The effects of stimulus modality on the development of equivalence relations in children with mild disabilities

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The effects of stimulus modality on the development of equivalence relations in children with mild disabilities
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Thesis (Ph. D.)--University of Florida, 1993.
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by Lori Jean Marks.
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THE EFFECTS OF STIMULUS MODALITY ON THE
DEVELOPMENT OF EQUIVALENCE RELATIONS
IN CHILDREN WITH MILD DISABILITIES






BY






LORI JEAN MARKS


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

1993













ACKNOWLEDGMENTS

I would like to thank my committee members, Roy Bolduc,

Mary K. Dykes, William Reid, Paul Sindelar, and William

Wolking for their valuable feedback, guidance, and

encouragement. My very warmest appreciation is extended to

mentor and friend, William Wolking, for sharing with me his

valuable time, his inspirations, and his expertise in

experimental design and data analysis.

I wish to extend my sincere gratitude to Lisa Hopkins

for allowing me to conduct research in her classroom. I would

also like to thank the students at Stephen C. Foster

Elementary School for being so willing to work and for adding

some extra cheer to in my life.

Finally, very special thanks are offered to my husband,

Mike, for all the loving support and encouragement he gave me

during the years that I was a doctoral student.















TABLE OF CONTENTS
Pace

ACKNOWLEDGMENTS ......................................... ii

LIST OF TABLES ..................................... ...... V

LIST OF FIGURES ......................................... vi

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

CHAPTERS

I INTRODUCTION ........................................ 1

Introduction to the Problem ........................ 1
Stimulus Equivalence ................................ 3
Statement of Purpose ................................ 6
Rationale ........................................... 8
Delimitations ....................................... 12
Limitations ........................................ 12
Summary ............................................... 12

II REVIEW OF THE LITERATURE ........................... 14

Selection of Relevant Literature .................... 14
Historical Background ............................... 16
Benefits of Stimulus Equivalence Instruction ....... 25
Emergence of Untaught Skills .................... 25
Skill Generalization ............................. 32
Long Term Maintenance of Equivalence Classes .... 40
Using the Stimulus Equivalence Model to Teach
Academic Skills ..................................... 42
Vocabulary and Reading Comprehension ............ 43
Spelling ......................................... 48
Money Skills ..................................... 50
Pre-arithmetic Skills ........................... 54
Foreign Language Vocabulary Development ......... 55
Variables that Influence Equivalence Class
Development ......................................... 56
Nodality ......................................... 57
Testing Sequence ................................. 60
Stimulus Modality ................................ 61
Summary ............................................. 63










Page

III METHOD ............................................. 65

Subjects ............................................ 65
Setting ............................................. 67
Apparatus ........................................... 68
Stimuli ............................................. 68
Variables Under Investigation ...................... 73
Experimental Design ............................... 76
Experimental Procedures ............................ 77
Experiment 1 ........................................ 80
Experiment 2 ........................................ 83

IV RESULTS ............................................. 87

Student 1 ........................................... 87
Student 2 ........................................... 96
Student 3 .......................................... 105
Student 4 .......................................... 112
Student 5 .......................................... 118
Student 6 .......................................... 122
Student 7 .......................................... 127
Questions Under Investigation ...................... 130
Development of Equivalence Relations ............ 130
Rate of Equivalenc Class Development ............ 133
Maintenance of Equivalence Relations ............ 135
Summary ............................................ 137

V DISCUSSION ......................................... 156

Equivalence Class Development ...................... 156
Effects of Modality on the Rate of Equivalence
Class Development .................................. 158
Maintenance ........................................ 160
Methodological Concerns ............................ 162
Problems and Limitations ........................... 164
Practical Implications ............................. 168
Further Research ................................... 171

REFERENCES .............................................. 175

APPENDICES

A DEFINITION OF TERMS ........................... 183

B PERMISSION FORMS .............................. 186

BIOGRAPHICAL SKETCH ..................................... 192














LIST OF TABLES

Table Page

3-1 Summary of Student Characteristics ................ 66

3-2 Equivalence Classes Trained in Experiment 1 ...... 82

3-3 Equivalence Classes Trained in Experiment 2 ...... 85

4-1 Evidence of Equivalence Class Development ........ 132

4-2 Percentage of Equivalence Relations Maintained ... 136














LIST OF FIGURES

Figure Page

2-1 Stimulus Equivalence paradigm used by Sidman,
1971, and Sidman and Cresson, 1973 ................ 18

2-2 Stimulus Equivalence paradigm used by Lazar et
al., 1984......................................... 28

2-3 Stimulus Equivalence instructional model used by
Osborne and Gatch, 1989 ........................... 47

2-4 Schematic representation of the stimulus
equivalence class demonstrated by McDonagh et
al., 1984.......................................... 52

2-5 Schematic representation of the teaching and
testing phases in the development of the
stimulus equivalence class demonstrated by
McDonagh et al., 1984 ............................. 53

2-6 Diagram of four-member equivalence classes with
different number of nodes......................... 58

3-1 Positions of sample and comparison stimuli
on the computer screen............................ 70

3-2 Stimulus sets that compose the all-visual and
cross-modal equivalence classes in Experiments 1
and 2.............................................. 79

4-1 Student 1. Percentage of correct responses
in Experiment 1.................................... 139

4-2 Student 1. Percentage of correct responses
in Experiment 2.................................... 140

4-3 Student 2. Percentage of correct responses
in Experiment 1.................................... 142

4-4 Student 2. Percentage of correct responses
in Experiment 2 ................................... 143

4-5 Student 3. Percentage of correct responses
in Experiment 1 .................................... 145









Page

4-6 Student 3. Percentage of correct responses
in Experiment 2.................................... 146

4-7 Student 4. Percentage of correct responses
in Experiment 1.................................... 147

4-8 Student 4. Percentage of correct responses
in Experiment 2 ................................... 148

4-9 Student 5. Percentage of correct responses
in Experiment 1.................................... 149

4-10 Student 5. Percentage of correct responses
in Experiment 2.................................... 150

4-11 Student 6. Percentage of correct responses
in Experiment 1.................................... 151

