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The effects of operant procedures and cognitive behavior modification on learning disabled students' math skills

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The effects of operant procedures and cognitive behavior modification on learning disabled students' math skills
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Pavchinski, Peter, 1954-
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Classrooms ( jstor )
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Learning ( jstor )
Learning disabilities ( jstor )
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Counselor Education thesis Ph. D
Dissertations, Academic -- Counselor Education -- UF
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Thesis (Ph. D.)--University of Florida, 1988.
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Includes bibliographical references.
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Typescript.
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Vita.
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by Peter Pavchinski.

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THE EFFECTS OF OPERANT PROCEDURES AND COGNITIVE BEHAVIOR MODIFICATION ON LEARNING DISABLED STUDENTS' MATH SKILLS




By

PETER PAVCHINSKI


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 FILORIDA

1988


W1*" !S ,, OF FLORIDA LIBRARIM























Copyright 1988

by
Peter Pavchinski














ACKNOWLEDGMENTS


Thanks are extended to the school principals and teachers for their cooperation and contribution to this study. Thanks also go to committee members Paul Fitzgerald and Cecil Mercer for their valuable input and support. Special thanks are extended to Jeff Braden for his support and impeccable editorial and analytical contributions to this study. Special thanks also go to my wife, Alexa, for her constant support through the past

4 years of arduous graduate study.













TABLE OF CONTENTS


PAGE

ACKNOW LEDG M ENTS ............................................................................. iii

LIST O F TABLES ........................................................................................ vi

LIST O F FIG URES .......................................................................................... vii

ABSTRACT ..................................................................................................... viii

CHAPTERS

1 INTRO DUCTIO N ............................................................................. 1

Operant Procedures and Learning Disabilities .......................... 2
Cognitive Behavior Modification and Learning Disabilities ......... 4 Significance of the Study .............................................................. 6
Statem ent of the Problem ............................................................... 7
Purpose of the Study .................................................................... 8
Hypotheses ..................................................................................... 8
Definition of Term s .......................................................................... 9
Overview of Rem ainder of Study ............................................... 10

2 REVIEW O F LITERATURE ........................................................... 11

Remediation of Learning Disabilities with
Operant Procedures ..................................................................... 11
Remediation of Learning Disabilities with
Cognitive Behavior M odification ............................................ 15
Design Issues for Intervention Studies ..................................... 25
Sum m ary of the Literature Review ............................................ 26

3 M ETHODO LOGY ........................................................................... 28

Overview of the Study .................................................................. 28
Subjects .......................................................................................... 28
Variables Under Investigation .................................................... 29
Apparatus ..................................................................................... 31
Procedure ..................................................................................... 32
Design ............................................................................................. 38














TABLE OF CONTENTS



Data Analyses .............................................................................. 39
Limitations of the Study ............................................................... 41


4 RESULTS ...................................................................................... 44

Classroom Timings ...................................................................... 44
Achievement Tests ....................................................................... 44
Treatment Integrity ....................................................................... 48
Social Validity ................................................................................ 50

5 DISCUSSION ................................................................................ 52

Conclusion ..................................................................................... 54
Implications for Future Research ................................................ 55

APPENDICES

A TIMINGS PROBE SHEET ........................................................... 58

B TEACHER REFERENCE--CBM ................................................. 59C TEACHER REFERENCE--OPERANT PROCEDURES ........... 60

D INVENTORY ................................................................................... 61

E TREATMENT INTEGRITY RATING ............................................. 62

F SOCIAL VALIDITY RATING INTERVIEW .................................. 63

REFERENCES ........................................................................................... 64

BIOGRAPHICAL SKETCH ....................................................................... 70













LIST OF TABLES


Table 1
Subject Characteristics ........................... 29

Table 2
Assignment of Condition Per Teacher and School ................. 40

Table 3
ANOVA Results of Classroom Timings for all Conditions ....... 46

Table 4
ANOVA Results of Achievement Tests for all Conditions ..... 48

Table 5
Within-Subject Analyses for Control, Operant, and
C BM Conditions .......................................................................... 49

Table 6
Effects Due to Operant and CBM Conditions ........................ 49













LIST OF FIGURES


Page
Figure 1
Classroom Timings Results for All Conditions .......................... 45

Figure 2
Stanford Diagnostic MathematicsTest Results for All
Conditions ..................................................................................... 47


vii













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 OPERANT PROCEDURES AND COGNITIVE
BEHAVIOR MODIFICATION ON LEARNING DISABLED STUDENTS' MATH SKILLS

By

Peter Pavchinski

August, 1988

Chairman: Jeffery P. Braden
Major Department: Counselor Education
A comparison between operant procedures and cognitive behavior modification was conducted in this study on elementary school learning disabled students' math skills. A control condition consisting of direct instruction of math skills was also used. Dependent measures were 2-minute classroom timings of basic addition and subtraction problems and the Stanford Diagnostic Mathematics Test.
Nine intact classrooms from four schools were selected for the study; the classrooms were randomly assigned to one of three conditions. A total of 94 students participated.
Treatment was provided for 4 weeks in daily 1-hour sessions. Retention of math skills over a 2-week period was also investigated. Performance trends across three testing periods were compared between


viii








the two treatments and the control condition. A repeated measures ANOVA design was used to analyze the data.
Significant differential gain between experimental and control groups in achievement test scores was found (F(4, 182) = 4.03, P<.01). Operant procedures and cognitive behavior modification were equally effective (F(2, 65) = 0.29, NS). All three groups improved with 2-minute classroom timings (F(2, 91) = 8.53, p<.001). Retention of skills for both treatments was maintained over the 2-week period of no treatment.
Teacher social validity ratings indicated differences between the two treatments relative to student behaviors and teacher roles. The operant procedure requires the teacher to maintain back-up reinforcers and to deliver token reinforcement. Students are not taught specific learning strategies, but are reinforced for correct classwork. Cognitive behavior modification requires a more active teacher role in terms of modeling and prompting self-instruction procedures. Students must learn and apply self-instruction for classwork.
Implications of the study are that both operant procedures and cognitive behavior modification are equally effective techniques to remediate learning disabled students' math skills despite their disparate theoretical orientation, and both are better than direct instruction. Both remediation techniques also are equally effective in producing retention of math skills over a 2-week period. Selection of one treatment over the other may depend upon desirability of the teacher's role for each treatment and specific student behaviors to be produced.














CHAPTER 1
INTRODUCTION

Learning disabilities are phenomena which manifest themselves in significant academic difficulties among certain students. Although many characteristics typify learning disabled (LD) students, discrepancy between academic achievement and estimated ability is one of the chief variables distinguishing LD students from normal students (Ferguson & Mamen,1 985; Mercer & Mercer, 1985). Other characteristics of LD students include below grade-level academic performance, language problems, perceptual disorders, motor dysfunctions, and memory and attention deficits (Mercer, 1987).
Theories of etiology and treatment of learning disabilities typically fall within two major models: medical or behavioral (Treiber & Lahey, 1983). Learning disabilities are viewed as symptoms of organic dysfunction in the medical model. Minimal brain injury and process deficits are diagnostic labels used to identify organic pathology associated with learning disabilities. A process deficit is defined as a disorder in basic psychological processes such as memory, language, or perceptual-motor skills which contributes to academic problems (Mercer, 1987).
Etiology is deemphasized in the behavioral model, and learning disabilities are viewed as behaviors that require modification (Throne, 1973; Treiber & Lahey, 1983). Rather than assigning diagnostic labels, treatment of learning disabilities involves direct instruction with weak





2


academic areas and manipulation of environmental contingencies in order to enhance learning (Treiber & Lahey, 1983).
Operant Procedures and Learning Disabilities
There have been various approaches for remediating learning disabilities, but few are effective (Lahey, Hobbs, Kupfer, & Delamater, 1979). One of the major remediation models shown to be effective with learning disabilities is the behavioral model (Treiber & Lahey, 1983). Most behavioral techniques for LD remediation are based on operant conditioning theory (Skinner, 1953). A principle of operant theory holds that rates of behavior increase when followed by positive reinforcement. Operant remediation of learning disabilities typically reinforces on-task behavior, rates of completed classwork, or other desired behaviors.
Application of operant procedures for LD remediation does not
hinge upon assignment of a label or categorization of a disorder within the student. Based on operant conditioning theory, LD students demonstrate academic difficulties because environmental contingencies do not reinforce learning, not because of organic or internal factors (Throne, 1973). Operant procedures typically result in modified behaviors through manipulation of external or environmental contingencies. Providing appropriate reinforcers for academic achievement in LD students increases academic gains (Skinner, 1968).
There are several types of reinforcers used with operant procedures. Primary reinforcers, such as edibles, are stimuli that have high biological importance. Secondary or conditioned reinforcers are those whose value has been learned or conditioned by the environment (Alberto & Troutman, 1986). Secondary reinforcers include praise, social approval, and tokens





3


(Stromer, 1977). Tokens and money are a special class of conditioned reinforcers termed generalized conditioned reinforcers because they provide access to a variety of primary and secondary reinforcers. Tokens are frequently used in educational research because of their high motivational properties (Alberto & Troutman, 1986).
Remediation of learning disabilities with operant procedures has been widely investigated and accepted as an effective remediation technique (Lahey et al., 1979). A number of academic areas have been targeted including reading comprehension (Lahey, McNees, & Brown, 1973), oral reading (Lovitt & Hansen, 1976), and math (Broughton & Lahey, 1978; Smith & Lovitt, 1976). Operant procedures also have been used to remediate a "process deficit" with perceptual-motor skills (Lahey, Busemeyer, O'Hara, & Beggs, 1977). Lahey et al. (1977) demonstrated the significant positive impact that operant procedures exert on behaviors attributed to organic dysfunction.
Generalization or retention of training is an important element in the learning process (Gagne, 1977; Wong, 1985). Despite the success of operant procedures for remediating learning disabilities, retention of skills after treatment has been poor (Rose, Koorland, & Epstein, 1982; Stokes & Baer, 1977). Generalization is defined as the occurrence of relevant behaviors under different, non-training conditions, such as across settings, instructors, tasks, or time, without the scheduling of the same events in those conditions as had been scheduled in the training conditions (Stokes & Baer, 1977). Most researchers with operant studies have not actively investigated retention of treatment. Despite available technology for generalization with operant procedures, the "train and hope" model of









treatment generalization has prevailed (Stokes & Baer, 1977). In this model of generalization retention of learning is documented if it occurs after treatment, but a specific methodology to account for its occurrence is not provided.

Cognitive Behavior Modification and Learning Disabilities
Cognitive behavior modification (CBM) is a relatively new and

popular cognitive treatment for learning disabilities (Meichenbaum, 1980; Swanson & Kozleski, 1985). It is related to metacognition, a general term referring to an awareness of one's own cognitive performance (Hallahan, Hall, lanna, Kneedler, Lloyd, Loper, & Reeve, 1983). Cognitive behavior modification is based on the research of two Soviet learning theorists: Vygotsky and Luria. Both Vygotsky (1962) and Luria (1961) independently posited that overt child behaviors can be governed by internal speech. Vygotsky hypothesized that private speech facilitates organization of problem-solving strategies in children. Luria theorized three stages when overt behaviors come under voluntary control during child development. During the first stage, the speech of others, usually adults, controls and directs a child's behavior. In the second stage, the child's overt speech becomes an effective regulator of behavior. Finally, the child's covert, or inner speech, assumes a self-governing role.

Cognitive behavior modification is a technique which utilizes selfinstruction to regulate or change behaviors (Meichenbaum, 1977). Selfinstruction involves self-verbalizations which aid in identifying and controlling new behaviors (Ledwidge, 1978). In this process, selfinstruction becomes a mediator between cognitive structures and behaviors. Self-instruction training contains five basic steps:









1. An adult model performs a task while talking to herself out loud (cognitive modeling);
2. The child performs the same task under the direction of the model's instructions (overt, external guidance);
3. The child performs the task while instructing herself out loud (overt self-guidance);
4. The child whispers the instructions to herself as she goes through the task (faded, overt self-guidance); and
5. The child performs the task while guiding her performance via private speech (covert self-instruction). (Meichenbaum, 1977, p. 32)

Normal students typically approach tasks in an active manner and spontaneously apply self-instruction to guide behaviors or solve tasks (Hallahan et al., 1983). However, academic deficits occur when students fail to use self-instruction to guide behavior (Meichenbaum, 1977). Learning disabled students are characterized as passive, inactive learners who do not spontaneously produce or apply appropriate self-instruction strategies for task solution (Hallahan et al., 1983; Ryan, Short, & Weed, 1986; Torgeson, 1977). Learning disabled students also fail to internalize rules or strategies that guide new learning situations. Based on the CBM model, LD students' academic problems are due to deficient application of self-instruction to academic tasks.
According to the CBM model, behavioral changes occur through internal controls or self-regulatory private speech. Training in selfinstruction should increase academic performance by allowing LD students to perform a kind of thinking that they do not normally produce (Meichenbaum & Asarnow, 1979). With CBM, the student is able to consistently apply problem-solving behaviors across differing environments (Meichenbaum, 1985).
Research with CBM and learning disabilities has primarily focused on remediation of impulsivity or other task-oriented behaviors









(Meichenbaum & Asarnow, 1979). General self-instruction procedures, such as self-monitoring, are used to address generic classes of behaviors rather than behaviors specific to academic tasks. Application of CBM for treatment of academic subjects in LD students has only recently received attention, and few studies exist (Gerber, 1983; Kneedler & Hallahan, 1981; Lloyd, 1980).
Specific self-instruction procedures have been developed to
promote academic remediation of LD students (Tarver, 1986). In several studies researchers have combined both general and specific selfinstruction training with academic remediation in LD students (Harris & Graham, 1985; Swanson & Scarpati, 1984). In these studies, application of general self-instruction is intended to enhance active learning styles, while specific self-instruction training focuses on task solution and facilitates treatment retention. It has been shown in the research literature that remediation of learning disabilities with self-instruction can increase problem-solving efficiency to the point where it is commensurate with normal learners (Harris, 1986). Cognitive behavior modification, like operant procedures, has been criticized for lack of treatment retention.
Significance of the Study

Although research based on CBM is suggestive of effective remediation with learning disabilities, there has been no careful comparison with other remediation models (Lahey & Strauss, 1982). Further, problems with methodology and lack of preliminary studies preclude making firm conclusions regarding CBM's efficacy (Gerber, 1983; Hobbs, Moguin, Tyroler, & Lahey, 1980; Meichenbaum, 1980; Rooney &








Hallahan, 1985; Swanson & Kozleski, 1985). Criticism of CBM methodology includes the following:

1. Students with different learning problems are used when
providing treatment. For example, in some group studies, nonLD students are combined with LD students within the treatment group.

2. Independent variables are not always clearly defined, so they confound interpretations of treatment gains.
3. Type I dependent measures are infrequently used to evaluate treatment gains. Type I dependent measures are direct measures of a socially valued treatment goal such as improvement in tested academic achievement (Lahey & Strauss, 1982).
4. Researchers do not utilize measures of classroom achievement gains as dependent measures.
5. Retention of treatment across time is not adequately demonstrated with CBM.

Thus, it is not clear how effective CBM is with academic remediation in LD students, or how it compares with operant procedures. This comparison, along with methodological issues, requires investigation in order to advance knowledge of education of LD students and to substantiate use of CBM as a remediation strategy with this student population.

Statement of the Problem
Few researchers have specifically investigated academic
remediation with LD students. Despite CBM's increasing promise as an LD remediation tool, there are no convincing empirical data to substantiate its effectiveness. Cognitive behavior modification studies have been








criticized for methodological weaknesses, which casts doubt on treatment effectiveness. There have been no careful comparisons between CBM and operant conditioning with academic remediation of LD students.
Purpose of the Study

A comparison of treatment effects was conducted in this study

between direct instruction, direct instruction with operant procedures, and CBM with remediation of addition and subtraction operations in elementary school LD students. Treatment effectiveness was measured by results from a standardized math test and classroom performances. Retention scores of math skills across time based on remediation techniques were collected and compared.
Hypotheses

The following hypotheses were investigated in this study.

1. Ho: There will be no significant difference (p>.05) in trend among direct instruction, direct instruction with operant procedures, and CBM with elementary school LD students' addition and subtraction operations as measured by classroom performance timings.

2. Ho: There will be no significant difference (p>.05) in trend among direct instruction, direct instruction with operant procedures, and CBM with elementary school LD students' addition and subtraction operations as measured by a standardized math test.
3. Ho: There will be no significant difference (p>.05) in trend between direct instruction with operant procedures and CBM with elementary school LD students' addition and subtraction operations as measured by classroom performance timings.









4. Ho: There will be no significant difference (p>.05) in trend between direct instruction with operant procedures and CBM with elementary school LD students' addition and subtraction operations as measured by a standardized math test.

Definition of Terms

Classroom performance timings-- This measure is the number of correct basic addition and subtraction problems completed .during a 2-minute period.

Cognitive behavior modification (CBM)-- This treatment is a type of cognitive remediation technique which employs self-instruction to guide overt behaviors.

Direct instruction-- Direct instruction is a systematic plan of

instruction which targets academic deficits and directs teaching toward increasing those deficits.
Learning disabled (LD) student-- An LD student is one who is

experiencing academic difficulties and who has met the following criteria:
(a) demonstrates a standard deviation discrepancy between IQ and math achievement and (b) has below average functioning in either perceptualmotor, short-term memory, or language processing skills. Learning disabled students attend resource or self-contained classrooms for remedial instruction with an exceptional education (LD) teacher.
Operant procedure-- This is a procedure which provides token
reinforcers immediately after and contingent upon a specified behavior in order to increase the probability of that behavior to recur.

Standardized math achievement test-- This is a test which has undergone a norming process that allows meaningful interindividual








comparisons. Reliability and validity data are usually reported for standardized tests.


Overview of Remainder of Study
A review of literature is presented in Chapter 2. Variables under investigation are discussed in Chapter 3. Methodological issues such as research design and statistical procedures are also described. Results of the data analysis and statistical summary tables are presented in Chapter
4. The results and implications for future research are discussed in Chapter 5.














