18. feet His feet were bare. 19. food What kind of food do you want? 20. her That belongs to her. I I

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97 Ten-Word List 1 for Marketa 1 . for This flower is for you. 2. stop Please stop doing that. 3. funny The clown was very funny. 4. look Look at the dog. 5. play Can I go out and play? 6. see See what I have. 7. black It was black inside. 8. she She will like it. 9. them Give them to me. 10. tell Tell me what you like.

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98 Twenty-Word List 2 for Marketa 1 . ship ^ I have never sailed on a ship before. 2. win Did we win the game? 3 . lamp The lamp shined brightly in the room. 4. tail That dog has a pretty tail. 5 . j oke That was a funny joke. 6. mop Take this mop and clean the floor. 7 . drum He banged loudly on his drum. o 8 . wood This table is made of wood. Q cow — See the cow in the field. 10. tub You can wash the dog in that tub. 11 . class Our whole class went on a field trip. 12. farm We live on a farm. 13. truck My dad drives a big truck. 14. wind The wind blew my hat off my head. 15. tooth I lost my front tooth. 16. fly There is a fly on the wall. 1 7. mouse The cat chased the mouse. 18. burn Did you burn yourself? 19. fish That is a big fish you caught. 20. tent The circus put up a big tent.

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99 Ten-Word List 2 for Markets 1 . hop 2. bean 3. fast 4. well 5. broom 6. cut 7. forty 8. river 9. clap 10. ring Watch the bunny rabbit hop. I planted a bean in the ground and watched it grow. How fast can you run? Are you feeling well today? Take this broom and sweep the front room. Don't cut yourself on that piece of glass. I am forty years old today. That is a long river. You can clap your hands now. That is a pretty ring on your finger.

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Twenty-Word List 1 for Matthew 100 1 . foolish It was a foolish thing to do. 2. anything I will do anything you ask. 3. turkeys We saw turkeys at the farm. 4. senseless They committed a senseless act. 5. hour The party will start in one hour. 6. dozen We have a dozen cookies to eat. 7. trail She followed the trail to the cabin. 8. machine The big machine made a lot of noise. 9. exercise He loves to exercise his dog outside. 10. disturbed The loud noise disturbed the class. 11. force The force of the blow knocked me down. 12. weather We do not know what the weather will be like. 13. rooster The rooster crows every morning at six. 14. mountains It is cold in the mountains. 15. island The ship wrecked on a tiny island. 16. settlers The settlers had to fight Indians. 17. hook The fish hook stuck in the wood. 18. guides We had two guides on our tour. 19. pitching Pitching a tent is not easy. 20. prepared She was prepared for the test.

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101 Ten-Word List 1 for Matthew 1 . nail Please bring the hammer and nail. 2. picture The picture on the wall was crooked. 3. discover Scientists discover many new things. 4. pencil You can erase with this pencil. 5. hose Take the hose and water the garden. 6. clothes We washed all the clothes. 7. crawl I watched the snail crawl. 8. crowd The crowd gathered quickly. 9. chased The dog chased the rabbit. 10. enough I have had enough to eat.

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1 02 Twenty-Word List 2 for Matthew 1 . patch Let's sit on that patch of grass. 2. smooth A smooth piece of wood won't give you splinters. 3 . whale That whale is the biggest fish I ever saw. 4. brick My house is made of brick blocks. 5 . throne The King sat on his throne. 6. danger There is much danger when you see a snake. 7. badge The sheriff showed me his badge. 8. claw The cat s claw was caught in the carpet. Q y • en j oy — Did you enjoy that movie? 10. alive The butterfly is still alive. 11 . bushes The animal ran into the bushes. 12. glass I did not break this glass. 13. chain The lion is tied up with a chain. 14. tray Don't drop your lunch tray. 15. chewed My dog chewed on his bone. 16. church I went to church last Sunday. 17. window Open the window for fresh air. 18. porch Let us sit on the porch now. 19. father My father is a plumber. 20. spoon Use your spoon for the soup.

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1 03 Ten-Word List 2 for Matthew 1 . 2. 3. 4. 5. 6. 7. 8. 9. 10. thick strike jacket almost attack spend coach dinner shirt snake This milk shake is very thick. I did not strike out at the baseball game. He wore his jacket to school today. We almost won the game. My dog did not attack your cat. Don't spend all your money in one place. The P.E. coach let us have free play. What did you have for dinner last night? That is a nice shirt you have on. That snake will bite you.