4-12 Student 6. Percentage of correct responses
in Experiment 2 ................................... 152

4-13 Student 7. Percentage of correct responses
in Experiment 1.................................... 153

4-14 Student 7. Percentage of correct responses
in Experiment 2.................................... 154

4-15 Number of training and testing sessions
required for equivalence class development........ 155















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 STIMULUS MODALITY ON THE DEVELOPMENT OF
EQUIVALENCE RELATIONS IN CHILDREN WITH MILD DISABILITIES

By

Lori Jean Marks

August, 1993



Chairman: William D. Wolking
Major Department: Special Education


The purpose of this study was to investigate the effects

of stimulus modality on equivalence class development. Time-

telling skills were taught and tested under two conditions of

stimulus presentation: an all-visual condition, and a cross-

modal condition. Seven elementary school students with mild

disabilities participated as subjects. The students were

given computer-based matching-to-sample instruction within a

stimulus equivalence model. Two experiments were conducted

using a single subject alternating treatments design within a

withdrawal strategy.

In Experiment 1 students were taught conditional

relations for six all-visual and six cross-modal equivalence

classes. Four of the seven students reached criterion level









on one of the experimental conditions. On post-training

equivalence tests, one student demonstrated stimulus

equivalence for all of the cross-modal classes and two of the

all-visual classes. A total of seven cross-modal equivalence

relations and no all-visual equivalence relations were

developed across the three remaining students.

Because low learning rates were demonstrated during the

training phase in Experiment 1, the number of equivalence

classes trained in Experiment 2 was reduced. In Experiment

2, students were taught conditional relations for two all-

visual and two cross-modal equivalence classes. All students

had higher rates of learning and were able to reach the

training criterion with the reduced set size. A total of 23

all-visual and 24 cross-modal equivalence relations were

developed across the seven students in Experiment 2. No

reliable differences in the expediency of formation of all-

visual or cross-modal equivalences were found with the

smaller set size.

Maintenance of equivalence relations was

investigated in Experiment 2. A majority of the equivalence

relations maintained at 2-week and 4-week intervals. There

were no clear differences between the maintenance

performances of all-visual and cross-modal relations.















CHAPTER I

INTRODUCTION

Introduction to the Problem

To meet the growing demands of our complex society,

education must become more efficient. A solution to

educational inefficiency is to use a technology of teaching

based on principles of learning from behavioral science

(Skinner, 1960). Under experimental conditions, behavioral

scientists have identified a number of interventions that

address the learning problems of students with mild

disabilities (Axelrod, 1992; MacMillan, Keogh, & Jones,

1986). Applied instructional interventions based on

behavioral technology have proven to be highly effective

(Selinske, Greer, & Lodhi, 1991; Sulzer-Azaroff & Mayer,

1986). Despite the number of successful applications of the

natural science principles of behavior to practical classroom

use, there remains a disparity between available behavioral

technology and educational practice. The failure to

translate scientific knowledge of learning into a technology

of instruction may be a major variable affecting the widely

recognized need for more effective schooling for students

with mild disabilities.









The formation of equivalence relations, or stimulus

equivalence, is an instructional procedure derived from the

experimental analysis of behavior. Stimulus equivalence has

been successfully used under experimental conditions to teach

a variety of skills to a wide range of student populations.

Although stimulus equivalence was originally intended to

explain rules of verbal behavior and language acquisition,

applied researchers have shown that the procedures used to

develop equivalence relations can be an effective method for

teaching academic subject matter.

Equivalence class formation typically has been

investigated in a delayed matching-to-sample format.

Matching-to-sample is a procedure in which, in the presence

of a particular stimulus, an individual is taught to select a

corresponding stimulus from an array of stimuli (Green,

Mackay, McIlvane, Saunders, & Soraci, 1990). A matching-to-

sample trial begins when a sample stimulus is presented

(e.g., the printed word "cat"). The learner is required to

respond in some way to the sample stimulus, usually by

touching it, and subsequently an array of comparison stimuli

are displayed (e.g., pictures of a cat, a dog, and a rabbit).

One comparison stimulus is defined as correct (the cat, in

this example), and the others) as incorrect (e.g., the dog

and the rabbit). Conditional relations between stimuli









(e.g., the printed word "cat" and the picture of a cat) are

established by reinforcing the learner for selecting the

correct comparison and extinguishing incorrect choices.

Stimulus Equivalence

Not all conditional relations are equivalence relations

(Sidman & Tailby, 1982). An equivalence relation is defined

by the properties of reflexivity, symmetry, and transitivity.

To fulfill the definition of an equivalence relation, a

relation (R) must possess all three properties (Sidman,

Rauzin, Lazar, Cunningham, Tailby, & Carrigan, 1982).

Therefore, tests for the properties of reflexivity, symmetry,

and transitivity are necessary to confirm equivalence class

formation.

The reflexive property requires a stimulus to be related

to itself (aRa; "a" is related to "a"). A test of

generalized identity matching is used to determine whether

the equivalence relation has the property of reflexivity.

For example, when given a picture of a mouse as a sample

stimulus, the reflexive property is demonstrated if, without

reinforcement, the learner selects the picture of the mouse

that is presented as a choice among comparison stimuli.

Symmetry, or functional sample-comparison reversibility,

requires sample and comparison stimuli to be interchangeable.

If sample "a" is conditionally related to "b" (aRb), then the

relation must also hold true when "b" is the sample and "a"

is the comparison (bRa). Suppose a student is taught to









match a picture of a cat when presented with the printed word

"cat" as a sample stimulus (aRb). Symmetry is demonstrated

when the student can, without further training or

reinforcement, match the printed word "cat" when presented

with the picture of the cat as a sample stimulus (bRa).

Transitivity, the final property required to confirm

equivalence class formation, involves the introduction of a

third stimulus ("c"). Two conditional relations, aRb and

bRc, are established using the matching-to-sample procedure.

The test of transitivity requires the emergence of the

untaught relation, aRc, in which the student matches the

sample stimulus from the first conditional relation ("a") to

the comparison from the second ("c"). For example, having

learned to relate the printed word "cat" as a sample to the

picture of a cat as a comparison (aRb), and the picture of a

cat as a sample to the spoken word "cat" as a comparison

(bRc), the student must then be able to relate the printed

word "cat" to the spoken word (aRc).