CHAPTER 2
REVIEW OF LITERATURE

This review is divided into three sections. The first section is an
overview of math remediation of LD students with operant procedures. A comprehensive review of academic remediation with CBM of LD students is presented in the second section. Specific methodological issues pertinent to this study are reviewed in the third section.
Remediation of Learning Disabilities With Operant Procedures

Operant procedures are based on operant conditioning theory
(Skinner, 1953). Operant procedures typically arrange environmental or external consequences in order to modify behaviors. Positive reinforcement is a widely used operant procedure and one of the most effective methods for increasing rates of behavior (Alberto & Troutman, 1986; Hilgard & Bower, 1975). A positive reinforcer is a consequential stimulus that (a) increases or maintains future rates of behaviors, (b) is administered contingent upon the production of a desired behavior, and (c) is administered immediately following the desired behavior (Alberto & Troutman, 1986)
Remediation of LD students with operant procedures is concerned with changing academic behaviors or characteristics rather than assigning labels or searching for causes of academic dysfunction (Treiber & Lahey, 1983). Operant procedures are used to manipulate environmental contingencies in order to increase academic functioning in LD students.








Operant procedures have been used to effectively remediate many academic areas (Lovitt, 1975). Operant procedures also have been used to effectively remediate a severe "process deficit" typically attributed to organic dysfunction (Lahey et al., 1977). That is, two severely handicapped LD males with perceptual-motor deficits significantly improved copying skills when token reinforcement was instituted.
Academic remediation with operant procedures typically includes the following characteristics:
1. Direct instruction--specifically teaching weak academic areas.
2. Emphasis on measurement--continuous measurement of

behaviors being remediated are used for immediate feedback of treatment effectiveness.
3. Manipulation of environmental contingencies (Treiber & Lahey, 1983).
Math Remediation of LD Students With Operant Procedures
Smith and Lovitt (1976) investigated conditions for appropriate
application of operant procedures with math remediation. Seven LD males participated in the study which employed a single-subject reversal design. Subjects had opportunity to earn points toward a chosen toy by successfully completing math problems. Initially, none of the students earned points. However, once the students were shown how to compute the problems, points were earned and task accuracy increased. Smith and Lovitt (1976) concluded that reinforcement contingencies are only effective when desired behaviors are part of the subject's repertoire of behaviors.

Broughton and Lahey (1978) conducted a study investigating effects of positive reinforcement, response cost, and combination of positive








reinforcement and response cost with remediation of subtraction. Thirtythree fourth and fifth graders with math disabilities served as subjects. The subjects were assigned to either positive reinforcement, response cost, combination positive reinforcement and response cost, or control group. A reversal design was used with each treatment group. Reinforcement occurred as points which were exchanged for various activities during free time. Points were awarded for correct subtraction responses in the positive reinforcement group. The response cost treatment group initially received 20 points per day to spend during free time. Points were lost for each incorrect subtraction response. The procedure for the combination treatment group combined both contingencies for either correct or incorrect responses.
Significant positive gains were found for the results from all three treatments. Although significant differences were not shown among treatment groups, the response cost group and positive reinforcement group produced more immediate changes in subtraction performance than did the combination treatment group. A reason for this observation may have been lack of immediacy in determining number of earned points by students in this condition. That is, the subjects had to ask the teacher frequently for cumulative point totals. Increases in on-task behavior also occurred as academic gains were made. It was posited that successful academic progress may be a prerequisite for increasing on-task behaviors.
Blankenship and Baumgartner (1982) investigated remediation and generalization of math skills with operant procedures in LD students. In this study procedures for generalization across task were specifically addressed. Subjects were 4 female and 5 male LD students ranging from








8 through 11 years of age. A single-subject multiple-baseline design was used. After subjects showed proficiency with math computation, they were presented with a worksheet of noninstructed math problems to complete. Points as reinforcers were delivered for correct responses on the worksheet and were exchanged for school supplies. This procedure served as the attempt for generalization across task of instructed math problems.
Results varied as to the extent to which students acquired and

generalized math skills. However, when treatment procedures added a relevant algorithm aiding math computation along with a variable schedule of reinforcement, all students increased accuracy and generalization to noninstructed problems.
A departure from the "train and hope" model of generalization with operant procedures was demonstrated in this experiment. Rather than hoping for transfer of learning to occur after treatment, this study included prescribed, specific procedures for assessing and increasing the probability of generalization across task. Summary of Math Remediation of LD Students With Operant Procedures
Remediation of math in LD students with operant procedures

typically employs direct instruction and reinforcers to increase academic skills. Etiology of learning disabilities is not a concern in operant studies. Instead, overt behaviors requiring change are focused upon. Singlesubject designs with multiple-baseline and reversal features dominate operant research. Few statistical measures are used to show treatment significance. Instead, descriptive or qualitative data are often graphed to








show treatment changes relative to baseline conditions. Retention of treatment gains has been limited.
Remediation Of Learning Disabilities With Cognitive Behavior Modification
Meichenbaum is credited for seminal research with CBM (Wong, 1985). Cognitive behavior modification first emerged as a technique to remediate a generic class of behaviors including impulsivity and off-task behavior. Meichenbaum and Goodman's (1971) two-part study is among the first in which the role of self-instruction on overt behaviors was investigated (Craighead, 1982). The researchers used self-instruction to modify impulsivity in 15 second graders ranging from 7 to 9 years of age. Several other studies have examined the role of CBM with task-oriented behaviors of LD students (Hallahan, Marshall, & Lloyd, 1981; Rooney, Polloway, & Hallahan, 1985; Tollefson, Tracy, Johnsen, & Chatman, 1986).
Investigation of specific academic areas among LD students with CBM has only recently received attention. General self-instruction techniques similar to those employed for remediation of task-oriented behaviors were utilized in earlier studies. Contemporary researchers have combined general and specific self-instruction in order to increase academic achievement and retention of skills. Academic Remediation of Learning Disabilities With CBM
Writing. Robin, Armel, and O'Leary (1975) remediated handwriting deficiencies with CBM. Thirty kindergarten subjects were not specifically identified as LD, but reportedly scored poorly on a handwriting measure. The subjects were divided into a self-instruction group, direct training with social reinforcement group, and control group. The main components of direct training were corrective feedback and social reinforcement. The self-









instruction group also received social reinforcement, and this procedure may have confounded the results (Lahey et al., 1979). Treatment consisted of 20 training sessions spanning a 7-week period. Selfinstruction training consisted of the following steps:

1. Question about the task: "What is it I have to do?"
2. Answer in the form of planning: "I have to make a 'P'."
3. Appropriate directive comment: "I have to go down, down,
slow, stop at the bottom, stop."
4. Correction of error: "No, that's not straight; I have to make a
straight line, like a stick."
5. Self-reinforcement: "It's done and I made a good letter." (p.
182)

Based on results from an analysis of variance (ANOVA), it was shown that CBM treatment was more effective than direct training with reinforcement. Both treatments were superior to the control group. Cognitive behavior modification's superior results were attributed to its incremental task strategy. That is, the copying task was partitioned by CBM into more discrete components as compared with direct training.
Several issues with practicality of CBM treatment arose from this study. Despite demonstration of self-instruction by the experimenter, students often abbreviated the procedure. Most students developed their own idiosyncratic style of self-instructing. Secondly, higher rates of overt verbalization were not correlated with superior performance. However, some children may have covertly guided their behavior, making such an inference inaccurate. Finally, overt self-instruction was deerred cumbersome because of disruptive effects in the classroom.
Kosiewicz, Hallahan, Lloyd, and Graves (1982) more recently
investigated CBM treatment of poor handwriting in a 10-year-old LD male. A multiple-baseline reversal design was used. Sixty-five treatment








sessions at 1-5 minutes per session spanned 120 days. Dependent measures were percent of correctly reproduced letters. Significant improvements in handwriting were found. However, a potential methodological problem was cited with confounding effects of sequential treatment order. It may be impossible to completely withdraw a cognitive strategy such as self-instruction once it has been taught. Thus, a reversal design may be inappropriate with CBM.
The experimenters did not experience the cumbersome aspect of classroom self-instruction previously cited by Robin et al. (1975). The student in the current study seemed to progress spontaneously to the covert self-instruction stage. Reasons for the smooth transition from overt to covert self-instruction may have been the 10-year-old's higher language skills than a kindergartener's, and prior knowledge of letter formation. Thus, CBM's effectiveness may be facilitated with older subjects, or those with established language skills.

Composition writing. Harris and Graham (1985) investigated
improvement of composition writing in LD students with CBM. Two 12year-old LD students served as subjects. For treatment, Harris and Graham introduced self-control as an adaptation of self-instruction training. Self-control training includes specific task-appropriate strategies and metacognitive training. Metacognitive training is defined as training in the self-regulation of appropriate self-instruction strategies. Self-control training contains the following four procedures: (a) self-instruction, (b) selfdetermined criteria for academic performance, (c) self-assessment, and (d) self-reinforcement.








Treatment began with skill building in recognition of "action words." Then, the importance of increasing writing skills was discussed with the student. A five-step strategy for writing good stories followed which was modeled by the instructor and written out on a small chart for students:

1. Look at the picture and write down good action words.
2. Think of a good story idea to use my words in.
3. Write my story--make sense and use good action words.
4. Read my story and ask--did I write a good story? Did I use
good action words?
5. Fix my story--can I use more good action words? (p. 29)
After training of these components, metacognitive procedures for selfcontrol training were presented.
Dependent measures for written stories were frequency of different action words, action helpers, descriptive words, and total number of words. Significant improvements in the quality of written compositions in both subjects were demonstrated. Post-treatment retention was shown after 2 weeks, but inconsistencies occurred after 14 weeks. Both subjects maintained retention of training steps after 14 weeks, but implementation of training was inconsistent.

Math. Several studies (e.g., Grimm, Bijou, & Parsons, 1973; Lovitt & Curtiss, 1968) have focused on the role of verbal mediation with math in handicapped children. However, Leon and Pepe (1983) were among the first to investigate CBM remediation of math with LD students. Their sample consisted of 13 LD and 24 educable mentally handicapped (EMH) students ranging from 9 through 12 years of age. Learning disabled and EMH students were combined in treatment and control groups. Dependent measures were results from standardized and curriculum-based math tests





19


of basic math operations. Training consisted of 35 sessions during a 7week period. Self-instruction training contained the following steps:

1. Teacher provided modeling by computing the problem using overt verbalization.
2. Teacher and student computed the problem together using overt verbalization.

3. Student computed the problem with overt verbalization and teacher supervision.

4. Student computed the problem while whispering self-instruction (fading of overt verbalization).
5. Student computed the problem with covert verbalization.
Significant math increases were found in the treatment group, and learning disabled students scored higher than EMH students on dependent measures. Generalization of self-instruction training was reported to occur across math tasks.
Schunk and Cox (1986) further investigated math remediation with CBM in LD students by adding an effort attribution variable and differentiating between overt and covert verbalization. Subjects included 90 LD students ranging from 11 through 16 years of age. Treatment math operations were subtraction problems involving regrouping. Selfinstruction training consisted of six 45-minute sessions. After a modeled example, the overt verbalization group received the following instructions:

I'm really interested in knowing what students think about as
they solve problems. So as you're working problems, I'd like you to
think out loud; that is, say out loud what you're thinking about, just like I did while I was solving problems. You'll probably be
thinking about what to do next, what numbers to use, how much is
one number minus another, and so on. Remember, say out loud
what you're thinking about, just as I did. (p. 204)








The covert verbalization group received the same instructions, but was asked not to talk out loud after the third session. Besides general selfinstruction training, students received attribution feedback for effort after successful problem solving. Effort feedback was delivered either during the first or second half of training, or not at all. Dependent measures included a subtraction skill test and self-efficacy rating scale for attribution.
Based on results from the multivariate analysis of covariance (MANCOVA), self-instruction was found to increase subtraction skills. Covert self-instruction was not as successful as overt self-instruction. The authors concluded that the subjects had difficulty internalizing the strategies, i.e., in Meichenbaum's fifth step in self-instruction training. This difficulty also may have been due to application of only general selfinstruction training academics. Specific self-instruction training may have produced better results (Wong, 1985). Effort attribution feedback led to higher self-efficacy and subtraction skills. However, there was no difference between first or second-half effort feedback conditions.
Reading. Wong and Jones (1982) investigated treatment of reading comprehension with a CBM-related procedure. The sample consisted of 120 LD and normal eighth and ninth graders. Treatment effects were compared between normal and LD students. Two-day treatment consisted of a self-questioning procedure focusing on reading comprehension strategies:

1. What are you studying this passage for?
2. Find the main idea/ideas.., and underline them.
3. Think of a question about the main idea you have underlined.
Remember what a good question should look like.
4. Learn the answer to your question.





21


5. Always look back at the questions and answers to see how each
successive question and answer provide you with more
information. (p. 231)

Significant comprehension gains occurred in the LD treatment
group. No significant gains were found among normal students. The lack of training effects among normal students may be attributed to the fact that normal students spontaneously monitor their comprehension without requiring specific training. This hypothesis is consistent with CBM theory and the prediction of a verbal mediation deficit among LD students.

Kupietz (1980) attempted to modify impulsivity and increase
reading in 30 second and third graders. Effects of general versus specific self-instruction were compared on these variables. Dependent measures for reading were results from standardized tests. Although subjects showed a decrease in impulsivity, there were no significant gains made in reading. A significant difference was not found between general and specific self-instruction with reading gains. Several confounding variables were cited, including problems with student discipline and limited training time for treatment.
Swanson and Scarpati (1984) conducted two experiments in which they investigated reading, spelling, and math remediation with CBM in LD students. Several aspects of generalization also were analyzed. Subjects were 2 LD eighth and ninth-grade males. A single-subject design was used. Similar to Harris and Graham (1985), the researchers used general self-instruction for error monitoring and self-reinforcement. Task specific strategies focused directly on academic problem solving. Training in Part I consisted of 45-minute treatments for a minimum of eight sessions. Delivery of token reinforcers was part of the existing classroom behavior





22


management program, and subjects continued to earn them. This motivational variable may have confounded results (Lahey et al., 1979).

Generalization across setting, instructor, and task was conducted immediately following the treatment condition. In the setting phase, the 2 subjects attempted learning activities with the same teacher used for CBM training, but in a setting different from the baseline or treatment conditions. Setting differences included changes in room color and seating arrangement. For the generalization procedure across instructor, a teacher who was familiar to the students, but who had not taught reading or spelling to the students was used. Generalization across task exposed the students to new learning activities commensurate with training item difficulty.

Based on results to Part I, the researchers concluded that

self-instruction significantly increased LD students' reading and spelling performances. Generalization across instructor and task was shown with reading and spelling. However, generalization across setting in a nontreatment classroom did not occur. Possible reasons were attributed to a radically different classroom environment as compared to treatment setting.

In Part II, math remediation and generalization of math skills across setting in a 13-year-old LD male were investigated. A reversal design was used in this phase. Initially, treatment was conducted in one corner of the student's LD classroom. Twenty-eight 30-minute treatment sessions were conducted. Generalization was assessed when the subject returned to his regular seat in the same classroom. The student's math performance in this setting remained at a rate commensurate with treatment setting. The









researchers hypothesized that when classroom settings are changed in smaller increments from treatment settings, generalization is more likely to
occur.

Swanson and Scarpati (1984) noted difficulties similar to those cited by Kosiewicz et al. (1982) with a reversal design and CBM treatment. Confounded results occur when CBM treatment is withdrawn.
Puzzle task. Harris (1986) investigated differences between LD and normal students with private speech and puzzle performance. Subjects were 30 LD and 30 normal 7 and 8-year-old students. The students were assigned to complete an insolvable puzzle. The treatment group was exposed to self-instruction training relative to puzzle tasks. Four dependent measures were collected: rate of private speech (only overt verbalizations were measured), proportion of task-relevant private speech, time required to complete solvable portion of puzzle, and persistence time.
Three significant differences between LD and normal students were found: (a) LD students showed lower proportion of task-relevant verbalizations, (b) LD students required more time to solve the task, and (c) LD students showed shorter persistence times. In addition, LD students produced more negative self-statements than normal students while solving the puzzle.

Three significant differences also were found between treatment and control groups. The treatment group showed a higher proportion of task-relevant private speech and higher rate of private speech in general. The treatment group also had longer persistence times. Interestingly, treatment group LD students performed as well as normal control group students.





24


These results are significant in that they support further the

hypothesis that LD students have a verbal mediation deficit in academic processes. In addition, CBM remediation can produce task efficiency among LD students that is commensurate with nonLD students. Summary of CBM Research
Research with CBM and task-oriented behaviors was pioneered by Meichenbaum. Cognitive behavior modification emerged as a remediation strategy for impulsivity and hyperactivity. General self-instruction methods were applied to remediate these behaviors. Based on verbal mediation deficits, CBM was then applied to academic remediation with LD students. Specific self-instruction procedures have been developed that directly focus on academic problem-solving strategies.
Design characteristics with CBM research include both
single-subject and group designs. However, single-subject reversal designs with CBM are a problem. Reversal, alternating treatments, and changing conditions designs are inappropriate with CBM because of difficulties encountered when withdrawing a cognitive remediation strategy (Kosiewicz et al. 1982; Swanson & Scarpati, 1984). When CBM treatment is withdrawn in a reversal design, it cannot be assumed that learned cognitions in the treatment phase are withdrawn from the student. Similarly, with alternating treatments or changing conditions designs such as ABCBC, cognitive training (for example, B) can be carried over to the next treatment phase (C) and confound results.
As with operant studies, retention of treatment across time has not been adequately shown with CBM research. The hypothesis that CBM





25


produces greater treatment gains and skill retention than operant procedures is untested.


Design Issues for Intervention Studies Reinforcers
Token reinforcement systems are widely used in educational

research because they allow for greater versatility over other reinforcement systems (Alberto & Troutman, 1986). Token reinforcers are generalized conditioned reinforcers because they are associated with a variety of behaviors or other reinforcing items termed back-up reinforcers (Alberto & Troutman, 1986). Thus, tokens are particularly motivating because of this variety of choice for exchange.