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1 04 Twenty-Word List 1 for Mikki 1 . scientist 3. examined 4 5. delicious 6. octave 7. terrific 8. salmon 9. brisklv 10. amount 11 . sharpness 12. hymn 13. whether 14. strutted 15. rumored 16. pounce 17. sentinel 18. nostrils 19. sensitive 20. wreath Scientists do important work. He took a considerable amount of time to complete the test. My physician examined me. Her cry was muffled. The pie was delicious. The third octave was what I wanted to play. They were terrific at their work. I like to eat smoked salmon. The wind blew briskly. What is the amount I owe you? The sharpness of the knife made it dangerous . We sang a Christmas hymn. I cannot decide whether I want to go to town or not. The chicken strutted across the yard. He was rumored to be missing. I saw the cat pounce on the mouse. The sentinel stood guard at the fort. His nostrils widened when he smelled smoke . She is sensitive to that perfume. She made the Christmas wreath.

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105 Ten-Word List 1 for Mikki 1 . instinct He worked solely on instinct. 2. dozen We have a dozen cookies to eat. 3. exercise He loves to exercise his dog outside. 4. disturbed The loud noise disturbed the class. 5. force Please do not force the window open. 6. weather We do not know what the weather will be like. 7. mountains It is cold in the mountains. 8. island The ship wrecked on a tiny island. 9. guides We had two guides on our tour. 10. trail She followed the trail to the cabin.

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1 06 Twenty-Word List 2 for Mikki 4 \ I 1 . autumn 2. truthful 3. weightless 4. disappear 5 . unusual 6. museum saxophone 8. imperfect 9. prehistoric 10. quiver 11 . clipped transferred 13. excitement 1 4. puncture 15. parachute 1 6. giraffe 17. tongue 18. earthquake 19. eyesight 20. favorably Autumn is one of the four seasons of the year. An honest person is always truthful. The astronaut was weightless in outer space. The magician made the rabbit disappear. That is an unusual bug on the ground. I went to an art museum today. He plays the saxophone in band. This diamond is imperfect because of a crack. The dinosaur was a prehistoric animal. There were six arrows left in the quiver. She clipped her fingernails last night. I was transferred to a different classroom. The class showed excitement when they went on a field trip. Be careful not to puncture yourself with that nail. He used a parachute after he jumped out of the plane. A giraffe can be up to thirty feet tall. Don't stick your tongue out at me. The earthquake destroyed many buildings. My doctor helped me get my eyesight back. The supervisor looked favorably at his workers.

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107 Ten-Word List 2 for Mlkki 1 . tomorrow i . unwrap •3 J • v\ ^ V* ^4 Kniccea — 4. autograph 5. injured 6. quicken 7. appointment 8. plumber 9. wonderful 10. everywhere You can finish your work tomorrow. I want to unwrap my Christmas present. She knitted a pretty sweater. Can I have your autograph? The football player was injured in last night's game. We must quicken our pace to catch up with them. Your appointment is for two o'clock today. Call the plumber to fix our kitchen sink. We had a wonderful time at the party. They were everywhere around us.

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APPENDIX C DATA RECORDING FORM Name C.A. Count Time Rate Date (#Cor/#Err) (Min. Fraction (Cor/Err) of Min.) Day 1 (Small) (Large ) Day 2 (Small) (Large) Day 3 (Small) (Large ) Day 4 (Small) (Large) Day 5 (Small) (Large ) Day 6 (Small) (Large) Day 7 (Small) (Large ) Day 8 (Small) (Large) Day 9 (Small) (Large) Day 1 0 (Small) (Large) 1 08

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APPENDIX D FREQUENCY MULTIPLIERS FOR CELERATIONS, MASTERIES, AND ACCURACIES