Tests for reflexivity, symmetry, and transitivity must

be given without programmed consequences (Sidman, 1990).

When all three properties are demonstrated through testing,

the stimuli involved in the conditional relations are related

by equivalence (Saunders & Green, 1992). Stimuli in an

equivalence relation are regarded as members of an

equivalence class. If tests do not confirm the relational

properties of reflexivity, symmetry, and transitivity, then









the relation is not an equivalence relation. Instead, the

stimuli involved are only related conditionally in an

"if...then..." relation (Mackay & Sidman, 1984).

Despite the many demonstrations and confirmations of

stimulus equivalence, little is known about variables that

expedite or retard equivalence class development (Green,

1990). A variable that may effect the efficiency of

equivalence class development and the longevity of retention

is the modality of stimulus presentation. The evidence

allows for the conclusion that persons with mental

retardation develop equivalence classes that include auditory

stimuli more quickly than classes consisting entirely of

visual stimuli (Green, 1990; Sidman, Wilson-Morris, & Kirk,

1986). The effects of the modality of stimulus presentation

on the formation of equivalence classes with other

populations has not yet been researched.

Instruction that establishes equivalence classes has

implications for teaching all children, but learning outcomes

may be especially beneficial to students with mild

disabilities. Students with mild disabilities typically

exhibit deficits in academic and language skills. These

students often have problems remembering auditory and visual

stimuli, and they have difficulty in maintaining and

generalizing skills (Bos & Vaughn, 1988; Mercer, 1987).

Educational benefits of stimulus equivalence instruction

include the emergence of untrained skills (Sidman, 1971),









generalization of skills (Mackay & Ratti, 1990; Stoddard,

Bradley, & McIlvane, 1987), and maintenance of skills for

long periods of time (Saunders, Saunders, & Spradlin, 1990;

Saunders, Saunders, Kirby, & Spradlin, 1988). The benefits

of stimulus equivalence instruction closely match the needs

of students who have mild disabilities.

The match between the academic needs of students with

mild disabilities and learning outcomes reported in stimulus

equivalence research indicates that students with mild

disabilities should profit academically from instruction that

results in the development of equivalence classes.

Investigations of stimulus equivalence instruction with

students with mild disabilities, however, is limited. Ferro

(1990) investigated the effects of all-visual stimulus

equivalence instruction on the learning of bilingual students

who were identified as learning disabled in their native

countries. Ferro's is the only published research report on

stimulus equivalence instruction with students with mild

disabilities, however in a chapter on the teaching

implications of the stimulus equivalence model, Stromer

(1991) reported that he had used the model to teach reading

and spelling to learning-disabled children.

Statement of Purpose

This study was conducted to determine whether stimulus

equivalence instruction is an effective technique for

teaching basic academic skills to students with mild









disabilities. Time-telling was the specific skill taught.

Two methods of stimulus presentation were investigated. The

first method used three forms of visual stimuli. The second

method incorporated a spoken stimulus and two forms of visual

stimuli. Both methods were conducted within a desktop

computer HyperCard environment. The following questions were

addressed:

1. When provided with matching-to-sample computer-

based instruction, will students with mild

disabilities develop equivalence classes that are

composed of all-visual stimuli and classes composed

of cross-modal stimuli?

2. Will equivalence classes composed of all-visual

stimuli and classes composed of cross-modal stimuli

emerge at the same rate?

3. Will performance of skills developed through

stimulus class formation be maintained after 2- and

4-week follow-up intervals?

4. On maintenance probes, are there performance

differences between classes that consist entirely

of visual stimuli and those that include cross-

modal stimuli?

Importance

This study is important for several reasons. First, it

will contribute to data related to the formation and

maintenance of equivalence classes that include both spoken









and visual stimuli, and those that consist only of visual

stimuli. Second, this study will provide information about

the effectiveness of the stimulus equivalence procedure as a

teaching technique for students with mild learning problems.

Third, this study will add to research data on the use of the

stimulus equivalence paradigm to teach functional academic

skills. Specifically, this study will address the use of the

equivalence procedure to teach time-telling skills, an

academic subject that has not been addressed by stimulus

equivalence researchers. Fourth, this study will add to data

regarding the applicability of a traditionally experimental

procedure to the classroom setting. Finally, this study will

address the usefulness of the desktop computer HyperCard

environment for presentation of spoken and visual stimuli in

stimulus equivalence development.
Rationale

The stimulus equivalence paradigm has been used to

instruct several subject populations. Much of the research

has been with individuals with moderate to severe mental

retardation (e.g., Dixon & Spradlin, 1976; Mackay, 1985;

Sidman, 1971; Sidman & Cresson, 1973). A number of studies,

however, have involved other populations, including normally

functioning young children (Gast, VanBiervliet, & Spradlin,

1979; Joyce & Wolking, 1989), children with hearing

impairments (Osborne & Gatch, 1989), adolescents who had

sustained brain injuries (Joyce, Joyce, & Wellington, in









press), and students with limited proficiency in English

(Ferro, 1990). Equivalence class formation has been produced

in all human populations heretofore studied.

Sidman et al. (1986) and Green (1990) conducted the only

investigations that have systematically addressed the

modality of stimulus presentation in equivalence class

formation. The participants in both of these studies were

young men and women with moderate to severe mental

retardation. Both studies demonstrated that when equivalence

relations developed, classes that included cross-modal

stimuli emerged in fewer training and testing trials than did

classes consisting entirely of visual stimuli. The

accelerated emergence of equivalence classes comprised of

cross-modal stimuli may not be evident in all populations.

Sidman et al. (1986) also reported that young children with

normal intelligence showed no difference between the

development of equivalence classes that were composed of

cross-modal stimuli and those consisting only of visual

stimuli. The effects of modality of stimulus presentation in

the development of equivalence classes in students with mild

disabilities is unknown.