There are additional advantages of the use of token reinforcers over other reinforcement procedures. Token reinforcers maintain performance over extended periods of time because they are less subject to satiation effects and deprivation states than primary reinforcers. Token reinforcers provide the same reinforcement for individuals who have different back-up preferences. Finally, use of tokens provides the student with a tangible means of continuous feedback (Alberto & Troutman, 1986). Treatment Integrity
Treatment integrity refers to the extent to which a specified treatment is actually implemented in the manner prescribed by the methodology. Treatment integrity should be included in contemporary research, especially with group designs, but few researchers address it (Shapiro, 1987). Documentation of treatment integrity is important for ethical





26


considerations and practical reasons such as replication of research (Shapiro, 1987).

Social Validity
Social validity refers to the evaluation of treatment by consumers or relevant observers and is often assessed qualitatively (Shapiro, 1987). Social validity of treatment effectiveness and related issues is an important aspect of contemporary educational research.

Summary of the Literature Review

Three topics were highlighted in the literature review: operant
treatment of LD students' math deficiencies, CBM treatment of LD students' academic deficiencies, and design issues for intervention studies.

Operant procedures have been shown to increase successfully LD students' math skills primarily with the use of extrinsic reinforcers and direct instruction. Cognitive behavior modification has been shown to remediate effectively LD students' academic deficits by enhancing self-guiding behaviors with internal dialogue, or self-instruction. General self-instruction has been designed to increase task-oriented behaviors, while specific self-instruction has been used to improve specific academic skills. The effects of CBM and operant procedures on LD students' math skills have not been directly compared.
The following design issues for contemporary intervention research were reviewed: token reinforcement, measures of treatment integrity, and social validity. Use of token reinforcers has advantages because they are associated with a variety of back-up reinforcers. Measures of treatment integrity should be conducted in intervention research to substantiate treatment implementation as prescribed by the methodology. Social





27


validity is an important aspect of intervention research because it allows for the evaluation of the treatment by relevant consumers.














CHAPTER 3
METHODOLOGY
Overview of the Study

Operant conditioning and CBM are two models for treating learning disabilities. Environmental contingencies are manipulated when using operant procedures in order to change academic behaviors without regard to etiology of learning disabilities. Cognition does not play a role in operant procedures. On the other hand, behavioral changes due to CBM occur through self-regulatory private speech. It has been hypothesized that LD students show deficient self-instruction strategies for academic problem solving. Both remediation models have poor treatment retention over time.
The purpose of this study was to compare treatment effectiveness between CBM and operant procedures with addition and subtraction problems in elementary school LD students. Treatment retention between the two models was also compared.

Subjects
This study was conducted in Duval County public schools,

Jacksonville, Florida. Ninety-four students participated in the study. There were 27 students in the control group, 32 in the CBM group, and 35 in the operant group. All students were identified formally as learning disabled. The LD students attended nine exceptional education classrooms from four different Duval County schools. The students were deficient in math skills








and were receiving remedial math instruction from a state-certified exceptional education teacher.

Socioeconomic status of students was determined by free lunch eligibility and teacher input. The mean IQ for all students was 99.03 (SD=9.62) and the mean achievement score was 78.05 (SD=1 1.41). Relevant subject characteristics are shown in Table 1.


Table 1

Subject Characteristics


Number of Students 1st 2nd 3rd 4th 5th Per Grade Level
8 9 25 26 26


Gender Females Males 31 63

Race Black White Other 28 61 5 SES High Middle Low 8 33 53

Variables Under Investigation Independent Variable
There were three levels of treatment as independent variables

under investigation in this study. The first level was CBM as a remediation technique. This included general self-instruction for task oriented behaviors, such as attention to task and specific self-instruction for math problem solving.








The second level was an operant procedure with direct instruction of math skills. Token reinforcers were given for each correctly solved math problem. The reinforcement schedule was continuous reinforcement per correct response, or fixed ratio per correct unit response (FR 1) (Miller, 1980).
The third level was an alternative treatment control condition
consisting of direct instruction of math skills without token reinforcement. This condition served as a control for the other two treatments. Dependent Variable
Math measures were chosen for dependent variables in this study because authors of both CBM and operant studies report successful remediation with this academic area (Blankenship & Baumgartner, 1982; Schunk & Cox, 1986). Math gains are quickly assessed without subjectivity in scoring. Finally, fewer researchers have investigated math compared to other academic areas with LD students (Mercer & Mercer, 1985).
Two dependent variables were used in this study: standardized achievement and timings of math work. The computation portion of the Stanford Diagnostic Mathematics Test (Beatty, Madden, Gardner, & Karlsen, 1986) was used as the standardized achievement measure. This test was chosen because it (a) is group administered, (b) focuses on computation skills, and (c) has excellent normative characteristics (Salvia & Ysseldyke, 1981).
Rate of problems correct, or timings of basic addition and subtraction problems, was the dependent variable relevant to classroom instruction. Timings are an accurate method to assess understanding and proficiency








with basic math skills (Alberto & Troutman, 1986). Timings of academic performance are also Type I dependent variables (Lahey & Strauss, 1982). Time interval for work on these problems was 2 minutes.
Apparatus

A mixed probe consisting of 25 basic addition and 30 basic

subtraction problems was used for the timings (see Appendix A). The mixed probe was developed according to addition and subtFaction skill hierarchies (Evans, Evans, & Mercer, 1986). The problems were arranged in complexity from top to page bottom. The addition problems required the students to demonstrate the following skills:
1. Computation of sums 0-9.

2. Computation of sums 10-18; both addends less than 10.

3. Calculation of two-digits plus one-digit or two-digits without regrouping.
4. Computation of two-digits plus one-digit or two-digits with regrouping.
5. Computation of two-digits plus two-digits plus two-digits with sums of ones greater than 20.

6. Calculation of three-digits plus three-digits with and without regrouping.
The subtraction problems required the students to demonstrate the following skills:
1. Computation of basic subtraction facts with minuends 1-17 and answers 0-9.
2. Computation between two-digit and one-digit or two-digit problems without regrouping.









3. Calculation of two-digit and one-digit or two-digit problems with regrouping.
4. Computation between three-digit and three-digit problems with single regrouping.
5. Calculation of three-digit and two-digit problems with double regrouping.

Procedure
Nine classrooms serving LD children were selected for this study

based on subject availability, teacher cooperation, and permission from the school principal. The participating teachers were given a $25 stipend for 1-2 hours of training time after school hours. The experimenter contacted teachers with treatment conditions twice per week to answer questions and observe treatment delivery. Teachers also were encouraged to call upon the experimenter at any time during the study if questions arose. Besides a copy of the procedure, summaries of both experimental treatments were given to teachers as a reference guide (see Appendices B and C). Because of its relatively straight-forward procedure, the control group teachers did not receive a reference guide. The experimenter and teachers collected all data.

Both dependent measures were administered as pretests, posttests, and retention measures. Standardized instructions for group administration as prescribed by the Stanford Diagnostic Mathematics Test manual were followed when administering the test.
The following instructions were given when administering the probe sheet: "I am passing out some math problems (face down) for you to do. When I say go, turn over your papers and begin working. Do as many









problems as you can. Any questions? Go." After 2 minutes, the teacher said "stop" and collected the papers.
Treatment consisted of nineteen 60-minute sessions spanning 4
weeks. Administration of the pretests occurred immediately preceding the first day of treatment. The posttests were administered at the end of the 19th session. The measure of treatment retention was conducted by readministering the probe sheets and standardized tests after.2 weeks following the final day of treatment.

Seven students (across all conditions) were absent from one of the testing sessions and were tested the following school day. Three students were absent for more than one day beyond the group test day and were eliminated from the study.
Subject mortality was essentially equivalent across groups. Of 107 original subjects, 94 subjects remained for the duration of the study. The control and operant conditions each lost 4 students, and the CBM condition lost 5 students. Six losses were due to moves, 4 were due to class changes, and 3 were due to extended illness. CBM Treatment
Implementation of general self-instruction was intended to promote an active learning style within the LD student (Hallahan et al., 1983; Torgeson, 1977). General self-instruction procedures based on Meichenbaum and Goodman's (1971) model were applied to a set of selfstatements like the following:
1. "What is my assignment for today?"

2. "1 need to start working now."

3. "Good, I'm finished."





34


4. "Now I need to check my work. Good, I'm done."

Specific self-instruction training is designed to target specific academic strategies and steps toward task solution. This technique enhances treatment retention (Tarver, 1986; Meichenbaum, 1980; Wong 1985).

For specific self-instruction training, Meichenbaum and Goodman's (1971) model was applied to specific problems such as 24..
+9


1. "What kind of problem is this, addition or subtraction? What does the sign say?"
2. "OK, it's addition--that means I'll be adding numbers."

3. "First I add the first column of numbers-- that's 9+4."
4. "That equals 13, but I have to remember to only put down 3 and carry the 1 over to the tens column."
5. "Now I add 2+1 in the tens column. That's 3--and I write it down here. My answer is 34."
The following is an example of specific self-instruction for subtraction using the same math problem.

1. "What kind of problem is this, addition or subtraction? What does the sign say?"
2. "OK, it's subtraction--that means take-away."
3. "Will I need to borrow? Yes, because the bottom number is bigger than the top number."

4. "1 borrow 1 from the tens column, cross out the 2 and put 1, and bring 1 over to the 4 to make 14."
5. "Now I take away 9 from 14. That's 5, so I write it down here."









6. "What's left in the tens column? A 1, so I write it down here. My answer is 15."
The self-instruction procedure integrating general and specific selfinstruction was the specific format for CBM treatment in this study. The following is an example of the way in which general and specific selfinstruction was integrated into the treatment package (see Appendix B):

1. "What is my assignment for today? It's math problems 1 through 15."
2. "1 need to start working now."

3. "What kind of problem is this, addition or subtraction? What does the sign say?"
4. "OK, it's addition, that means....

5. "Good, I've finished that problem. I need to keep working."
6. "Good, I'm finished. I've checked my work and I'm done."
The students were initially informed of the treatment with the

following explanation: "For the next few weeks, we will be doing our math in a different way. Watch how I do a problem with this new way." The integrated package of general and specific self-instruction was delivered by the teachers in four steps.
1. The teachers modeled the procedure by talking to themselves while solving a sample problem at the beginning of every class.
2. The students were instructed to talk aloud as they performed math tasks.
3. The teachers provided guidance and prompts for self-talk as students performed math tasks.








4. After the second week, students were instructed to talk to themselves while performing math tasks. Operant Treatment
Students in the operant treatment condition received direct math instruction (see Appendix C). Direct instruction included the following steps:
1. Clearly explain the task objectives and goals.

2. Demonstrate the skill for the students.
3. Provide appropriate drill and practice.
4. Give corrective feedback.
5. Assess students' progress (Haring & Gentry, 1976; Mercer & Mercer, 1985).
The reinforcement procedure was initially explained to students in the following manner: "You will get one token (chip) for each correct addition or subtraction problem you complete in class. You will be given the tokens (chips) you earn near the end of class." Back-up reinforcers were explained as follows: "These are items that you can buy as soon as you earn enough tokens for that item."
Poker chips were used as tokens in this study. The poker chip was chosen as the preferred token because it is portable, durable, and easy to handle (Alberto & Troutman, 1986). Each teacher was given a "bank" of 300 red, white, and blue tokens. Blue tokens were assigned a value of 10 problems correct, red = 5 problems correct, and white = 1 correct. Students were able to earn a daily token value equivalent to the correct number of classwork math problems. Earned tokens were kept in clear envelopes for each student. The envelopes were passed out to the students at the








beginning of class and were collected at the very end of each class. Tokens were delivered 10-15 minutes prior to the end of each class period. Students exchanged tokens for stickers, stationery items, or small toys (not exceeding $3 each) prior to the end of each class period (see Appendix D for back-up reinforcer inventory). Back-up reinforcers were selected in an attempt to appeal equally to both genders. Back-up reinforcers were kept in a metal or wood cabinet in the classroom. One teacher kept back-up reinforcers in clear plastic bags hooked on a peg board. The back-up reinforcers were available for display during class and locked away when teachers were not present.
Twenty to 30 daily assigned math problems were typically available for token reinforcement in all three classrooms. The cost of back-up reinforcers was mutually established by the experimenter and teachers. The cost was based upon perceived student demands for each item. Several back-up reinforcers (raisins, folders, and notepads) required a cost increase because of unusually high demand for these items. It was the experimenter's responsibility to maintain adequate supplies of back-up reinforcers. Total purchase cost for the back-up reinforcers amounted to $74.10.
Control GrouD (Direct Instruction)
The direct instruction group received direct math instruction (as described in the operant procedure) without token reinforcement.

Following the 4-week treatment period, math instruction for all
classes resumed to normal pretreatment settings. None of the treatment conditions were provided during the 2-week period prior to the retention measure.








Treatment Integrity

Treatment integrity ratings of the experimental conditions were conducted by sets of two school psychologists not associated with the study. Sample class periods were videotaped for the ratings. One taping per experimental treatment was made for a total of 12 ratings. Treatment integrity was rated according to the extent of conformity with the procedures (see Appendix E). To prevent bias, raters were.not told which conditions they were observing. Interrater agreement was also calculated. Social Validity
Social validity of treatment effectiveness refers to the evaluation of treatment by consumers or relevant observers (Shapiro, 1987). Social validity was conducted at the conclusion of treatment with participating teachers (see Appendix F). Individual open-ended interviews were scheduled with teachers to discuss treatment topics, including
1. How long did it take for you to feel comfortable in delivering the treatment?
2. Were there any negative side-effects to the treatment?
3. Were there any positive side-effects to the treatment?

4. Would you adopt this treatment for regular use in your classroom?
The experimenter recorded interview data.
Design

The design in this study was a nonequivalent pretest-posttest control group design. This design is prevalent in educational research and used with intact classrooms when randomization of subjects is difficult or impossible (Campbell & Stanley,1963; McMillan & Schumacher, 1984).









This type of design can be used to control for subject reactivity which can occur when subjects are removed from their natural setting for treatment (Huck, Cormier, & Bounds, 1974). It also can be used to control for main effects of history, maturation, testing, and instrumentation (Campbell & Stanley,1963). Use of a control group further guards against threats to internal validity.

Using intact classrooms is common in educational research and has several advantages. Threats to ecological external validity occur when subjects are removed from their normal environment to conduct the experiment (McMillan & Schumacher, 1984). This threat was not a variable in this study since subjects received treatment in their normally scheduled exceptional education classrooms. The Hawthorne effect probably did not play a confounding role because the subjects' teachers continued math instruction and only varied teaching methods.
Teachers were randomly assigned to an experimental or control
condition. Three groups of three teachers each provided treatments. This procedure greatly reduced the likelihood that teacher-treatment interaction and nesting variables would affect results. Assignments of conditions per teacher and school are shown in Table 2.
Data Analyses

A within-subjects or repeated measures design (Winer, 1971) was used as the statistical design in this study. This design is also termed Lindquist Type I ANOVA, split plot ANOVA, or mixed design (Huck et al., 1974). This type of statistical design is frequently used to study learning phenomena in education (Keppel, 1982). It is suitable when subjects are measured on a dependent variable several times during an experiment.





40


Table 2

Assignment of Condition Per Teacher and School


Teacher School Control Gu 1 #4 2 #4 3 #1

CBM Group 4 #2 5 #2 6 #4
Operant GrQup
7 #4 8 #3
9 #1


Although the assumption of true random selection was violated in this study, this statistical design is robust despite violations of random assignment (Glass & Stanley, 1970; Kirk, 1982).
The repeated measures design was used to investigate a main effect of repeated measures (within-subjects factor). Overall trend significance among groups was determined with this procedure. An interaction between group performance and repeated measures was also investigated. The interaction illustrated trend differences among groups across three testing periods.

Hypothesis #1, stating no significant difference in trend among direct instruction, direct instruction with operant procedures, and CBM with elementary school LD students' addition and subtraction operations as measured by classroom performance timings, is rejected if the F for repeated measures X group interaction is significant (p< .05).








Hypothesis #2, stating no significant difference in trend among direct instruction, direct instruction with operant procedures, and CBM with elementary school LD students' addition and subtraction operations as measured by a standardized math test, is rejected if the F for repeated measures X group interaction is significant (p< .05).
Hypothesis #3, stating no significant difference in trend between
direct instruction with operant procedures and CBM with elementary school LD students' addition and subtraction operations as measured by classroom performance timings, is rejected if the F for repeated measures X group interaction is significant (p< .05).
Hypothesis #4, stating no significant difference in trend between

direct instruction with operant procedures and CBM with elementary school LD students' addition and subtraction operations as measured by a standardized math test, is rejected if the F for repeated measures X group interaction is significant (p < .05).

Limitations of the Study
Internal Validity
Internal validity refers to the efficacy with which extraneous variables are controlled in a study (McMillan & Schumacher, 1984). The most serious threat to internal validity in this study was lack of random selection and assignment of subjects. Without random selection and assignment to groups, a group of subjects may differ with a characteristic which could affect the dependent variable. However, assigning three teachers per condition minimized this threat, as did pretesting groups for initial differences.









Another possible threat to internal validity in this study was the

interaction between selection and maturation (Campbell & Stanley, 1963). Unplanned, extraneous events or natural changes within a specific group of subjects could have influenced the results, especially with lengthy treatment periods (McMillan & Schumacher, 1984). However, use of a control condition reduced these threats because they probably would have occurred equally across all conditions. Also, the treatment period was 4 weeks in duration.
Testing effects could have been a threat to internal validity, but were not expected to be a major concern in this study. Testing effects are usually a threat with attitude or values research where pretest sensitivity could markedly influence posttest scores (Ary, Jacobs, & Razavieh, 1979). Testing effects could also bias measurement of achievement gains over a short period of time. Three sessions of math achievement testing were conducted over 6 weeks and probably did not affect posttest and retention scores. However, even if testing effects occurred, there is no reason to believe these effects would differ across groups. External Validity
External validity is the extent to which results and conclusions can be generalized to other people and settings (McMillan & Schumacher, (1984). Population external validity is limited to elementary school students in large urban districts who are identified as LD with the same criteria as in Duval County, Florida.
Ecological external validity refers to the conditions of the research and the extent to which results can be generalized to similar conditions. Results from this study can be generalized to math remediation of learning








disabilities by LD teachers in public elementary school exceptional education classrooms.