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' i n u H " O .•H f > u a « 0) c c x: u cn (0 S c CO s cn CQ 0) N -H w 0) w to T3 0 tn •H >1 >1 n o a) 0 -H 4J 4J 4J CO cn (0 o o n O OD ^ O '!P fO 1 >1 m ^^ 0 0) 0) -H 4J -P 4-) tn CO 03 (0 to OS m CM CO 00 in TCN n r>Trrn • • • o o VD ro O TO O to o CN t4J CQ -iH iJ T3 u o CO u >l >1 0) CO (0 o o o o in vo CN »(N O O rt(N O O Tro "I* n o o ro o o ^ o o CN (0 (d 4J J-) n] « c c •H -H u o •H -H
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115 C a to s >1 >1 J-l o 0) -H CO j H Ui o 4J JJ 4J 01 m (0 o o 1 >i u u o +J 4J 4J CO CO 05 (0 m OS rCM in fN ^ CM »a s m rCM ro m o o 00 (N (N (N CN O O Tr-< o rO • • • O O TCN pr» ^ ^ TJ< • • • O O (N u n (0 N •H w 0) CO 4J (0 •H iJ TJ Vj O +J CO u •H 1 0 H 4J Q. 0) u X Q Q cn Q CO Q CQ

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REFERENCE LIST Adamson, W. C. , & Adamson, K. K. (1979). A handbook for specific learning disabilities . New York: Gardner Press. All, P. (1977). From get truckin' to jaws, students improve their learning picture . Unpublished master' thesis, University of Kansas, Lawrence, KS. Alley, G. , & Deshler, D. (1979). Teaching the learning disabled adolescent: Strategies and methods . Denver Love. Alper, T. G. , & White, O. R. (1971). Precision teaching A tool for the school psychologist and teacher. Journal of School Psychology , 9_, 445-454. Baer, D. M., Wolf, M. M., & Risley, T. R. (1968). Some current dimensions of applied behavior analysis. Journal of Applied Behavior Analysis , 1_, 91-97. Bailey, J. S. (1977). A handbook of research methods in applied behavior analysis . Tallahassee: Florida State University. Barlow, D. H., & Hayes, S. C. (1979). Alternating treatments design: One strategy for comparing the effects of two treatments in a single subject. Journal of Applied Behavior Analysis , 1 2 , 199-210. Barrett, B. (1979). Communitization and the measured message of normal behavior. In R. York & E. Edgar (Eds.), Teaching the severely handicapped (Vol. 4 pp. 389-406). Columbus, OH: Special Press. Beck, R. (1977). Precision teaching project: Implementation handbook . The Sacajawea plan . Montana: Great Falls Public Schools. Bijou, S. W. (1970). What psychology has to offer education-now. Journal of Applied Behavior Analysis 3, 65-75. 1 1 9

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1 20 Blake, K. A. (1975). Amount of material and retarded and normal pupils' learning. Journal of Research and Development in Education , 8_, 1 28-1 36. Blake, K. A. (1976). The mentally retarded; An educational psychology . Englewood Cliffs, NJ: Prentice Hall. Bower, R., & Orgel, R. (1981). To err is divine. Journal of Precision Teaching , 2, 3-12. Bradfield, R. H. , Brown, J., Kaplan, P., Rickert, E. , & Stannard, R. (1973). The special child in the regular classroom. Exceptional Child , 39 , 384-390. Bruininks, R. H., Rynders, J. E. , & Gross, J. C. (1974). Social acceptance of mildly retarded pupils in resource rooms and regular classes. Journal of Mental Deficiency , 78 , 377-383. Caplan, G. (1970). The theory and practice of mental health consultation . New York: Basic Books. Gorman, L., & Gottlieb, J. (1978). Mainstreaming mentally retarded children: A review of research. In N. R. Ellis (Ed.), International review of research in mental retardation (Vol. 9 pp. 251-275). New York: Academic Press. Eaton, M. D. , & Wittman, V. (1982). Leap-ups: Acceleration of learning through increasing material difficulty. Journal of Precision Teaching , 3, 29-33. Eshleman, J. W. (1983, March). All the known precision teaching/standard chart references . Paper presented at the third annual meeting of the Precision Teaching Winter Conference, Orlando, FL. Evans, S. S. (1981). The relationship of skill rate to subsequent skill acquisition with learning disabled children (Doctoral dissertation. University of Florida, 1981). Dissertation Abstracts International , 42, 3945 A. Evans, S. S. & Evans, W. H. (1985). Frequencies that ensure skill competency. Journal of Precision Teaching , 6, 25-30.