The stimulus equivalence procedure can be used as a

model for teaching academic skills. Most stimulus

equivalence investigations have been conducted in carefully

controlled laboratory environments; a number have resulted in

potentially functional academic skills. Studies conducted in









classroom settings have provided evidence that supports a

tentative conclusion that the stimulus equivalence procedure

offers an effective and efficient instructional technique for

most students (Ferro, 1990; Hollis, Fulton, & Larson, 1986;

Joyce & Wolking, 1989; Osborne & Gatch, 1989). Application,

however, has been limited to the following academic areas:

vocabulary and reading comprehension (Joyce & Wolking, 1989;

Sidman, 1971; Sidman & Cresson, 1973), money skills

(McDonagh, McIlvane, & Stoddard, 1984; Stoddard et al.,

1987), spelling (Mackay, 1985), number concepts (Gast et al.,

1979), and foreign language learning (Ferro, 1990; Joyce et

al., in press).

Microcomputers and Stimulus Equivalence

With appropriate programming, the microcomputer can

present instruction based on well-documented principles of

learning and behavior. The microcomputer has become a

popular medium for presenting stimulus equivalence

instruction. Unlike elaborate electro-mechanical apparatus

traditionally used to study equivalence class formation, the

availability and ease in programming the modern microcomputer

makes the microcomputer a tool that easily adapts the

stimulus equivalence paradigm for widespread classroom use.

For example, the microcomputer can support a high rate of

student response; rapidly process information provided by

student responses; provide immediate feedback for each

response; analyze correct and incorrect responding and









accordingly prescribe appropriate instructional

contingencies; arrange stimulus materials so that errors in

learning are decreased; and automatically save, chart, and

analyze student data (Dube & Mcllvane, 1989; LeBlanc, Hoko,

Aangeenbrug, & Etzel, 1985).

There is evidence that the microcomputer can effectively

provide instruction of new skills to students with mild

disabilities (Ellis & Sabornie, 1986; Fuchs, Fuchs, &

Hamlett, 1989; Horton, Lovitt, Givens, & Nelson, 1989;

Woodward, Carnine, & Gersten, 1988). The effectiveness of

computer-based instruction depends on well-designed software.

Technological sophistication of the microcomputer far exceeds

the sophistication of teaching procedures often used in

commercial educational software (LeBlanc et al., 1985).

Furthermore, operant learning principles are not often

systematically incorporated in software design (Tudor &

Bostow, 1991). Most educators have limited experience with

computer programming and software development and therefore

are unable to develop their own instructional programs.

Educators are dependent upon developers to provide software

that teaches effectively and efficiently. Developers must

begin to incorporate and evaluate the effects of principles

of learning and behavior in their software design, and

provide educators with empirical evidence of the software's

effectiveness.









Delimitations

This study is delimited in several ways. The study will

be conducted in Alachua county, a medium-sized county located

in north-central Florida. Participants in the study will be

elementary students with mild disabilities. Only students

who are enrolled in public schools and who are provided with

special education services will be included. No

consideration will be given to the sex or socioeconomic

status of the participants.

Limitations

The findings of this study should not be generalized to

middle-or high-school grade students or to students without

disabilities. Generalization to non-computerized

presentation of stimuli or to academic tasks other than time-

telling tasks should not be made without systematic

replications. Seven students will participate in this study.

The small number of students may not provide a convincing

basis for conclusion regarding all students of similar age

with mild disabilities.

Summary

The systematic development of equivalence classes has

strong educational implications. Stimulus equivalence can

result in the emergence of large numbers of previously

untrained and unreinforced performances. Consequently, the

number of performances that must be directly taught in the

classroom is reduced. Generalization of skills and long term









maintenance of relations are additional benefits of

equivalence relations. Researchers have shown that stimulus

equivalence can be an effective and efficient procedure for

teaching academic skills. This study will extend the

stimulus equivalence research to a new student population and

academic skill. The emergence of time-telling skills in

students with mild disabilities will be investigated. In

addition, the modality of stimulus presentation, a variable

that may expedite the formation of equivalence classes, will

be investigated.

A review of research related to this study is presented

in Chapter II. The methods and procedures used in this

research are described in Chapter III. The results are

reported in Chapter IV and the discussion and research

implications are presented in Chapter V.















CHAPTER II

REVIEW OF THE LITERATURE

The purpose of this chapter is to summarize and analyze

research on stimulus equivalence development. The review of

stimulus equivalence research is selective; criteria for

inclusion in the review and the sources of selection are

addressed first. The five areas of stimulus equivalence

research discussed in this chapter are: a historical

background of equivalence class development, benefits of

stimulus equivalence instruction, use of the stimulus

equivalence model to teach functional academic skills, and

variables that may enhance the development of equivalence

classes. The chapter concludes with an examination of the

implications of previous research for the present study.

Selection of Relevant Literature

The goal of the literature search was that of locating

and examining all stimulus equivalence studies that were

relevant to the application of the stimulus equivalence model

for teaching academic skills. The major criterion for

inclusion of a stimulus equivalence study was that the study

must have tested for most or all of the relations between

stimuli as defined by Sidman and Tailby (1982). There are

many references to "equivalence" and "stimulus equivalence"









in studies of relational learning. Many such referents

concern functional equivalence rather than stimulus

equivalence. In functional equivalence, members of a

stimulus class are considered "equivalent" because of their

functional control over behavior (Goldiamond, 1966).

Functional equivalence is not identified by tests of

reflexivity, symmetry, and transitivity, as is stimulus

equivalence. Studies of functional equivalence, and other

studies that assumed but did not test for stimulus

equivalence, were not included in the review.

Much of the research on stimulus equivalence has been

conducted in laboratory environments and has been directed

toward the identification of the limits of equivalence class

development. Studies that were determined to be irrelevant

to the application of the stimulus equivalence model for

teaching useful academic skills were not included in the

review. For example, a recent focus of stimulus equivalence

research is the study of contextual control over equivalence

class development. Contextual control has little relevance

to the proposed study, consequently studies of contextual

control were not included in the review. Furthermore, only

studies that had reports that contained a description of

subjects, method of stimulus presentation, teaching and

testing sequences, and results, were included.