CHAPTER 4
RESULTS

A repeated measures ANOVA was used for the data analysis in this study. Specifically, within-subjects factors and interactions between subjects and time were analyzed for significant differences in trend between groups.
Classroom Timings
Subjects improved with classroom timings over time in all

experimental groups (E(2, 91) = 8.53, 1=.0003). However, there was no interaction between subjects and time (E(4, 182) = 0.56, NS). Therefore, differences with timings among the three groups did not vary over testing periods. The following null hypotheses were not rejected: Ho#1--There will be no significant difference (12>.05) in trend among direct instruction, direct instruction with operant procedures, and CBM with elementary school LD students' addition and subtraction operations as measured by classroom timings; and Ho#3--There will be no significant difference (1>.05) in trend between direct instruction with operant procedures and CBM with elementary school LD students' addition and subtraction operations as measured by classroom timings. Timings results are illustrated in Figure 1 and summarized in Table 3.
Achievement Tests

Subjects in all three groups improved in math achievement over

time (F(2, 91) = 13.98, 2=.0001). However, groups were not equal in their












no- 19


T 18
0
cn 17

H- 16
c
coo

15
Pre Post Maint.
Day 0 Day 25 Day 39



U] CBM

El Operant O Control


Figure 1. Classroom Timings Results for All Conditions





46


Table 3

ANOVA Results of Classroom Timings for all Conditions


Source of df Sum of Variation Squares

Between sub. 2 218.37
Error 91 16873.43
Within sub. 2 211.72 Sub. x Time 4 28.03 Error 182 2258.44

Means and SDs for Timings (number of

Test 1 (SD) Test 2 (SD)

Control 16.0 (9.4) 15.2 (8.7) CBM 17.2 (6.0) 17.5 (6.6) Operant 15.3 (8.7) 16.0 (8.2)


Mean
Square

109.18 185.42 105.86
7.01
12.41

problems correct)
Test 3 (SD)

16.8 (9.8)
19.5 (7.2) 17.8 (8.5)


rates of improvement (U(4, 182) = 4.03, 1=.0037). Therefore, trends for the three groups varied significantly. The following null hypothesis was rejected: Ho#2--There will be no significant difference (12>.05) in trend among direct instruction, direct instruction with operant procedures, and CBM with elementary school LD students' addition and subtraction operations as measured by a standardized math test. Achievement test results are illustrated in Figure 2 and summarized in Table 4.
In order to identify how groups differed on the achievement test, separate within-subject analyses were partialed with control, CBM, and operant groups. Subjects in CBM and operant groups scored significantly higher than control group subjects (E(2, 31) =14.86 and E(2, 34) = 9.71, p<.05). Based on these results, trend differences with CBM and operant groups were significantly higher than the control group. These results are


0.58 8.53 0.56


.5571 .0003 .6885








540 530 520 C,)
W
510
-2_ 0
-o 500
C

490


480 470 460
Pre Post Maint.
Day 0 Day 25 Day 39



*CBM

O Operant LI Control






Figure 2. Stanford Diagnostic Mathematics Test Results for All Conditions





48


Table 4
ANOVA Results of Achievement Tests for all Conditions


Source of df Sum of Mean F Variation Squares Square

Between sub. 2 109435.77 54717.88 1.73 .1828
Error 91 2875670.93 31600.78
Within sub. 2 31841.47 15920.73 13:98 .0001
Sub. x Time 4 18355.12 4591.53 4.03 .0037
Error 182 207227.55 1138.61


summarized in Table 5.
To determine if significant differences in gains existed between operant and CBM groups, the effects due to these two treatments were examined. Subjects scored equally well in operant and CBM groups (F(2, 65) = 0.29, NS). Therefore, trend differences for posttest and retention measures between these two conditions were not significant. The following null hypothesis was not rejected: Ho#4--There will be no significant difference (p>.05) in trend between direct instruction with operant procedures and CBM with elementary school LD students' addition and subtraction operations as measured by a standardized math test. The effects due to operant procedures and CBM are summarized in Table 6.
Treatment Integrity
Treatment integrity was rated by three school psychologists not

associated with the study for each experimental classroom. Ratings were based on the criteria defined by the treatment integrity form (see Appendix D). A class period midway through the treatment phase was videotaped for










Table 5


Within-Subiect


Analyses for Control. Ooerant, andC CBM Conditions


Sum of
Square$


Source of Variation


Mean
Square


F P


Control sub. Within sub.
Error

Operant sub. Within sub.
Error

CBM sub. Within sub.
Error


1690994.24
2299.72
64923.60

853260.05
25005.48 87492.51

331416.62 26284.56 54811.43


65038.24 1149.86 1248.53

25095.88 12502.74 1286.65

10690.86 13142.28
884.05


0.92 .4045 9.71 .0002 14.86 .0001


Means and SDs for Achievement Test


Standard Scores


Test 1 (DS


469.11 476.80 498.69


(153.7) (86.5) (71.6)


lest 2 (SD

479.66 (149.6) 494.40 (92.9) 524.78 (60.4)


Test a (SD


467.74 514.57 538.59


(139.1) (103.8) (61.8)


Table 6

Effects Due to Operant and CBM Conditions

Source of df Sum of Mean E 12 Variation Squares Square

Between sub. 1 32431.67 32431.67 1.77 .1869
Error 65 1184676.68 18225.79
Within sub. 2 50694.61 25347.30 23.15 .0001 Sub. x Time 2 652.70 326.35 0.29 .7427


Control Operant CBM


Within-Subiect nalvses for Control Ooerant, and CBM Conditions


Means and S -q for Achievement TestStandard Score








all experimental conditions. The raters were given rating forms prior to viewing videotaped classroom sessions. All three raters correctly classified the experimental conditions with 100% agreement.
Teachers were specifically instructed not to provide treatments

during the retention phase. Materials from operant teachers were collected and daily contacts were made with all teachers to insure nontreatment conditions.
Social Validity

Social validity of treatment perspectives was measured with operant and CBM teachers after the experimental phase of the study. Teachers responded to at least four questions presented by the social validity rating interview (see Appendix F).

Operant
All three operant condition teachers reported feeling comfortable with treatment delivery after a maximum of 2 days. Two teachers felt comfortable with the procedure after the 1st day of treatment. None of the teachers cited any negative side effects to operant treatment relative to the students. However, two teachers reported that the token delivery and exchange procedure for back-up reinforcers was time consuming.
There were consistent reports of positive side effects among all

three teachers. All teachers reported that the operant treatment increased motivation and on-task behavior. In addition, teachers reported (a) increased enthusiasm for math classwork, (b) increased math grades, (c) increased knowledge of money and expenditures, and (d) increased attention to detail with math classwork due to immediate feedback and consequences.








All three teachers found the operant treatment appealing and
planned to use it in their classrooms. In order to save time, one teacher reported that she would restructure the procedure by allowing purchase of back-up reinforcers once per week, instead of five times per week as in the experiment.
Cognitive Behavior Modification
All three teachers with the CBM condition reported a period of 2 days for becoming comfortable with treatment delivery. None of the teachers indicated negative side effects, but all three reported initial reluctance among a few students to talk aloud while working. This condition did not persist as self-talk quickly became the norm in the CBM classrooms. None of the teachers reported increased distraction among students due to overt self-talk. In fact, one teacher specifically noted a decrease in non-task oriented conversation during class.
While all three teachers reported gains in classwork grades during treatment, one teacher saw especially dramatic grade changes from Cs and Ds to As and Bs. Other positive observations included (a) increased on-task behavior, (b) increased task completion, and (c) increased retention of skills. Two teachers, who also taught reading, observed students transferring general self-instruction components of CBM to reading tasks. Maintenance of self-talk was observed during the retention phase, but at a lower rate than during treatment.
Two of three teachers expressed great enthusiasm for CBM and its apparent success. All three teachers reported that they were going to use CBM with classroom instruction.














CHAPTER 5
DISCUSSION

Based on the results, CBM and operant treatments are not better than no treatment for improving the rate of correct math behavior. Even though the control group mean dropped slightly at posttest, overall differences in classroom timings among conditions were not significant. Thus, all three remediation techniques were effective, but none was clearly superior to others. Interestingly, CBM did not slow the rate of problem solving more than the other procedures. Apparently, using self-talk while solving math problems does not add to nor interfere with the overall time required to complete such tasks.
Standardized math achievement was improved by some treatments more than others. Performances by students in operant and CBM conditions were better than the no treatment condition. But no significant differences existed between CBM and operant treatment effectiveness. Positive academic gains with both CBM and operant procedures are consistent with current literature.
Significant achievement test results may be related to the fact that the test is essentially a power test. It allows time for most or all items to be completed at the student's own pace. It is possible that this format for measuring math gains may be more sensitive to treatment differences than brief timed performances.








Student performances on the timings were suggestive of limited
variability on this measure. The results are below expected fluency rates for math skills (Mercer & Mercer, 1985). Many subjects did not get beyond basic math facts on the 2-minute probe. Students had more time to sample a variety of math operations on the achievement test, thus utilizing more than rote memory for problem solving.
Learning trends with operant and CBM groups continued over time and did not drop off as predicted by some researchers. Despite claims of poor maintenance of academic skills with CBM and operant procedures, maintenance or retention of achievement due to these treatments persisted over a 2-week period. Thus, the operant group did not require specific generalization instruction for short-term retention to occur. Inclusion of task-specific self-instruction may have facilitated maintenance of skills with the CBM group.
Treatment retention in this study may also be due to the intensity of the treatment. The treatment period of nineteen 1-hour treatments was delivered in this experiment, as opposed to six 45-minute sessions provided in another math CBM study (Schunk & Cox, 1986). Due to the hierarchial nature of math instruction, it is reasonable to assume that an intensive, effective treatment will show carry-over effects following treatment.
Cognitive behavior modification and operant procedures do not differ with respect to math gains for posttest and retention measures, but social validity ratings may offer additional insight into treatment differences and similarities. Both sets of teachers observed math gains in students'









classwork and reported that they would incorporate respective treatments into their classroom curricula.
Interestingly, student behaviors that are often attributed to operant procedures, such as increased on-task behavior and task completion, also resulted from CBM treatment. The prescribed general task-orienting selfinstruction in this study apparently increased task awareness without requiring extrinsic tangible reinforcement for these behaviors.

Transfer of CBM to a nontreatment academic subject was also

observed. Two CBM teachers observed their students transferring general self-instruction strategies to reading tasks. This observation is consistent with CBM theory. Operant procedures were not noted to produce similar effects, perhaps because they operate extrinsically upon the student. On the other hand, CBM components must first be learned by students in order to apply the treatment to academic subjects.
Cognitive behavior modification does not contribute to disrupting or distracting effects among students as did occur in a previous study (Robin, Armel, & O'Leary, 1975). However, CBM requires a short "break-in" period for some students in order to gain a comfort level while talking out-loud. The operant treatment condition requires additional class time in excess of actual instruction. The operant condition also requires a budget to purchase back-up reinforcers. Teacher training time and time needed for comfortable treatment delivery are basically uniform for both groups.

Conclusion
Cognitive behavior modification and operant procedures are
effective remediation techniques for LD students. Despite polar theoretical etiology, both remediation techniques produce similar desirable classroom








behaviors. Differences with treatments exist in terms of specific procedures, available class time for treatment delivery, teachers' roles (modeling), required student behaviors (self-talk), necessary equipment (storage cabinet, tokens), and budget for tangible back-up reinforcers. Transfer of CBM strategies to other academic subjects may be a potential benefit over operant procedures, but there is little evidence to corroborate this speculation. Ultimately, choices between CBM and operant treatments may depend upon aforementioned factors and teachers' training backgrounds and affinity for one treatment over the other.

Implications for Future Research

Treatment generalization issues should be investigated with future research. Retention of treatment gains was shown over a 2-week period by both treatments in this study; however, retention over longer periods is uncertain. A comparison of generalization to other academic subjects between treatments should also be investigated. Students were observed generalizing CBM to reading in this study, but no data exist comparing generalization efficacy between operant and CBM treatments with academic subjects.
Both treatments worked equally well with LD students' math skills in this study, but findings might differ with other academic subjects or exceptional student groups. Future research with operant and CBM treatment effectiveness should be explored with different academic subjects and exceptional student populations.
Other time intervals for classroom math measures should be
investigated. Although 2-minute classroom timings produced treatment





56


gains, the short time interval may not be sensitive enough to discriminate effectiveness between treatments.












APPENDICES











APPENDIX A
TIMINGS PROBE SHEET


8 9 3 4 6 6 7 2 +7 +9 +5 +2 +7 -3 -6 -2


10 52 84 43 63 +9 +4 +13 +24 +n6


11 17 13
-4 -8 -7


24 73 56 69 67 86 38 59 63 95 +8 +9 +17 +23 +64 -2 -3 -19 -22 -


28 85 46 75 36 37 19 48 67 26 +16 +28 +48 +58 +39


43 71 65 28 84
-4 -3 2 -19 -45


281 770 746 552 945 242 +304 +216 +132 +453 +376 -139


372
-m3


463
-204


434
-58


552
-77


223
-49


850
-32


141
-m2


945
-96


321
-54














APPENDIX B
TEACHER REFERENCE--CBM


1. Remember to explain the procedure with the following: "For the next few weeks, we will be doing our math in a different way. Watch how I do a problem with this new way."

2. Remember to model a sample problem at the beginning of each CBM session. Example statements:

1. "What is my assignment for today? It's math problems 1

through 15."
2. "1 need to start working now."
3. "What kind of problem is this, addition or subtraction? What

does the sign say?"
4. "OK, it's addition, that means ......

5. "Good, I've finished that problem. I need to keep working."

6. "Good, I'm finished. I've checked my work and I'm done."
3. Prompt the students to talk to themselves as they work.

4. Remember to keep reinforcers out of sight during CBM treatment. Instructions for administering timings:

"I am passing out some math problems (face down) for you to do. When I say go, turn over your papers and begin working. Work as quickly as you can without making careless mistakes. Any questions? Go." After

2 minutes, say "stop" and collect the papers.














APPENDIX C
TEACHER REFERENCE--OPERANT PROCEDURES


1. Clearly explain the task objectives and goals.
2. Demonstrate the skill.
3. Provide drill and practice. 4. Give corrective feedback.
5. Remember to explain the reinforcement:
"You will get one token (chip) for each correct addition or

subtraction problem you complete in class. You will be given the tokens (chips) you earn near the end of class." Back-up reinforcers will be explained as: "These are items that you can buy with your tokens."
6. Check classwork 15 minutes prior to end of class and place earned tokens in students' envelopes.
7. Allow students to exchange tokens for back-ups 5 minutes prior to end of class.

8. Remember to close and lock the back-up cabinet after each operant session.













APPENDIX D
INVENTORY


ITEM COST (# of tokens)

Sticker 20 Eraser 25 Large sticker 25 Story book 30 Snoopy Pencil 30 Cowboy or Indian Character 30 Ninja Character 35 Box of Crayons 40 Large Pencil 40 Crayola Marker 40 Designer School Folder 50 Snoopy Notepad 50 Pencil Sharpener 50 Matchbox Car or Truck 60 Four-color Pen 60 Pencil Case 60 Lifesaver Scented Marker 70 Barbie Doll Outfit 70 California Raisin Character 80














APPENDIX E
TREATMENT INTEGRITY RATING




Dear Rater: Please circle the number of each item observed during the videotaped class session.


1. Did the teacher model at least one sample problem at the beginning of class?
2. Did the teacher talk to herself as she modeled the sample problem?
3. Were tokens given to students for correct classwork?
4. Were students instructed to talk to themselves while solving math problems?
5. Was there opportunity for exchange of tokens for back-up reinforcers prior to the end of class?
6. Were back-up reinforcers available for display in the classroom?













APPENDIX F
SOCIAL VALIDITY RATING INTERVIEW


1. How long did it take for you to feel comfortable in delivering the treatment?






2. Were there any negative side-effects to the treatment?






3. Were there any positive side-effects to the treatment?





4. Would you adopt this treatment for regular use in your classroom? Additional comments:













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BIOGRAPHICAL SKETCH
Peter Pavchinski was born in Canada in 1954 to immigrant parents. Having no money or possessions, his parents risked their lives by fleeing the oppression of war-torn eastern Europe. Pete was able to learn the lessons of survival first-hand from his parents. After living in Canada for 8 years, Pete's family moved to the United States to seek greater opportunity. In concert with this credo, his parents offered him musical training in several instruments. Despite required practice time for proper beats and note values, he still managed to acquire a penchant for baseball and tennis.
While at Rutgers University, Pete sampled a number of academic disciplines. He first enjoyed the natural sciences, but later changed to the study of Russian language. It wasn't until transferring to New College of the University of South Florida, a unique and challenging school, that his studies became concentrated in psychology. Several years later, Pete earned his Master of Arts and Education Specialist degrees in school psychology from the University of South Florida.
Pete is currently employed by the Duval County School Board as a school psychologist in Jacksonville, Florida. Pete has been instrumental in expanding the role of school psychologists in Duval County public schools. He has developed and implemented suicide awareness and training programs, behavior management workshops, and mental health programs for students.





71


Pete is married to a loving and conscientious wife who is pursuing a law degree at the University of Florida.










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.


Jetlfrf P.\Braden, Chairman
Assi tant 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.


Paul W. Fitzgel'ald
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.



Cecil D. Mercer
Professor of Special Education











This dissertation was submitted to the Graduate Faculty of the College of Education and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy.