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121 Evans, S. S., Mercer, C. D. , & Evans, W. H. (1983). The relationship of frequency to subsequent skill acquisition. Journal of Precision Teaching , 4^, 28-34. Fine, M. J. (1967). Attitudes of regular and special class teachers toward the educable mentally retarded child. Exceptional Children , 33 , 429-430. Gallagher, J. J. (1967). New directions in special education. Exceptional Children , 33 , 441-447. Cerent, M. C. (1985). The effects of initially high error tasks on short-term learning for mildly handicapped students (Doctoral dissertation. University of Florida, 1985). Dissertation Abstracts International , 45 , 2834A. Guskin, S. L., & Spicker, H. H. (1968). Educational research in mental retardation. In N. R. Ellis (Ed.), International Review of Research in Mental Retardation (Vol. 3 pp. 217-278). New York: Academic Press. Haring, N. G., & Bateman, B. (1977). Teaching the learning disabled . Englewood Cliffs, NJ: Prentice-Hall. Haring, N. G. , Lovitt, T. , Eaton, M. , & Hansen, C. (1978). The fourth R; Research in the classroom . Columbus, OH: Charles E. Merrill. Howell, K. W. (1979). Evaluating exceptional children: A task analysis approach . Columbus, OH: Charles E. Merrill. Johnson, G. O. (1961). A comparative study of the personal and social adjustment of mentally handicapped children who remain in special classes with mentally handicapped children who remain in regular classes. Syracuse: Syracuse University Research Institute, Office of Research in Special Education and Rehabilitation. Johnson, G. 0. (1962). Special education for the mentally handicapped: A paradox. Exceptiona l Children . 29 , 62-69. Johnston, J., & Pennypacker, H. (1980). Strategies and tac tics of human behavior research . Princeton, NJ: Lawrence Erlbaum Associates.

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1 Kauffman, J. M., & Payne, J. S. (Eds.). (1975). Mental retardation; Introduction and personal perspectives . Columbus: OH: Charles E. Merrill. Kirk, S. A., & Johnson, G. 0. (1951). Educating the retarded child . Boston: Houghton-Mifflin. Kjersted, C. L. (1919). The form of learning curves for memory. Psychological Monographs , 26 (No. 5). Klein, N. K., Pasch, M. , & Frew, T. W. (1979). Curriculum analysis and design for retarded learners Columbus, OH: Charles E. Merrill. Koenig, C. (1972). Charting the future course of behavior. Kansas City, KS: Precision Media. Lowenbraiim, S., & Affleck, J. Q. (Eds.). (1 976). Teaching mildly handicapped children in regular classes . Columbus, OH: Charles E. Merrill. MacMillan, D. L. (1971). The problem of motivation in the education of the mentally retarded. Exceptional Children, 37, 579-586. McGreevy, P. (1978). District-wide learning screening compared with average learning and learning picture products of resource teachers. Unpublished doctoral dissertation, Kansas University. McGreevy, P. (1980). Hard to do becomes easy to learn. Journal of Precision Teaching , 1_, 27-29. McGreevy, P., Thomas, J. G. , Lacy, L. , Krantz , S., & Salisbury, C. (1982). Can learning or variability be predicted from low initial performance? Implications for precision teachers and equal interval charters. Journal of Pr ecision Teaching, 3, 63-68. ~ — ^ Mercer, C. D. (1979). Children and adolescents with learning disabilities . Columbus, OH: Charles E. Merrill. Meyen, E. L. (1978). Exceptional children and youth: An introduction . Denver: Love.

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123 Miller, T. L., & Davis, E. E. (1982). The mildly handicapped: A rationale. In T. L. Miller, & E. E. Davis, (Eds.), The mildly handicapped student (pp. 3-15). New York: Grune & Stratton. Myers, P. I., & Hammill, D. D. (1976). Methods for learning disorders (2nd ed.). New York: Wiley. Neely, M. (1978). Six years of supervising a special education program by learning products. Unpublished doctoral dissertation. University of Kansas. Pennypacker, H. S., Koenig, C. H. , & Lindsley, 0. R. (1972). Handbook of the standard behavior chart . Kansas City, KS: Precision Media. Robinson, E. S., & Darrow, C. W. (1924). Effects of lengths of list upon memory for numbers. American Journal of Psychology , 35 , 235-243. Robinson, E. S., & Heron, W. T. (1922). Results in variations in length of memorized material. Journal • ' of Experimental Psychology , _5, 428-448. Robinson, N. , & Robinson, H. B. (1976). The mentally retarded child: A psychological approach . New York: McGraw-Hill. Rosenthal, R. (1966). Experimenter effects in behavioral research . New York: Appleton. Rosenthal, R., and Jacobsen, L. (1966). Teachers' expectancies: Determinants of pupils' IQ gains. Psychological Reports , 1 9 , 115-118. Rosenthal, R. , and Jacobsen, L. (1968). Pygmalion in the classroom . New York: Holt. Rothstein, J. H. (Ed.). (1962). Mental retardation . New York: Holt, Rinehart & Winston. Salvia, J., & Sindelar, P. T. (1982). Aptitude testing and alternative approaches to maximizing the effects of instruction. In T. L. Miller, & E. E. Davis, (Eds). The mildly handicapped student (pp. 221-240). New York: Grune & Stratton. Schmidt, L. J., & Nelson, C. C. (1969). The affective/cognitive attitude dimension of teachers of educable mentally retarded minors. Exceptiona l Children , 35/ 695-701 .