The major sources for locating relevant literature were

the reference sections of related articles, chapters, and

books. Other sources included Current Index of Journals in

Education (CIJE), Educational Resources Information Center

(ERIC), Library User Information Service (LUIS),

Psychological Abstracts Information Services (PsycINFO), and

a manual search through volumes of the Journal of the

Experimental Analysis of Behavior.

Historical Background

Many researchers have shown that when humans are taught

certain conditional relations among stimuli, other stimulus

relations often emerge, or become related to each other in

new ways, without explicit teaching. The emergence of

specific untrained relations confirms the formation of an

equivalence relation. Although the instructional model that

develops stimulus equivalence is virtually unheard of in the

typical educational environment, stimulus equivalence is a

well-documented and reliable phenomenon that has much to

offer academic instruction.

The first demonstrations of the stimulus equivalence

paradigm involved teaching receptive reading skills to

persons with severe mental retardation (Sidman, 1971; Sidman

& Cresson, 1973). Sidman's (1971) preeminent study

demonstrated an instructional procedure that resulted in the

emergence of reading comprehension. Reading comprehension

was defined as a visual task that emerged from a sequence of









explicitly taught and previously established auditory-visual

conditional relations. The participant in Sidman's study

demonstrated the formation of 20 four-member classes of

equivalent stimuli. Each stimulus set contained a dictated

name (A), a picture (B), a printed word (C), and the

participant's oral naming of the stimuli (D). Figure 2-1

illustrates the stimulus equivalence paradigm used in

Sidman's studies (Sidman, 1971; Sidman & Cresson, 1973). For

ease of presentation in this chapter, conditional relations

are named by a code for the sample stimulus and its

designated correct comparison. For example, AB denotes a

conditional relation in which A is the sample and B is the

correct comparison.

Sidman (1971) demonstrated, in the use of baseline

tests, that of the six basic conditional relations, the

participant was only able to match pictures to dictated names

(AB) and to orally name pictures (BD). The participant was

trained to match three-letter printed words to their

corresponding dictated word samples (AC). After training on

the AC conditional relation, three performances emerged

without additional teaching. On post-tests, in addition to

the AC performances, the participant was able to match

printed words to picture samples (BC), pictures to printed

word samples (CB), and he was able to orally name printed

words (CD).


































Figure 2-1. Stimulus Equivalence paradigm used by Sidman,
1971 and Sidman and Cresson, 1973.


Dictated Oral
AlI C __I I I I wasiner I









The results of Sidman's (1971) study were replicated by

Sidman and Cresson (1973) with two additional participants

who were severely mentally retarded. Baseline tests for both

participants showed that performance on all relations were at

chance levels. Participants were taught the following

sequence of relations: (a) identity matching of printed words

(CC), (b) auditory comprehension that required participants

to match pictures to dictated names (AB), (c) auditory

receptive reading that required participants to match three-

letter printed words to their corresponding dictated word

samples (AC) for 9 words, (d) auditory receptive reading (AC)

for the 9 words taught plus 5 additional words, and (e)

auditory receptive reading (AC) for the entire set of 20

words. Post-tests showed that the teaching sequence caused

four untaught relations to emerge. Without specific training

on the following four skills, participants were able to

orally name pictures (BD), match printed words to pictures

(BC), match pictures to printed words, and orally name

printed words (CD).

Sidman's findings were unexpected because the findings

contradicted verbal mediation theory. At that time, verbal

mediation theory held that dissimilar stimuli could be

established as equivalent by producing a common name for the

stimuli (Spradlin & Saunders, 1984). The participants in the

Sidman studies did not produce a common name for stimuli









until auditory receptive relations had already been

established. The unexpected findings sparked renewed

interest in the study of verbal mediation.

Sidman's studies were precedents in the use of automated

teaching machines for effective instruction of reading

comprehension skills to students with severe learning

deficits. Except for constructing the teaching sequences in

advance, the use of automated teaching equipment required

little teacher intervention. Sidman and Cresson (1973) did

indicate, however, that potentially significant aspects of

the methods of instruction, such as reinforcement schedules

and correction procedures, were changed several times to

overcome difficulties that were encountered in teaching. The

lack of undocumented changes in instructional procedures made

in Sidman and Cresson's (1973) study make replications of the

study problematic.

Sidman and Tailby (1982) and Sidman, Rauzin, Lazar,

Cunningham, Tailby, and Carrigan, (1982) clarified the

processes involved in stimulus class development by

describing the mathematically-based properties that

equivalence relations must possess. Procedures for

generating matching-to-sample performances may result in

conditional discrimination that do not form an equivalence

relation. Sidman and Tailby (1982) and Sidman, Rauzin,

Lazar, Cunningham, Tailby, and Carrigan (1982) described the

three properties--reflexivity, symmetry, and transitivity--









that are necessary to distinguish between conditional

discrimination performances and the generation of an

equivalence relation as a result of conditional-

discrimination procedures.

According to the three defining properties of stimulus

equivalence, certain relations may be taught, and other

relations must be left to emerge. Sidman and Tailby (1982)

noted that it is not appropriate to teach identity matching

(e.g., AA or BB) because of the reflexivity requirement that

specifies that a stimulus must be unconditionally related to

itself. If a student is taught the conditional relation

'AA', the researcher cannot be certain that the relation is

truly reflexive; there is no assurance that the relation is

not being controlled by an unidentified extraneous feature.

There are inconsistencies in Sidman and Tailby's (1982)

report regarding the issue of teaching identity matching.

Sidman and Tailby (1982) noted that it does not suffice to

teach identity matching (e.g., the conditional relations,

'AA' and 'BB'). In the same report, in their review of

earlier studies (ie., Sidman, 1971 and Sidman & Cresson,

1973), the authors noted that the participants were capable

of generalized identity matching, and thereby met the

reflexivity criterion. On the contrary, Sidman and Cresson

(1973) reported that both participants in the study had poor

scores on the word-word matching protests (CC) and were









subsequently taught word-word identity matching for each of

the 20 printed words involved in the conditional

discrimination.