August, 1988


Dean, College of Education


Dean, Graduate School




Full Text

PAGE 1

THE EFFECTS OF OPERANT PROCEDURES AND COGNITIVE BEHAVIOR MODIFICATION ON LEARNING DISABLED STUDENTS' MATH SKILLS By PETER PAVCHINSKI 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 1988 \ BlVERsmr OF Florida librarici

PAGE 2

Copyright 1988 by Peter Pavchinski

PAGE 3

ACKNOWLEDGMENTS Thanks are extended to the school principals and teachers for their cooperation and contribution to this study. Thanks also go to committee members Paul Fitzgerald and Cecil Mercer for their valuable input and support. Special thanks are extended to Jeff Braden for his support and impeccable editorial and analytical contributions to this study. Special thanks also go to my wife, Alexa, for her constant support through the past 4 years of arduous graduate study. i i i

PAGE 4

TABLE OF CONTENTS PAG E ACKNOWLEDGMENTS iii LIST OF TABLES [ vi LIST OF FIGURES vii ABSTRACT viii CHAPTERS 1 INTRODUCTION 1 Operant Procedures and Learning Disabilities 2 Cognitive Behavior Modification and Learning Disabilities 4 Significance of the Study 6 » Statement of the Problem 133...... 7 Purpose of the Study 8 f^ypotheses 8 Definition of Terms , 9 Overview of Remainder of Study 1 0 2 REVIEW OF LITERATURE 1 1 Remediation of Learning Disabilities with Operant Procedures 1 -i Remediation of Learning Disabilities with Cognitive Behavior Modification 1 5 Design Issues for Intervention Studies ""'''"'^^^^^^ Summary of the Literature Review .............26 3 METHODOLOGY 28 Overview of the Study 28 Subjects 28 Variables Under Investigation 29 Apparatus " o ^ Procedure 32 Design """''1'!"!"!""!!^!!"!!!! 38 I V

PAGE 5

TABLE OF CONTENTS Data Analyses 39 Limitations of the Study 4 1 4 RESULTS 44 Classroom Timings 44 Achievement Tests 44 Treatment Integrity 48 Social Validity 50 5 DISCUSSION 52 Conclusion 54 Implications for Future Research 55 APPENDICES A TIMINGS PROBE SHEET 58 B TEACHER REFERENCE--CBM 59 C TEACHER REFERENCE-OPERANT PROCEDURES 60 D INVENTORY 61 E TREATMENT INTEGRITY RATING 62 F SOCIAL VALIDITY RATING INTERVIEW 63 REFERENCES 64 BIOGRAPHICAL SKETCH 7n V

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LIST OF TABLES Pa ge Table 1 Subject Characteristics 29 Table 2 Assignment of Condition Per Teacher and School 40 Table 3 ANOVA Results of Classroom Timings for all Conditions 46 Table 4 ANOVA Results of Achievement Tests for all Conditions 48 Table 5 Within-Subject Analyses for Control, Operant, and CBM Conditions 49 Table 6 Effects Due to Operant and CBM Conditions 49 vi

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LIST OF FIGURES Page Figure 1 Classroom Timings Results for All Conditions 45 Figure 2 Stanford Diagnostic MathematicsTest Results for All Conditions 47 vii

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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 OPERANT PROCEDURES AND COGNITIVE BEHAVIOR MODIFICATION ON LEARNING DISABLED STUDENTS' MATH SKILLS By Peter Pavchlnski August, 1988 Chairman: Jeffery P. Braden Major Department: Counselor Education A comparison between operant procedures and cognitive behavior modification was conducted in this study on elementary school learning disabled students' math skills. A control condition consisting of direct instruction of math skills was also used. Dependent measures were 2-mlnute classroom timings of basic addition and subtraction problems and the Stanford Diagnostic Mathematics Test . Nine intact classrooms from four schools were selected for the study; the classrooms were randomly assigned to one of three conditions. A total of 94 students participated. Treatment was provided for 4 weeks in daily 1-hour sessions. Retention of math skills over a 2-week period was also investigated. Performance trends across three testing periods were compared between vi i i

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the two treatments and the control condition. A repeated measures ANOVA design was used to analyze the data. Significant differential gain between experimental and control groups in achievement test scores was found (F(4, 182) = 4.03, e< 01). Operant procedures and cognitive behavior modification were equally effective (F(2, 65) = 0.29. NS). All three groups improved with 2-minute classroom timings {£(2, 91 ) = 8.53, fi<.001 ). Retention of skills for both treatments was maintained over the 2-weel< period of no treatment. Teacher social validity ratings indicated differences between the two treatments relative to student behaviors and teacher roles. The operant procedure requires the teacher to maintain back-up reinforcers and to deliver token reinforcement. Students are not taught specific learning strategies, but are reinforced for correct classwork. Cognitive behavior modification requires a more active teacher role in terms of modeling and prompting self-instruction procedures. Students must learn and apply self-instruction for classwork. Implications of the study are that both operant procedures and cognitive behavior modification are equally effective techniques to remediate learning disabled students' math skills despite their disparate theoretical orientation, and both are better than direct instruction. Both remediation techniques also are equally effective in producing retention of math skills over a 2-week period. Selection of one treatment over the other may depend upon desirability of the teacher's role for each treatment and specific student behaviors to be produced.

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CHAPTER 1 INTRODUCTION Learning disabilities are phenomena which manifest themselves in significant academic difficulties among certain students. Although many characteristics typify learning disabled (LD) students, discrepancy between academic achievement and estimated ability is one of the chief variables distinguishing LD students from normal students (Ferguson & Mamen,1985; Mercer & Mercer, 1985). Other characteristics of LD students include below grade-level academic performance, language problems, perceptual disorders, motor dysfunctions, and memory and attention deficits (Mercer, 1987). Theories of etiology and treatment of learning disabilities typically fall within two major models; medical or behavioral (Treiber & Lahey, 1983). Learning disabilities are viewed as symptoms of organic dysfunction in the medical model. Minimal brain injury and process deficits are diagnostic labels used to identify organic pathology associated with learning disabilities. A process deficit is defined as a disorder in basic psychological processes such as memory, language, or perceptual-motor skills which contributes to academic problems (Mercer, 1987). Etiology is deemphasized in the behavioral model, and learning disabilities are viewed as behaviors that require modification (Throne, 1973; Treiber & Lahey, 1983). Rather than assigning diagnostic labels, treatment of learning disabilities involves direct instruction with weak 1

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academic areas and manipulation of environmental contingencies in order to enhance learning (Treiber & Lahey, 1983). Operant Procedures and Learning Disabilities There have been various approaches for remediating learning disabilities, but few are effective (Lahey, Hobbs, Kupfer, & Delamater, 1979). One of the major remediation models shown to be effective with learning disabilities is the behavioral model (Treiber & Lahey, 1983). Most behavioral techniques for LD remediation are based on operant conditioning theory (Skinner, 1953). A principle of operant theory holds that rates of behavior increase when followed by positive reinforcement. Operant remediation of learning disabilities typically reinforces on-task behavior, rates of completed classwork, or other desired behaviors. Application of operant procedures for LD remediation does not hinge upon assignment of a label or categorization of a disorder within the student. Based on operant conditioning theory, LD students demonstrate academic difficulties because environmental contingencies do not reinforce learning, not because of organic or internal factors (Throne, 1973). Operant procedures typically result in modified behaviors through manipulation of external or environmental contingencies. Providing appropriate reinforcers for academic achievement in LD students increases academic gains (Skinner, 1968). There are several types of reinforcers used with operant procedures. Primary reinforcers, such as edibles, are stimuli that have high biological importance. Secondary or conditioned reinforcers are those whose value has been learned or conditioned by the environment (Alberto & Troutman, 1986). Secondary reinforcers include praise, social approval, and tokens

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3 (Stromer, 1977). Tokens and money are a special class of conditioned reinforcers termed generalized conditioned reinforcers because they provide access to a variety of primary and secondary reinforcers. Tokens are frequently used in educational research because of their high motivational properties (Alberto & Troutman, 1986). Remediation of learning disabilities with operant procedures has been widely investigated and accepted as an effective remediation technique (Lahey et al., 1979). A number of academic areas have been targeted including reading comprehension (Lahey, McNees, & Brown, 1973), oral reading (Lovitt & Hansen, 1976), and math (Broughton & Lahey, 1978; Smith & Lovitt, 1976). Operant procedures also have been used to remediate a "process deficit" with perceptual-motor skills (Lahey, Busemeyer, O'Hara, & Beggs, 1977). Lahey et al. (1977) demonstrated the significant positive impact that operant procedures exert on behaviors attributed to organic dysfunction. Generalization or retention of training is an important element in the learning process (Gagne, 1977; Wong, 1985). Despite the success of operant procedures for remediating learning disabilities, retention of skills after treatment has been poor (Rose, Koorland, & Epstein, 1982; Stokes & Baer, 1977). Generalization is defined as the occurrence of relevant behaviors under different, non-training conditions, such as across settings, instructors, tasks, or time, without the scheduling of the same events in those conditions as had been scheduled in the training conditions (Stokes & Baer, 1977). Most researchers with operant studies have not actively investigated retention of treatment. Despite available technology for generalization with operant procedures, the "train and hope" model of

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4 treatment generalization has prevailed (Stokes & Baer, 1977). In this model of generalization retention of learning is documented if it occurs after treatment, but a specific methodology to account for its occurrence is not provided. Coonitive Behavior Modification and Learnino Disabilities Cognitive behavior modification (CBM) is a relatively new and popular cognitive treatment for learning disabilities (Meichenbaum, 1980; Swanson & Kozleski, 1985). It is related to metacognition, a general term referring to an awareness of one's own cognitive performance (Hallahan, Hall, lanna, Kneedler, Lloyd, Loper, & Reeve, 1983). Cognitive behavior modification is based on the research of two Soviet learning theorists: Vygotsky and Luria. Both Vygotsky (1962) and Luria (1961) independently posited that overt child behaviors can be governed by internal speech. Vygotsky hypothesized that private speech facilitates organization of problem-solving strategies in children. Luria theorized three stages when overt behaviors come under voluntary control during child development. During the first stage, the speech of others, usually adults, controls and directs a child's behavior. In the second stage, the child's overt speech becomes an effective regulator of behavior. Finally, the child's covert, or inner speech, assumes a self-governing role. Cognitive behavior modification is a technique which utilizes selfinstruction to regulate or change behaviors (Meichenbaum, 1977). Selfinstruction involves self-verbalizations which aid in identifying and controlling new behaviors (Ledwidge, 1978). In this process, selfinstruction becomes a mediator between cognitive structures and behaviors. Self-instruction training contains five basic steps:

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1 . An adult model performs a task while talking to herself out loud (cognitive modeling); 2. The child performs the same task under the direction of the model's instructions (overt, external guidance); 3. The child performs the task while instructing herself out loud (overt self-guidance); 4. The child whispers the instructions to herself as she goes through the task (faded, overt self-guidance); and 5. The child performs the task while guiding her performance via private speech (covert self-instruction). (Meichenbaum, 1977, p. 32) Normal students typically approach tasks in an active manner and spontaneously apply self-instruction to guide behaviors or solve tasks (Hallahan et al., 1983). However, academic deficits occur when students fail to use self-instruction to guide behavior (Meichenbaum, 1977). Learning disabled students are characterized as passive, inactive learners who do not spontaneously produce or apply appropriate self-instruction strategies for task solution (Hallahan et al., 1983; Ryan, Short, & Weed, 1986; Torgeson, 1977). Learning disabled students also fail to internalize rules or strategies that guide new learning situations. Based on the CBM model, LD students' academic problems are due to deficient application of self-instruction to academic tasks. According to the CBM model, behavioral changes occur through internal controls or self-regulatory private speech. Training in selfinstruction should increase academic performance by allowing LD students to perform a kind of thinking that they do not normally produce (Meichenbaum & Asarnow, 1979). With CBM, the student is able to consistently apply problem-solving behaviors across differing environments (Meichenbaum, 1985). Research with CBM and learning disabilities has primarily focused on remediation of impulsivity or other task-oriented behaviors

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6 (Meichenbaum & Asarnow, 1979). General self-instruction procedures, such as self-monitoring, are used to address generic classes of behaviors rather than behaviors specific to academic tasks. Application of CBM for treatment of academic subjects in LD students has only recently received attention, and few studies exist (Gerber, 1983; Kneedler & Hallahan, 1981 ; Lloyd, 1980). Specific self-instruction procedures have been developed to promote academic remediation of LD students (Tarver, 1986). In several studies researchers have combined both general and specific selfinstruction training with academic remediation in LD students (Harris & Graham, 1985; Swanson & Scarpati, 1984). In these studies, application of general self-instruction is intended to enhance active learning styles, while specific self-instruction training focuses on task solution and facilitates treatment retention. It has been shown in the research literature that remediation of learning disabilities with self-instruction can increase problem-solving efficiency to the point where it is commensurate with normal learners (Harris, 1986). Cognitive behavior modification, like operant procedures, has been criticized for lack of treatment retention. Significance of the Study Although research based on CBM is suggestive of effective remediation with learning disabilities, there has been no careful comparison with other remediation models (Lahey & Strauss, 1982). Further, problems with methodology and lack of preliminary studies preclude making firm conclusions regarding CBM's efficacy (Gerber, 1983; Hobbs, Moguin, Tyroler, & Lahey, 1980; fVieichenbaum, 1980; Rooney &

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Hallahan, 1985; Swanson & Kozleski, 1985). Criticism of CBM methodology includes the following: 1. Students with different learning problems are used when providing treatment. For example, in some group studies, nonLD students are combined with LD students within the treatment group. 2. Independent variables are not always clearly defined, so they confound interpretations of treatment gains. 3. Type I dependent measures are infrequently used to evaluate treatment gains. Type I dependent measures are direct measures of a socially valued treatment goal such as improvement in tested academic achievement (Lahey & Strauss, 1982). 4. Researchers do not utilize measures of classroom achievement gains as dependent measures. 5. Retention of treatment across time is not adequately demonstrated with CBM. Thus, it is not clear how effective CBM is with academic remediation in LD students, or how it compares with operant procedures. This comparison, along with methodological issues, requires investigation in order to advance knowledge of education of LD students and to substantiate use of CBM as a remediation strategy with this student population. Statement of the Problem Few researchers have specifically investigated academic remediation with LD students. Despite CBM's increasing promise as an LD remediation tool, there are no convincing empirical data to substantiate its effectiveness. Cognitive behavior modification studies have been

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8 criticized for methodological weaknesses, which casts doubt on treatment effectiveness. There have been no careful comparisons between CBM and operant conditioning with academic remediation of LD students. Purpose of the Study A comparison of treatment effects was conducted in this study between direct instruction, direct instruction with operant procedures, and CBM with remediation of addition and subtraction operations in elementary school LD students. Treatment effectiveness was measured by results from a standardized math test and classroom performances. Retention scores of math skills across time based on remediation techniques were collected and compared. Hypotheses The following hypotheses were investigated in this study. 1. Ho: There will be no significant difference (e>. 05) in trend among direct instruction, direct instruction with operant procedures, and CBM with elementary school LD students' addition and subtraction operations as measured by classroom performance timings. 2. Ho: There will be no significant difference (e>.05) in trend among direct instruction, direct instruction with operant procedures, and CBM with elementary school LD students' addition and subtraction operations as measured by a standardized math test. 3. Ho: There will be no significant difference (a>.05) in trend between direct instruction with operant procedures and CBM with elementary school LD students' addition and subtraction operations as measured by classroom performance timings.

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9 4. Ho: There will be no significant difference (fi>.05) in trend between direct instruction with operant procedures and CBM with elementary school LD students' addition and subtraction operations as measured by a standardized math test. Definition of Terms Classroom performance timings-This measure is the number of correct basic addition and subtraction problems completed during a 2-minute period. Cognitive behavior modification (CBM)This treatment is a type of cognitive remediation technique which employs self-instruction to guide overt behaviors. Direct instructionDirect instruction is a systematic plan of instruction which targets academic deficits and directs teaching toward increasing those deficits. Learning disabled (LD) studentAn LD student is one who is experiencing academic difficulties and who has met the following criteria: (a) demonstrates a standard deviation discrepancy between IQ and math achievement and (b) has below average functioning in either perceptualmotor, short-term memory, or language processing skills. Learning disabled students attend resource or self-contained classrooms for remedial instruction with an exceptional education (LD) teacher. Operant procedureThis is a procedure which provides token reinforcers immediately after and contingent upon a specified behavior in order to increase the probability of that behavior to recur. Standardized math achievement testThis is a test which has undergone a norming process that allows meaningful interindividual

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comparisons. Reliability and validity data are usually reported for standardized tests. Overview of Remainder of Study A review of literature is presented in Chapter 2. Variables under investigation are discussed in Chapter 3. Methodological issues such as research design and statistical procedures are also described. Results of the data analysis and statistical summary tables are presented in Chapter 4. The results and implications for future research are discussed in Chapter 5.