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1 24 School enrollment data . (1986). (Available from Marion County School System, Office of Student Information and Services, P. O. Box 670, Ocala, Florida 32678). Sidman, M. (1960). Tactics of scientific research: Evaluating experimental data in psychology . New York: Basic Books. Sidman, M., & Stoddard, L. T. (1966). Programming perception and learning for retarded children. In N. R. Ellis (Ed.), International review of research in mental retardation (Vol. 2 pp. 151-208). New York: Academic Press. Sidman, M. , & Stoddard, L. T. (1967). The effectiveness of fading in programming a simultaneous form discrimination for retarded children. Journal of Experimental Analysis of Behavior , 1 0 , 3-15. Siegel, E. (1969). Special education in the regular classroom . New York: John Day. Silvaroli, N. J. (1965). Classroom Reading Inventory (3rd ed.). Dubuque, lA: Brown. Smead, V. S. (1977). Ability training and task analysis in diagnostic prescriptive teaching. Journal of Special Education , 1 1 , 113-125. Smith, R. M. (1974). Clinical teaching; Methods of instruction for the mentally retarded (2nd ed.). New York: McGraw-Hill. Sparks, H. L., & Blackman, L. S. (1965). What is special about special education revisited: The mentally retarded. Exceptional Children . 31 , 242-247. Stainback, W. , & Stainback, S. (1984). A rationale for the merger of special and regular education. Exceptional Children , 51 , 102-111. Stoddard, L. T., & Sidman, M. (1967). The effects of errors on children's performance on a circle-ellipse discrimination. Journal of Experimental Analysis of Behavior , 10, 261-270. Stromberg, G. , & Chappell, M. (1980). Poster session at the Association for Behavioral Analysis Fifth Annual Convention.

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125 Sulzer-Azarof f , B., & Mayer, G. R. (1977). Applying behavior analysis procedures with children and youth . New York: Holt, Rinehart & Winston. Tawney, J., & Gast, D. (1984). Single subject research in special education . Columbus, OH: Charles E. Merrill. Tenenbaum, H. A. (1984). Effects of oral reading rate and inflection on comprehension and its maintenance. (Doctoral dissertation. University of Florida, 1983). Dissertation Abstracts International , 45 , 1086A. Wallace, E. E. (1984). The Riverside Spelling Program . Chicago: Riverside. Weatherby, R. , & Lipsky, M. (1977). Street-level bureaucrats and institutional innovation: Implementing special education reform. Harvard Educational Review , 47 , 171-197. Wehman, P., & McLaughlin, P. J. (1981). Program development in special education: Designing individualized education programs . New York: McGraw-Hill.

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BIOGRAPHICAL SKETCH Michael Mishkin was born on February 24, 1951, in Staten Island, New York. He graduated from West Hill High School, Montreal, Canada, in 1968. He graduated from the University of Florida in 1972 with a Bachelor of Science degree. He received a Master of Arts degree from the University of Alabama in Birmingham in 1978. He resumed his graduate studies at the University of Florida in 1979, receiving a Specialist in Education degree in 1981. Mr. Mishkin has been employed by the Marion County School Board since 1978. He was a school psychometrist for the first two years and, upon certification, became employed as a school psychologist in Marion County. He has been a certified school psychologist for the past seven years. Mr. Mishkin has been involved in the community in a variety of capacities. He has been on the school board for Cornerstone School for more than three years. He has been involved in the Marion Association of Counseling and Development for two years as a general member and officer. 1 26

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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. William Wolking, Cifalrman Professor of Counselor Education I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor-^ of Philosophy. Education I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Associate Professor of Foundations of Education This dissertation was submitted to the Graduate Faculty of the College of Engineering and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. December 1987 Dean, Graduate School