Of the studies reported in the present review of the

literature, there are only two other instances of

nonconformance with the definitive properties of equivalence

relations. One (Sidman, Cresson, & Willson-Morris, 1974)

occurred prior to the publication of Sidman and Tailby's

(1982) description of the defining properties of stimulus

equivalence, and the other (Hollis et al., 1986) occurred

after the 1982 publication. Both of these studies taught

identity matching of stimuli before the other conditional

relations were taught. For participants who needed the

instruction, Hollis et al. (1986) taught identity matching of

both pictures and words. Sidman et al. (1974), in one

experiment, taught identity matching of printed words to

printed words. In a second experiment (Sidman et al., 1974),

a participant was first taught to match lower-case letter to

upper-case letters (AB), and subsequently taught to match

upper-case letters to lower-case letters (BA). Performances

on tests for symmetry were invalid because the BA relation

was specifically taught rather than allowed to emerge.

Theoretically, the three properties that define an

equivalence relation are hierarchical (Spradlin & Saunders,

1984). That is, reflexivity must precede symmetry, and

symmetry must precede transitivity. According to this









hierarchy, it is necessary for students to demonstrate

generalized identity matching before attempts are made to

teach the student higher level equivalence skills.

Trained relations cannot be assumed to have the property

of symmetry. Because a student has learned a conditional

relation (AB), it does not necessarily follow that the BA

relation will automatically emerge. In fact, there are

reports that the the symmetric property was not demonstrated

even after protracted conditional discrimination instruction

(Sidman & Tailby, 1982; Spradlin & Saunders, 1986).

Equivalence classes can include cross-modality relations

(e.g., printed words matched to dictated words). Auditory-

visual relations cannot be tested directly for symmetry

because it is not possible to present several auditory

stimuli simultaneously as comparisons without destroying

their intelligibility (Mackay & Sidman, 1984). Symmetry can

be tested indirectly, however (Sidman & Tailby, 1982). If a

student is taught the relations AB and AC, where A is an

auditory stimulus and B and C are visual stimuli, then

testing the BC and CB relations provides evidence of both the

symmetric and transitive properties. If the symmetric

property is true, then the AB and AC relations establish BA

and CA relations. If the transitivity property is true, then

the BC emerges from BA (which emerged through symmetry) and

AC (which was taught directly), and CB emerges from CA (which

emerged through symmetry) and AB (which was taught directly).









Similarly, if a student is taught the relations AB and

BC, where all stimuli are visual, testing the CA relation

provides both tests of symmetry and transitivity. A positive

outcome on the CA test is possible only if the the explicitly

taught relations have the properties of symmetry and

transitivity. Sidman and Tailby (1982) referred to the

combined test as a simultaneous test for symmetry and

transitivity, Sidman (1986) called it a global test for

equivalence, and an equivalence test (Sidman, 1990).

The hierarchical nature of the properties that define an

equivalence relation is further demonstrated when students

fail to display transitivity. When a student demonstrates

that trained relations have the property of transitivity,

further testing will show that all underlying relations,

including those relations that confirm the properties of

reflexivity and symmetry, are in the student's performance

repertoire. When tests have shown that students failed to

display transitivity, additional testing has revealed that

prerequisite relations are also deficient (Sidman, Kirk, &

Willson-Morris, 1985; Spradlin & Saunders, 1986).

Sufficient evidence is available to confirm that the

development of equivalence relations occurs only in humans

(D'Amato, Salmon, Loukas, & Tomie, 1985; Hayes, 1989;

Lipkens, Kop, & Matthijs, 1988; Sidman, Rauzin, Lazar,

Cunningham, Tailby, & Carrigan, 1982). Even such high-level

animals as Rhesus monkeys and baboons do not exhibit









transitivity or symmetry (Sidman, Rauzin, Lazar, Cunningham,

Tailby, & Carrigan,.1982). For persons with severe learning

deficits who have failed to demonstrate reflexivity or

symmetry, it is unclear whether the failure is a nonremedial

deficit inherent in the learner, or whether it is possible to

teach these skills through exposure to multiple examples.

Benefits of Stimulus Equivalence Instruction

The stimulus equivalence model provides the basis for a

powerful instructional technology for remediating or teaching

new functional academic skills. Learning outcomes of

stimulus equivalence instruction include the emergence of

untaught conditional relations, skill generalization, and

long term maintenance of equivalence classes. Emergence,

generalization, and long term maintenance of skills may be

especially beneficial to students who have deficits in

learning, retention, or both.

Emergence of Untaught Skills

When students are taught a sequence of conditional

relations specified by the stimulus equivalence model, other

untaught conditional relations on unreinforced tests emerge.

According to the stimulus equivalence model, the emergence of

untaught relations, demonstrated by the properties of

symmetry and transitivity, provides evidence of the formation

of a stimulus equivalence class (Sidman, 1977). For example,

when AB and AC conditional relations are taught, the untaught









BA, CA, BC, and CB relations can emerge. The emergence of

untaught performances is necessary to confirm the formation

of an equivalence class.

The emergent skills phenomena makes the systematic

development of equivalence classes an efficient technology

for teaching skill repertoires that require mastery of large

numbers of individual performances (McDonagh et al., 1984).

When instruction is systematically designed so that untaught

relations emerge as a result, the number of performances that

must be explicitly taught is consequently reduced. In a

series of three experiments, for example, Sidman et al.

(1985) taught participants with normal intelligence 15

conditional relations. As a result of the systematically

designed instruction, three six-member equivalence classes

were generated, and 60 untaught relations emerged.

During typical classroom instruction, teachers may

unknowingly provide instruction that results in equivalence

class development. For example, a reading teacher may orally

read a printed word to the class (AB), provide the name for a

picture that illustrates the word (AC), and then ask a

student to match the word to its picture (BC). Proficient

learners may be able to develop the underlying conditional

relations (AB and AC) and emergent relations (BC and CB)

through exposure to natural contingencies provided in the

classroom (Sidman, 1977). Less fortunate learners may not

develop equivalence classes and would therefore leave the









teacher with two options. One option is that the teacher

could explicitly teach each conditional relation between

related stimuli. This instruction would be inefficient

because it would not take advantage of the emergent skills

phenomena of stimulus equivalence instruction. A second

option is that the untaught skill could remain as a learning

deficit that may or may not be remediated in future

instruction.