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CHAPTER 2 REVIEW OF LITERATURE This review is divided into three sections. The first section is an overview of math remediation of LD students with operant procedures. A comprehensive review of academic remediation with CBM of LD students is presented in the second section. Specific methodological issues pertinent to this study are reviewed in the third section. Remediation of Learning Disabilities With Operant Procedures Operant procedures are based on operant conditioning theory (Skinner, 1953). Operant procedures typically arrange environmental or external consequences in order to modify behaviors. Positive reinforcement is a widely used operant procedure and one of the most effective methods for increasing rates of behavior (Alberto & Troutman, 1986; Hilgard & Bower, 1975). A positive reinforcer is a consequential stimulus that (a) increases or maintains future rates of behaviors, (b) is administered contingent upon the production of a desired behavior, and (c) Is administered immediately following the desired behavior (Alberto & Troutman, 1986) Remediation of LD students with operant procedures is concerned with changing academic behaviors or characteristics rather than assigning labels or searching for causes of academic dysfunction (Treiber & Lahey, 1983). Operant procedures are used to manipulate environmental contingencies in order to increase academic functioning in LD students. 11

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Operant procedures have been used to effectively remediate many academic areas (Lovitt, 1975). Operant procedures also have been used to effectively remediate a severe "process deficit" typically attributed to organic dysfunction (Lahey et al., 1977). That is, two severely handicapped LD males with perceptual-motor deficits significantly improved copying skills when token reinforcement was instituted. Academic remediation with operant procedures typically includes the following characteristics: 1 . Direct instruction-specifically teaching weak academic areas. 2. Emphasis on measurement-continuous measurement of behaviors being remediated are used for immediate feedback of treatment effectiveness. 3. Manipulation of environmental contingencies (Treiber & Lahey, 1983). Math Remediation of LD Students With Operant Procedures Smith and Lovitt (1976) investigated conditions for appropriate application of operant procedures with math remediation. Seven LD males participated in the study which employed a single-subject reversal design. Subjects had opportunity to earn points toward a chosen toy by successfully completing math problems. Initially, none of the students earned points. However, once the students were shown how to compute the problems, points were earned and task accuracy increased. Smith and Lovitt (1976) concluded that reinforcement contingencies are only effective when desired behaviors are part of the subject's repertoire of behaviors. Broughton and Lahey (1978) conducted a study investigating effects of positive reinforcement, response cost, and combination of positive

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reinforcement and response cost with remediation of subtraction. Thirtythree fourth and fifth graders with math disabilities served as subjects. The subjects were assigned to either positive reinforcement, response cost, combination positive reinforcement and response cost, or control group. A reversal design was used with each treatment group. Reinforcement occurred as points which were exchanged for various activities during free time. Points were awarded for correct subtraction responses in the positive reinforcement group. The response cost treatment group initially received 20 points per day to spend during free time. Points were lost for each incorrect subtraction response. The procedure for the combination treatment group combined both contingencies for either correct or incorrect responses. Significant positive gains were found for the results from all three treatments. Although significant differences were not shown among treatment groups, the response cost group and positive reinforcement group produced more immediate changes in subtraction performance than did the combination treatment group. A reason for this observation may have been lack of immediacy in determining number of earned points by students in this condition. That is, the subjects had to ask the teacher frequently for cumulative point totals. Increases in on-task behavior also occurred as academic gains were made. It was posited that successful academic progress may be a prerequisite for increasing on-task behaviors. Blankenship and Baumgartner (1982) investigated remediation and generalization of math skills with operant procedures in LD students. In this study procedures for generalization across task were specifically addressed. Subjects were 4 female and 5 male LD students ranging from

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8 through 1 1 years of age. A single-subject multiple-baseline design was used. After subjects showed proficiency with math computation, they were presented with a worl
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show treatment changes relative to baseline conditions. Retention of treatment gains has been limited. Remediation Of Learning Disabilities With Cognitive Behavior Modification Meichenbaum is credited for seminal research with CBM (Wong, 1985). Cognitive behavior modification first emerged as a technique to remediate a generic class of behaviors including impulsivity and off-task behavior, f^yieichenbaum and Goodman's (1971) two-part study is among the first in which the role of self-instruction on overt behaviors was investigated (Craighead, 1982). The researchers used self-instruction to modify impulsivity in 15 second graders ranging from 7 to 9 years of age. Several other studies have examined the role of CBM with task-oriented behaviors of LD students (Hallahan, Marshall, & Lloyd, 1981; Rooney, Polloway, & Hallahan, 1985; Tollefson, Tracy, Johnsen, & Chatman, 1986). Investigation of specific academic areas among LD students with CBM has only recently received attention. General self-instruction techniques similar to those employed for remediation of task-oriented behaviors were utilized in earlier studies. Contemporary researchers have combined general and specific self-instruction in order to increase academic achievement and retention of skills. Academic Remediation of Learning Disabilities With CBM Writing. Robin, Armel, and O'Leary (1975) remediated handwriting deficiencies with CBM. Thirty kindergarten subjects were not specifically identified as LD, but reportedly scored poorly on a handwriting measure. The subjects were divided into a self-instruction group, direct training with social reinforcement group, and control group. The main components of direct training were corrective feedback and social reinforcement. The self-

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instruction group also received social reinforcement, and this procedure may have confounded the results (Lahey et al., 1979). Treatment consisted of 20 training sessions spanning a 7-week period. Selfinstruction training consisted of the following steps: 1 . Question about the task: "What is it I have to do?" 2. Answer in the form of planning: "I have to make a 'P'." 3. Appropriate directive comment: "I have to go down, down, slow, stop at the bottom, stop." 4. Correction of error: "No, that's not straight; I have to make a straight line, like a stick." 5. Self-reinforcement: "It's done and I made a good letter." (p. 182) Based on results from an analysis of variance (ANOVA), it was shown that CBM treatment was more effective than direct training with reinforcement. Both treatments were superior to the control group. Cognitive behavior modification's superior results were attributed to its incremental task strategy. That is, the copying task was partitioned by CBM into more discrete components as compared with direct training. Several issues with practicality of CBM treatment arose from this study. Despite demonstration of self-instruction by the experimenter, students often abbreviated the procedure. Most students developed their own idiosyncratic style of self-instructing. Secondly, higher rates of overt verbalization were not correlated with superior performance. However, some children may have covertly guided their behavior, making such an inference inaccurate. Finally, overt self-instruction was deem*ed cumbersome because of disruptive effects in the classroom. Kosiewicz, Hallahan, Lloyd, and Graves (1982) more recently investigated CBM treatment of poor handwriting in a 10-year-old LD male. A multiple-baseline reversal design was used. Sixty-five treatment

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sessions at 1-5 minutes per session spanned 120 days. Dependent measures were percent of correctly reproduced letters. Significant improvements in handwriting were found. However, a potential methodological problem was cited with confounding effects of sequential treatment order. It may be impossible to completely withdraw a cognitive strategy such as self-instruction once it has been taught. Thus, a reversal design may be inappropriate with CBM. * The experimenters did not experience the cumbersome aspect of classroom self-instruction previously cited by Robin et al. (1975). The student in the current study seemed to progress spontaneously to the covert self-instruction stage. Reasons for the smooth transition from overt to covert self-instruction may have been the 10-year-old's higher language skills than a kindergartener's, and prior knowledge of letter formation. Thus, CBfVI's effectiveness may be facilitated with older subjects, or those with established language skills. Composition writing Harris and Graham (1985) investigated improvement of composition writing in LD students with CBM. Two 12year-old LD students served as subjects. For treatment, Harris and Graham introduced self-control as an adaptation of self-instruction training. Self-control training includes specific task-appropriate strategies and metacognitive training. Metacognitive training is defined as training in the self-regulation of appropriate self-instruction strategies. Self-control training contains the following four procedures: (a) self-instruction, (b) selfdetermined criteria for academic performance, (c) self-assessment, and (d) self-reinforcement.

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Treatment began with skill building in recognition of "action words." Then, the importance of increasing writing skills was discussed with the student. A five-step strategy for writing good stories followed which was modeled by the instructor and written out on a small chart for students: 1 . Look at the picture and write down good action words. 2. Think of a good story idea to use my words in. 3. Write my story--make sense and use good action words. 4. Read my story and ask--did I write a good story? Did I use good action words? 5. Fix my story--can I use more good action words? (p. 29) After training of these components, metacognitive procedures for selfcontrol training were presented. Dependent measures for written stories were frequency of different action words, action helpers, descriptive words, and total number of words. Significant improvements in the quality of written compositions in both subjects were demonstrated. Post-treatment retention was shown after 2 weeks, but inconsistencies occurred after 14 weeks. Both subjects maintained retention of training steps after 14 weeks, but implementation of training was inconsistent. Malh. Several studies (e.g., Grimm, Bijou. & Parsons, 1973; Lovitt & Curtiss, 1968) have focused on the role of verbal mediation with math in handicapped children. However, Leon and Pepe (1983) were among the first to investigate CBM remediation of math with LD students. Their sample consisted of 13 LD and 24 educable mentally handicapped (EMH) students ranging from 9 through 12 years of age. Learning disabled and EMH students were combined in treatment and control groups. Dependent measures were results from standardized and curriculum-based math tests

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of basic math operations. Training consisted of 35 sessions during a 7week period. Self-instruction training contained the following steps: 1. Teacher provided modeling by computing the problem using overt verbalization. 2. Teacher and student computed the problem together using overt verbalization. 3. Student computed the problem with overt verbalization and teacher supervision. 4. Student computed the problem while whispering self-instruction (fading of overt verbalization). 5. Student computed the problem with covert verbalization. Significant math increases were found in the treatment group, and learning disabled students scored higher than EMH students on dependent measures. Generalization of self-instruction training was reported to occur across math tasks. Schunk and Cox (1986) further investigated math remediation with CBM in LD students by adding an effort attribution variable and differentiating between overt and covert verbalization. Subjects included 90 LD students ranging from 1 1 through 16 years of age. Treatment math operations were subtraction problems involving regrouping. SelfInstruction training consisted of six 45-minute sessions. After a modeled example, the overt verbalization group received the following instructions: I'm really interested in knowing what students think about as they solve problems. So as you're working problems, I'd like you to think out loud; that is, say out loud what you're thinking about just like I did while I was solving problems. You'll probably be thinking about what to do next, what numbers to use, how much is one number minus another, and so on. Remember, say out loud what you're thinking about, just as I did. (p. 204)

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The covert verbalization group received the same instructions, but was asked not to talk out loud after the third session. Besides general selfinstruction training, students received attribution feedback for effort after successful problem solving. Effort feedback was delivered either during the first or second half of training, or not at all. Dependent measures included a subtraction skill test and self-efficacy rating scale for attribution. Based on results from the multivariate analysis of covariance (MANCOVA), self-instruction was found to increase subtraction skills. Covert self-instruction was not as successful as overt self-instruction. The authors concluded that the subjects had difficulty internalizing the strategies, i.e., in Meichenbaum's fifth step in self-instruction training. This difficulty also may have been due to application of only general selfinstruction training academics. Specific self-instruction training may have produced better results (Wong, 1985). Effort attribution feedback led to higher self-efficacy and subtraction skills. However, there was no difference between first or second-half effort feedback conditions. Rggding. Wong and Jones (1982) investigated treatment of reading comprehension with a CBM-related procedure. The sample consisted of 120 LD and normal eighth and ninth graders. Treatment effects were compared between normal and LD students. Two-day treatment consisted of a self-questioning procedure focusing on reading comprehension strategies: 1. What are you studying this passage for? 2. Find the main idea/ideas. . . and underline them. 3. Think of a question about the main idea you have underlined Remember what a good question should look like. 4. Learn the answer to your question.

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5. Always look back at the questions and answers to see how each successive question and answer provide you with more information, (p. 231) Significant comprehension gains occurred in the LD treatment group. No significant gains were found among normal students. The lack of training effects among normal students may be attributed to the fact that normal students spontaneously monitor their comprehension without requiring specific training. This hypothesis is consistent with CBM theory and the prediction of a verbal mediation deficit among LD students. Kupietz (1980) attempted to modify impulsivity and increase reading in 30 second and third graders. Effects of general versus specific self-instruction were compared on these variables. Dependent measures for reading were results from standardized tests. Although subjects showed a decrease in impulsivity, there were no significant gains made In reading. A significant difference was not found between general and specific self-instruction with reading gains. Several confounding variables were cited, including problems with student discipline and limited training time for treatment. Swanson and Scarpati (1984) conducted two experiments in which they investigated reading, spelling, and math remediation with CBM in LD students. Several aspects of generalization also were analyzed. Subjects were 2 LD eighth and ninth-grade males. A single-subject design was used. Similar to Harris and Graham (1985), the researchers used general self-Instruction for error monitoring and self-reinforcement. Task specific strategies focused directly on academic problem solving. Training in Part I consisted of 45-minute treatments for a minimum of eight sessions. Delivery of token reinforcers was part of the existing classroom behavior

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management program, and subjects continued to earn them. This motivational variable may have confounded results (Lahey et al., 1979). Generalization across setting, instructor, and task was conducted immediately following the treatment condition. In the setting phase, the 2 subjects attempted learning activities with the same teacher used for CBM training, but in a setting different from the baseline or treatment conditions. Setting differences included changes in room color and seating arrangement. For the generalization procedure across instructor, a teacher who was familiar to the students, but who had not taught reading or spelling to the students was used. Generalization across task exposed the students to new learning activities commensurate with training item difficulty. Based on results to Part I, the researchers concluded that self-instruction significantly increased LD students' reading and spelling performances. Generalization across instructor and task was shown with reading and spelling. However, generalization across setting in a nontreatment classroom did not occur. Possible reasons were attributed to a radically different classroom environment as compared to treatment setting. In Part II, math remediation and generalization of math skills across setting in a 13-year-old LD male were investigated. A reversal design was used in this phase. Initially, treatment was conducted in one corner of the student's LD classroom. Twenty-eight 30-minute treatment sessions were conducted. Generalization was assessed when the subject returned to his regular seat in the same classroom. The student's math performance in this setting remained at a rate commensurate with treatment setting. The

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researchers hypothesized that when classroom settings are changed in smaller increments from treatment settings, generalization is more likely to occur. Swanson and Scarpati (1984) noted difficulties similar to those cited by Kosiewicz et al. (1982) with a reversal design and CBM treatment. Confounded results occur when CBM treatment is withdrawn. Puzzle task . Harris (1986) investigated differences between LD and normal students with private speech and puzzle performance. Subjects were 30 LD and 30 normal 7 and 8-year-old students. The students were assigned to complete an insolvable puzzle. The treatment group was exposed to self-instruction training relative to puzzle tasks. Four dependent measures were collected: rate of private speech (only overt verbalizations were measured), proportion of task-relevant private speech, time required to complete solvable portion of puzzle, and persistence time. Three significant differences between LD and normal students were found: (a) LD students showed lower proportion of task-relevant verbalizations, (b) LD students required more time to solve the task, and (c) LD students showed shorter persistence times. In addition, LD students produced more negative self-statements than normal students while solving the puzzle. Three significant differences also were found between treatment and control groups. The treatment group showed a higher proportion of task-relevant private speech and higher rate of private speech in general. The treatment group also had longer persistence times. Interestingly, treatment group LD students performed as well as normal control group students.

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These results are significant in tliat they support further the hypothesis that LD students have a verbal mediation deficit in academic processes. In addition, CBf^ remediation can produce task efficiency among LD students that is commensurate with nonLD students. Summarv of CBM Research Research with CBM and task-oriented behaviors was pioneered by Meichenbaum. Cognitive behavior modification emerged as a remediation strategy for impulsivity and hyperactivity. General self-instruction methods were applied to remediate these behaviors. Based on verbal mediation deficits, CBM was then applied to academic remediation with LD students. Specific self-instruction procedures have been developed that directly focus on academic problem-solving strategies. Design characteristics with CBM research include both single-subject and group designs. However, single-subject reversal designs with CBM are a problem. Reversal, alternating treatments, and changing conditions designs are inappropriate with CBM because of difficulties encountered when withdrawing a cognitive remediation strategy (Kosiewicz et al. 1982; Swanson & Scarpati, 1984). When CBM treatment is withdrawn in a reversal design, it cannot be assumed that learned cognitions in the treatment phase are withdrawn from the student. Similarly, with alternating treatments or changing conditions designs such as ABCBC, cognitive training (for example, B) can be carried over to the next treatment phase (C) and confound results. As with operant studies, retention of treatment across time has not been adequately shown with CBM research. The hypothesis that CBM

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produces greater treatment gains and skill retention than operant procedures is untested. Design Issues for Intervention Studies Reinforcers Token reinforcement systems are widely used in educational research because they allow for greater versatility over other reinforcement systems (Alberto & Troutman, 1986). Token reinforcers are generalized conditioned reinforcers because they are associated with a variety of behaviors or other reinforcing items termed back-up reinforcers (Alberto & Troutman, 1986). Thus, tokens are particularly motivating because of this variety of choice for exchange. There are additional advantages of the use of token reinforcers over other reinforcement procedures. Token reinforcers maintain performance over extended periods of time because they are less subject to satiation effects and deprivation states than primary reinforcers. Token reinforcers provide the same reinforcement for individuals who have different back-up preferences. Finally, use of tokens provides the student with a tangible means of continuous feedback (Alberto & Troutman, 1986). Treatment Integrity Treatment integrity refers to the extent to which a specified treatment is actually implemented in the manner prescribed by the methodology. Treatment integrity should be included in contemporary research, especially with group designs, but few researchers address it (Shapiro, 1987). Documentation of treatment integrity is important for ethical

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considerations and practical reasons such as replication of research (Shapiro, 1987). Social Validity Social validity refers to the evaluation of treatment by consumers or relevant observers and is often assessed qualitatively (Shapiro, 1987). Social validity of treatment effectiveness and related issues is an important aspect of contemporary educational research. Summary of the Literature Review Three topics were highlighted in the literature review: operant treatment of LD students' math deficiencies, CBM treatment of LD students' academic deficiencies, and design issues for intervention studies. Operant procedures have been shown to increase successfully LD students' math skills primarily with the use of extrinsic reinforcers and direct instruction. Cognitive behavior modification has been shown to remediate effectively LD students' academic deficits by enhancing self-guiding behaviors with internal dialogue, or self-instruction. General self-instruction has been designed to increase task-oriented behaviors, while specific self-instruction has been used to improve specific academic skills. The effects of CBM and operant procedures on LD students' math skills have not been directly compared. The following design issues for contemporary intervention research were reviewed: token reinforcement, measures of treatment integrity, and social validity. Use of token reinforcers has advantages because they are associated with a variety of back-up reinforcers. Measures of treatment integrity should be conducted in intervention research to substantiate treatment implementation as prescribed by the methodology. Social

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validity is an important aspect of intervention research because it allows for the evaluation of the treatment by relevant consumers.

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CHAPTER 3 METHODOLOGY Overview of the Study Operant conditioning and CBM are two models for treating learning disabilities. Environmental contingencies are manipulated when using operant procedures in order to change academic behaviors without regard to etiology of learning disabilities. Cognition does not play a role in operant procedures. On the other hand, behavioral changes due to CBM occur through selfregulatory private speech. It has been hypothesized that LD students show deficient self-instruction strategies for academic problem solving. Both remediation models have poor treatment retention over time. The purpose of this study was to compare treatment effectiveness between CBM and operant procedures with addition and subtraction problems in elementary school LD students. Treatment retention between the two models was also compared. Subjects This study was conducted in Duval County public schools, Jacksonville, Florida. Ninety-four students participated in the study. There were 27 students in the control group, 32 in the CBM group, and 35 in the operant group. All students were identified formally as learning disabled. The LD students attended nine exceptional education classrooms from four different Duval County schools. The students were deficient in math skills 28

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and were receiving remedial math instruction from a state-certified exceptional education teacher. Socioeconomic status of students was determined by free lunch eligibility and teacher input. The mean IQ for all students was 99.03 (SD=9.62) and the mean achievement score was 78.05 (SD=11.41). Relevant subject characteristics are shown in Table 1 . Table 1 Subject Characteristics Number of Students 1st 2nd 3rd 4th Per Grade Level 8 9 25 26 Gender Females Males 31 63 Race Black White Other 28 61 5 SES Hich Middle Low 8 33 53 Variables Un der Inve.qtig atinn independent Variable There were three levels of treatment as independent variables under investigation in this study. The first level was CBM as a remediation technique. This included general self-instruction for task oriented behaviors, such as attention to task and specific self-instruction for math problem solving.