The spontaneous emergence of untaught relations as a

result of carefully sequenced stimulus equivalence

instruction has been repeated many times with a variety of

different teaching stimuli. Although many students have

shown equivalence on the first posttest for equivalence, the

gradual emergence of untrained equivalence relations over

repeated tests has been frequently observed in stimulus

equivalence research (Cowley, Green, & Braunling-McMorrow,

1992; Devany, Hayes, & Nelson, 1986; Ferro, 1990; Fields,

Adams, Verhave, & Newman, 1990; Green, 1990; Joyce et al., in

press, Joyce & Wolking, 1989; Lazar, Davis-Lang, & Sanchez,

1984; Saunders, Wachter, & Spradlin, 1988; Sidman et al.,

1974; Sidman et al., 1985; Sidman et al., 1986;

Sigurdardottir, Green, & Saunders, 1990; Spradlin, Cotter, &

Baxley, 1973).

Lazar et al. (1984) taught four normally functioning

children to develop five-member classes of purely visual

abstract stimuli. Figure 2-2 is a schematic representation








































Figure 2-2. Stimulus Equivalence paradigm used by Lazar et
al., 1984.
Note. Solid lines represent taught relations. Dotted lines
represent represent relations that emerged.


.. .








la









of the stimulus equivalence paradigm. The children were

first taught AD and DC relations and were able to perform AC

and CA matching without additional training. Next, ED was

taught, and AE, EA, EC, and CE performances emerged.

Finally, CB relations were taught, and AB, BA, EB, BE, DB,

and BD relations emerged.

In the study just described, Lazar et al. (1984)

reported that no participant demonstrated equivalence on the

first test session following CB training. Although there was

variability across children on relations that required

multiple testing, every child required multiple testing on at

least two equivalence tasks (CB and one other emerging

relation). The most extreme example of increased accuracy

across test sessions occurred for a participant on the

performance of the EB and BE emergent relations. This child

required four test administrations to reach a criterion level

of 92% correct. Across the test administrations, the

participant's scores gradually increased from 58% to 92%

correct. Another child required three test administrations

before the EB relation emerged to criterion level (scores

were 67%, 71%, and 92%, respectively) and two test

administrations before the BE relation emerged to an above-

criterion level (scores were 79% and 100%).

There is not a clear explanation for the gradual

emergence of relations during extinction; however, three

theories have been proposed. One explanation is that the









testing process is necessary for equivalence classes to form.

Sidman et al. (1985) proposed that equivalence classes do not

exist until they are tested; teaching the baseline

conditional relations only creates the potential for

equivalence class development. Saunders, Wachter, and

Spradlin (1988) argued against Sidman's theory. Saunders and

colleagues noted that in many cases, baseline training

conditions are sufficient for the formation of equivalence.

It is not uncommon for students to perform with 100% accuracy

on their first test for equivalence.

A second explanation is that the gradual emergence

during repeated testing reflects progressively diminishing

stimulus control by sources other than stimulus equivalence

(Cowley et al., 1992; Devany et al., 1986; Saunders & Green,

1992). Devany et al. suggested that other inconsistent

sources of control, such as the physical similarity between a

sample and a comparison, may be strong initially. The

inconsistent sources of control, which were not consistently

reinforced in past experiences, gradually decrease in

strength over repeated test trials. Equivalent relations

provide the only consistent (stronger) source of control.

According to this explanation, although they do not provide

direct consequences as do the trials during instruction,

unreinforced test trials somehow teach the student to perform

consistently to the experimenter-defined equivalence

relations.









A third explanation for the gradual emergence of

relations is that there are other uncontrolled variables

affecting the development of equivalence classes during

testing (Cowley et al, 1992; Lazar et al., 1984).

Unprogrammed consequences, such as subtle cues emitted by the

experimenter in experimenter-controlled procedures, is one

possible uncontrolled variable. Commonly used automated or

computerized stimulus control has been shown to prevent the

possibility of differential feedback, leaving the explanation

to other unidentified variables.

Saunders and Green (1992) suggested that a change in

experimental procedures may be a variable that has control

over the gradual emergence of relations in extinction. If a

student is reinforced by a change in experimental procedures

(e.g., presentation of new stimuli or an end to the session),

then repeated or prolonged testing may provide the student

with the cue that the correct response has not been produced.

Seeking reinforcement, the student might change an emitted

response pattern when tests are prolonged or repeated. If

this explanation is true, then the newly developed relations

may actually be trained relations rather than emergent

relations.

Regardless of its explanation, the gradual emergence of

performances across testing is a common occurrence in

stimulus equivalence experiments. In applied stimulus

equivalence instruction that involves teaching functional









academic skills, an implication of the gradual emergence of

equivalence is that if skills do not emerge on initial

testing, it may not be necessary to review the underlying

conditional relations. A more efficient strategy may be to

conduct repeated test sessions. The gradual emergence of

equivalence relations in extinction is still poorly

understood and is an important topic for future research.

Skill Generalization

Skill generalization is a beneficial learning outcome of

stimulus equivalence instruction. Several types of skill

generalization have been reported in the stimulus equivalence

literature. Examples of skill generalization reported in the

stimulus equivalence literature include generalization of

skills learned to new contexts (Mackay & Ratti, 1990),

generalization of stimulus control to novel stimuli (Fields,

Reeve, Adams, & Verhave, 1991), generalization of verbal

labels to all members of an equivalence class (Dixon &

Spradlin, 1976; Saunders, Wachter, & Spradlin, 1988; Spradlin

& Dixon, 1976), and the facile expansion of equivalence

classes (Dixon & Spradlin, 1976; Lazar et al, 1984; Saunders,

Saunders, Kirby, & Spradlin, 1988; Saunders, Wachter, &

Spradlin, 1988; Sidman & Tailby, 1982; Sidman et al., 1986;

Stromer & Osborne, 1982; Wetherby, Karlan, & Spradlin, 1983).