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The second level was an operant procedure with direct instruction of math skills. Token reinforcers were given for each correctly solved math problem. The reinforcement schedule was continuous reinforcement per correct response, or fixed ratio per correct unit response (FR 1) (Miller, 1980). The third level was an alternative treatment control condition consisting of direct instruction of math skills without token reinforcement. This condition served as a control for the other two treatments. Dependent Variable Math measures were chosen for dependent variables in this study because authors of both CBM and operant studies report successful remediation with this academic area (Blankenship & Baumgartner, 1982; Schunk & Cox, 1986). Math gains are quickly assessed without subjectivity in scoring. Finally, fewer researchers have investigated math compared to other academic areas with LD students (Mercer & Mercer, 1985). Two dependent variables were used in this study: standardized achievement and timings of math work. The computation portion of the Stanford Diagnostic Mathematics Test (Beatty, Madden, Gardner, & Karlsen, 1986) was used as the standardized achievement measure. This test was chosen because it (a) is group administered, (b) focuses on computation skills, and (c) has excellent normative characteristics (Salvia & Ysseldyke, 1981). Rate of problems correct, or timings of basic addition and subtraction problems, was the dependent variable relevant to classroom instruction. Timings are an accurate method to assess understanding and proficiency

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with basic math skills (Alberto & Troutman, 1986). Timings of academic performance are also Type I dependent variables (Lahey & Strauss, 1982). Time interval for work on these problems was 2 minutes. Apparatus A mixed probe consisting of 25 basic addition and 30 basic subtraction problems was used for the timings (see Appendix A). The mixed probe was developed according to addition and subtraction skill hierarchies (Evans, Evans, & Mercer, 1986). The problems were arranged in complexity from top to page bottom. The addition problems required the students to demonstrate the following skills: 1. Computation of sums 0-9. 2. Computation of sums 10-18; both addends less than 10. 3. Calculation of two-digits plus one-digit or two-digits without regrouping. 4. Computation of two-digits plus one-digit or two-digits with regrouping. 5. Computation of two-digits plus two-digits plus two-digits with sums of ones greater than 20. 6. Calculation of three-digits plus three-digits with and without regrouping. The subtraction problems required the students to demonstrate the following skills: 1. Computation of basic subtraction facts with minuends 1-17 and answers 0-9. 2. Computation between two-digit and one-digit or two-digit problems without regrouping.

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3. Calculation of two-digit and one-digit or two-digit problems with regrouping. 4. Computation between three-digit and three-digit problems with single regrouping. 5. Calculation of three-digit and two-digit problems with double regrouping. Procedure Nine classrooms serving LD children were selected for this study based on subject availability, teacher cooperation, and permission from the school principal. The participating teachers were given a $25 stipend for 1-2 hours of training time after school hours. The experimenter contacted teachers with treatment conditions twice per week to answer questions and observe treatment delivery. Teachers also were encouraged to call upon the experimenter at any time during the study if questions arose. Besides a copy of the procedure, summaries of both experimental treatments were given to teachers as a reference guide (see Appendices B and C). Because of its relatively straight-forward procedure, the control group teachers did not receive a reference guide. The experimenter and teachers collected all data. Both dependent measures were administered as pretests, posttests, and retention measures. Standardized instructions for group administration as prescribed by the Stanford Diagnostic f\^athematics Test manual were followed when administering the test. The following instructions were given when administering the probe sheet: "I am passing out some math problems (face down) for you to do. When I say go, turn over your papers and begin working. Do as many

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problems as you can. Any questions? Go." After 2 minutes, the teacher said "stop" and collected the papers. Treatment consisted of nineteen 60-mlnute sessions spanning 4 weeks. Administration of the pretests occurred immediately preceding the first day of treatment. The posttests were administered at the end of the 19th session. The measure of treatment retention was conducted by readministering the probe sheets and standardized tests after-2 weeks following the final day of treatment. Seven students (across all conditions) were absent from one of the testing sessions and were tested the following school day. Three students were absent for more than one day beyond the group test day and were eliminated from the study. Subject mortality was essentially equivalent across groups. Of 107 original subjects, 94 subjects remained for the duration of the study. The control and operant conditions each lost 4 students, and the CBM condition lost 5 students. Six losses were due to moves, 4 were due to class changes, and 3 were due to extended illness. CBM Treatment Implementation of general self-instruction was intended to promote an active learning style within the LD student (Hallahan et al., 1983; Torgeson, 1977). General self-instruction procedures based on Meichenbaum and Goodman's (1971) model were applied to a set of selfstatements like the following: 1 . "What is my assignment for today?" 2. "I need to start working now." 3. "Good, I'm finished."

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4. "Now I need to check my work. Good, I'm done." Specific self-instruction training is designed to target specific academic strategies and steps toward task solution. This technique enhances treatment retention (Tarver, 1986; Meichenbaum, 1980; Wong 1985). For specific self-instruction training, Meichenbaum and Goodman's (1971) model was applied to specific problems such as 24.±2 1. "What kind of problem is this, addition or subtraction? What does the sign say?" 2. "OK, it's addition-thai means I'll be adding numbers." 3. "First I add the first column of numbersthat's 9+4." 4. "That equals 13, but I have to remember to only put down 3 and carry the 1 over to the tens column." 5. "Now I add 2+1 in the tens column. That's 3-and I write it down here. My answer is 34." The following is an example of specific self-instruction for subtraction using the same math problem. 1. "What kind of problem is this, addition or subtraction? What does the sign say?" 2. "OK, it's subtraction-that means take-away." 3. "Will I need to borrow? Yes, because the bottom number is bigger than the top number." 4. "I borrow 1 from the tens column, cross out the 2 and put 1, and bring 1 over to the 4 to make 14." 5. "Now I take away 9 from 14. That's 5, so I write it down here."

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6. "What's left in the tens column? A 1 , so I write it down here. My answer is 15." The self-instruction procedure integrating general and specific selfinstruction was the specific format for CBM treatment in this study. The following is an example of the way in which general and specific selfinstruction was integrated Into the treatment package (see Appendix B): 1. "What is my assignment for today? It's math problems 1 through 15." ' 2. "I need to start working now." • 3. "What kind of problem is this, addition or subtraction? What does the sign say?" 4. "OK, it's addition, that means " 5. "Good, I've finished that problem. I need to keep working." 6. "Good, I'm finished. I've checked my work and I'm done." The students were initially informed of the treatment with the following explanation: "For the next few weeks, we will be doing our math in a different way. Watch how I do a problem with this new way." The integrated package of general and specific self-instruction was delivered by the teachers in four steps. 1. The teachers modeled the procedure by talking to themselves while solving a sample problem at the beginning of every class. 2. The students were instructed to talk aloud as they performed math tasks. 3. The teachers provided guidance and prompts for self-talk as students performed math tasks.

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4. After the second week, students were instructed to talk to themselves while performing math tasks. Operant Treatment Students in the operant treatment condition received direct math instruction (see Appendix C). Direct instruction included the following steps: 1. Clearly explain the task objectives and goals. 2. Demonstrate the skill for the students. 3. Provide appropriate drill and practice. 4. Give corrective feedback. 5. Assess students' progress (Haring & Gentry, 1976; Mercer & Mercer, 1985). The reinforcement procedure was initially explained to students in the following manner: "You will get one token (chip) for each correct addition or subtraction problem you complete in class. You will be given the tokens (chips) you earn near the end of class." Back-up reinforcers were explained as follows: "These are items that you can buy as soon as you earn enough tokens for that item." Poker chips were used as tokens in this study. The poker chip was chosen as the preferred token because it is portable, durable, and easy to handle (Alberto & Troutman, 1986). Each teacher was given a "bank" of 300 red, white, and blue tokens. Blue tokens were assigned a value of 10 problems correct, red = 5 problems correct, and white = 1 correct. Students were able to earn a daily token value equivalent to the correct number of classwork math problems. Earned tokens were kept in clear envelopes for each student. The envelopes were passed out to the students at the

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beginning of class and were collected at the very end of each class. Tokens were delivered 10-15 minutes prior to the end of each class period. Students exchanged tokens for stickers, stationery items, or small toys (not exceeding $3 each) prior to the end of each class period (see Appendix D for back-up reinforcer inventory). Back-up reinforcers were selected in an attempt to appeal equally to both genders. Back-up reinforcers were kept in a metal or wood cabinet in the classroom. One teacher kept back-up reinforcers in clear plastic bags hooked on a peg board. The back-up reinforcers were available for display during class and locked away when teachers were not present. Twenty to 30 daily assigned math problems were typically available for token reinforcement in all three classrooms. The cost of back-up reinforcers was mutually established by the experimenter and teachers. The cost was based upon perceived student demands for each item. Several back-up reinforcers (raisins, folders, and notepads) required a cost increase because of unusually high demand for these items. It was the experimenter's responsibility to maintain adequate supplies of back-up reinforcers. Total purchase cost for the back-up reinforcers amounted to $74.10. Control Group (Direct Instruction^ The direct instruction group received direct math Instruction (as described in the operant procedure) without token reinforcement. Following the 4-week treatment period, math instruction for all classes resumed to normal pretreatment settings. None of the treatment conditions were provided during the 2-week period prior to the retention measure.

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Treatment Integrity Treatment integrity ratings of the experimental conditions were conducted by sets of two school psychologists not associated with the study. Sample class periods were videotaped for the ratings. One taping per experimental treatment was made for a total of 12 ratings. Treatment integrity was rated according to the extent of conformity with the procedures (see Appendix E). To prevent bias, raters were-not told which conditions they were observing. Interrater agreement was also calculated. Social Validity Social validity of treatment effectiveness refers to the evaluation of treatment by consumers or relevant observers (Shapiro, 1987). Social validity was conducted at the conclusion of treatment with participating teachers (see Appendix F). Individual open-ended interviews were scheduled with teachers to discuss treatment topics, including 1. How long did it take for you to feel comfortable in delivering the treatment? 2. Were there any negative side-effects to the treatment? 3. Were there any positive side-effects to the treatment? 4. Would you adopt this treatment for regular use in your classroom? The experimenter recorded interview data. Design The design in this study was a nonequivalent pretest-posttest control group design. This design is prevalent in educational research and used with intact classrooms when randomization of subjects is difficult or impossible (Campbell & Stanley,1963; McMillan & Schumacher. 1984).

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This type of design can be used to control for subject reactivity which can occur when subjects are removed from their natural setting for treatment (Huck, Cormier, & Bounds, 1974). It also can be used to control for main effects of history, maturation, testing, and instrumentation (Campbell & Stanley, 1 963). Use of a control group further guards against threats to internal validity. Using intact classrooms is common in educational research and has several advantages. Threats to ecological external validity occur when subjects are removed from their normal environment to conduct the experiment (McMillan & Schumacher, 1984). This threat was not a variable in this study since subjects received treatment in their normally scheduled exceptional education classrooms. The Hawthorne effect probably did not play a confounding role because the subjects' teachers continued math instruction and only varied teaching methods. Teachers were randomly assigned to an experimental or control condition. Three groups of three teachers each provided treatments. This procedure greatly reduced the likelihood that teacher-treatment interaction and nesting variables would affect results. Assignments of conditions per teacher and school are shown in Table 2. Data Analvses A within-subjects or repeated measures design (Winer, 1971) was used as the statistical design in this study. This design is also termed Lindquist Type I ANOVA, split plot ANOVA, or mixed design (Huck et al., 1974). This type of statistical design is frequently used to study learning phenomena in education (Keppel. 1982). It is suitable when subjects are measured on a dependent variable several times during an experiment.

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Table 2 Assignment of Condition Per Teacher and School Teacher School Control Group #4 #4 #1 2 3 CBM Group 4 5 6 #2 #2 #4 Operant Group 7 8 9 #4 #3 #1 Although the assumption of true random selection was violated in this study, this statistical design is robust despite violations of random assignment (Glass & Stanley, 1970; Kirk, 1982). The repeated measures design was used to investigate a main effect of repeated measures (within-subjects factor). Overall trend significance among groups was determined with this procedure. An interaction between group performance and repeated measures was also investigated. The interaction illustrated trend differences among groups across three testing periods . Hypothesis #1 , stating no significant difference in trend among direct instruction, direct instruction with operant procedures, and CBM with elementary school LD students' addition and subtraction operations as measured by classroom performance timings, is rejected if the F for repeated measures X group interaction is significant (fi< .05).

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Hypothesis #2, stating no significant difference in trend among direct instruction, direct instruction with operant procedures, and CBM with elementary school LD students' addition and subtraction operations as measured by a standardized math test, is rejected if the F for repeated measures X group interaction is significant {q< .05). Hypothesis #3, stating no significant difference in trend between direct instruction with operant procedures and CBM with elementary school LD students' addition and subtraction operations as measured by classroom performance timings, is rejected if the F for repeated measures X group interaction is significant {q,< .05). Hypothesis #4, stating no significant difference in trend between direct instruction with operant procedures and CBM with elementary school LD students' addition and subtraction operations as measured by a standardized math test, is rejected if the F for repeated measures X group interaction is significant (e< .05). Limitations of the Study Internal Validity Internal validity refers to the efficacy with which extraneous variables are controlled in a study (McMillan & Schumacher, 1984). The most serious threat to internal validity In this study was lack of random selection and assignment of subjects. Without random selection and assignment to groups, a group of subjects may differ with a characteristic which could affect the dependent variable. However, assigning three teachers per condition minimized this threat, as did pretesting groups for initial differences.

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Another possible threat to internal validity in this study was the interaction between selection and maturation (Campbell & Stanley, 1963). Unplanned, extraneous events or natural changes within a specific group of subjects could have influenced the results, especially with lengthy treatment periods (McMillan & Schumacher, 1984). However, use of a control condition reduced these threats because they probably would have occurred equally across all conditions. Also, the treatment period was 4 weeks in duration. Testing effects could have been a threat to internal validity, but were not expected to be a major concern in this study. Testing effects are usually a threat with attitude or values research where pretest sensitivity could markedly influence posttest scores (Ary, Jacobs, & Razavieh, 1979). Testing effects could also bias measurement of achievement gains over a short period of time. Three sessions of math achievement testing were conducted over 6 weeks and probably did not affect posttest and retention scores. However, even if testing effects occurred, there is no reason to believe these effects would differ across groups. External Validity External validity is the extent to which results and conclusions can be generalized to other people and settings (McMillan & Schumacher, (1984). Population external validity is limited to elementary school students in large urban districts who are identified as LD with the same criteria as in Duval County, Florida. Ecological external validity refers to the conditions of the research and the extent to which results can be generalized to similar conditions. Results from this study can be generalized to math remediation of leaminq

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disabilities by LD teachers in public elementary school exceptional education classrooms.

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CHAPTER 4 RESULTS A repeated measures ANOVA was used for the data analysis in this study. Specifically, within-subjects factors and interactions between subjects and time were analyzed for significant differences in trend between groups. Classroom Timing s Subjects improved with classroom timings over time in all experimental groups (£(2, 91) = 8.53, J2=.0003). However, there was no interaction between subjects and time (£(4, 182) = 0.56, NS). Therefore, differences with timings among the three groups did not vary over testing periods. The following null hypotheses were not rejected: Ho#1 --There will be no significant difference {c>.05) in trend among direct instruction, direct instruction with operant procedures, and CBM with elementary school LD students' addition and subtraction operations as measured by classroom timings; and Ho#3-There will be no significant difference (a>.05) in trend between direct instruction with operant procedures and CBM with elementary school LD students' addition and subtraction operations as measured by classroom timings. Timings results are illustrated in Figure 1 and summarized in Table 3. Achievement TPRf g Subjects in all three groups improved in math achievement over time (£(2, 91) = 13.98, c=.0001). However, groups were not equal in their 44

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45 Pre Post Maint. Day 0 Day 25 Day 39 CBM Operant O Control Figurg 1 . Classroom Timings Results for All Conditions

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Table 3 ANOVA Results of Classroom Timings for all Conditions Source of dL Sum of Mean L St Variation Squares Square Between sub. 2 218.37 109.18 0.58 .5571 Error 91 16873.43 185.42 Within sub. 2 211.72 105.86 8.53 .0003 Sub. X Time 4 28.03 7.01 0.56 .6885 Error 182 2258.44 12.41 fvleans and SDs for Timings (number of problems corrects Test 1 (SD^ Test 2 (SD) Test 3 (^D) Control 16.0 (9.4) 15.2 (8.7) 16.8 (9.8) CBM 17.2 (6.0) 17.5 (6.6) 19.5 (7.2) Operant 15.3 (8.7) 16.0 (8.2) 17.8 (8.5) rates of improvement (F(4, 182) = 4.03, ^=.0037). Therefore, trends for the three groups varied significantly. The following null hypothesis was rejected: Ho#2--There will be no significant difference {q>.05) in trend among direct instruction, direct instruction with operant procedures, and CBM with elementary school LD students' addition and subtraction operations as measured by a standardized math test. Achievement test results are illustrated in Figure 2 and summarized in Table 4. In order to identify how groups differed on the achievement test, separate within-subject analyses were partialed with control, CBM. and operant groups. Subjects in CBM and operant groups scored significantly higfierthan control group subjects (£(2, 31) =14.86 and E(2, 34) = 9.71, R<.05). Based on these results, trend differences with CBM and operant groups were significantly higher than the control group. These results are

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540 "^60 Pre Post Maint. Day 0 Day 25 Day 39 CBM O Operant Control 2. Stanford Diagnostic Mathematics Test Results for All Conditions

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Table 4 ANOVA Results of Achievement Tests for all Conditions Source of Sum of Mean F n H Variation Squares Square Between sub. 2 109435.77 54717.88 1.73 .1828 Error 91 2875670.93 31600.78 Within sub. 2 31841.47 15920.73 13:98 .0001 Sub. X Time 4 18355.12 4591.53 4.03 .0037 Error 182 207227.55 1138.61 summarized in Table 5. To determine if significant differences in gains existed between operant and CBM groups, the effects due to these two treatments were examined. Subjects scored equally well in operant and CBM groups (F{2, 65) = 0.29, NS). Therefore, trend differences for posttest and retention measures between these two conditions were not significant. The following null hypothesis was not rejected: Ho#4--There will be no significant difference (e>.05) in trend between direct instruction with operant procedures and CBM with elementary school LD students' addition and subtraction operations as measured by a standardized math test. The effects due to operant procedures and CBM are summarized in Table 6. Treatment Infpgrity Treatment integrity was rated by three school psychologists not associated with the study for each experimental classroom. Ratings were based on the criteria defined by the treatment integrity form (see Appendix D). A class period midway through the treatment phase was videotaped for

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49 Table 5 Within-Subiect Analyses for Control. Operant, and CBM Conditions Source of £1 Sum of Mean E. Q Variation Square? Square Control sub. 26 1690994.24 65038.24 Within sub. 2 2299.72 1149.86 0.92 .4045 Error 52 64923.60 1248.53 Operant sub. 34 853260.05 25095.88 Within sub. 2 25005.48 12502.74 9.71 .0002 Error 68 87492.51 1286.65 CBM sub. 31 331416.62 10690.86 Within sub. 2 26284.56 13142.28 14.86 .0001 Error 62 54811.43 884.05 Means and SDs for Achievement Test Standard Scores Testl (SD) Test 2 i^D) Test 3 fSD^ Control 469.11 (153.7) 479.66(149.6) 467.74 (139 1) Operant 476.80 (86.5) 494.40 (92.9) 514.57 (103 8) CBM 498.69(71.6) 524.78 (60.4) 538.59 (61 8) Table 6 Effects Due to Operant and CBM Cnnditinns Source of Variation Sum of Squares Mean Square £ J2 Between sub. Error Within sub. Sub. X Time 1 65 2 2 32431.67 1184676.68 50694.61 652.70 32431.67 18225.79 25347.30 326.35 1.77 23.15 0.29 .1869 .0001 .7427

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all experimental conditions. The raters were given rating forms prior to viewing videotaped classroom sessions. All three raters correctly classified the experimental conditions with 100% agreement. Teachers were specifically instructed not to provide treatments during the retention phase. Materials from operant teachers were collected and daily contacts were made with all teachers to insure nontreatment conditions. Social Validity Social validity of treatment perspectives was measured with operant and CBM teachers after the experimental phase of the study. Teachers responded to at least four questions presented by the social validity rating interview (see Appendix F). Operant All three operant condition teachers reported feeling comfortable with treatment delivery after a maximum of 2 days. Two teachers felt comfortable with the procedure after the 1 st day of treatment. None of the teachers cited any negative side effects to operant treatment relative to the students. However, two teachers reported that the token delivery and exchange procedure for back-up reinforcers was time consuming. There were consistent reports of positive side effects among all three teachers. All teachers reported that the operant treatment increased motivation and on-task behavior. In addition, teachers reported (a) increased enthusiasm for math classwork, (b) increased math grades, (c) increased knowledge of money and expenditures, and (d) increased attention to detail with math classwork due to immediate feedback and consequences.

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All three teachers found the operant treatment appealing and planned to use it in their classrooms. In order to save time, one teacher reported that she would restructure the procedure by allowing purchase of back-up reinforcers once per week, instead of five times per week as in the experiment. Coonitive Behavior Modification All three teachers with the CBM condition reported a period of 2 days for becoming comfortable with treatment delivery. None of the teachers indicated negative side effects, but all three reported initial reluctance among a few students to talk aloud while working. This condition did not persist as self-talk quickly became the norm in the CBM classrooms. None of the teachers reported increased distraction among students due to overt self-talk. In fact, one teacher specifically noted a decrease in non-task oriented conversation during class. While all three teachers reported gains in classwork grades during treatment, one teacher saw especially dramatic grade changes from Cs and Ds to As and Bs. Other positive observations included (a) increased on-task behavior, (b) increased task completion, and (c) increased retention of skills. Two teachers, who also taught reading, observed students transferring general self-instruction components of CBM to reading tasks. Maintenance of self-talk was observed during the retention phase, but at a lower rate than during treatment. Two of three teachers expressed great enthusiasm for CBM and its apparent success. All three teachers reported that they were going to use CBM with classroom instruction.

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CHAPTER 5 DISCUSSION Based on the results, CBM and operant treatments are not better than no treatment for improving the rate of correct math behavior. Even though the control group mean dropped slightly at posttest, overall differences in classroom timings among conditions were not significant. Thus, all three remediation techniques were effective, but none was clearly superior to others. Interestingly, CBM did not slow the rate of problem solving more than the other procedures. Apparently, using self-talk while solving math problems does not add to nor interfere with the overall time required to complete such tasks. Standardized math achievement was improved by some treatments more than others. Performances by students in operant and CBM conditions were better than the no treatment condition. But no significant differences existed between CBM and operant treatment effectiveness. Positive academic gains with both CBM and operant procedures are consistent with current literature. Significant achievement test results may be related to the fact that the test is essentially a power test. It allows time for most or all items to be completed at the student's own pace. It is possible that this format for measuring math gains may be more sensitive to treatment differences than brief timed performances. 52

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Student performances on the timings were suggestive of limited variability on this measure. The results are below expected fluency rates for math skills (Mercer & Mercer, 1985). Many subjects did not get beyond basic math facts on the 2-minute probe. Students had more time to sample a variety of math operations on the achievement test, thus utilizing more than rote memory for problem solving. Learning trends with operant and CBM groups continued over time and did not drop off as predicted by some researchers. Despite claims of poor maintenance of academic skills with CBM and operant procedures, maintenance or retention of achievement due to these treatments persisted over a 2-week period. Thus, the operant group did not require specific generalization instruction for short-term retention to occur. Inclusion of task-specific self-instruction may have facilitated maintenance of skills with the CBM group. Treatment retention in this study may also be due to the intensity of the treatment. The treatment period of nineteen 1-hour treatments was delivered in this experiment, as opposed to six 45-minute sessions provided in another math CBM study (Schunk & Cox, 1986). Due to the hierarchial nature of math instruction, it is reasonable to assume that an intensive, effective treatment will show carry-over effects following treatment. Cognitive behavior modification and operant procedures do not differ with respect to math gains for posttest and retention measures, but social validity ratings may offer additional insight into treatment differences and similarities. Both sets of teachers observed math gains in students'

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classwork and reported that they would incorporate respective treatments into their classroom curricula. Interestingly, student behaviors that are often attributed to operant procedures, such as increased on-task behavior and task completion, also resulted from CBM treatment. The prescribed general task-orienting selfinstruction in this study apparently increased task awareness without requiring extrinsic tangible reinforcement for these behaviors. Transfer of CBM to a nontreatment academic subject was also observed. Two CBM teachers observed their students transferring general self-instruction strategies to reading tasks. This observation is consistent with CBM theory. Operant procedures were not noted to produce similar effects, perhaps because they operate extrinsically upon the student. On the other hand, CBM components must first be learned by students in order to apply the treatment to academic subjects. Cognitive behavior modification does not contribute to disrupting or distracting effects among students as did occur in a previous study (Robin, Armel, & O'Leary, 1975). However, CBM requires a short "break-in" period for some students in order to gain a comfort level while talking out-loud. The operant treatment condition requires additional class time in excess of actual instruction. The operant condition also requires a budget to purchase back-up reinforcers. Teacher training time and time needed for comfortable treatment delivery are basically uniform for both groups. Conclusion Cognitive behavior modification and operant procedures are effective remediation techniques for LD students. Despite polar theoretical etiology, both remediation techniques produce similar desirable classroom

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behaviors. Differences witli treatments exist in terms of specific procedures, available class time for treatment delivery, teachers' roles (modeling), required student behaviors (self-talk), necessary equipment (storage cabinet, tokens), and budget for tangible back-up reinforcers. Transfer of CBM strategies to other academic subjects may be a potential benefit over operant procedures, but there is little evidence to corroborate this speculation. Ultimately, choices between CBM and operant treatments may depend upon aforementioned factors and teachers' training backgrounds and affinity for one treatment over the other. Implications for Future Research Treatment generalization issues should be investigated with future research. Retention of treatment gains was shown over a 2-week period by both treatments in this study; however, retention over longer periods is uncertain. A comparison of generalization to other academic subjects between treatments should also be investigated. Students were observed generalizing CBM to reading in this study, but no data exist comparing generalization efficacy between operant and CBM treatments with academic subjects. Both treatments worked equally well with LD students' math skills in this study, but findings might differ with other academic subjects or exceptional student groups. Future research with operant and CBM treatment effectiveness should be explored with different academic subjects and exceptional student populations. Other time intervals for classroom math measures should be investigated. Although 2-minute classroom timings produced treatment

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gains, the short time interval may not be sensitive enough to discriminate effectiveness between treatments.

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APPENDICES

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APPENDIX A TIMINGS PROBE SHEET 8 +7 9 ±9 3 ±5 4 +2 6 +7 6 7 i2 :6 2 -2 8 -4 9 -1 10 52 84 43 63 11 17 13 15 12 ±9 i4 +13 +24 +1S 4 :8 :7 :2 :Q 24 73 56 69 67 86 38 ±8 ±9 +17 +^ +64 -2 -3 59 -19 63 -22 95 -62 28 85 46 75 36 43 37 19 48 67 26 A +m +2S +4S + 71 i3 65 -26 28 -19 84 -46 281 +304 770 746 552 945 242 850 141 +21S +132 +453 +2Zg -139 -312 -m 372 463 434 552 -235 -204 :5g :ZZ 223 945 321 :49 :9S :54 58

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APPENDIX B TEACHER REFERENCE--CBM 1 . Remember to explain the procedure with the following: "For the next few weeks, we will be doing our math in a different way. Watch how I do a problem with this new way." 2. Remember to model a sample problem at the beginning of each CBM session. Example statements: 1 . "What is my assignment for today? It's math problems 1 through 15." 2. "I need to start working now." 3. "What kind of problem is this, addition or subtraction? What does the sign say?" 4. "OK, it's addition, that means...." 5. "Good, I've finished that problem. I need to keep working." 6. "Good, I'm finished. I've checked my work and I'm done." 3. Prompt the students to talk to themselves as they work. 4. Remember to keep reinforcers out of sight during CBM treatment. Instructions for administering timings: "I am passing out some math problems (face down) for you to do. When I say go, turn over your papers and begin working. Work as quickly as you can without making careless mistakes. Any questions? Go." After 2 minutes, say "stop" and collect the papers. 59

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APPENDIX C TEACHER REFERENCE--OPERANT PROCEDURES 1 . Clearly explain the task objectives and goals. 2. Demonstrate the skill. 3. Provide drill and practice. 4. Give corrective feedback. 5. Remember to explain the reinforcement: "You will get one token (chip) for each correct addition or subtraction problem you complete in class. You will be given the tokens (chips) you earn near the end of class." Back-up reinforcers will be explained as: "These are items that you can buy with your tokens." 6. Check classwork 15 minutes prior to end of class and place earned tokens in students' envelopes. 7. Allow students to exchange tokens for back-ups 5 minutes prior to end of class. 8. Remember to close and lock the back-up cabinet after each operant session. 60

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APPENDIX D INVENTORY ITEM COST (# of tokens^ Sticker 20 Eraser 25 Large sticker 25 Story book 30 Snoopy Pencil 30 Cowboy or Indian Character 30 Ninja Character 35 Box of Crayons 40 Large Pencil 40 4u Designer School Folder 50 Snoopy Notepad 50 Pencil Sharpener 50 Matchbox Car or Truck 60 Four-color Pen 60 Pencil Case 60 Lifesaver Scented Marker 70 Barbie Doll Outfit 70 California Raisin Character 80 61

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APPENDIX E TREATMENT INTEGRIPt' RATING Dear Rater; Please circle the number of each item observed during the videotaped class session. 1 . Did the teacher model at least one sample problem at the beginning of class? 2. Did the teacher talk to herself as she modeled the sample problem? 3. Were tokens given to students for correct classwork? 4. Were students instructed to talk to themselves while solving math problems? 5. Was there opportunity for exchange of tokens for back-up reinforcers prior to the end of class? 6. Were back-up reinforcers available for display in the classroom?

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APPENDIX F SOCIAL VALIDITY RATING INTERVIEW 1 . How long did it take for you to fee! comfortable in delivering the treatment? 2. Were there any negative side-effects to the treatment? 3. Were there any positive side-effects to the treatment? 4. Would you adopt this treatment for regular use in your classroom? Additional comments:

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Lovitt, T. C, & Hansen, C. L. (1976). The use of contingent skipping and drilling to improve oral reading and comprehension. Journal of Learning Disabilities. 9^481 -487. Luria, A. (1961). The role of speech in the regulation of normal and abnormal behaviors . New York: Liveright. McMillan, J. H., & Schumacher, S. (1984). Research in education: A conceptual approach. Boston: Little, Brown & Company. Meichenbaum, D. (1977). Cognitive behavior modification: An integrative approach. New York: Plenum Press. Meichenbaum, D. (1980). Cognitive behavior modification with exceptional children: A promise yet unfulfilled. Exceptional Children Quarterly. 1, 83-88. Meichenbaum, D. (1985). Teaching thinking: A cognitive-behavioral persepctive. In S. Chipman, J Segal, & R. Glaser (Eds.), Thinking and learning skills (Vol. 2): Research and open questions (pp. 407-426). Hillsdale, NJ: Lawrence Eribaum Associates. Meichenbaum, D., & Asarnow, J. (1979). Cognitive-behavioral t modification and metacognitive development: Implications for the classroom. In P. C. Kendall & S. D. Hollon (Eds.), Cognitivebeh avioral interventions: theorv. re.search. and procedures (pp. 1 1 35). New York: Academic Press. Meichenbaum, D. H., & Goodman, J. (1971). Training Impulsive children to talk to themselves: A means of developing self-control. Journal of Abnormal P svchology. 77. 115-126. Mercer, C. D. (1987). Students with learning disahiliti^ .q (3rd ed ) Columbus, OH: Charles E. Merrill. Mercer, C. D.. & Mercer, A. R. (1985). Teaching students with learninn prgblemg (2nd ed.). Columbus, OH: Charles E. Merrill. Miller, L K. (1980). Principles of evervdav behavior analvsi.s (2nd ed ) Monterey, CA: Brooks/Cole. Robin, A. L., Armel, S., & O'Leary, K. D. (1975). The effects of selfinstruction on writing deficiencies. Behavior Therapy , 178-187. Rooney, K. J., & Hallahan, D. P. (1985). Future directions for cognitive behavior modification research: A quest for cognitive changp Remedial a nd Special Fdnra^ inn, k 46-51.

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69 Tarver, S. G. (1986). Cognitive behavior modification, direct instruction and holistic approaches to the education of students with learning disabilities. Journal of Learning Disabilities. 19. 368-375. Throne, J. M. (1973). Learning disabilities: A radical behaviorist point of view. Journal of Learning Disabilities. 6. 543-546. Tollefson, N., Tracy, D. B., Johnsen, E. P., & Chatman, J. (1986). Teaching learning disabled students goal-implementation skills. Psychology in the Schools. 23. 194-204. Torgeson, J. K. (1977). The role of nonspecific factors in the task performance of learning disabled children: A theoretical assessment Journal of Learning Disabilities. 10. 27-34. Treiber, F. A., & Lahey, B. B. (1983). Toward a behavioral model of academic remediation with learning disabled children. Journal of Learning Disabilities. 16. 111-116. Vygotsky, L. (1962). Thought and language. New York: Wiley. Winer, B. J. (1971). Statistical principles in experimental design. New York: McGraw-Hill. Wong, B. Y. (1985). Issues in cognitive-behavioral interventions in academic skill areas. Journal of Abnormal Child Psvcholnnv 13, 425-442. ^ Wong, B. Y., & Jones, W. (1982). Increasing metacomprehension in learning disabled and normally achieving students through selfquestioning training. Learning Dis ability Quarterly 5, PP»-P4n

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BIOGRAPHICAL SKETCH Peter Pavchinski was born in Canada in 1954 to immigrant parents. Having no money or possessions, his parents risked their lives by fleeing the oppression of war-torn eastern Europe. Pete was able to learn the lessons of survival first-hand from his parents. After living in Canada for 8 years, Pete's family moved to the United States to seek greater opportunity. In concert with this credo, his parents offered him musical training in several instruments. Despite required practice time for proper beats and note values, he still managed to acquire a penchant for baseball and tennis. While at Rutgers University, Pete sampled a number of academic disciplines. He first enjoyed the natural sciences, but later changed to the study of Russian language. It wasn't until transferring to New College of the University of South Florida, a unique and challenging school, that his studies became concentrated in psychology. Several years later, Pete earned his Master of Arts and Education Specialist degrees in school psychology from the University of South Florida. Pete is currently employed by the Duval County School Board as a school psychologist in Jacksonville, Florida. Pete has been instrumental in expanding the role of school psychologists in Duval County public schools. He has developed and implemented suicide awareness and training programs, behavior management workshops, and mental health programs for students. 70

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Pete is married to a loving and conscientious wife who is pursuing degree at the University of Florida.

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Jetfar^ P\B]raden, Chairman Assistant f^rofessor 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. Paul W. Fitzgerkfd 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. Cecil D. Mercer Professor of Special Education

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This dissertation was submitted to the Graduate Faculty of the College of Education and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. August, 1988 rf^A^^ fV ^ . ?97vJJ-fN^ Dean, College of Education Dean, Graduate School