Generalization to new contexts

Mackay and Ratti (1990) demonstrated that equivalence

relations established in a matching-to-sample context can

result in increased accuracy on a skill performed in a new

context. Using the stimulus equivalence model, Mackay and

Ratti taught 3 adults with severe mental retardation to

establish equivalence relations consisting of dictated number

names (A), nine positions on a modified form of a delayed

recognition span test board (B), printed numbers (C), and

oral number names spoken by the adult (D). Before

equivalence training, the adults were pretested for

equivalence class development. Pretests showed that the

participants were able to do generalized identity matching of

numbers (CC), and were able to match printed numbers to their

dictated names (AC) and to orally name the numbers (CD). The

participants were also given a delayed position recognition

span test (a test used to assess memory of persons who have

neurological impairments). The participants obtained scores

of 3 to 5 on the recognition span pretest (the maximum score

possible is nine--one point for each position on the span

board).

The participants were taught to match printed numbers to

their spatial positions on the recognition span board (BC).

Following the BC instruction, without further training, the

adults were able to match positions to printed numbers (CB),

and positions to dictated number names (AB), and they were









able to orally name the number that corresponded to each

position on the test board (BD). With confirmation of the

emergent performances, it was determined that each

participant had learned 9 three-member equivalence classes,

each class consisting of a number name, a printed number, and

a position on the test board.

The skills learned in the matching-to-sample context

affected the performances on recognition span posttests. One

participant, who had a pretest score of 3, obtained the

maximum score of 9 on the delayed recognition span posttest.

Data obtained from this participant's performance enabled the

determination to be made that equivalence relations

established in a matching-to-sample context can result in

increased accuracy on a skill performed in a new context.

The remaining 2 participants did not receive improved scores

on the first delayed recognition span test. On a subsequent

test, the participants were given the instructions to orally

name the stimuli. As a result of their naming, both

participants obtained a perfect score on the second testing.

It is unclear whether the 2 participants would also have had

improved scores on delayed recognition span protests if they

had been asked to name the stimuli during protesting.

Generalization to novel stimuli

In most demonstrations of stimulus equivalence, each

member of a class is a singular stimulus. In reading

instruction, for example, a student is taught to match a









drawing of a dog to its printed name and dictated name. The

student's generalization of matching printed and dictated

names to a variant of the dog illustration remains unknown.

If the student learned to select a blackline drawing of a dog

when presented with the printed word "dog", would the

student, without additional training be able to select a

photograph of a dog when presented with the printed word?

The stimulus equivalence model does not require the use of

variations in illustrative stimuli. In naturally occurring

categories, however, singular stimuli are more often the

exception than the rule (Fields et al., 1991).

Fields et al. (1991) demonstrated that the development

of complex naturally occurring categories can be explained by

equivalence class formation and stimulus generalization.

Five undergraduate college students were taught arbitrary

conditional relations consisting of nonsense syllables and

sets of "short" and "long" lines. The students were taught

two classes of stimuli; each class consisted of two nonsense

syllables (A and B) and two lines (C and D). Long lines were

presented as stimuli in one class and short lines in the

other. After stimulus equivalence was established, novel

stimuli of differing line lengths were substituted for the

trained lines in transitivity tests. Test results allowed

for the conclusion that the novel stimuli exerted the same

control as the trained stimuli. As a result of testing with









novel stimuli, the stimuli in the trained equivalence class

became related not only to each other, but also to novel

stimuli (lines of similar length).

Generalization of spoken labels

Data from several studies allow the conclusion to be

drawn that once a stimulus class consisting entirely of

visual stimuli has been developed, a spoken label can be

taught for that class by explicit training with a subset of

the class, and that label will generalize to the remaining

members of the class (Dixon & Spradlin, 1976; Saunders,

Wachter, & Spradlin, 1988; Spradlin & Dixon, 1976). Dixon

and Spradlin used abstract visual stimuli and nonsense

auditory stimuli to determine whether a set of visual stimuli

would function as a stimulus class in an auditory conditional

discrimination task if the stimuli had been established first

as equivalent in a visual matching-to-sample task. Six

participants with mild mental retardation were first taught

two classes of visual stimuli (Class A and Class B). Each

class consisted of four abstract stimuli. After participants

reached 100% accuracy on the visual conditional

discrimination training, auditory conditional discrimination

training was provided. One visual stimulus in each class was

selected as the correct comparison for an auditory stimulus

("La" for Class A and "De" for Class B). After the

participants reached 100% accuracy on the new auditory-visual









conditional discrimination, they were tested to determine

whether the auditory stimuli controlled other members of the

corresponding class.

Three of the 6 participants showed generalized control

of the auditory stimulus to the remaining three unreinforced

visual stimuli. The remaining 3 participants performed near

chance level on the untaught auditory-visual discrimination.

The experimental results enabled the investigators to

determine that when a response to one member of a class is

brought under the control of an auditory stimulus, the

control of that auditory stimulus can be generalized to other

established members of that class.

Spradlin and Dixon (1976) conducted a second experiment

using the same abstract visual stimuli that Dixon and

Spradlin (1976) used, but different auditory stimuli. The 2

participants in Spradlin and Dixon's experiment were more

severely retarded than the participants in the previously

reported experiment. Spradlin and Dixon obtained similar

results except they found that it was necessary to train the

auditory label to two members of each class before the

auditory stimulus controlled all other members. One

auditory-visual conditional relation did not provide

sufficient control.

Saunders, Wachter, and Spradlin (1988) described another

similar experiment in which 4 participants with moderate

mental retardation were taught two eight-member equivalence









classes of abstract visual stimuli. The participants were

taught to select one visual stimulus from each class in

response to a verbal stimulus. The participants were then

tested to determine whether the verbal stimulus controlled

responding to the remaining seven members of the class.

Generalized control of the remaining visual stimuli occurred

for 3 of the participants. For the 4th participant,

generalization occurred only after a second pair of visual

stimuli were trained.

Expansion of equivalence classes

An advantage of expanding equivalence classes is that

little training time needs to be invested to develop complex

and intricately related relations (Wulz & Hollis, 1979).

When a student is taught to relate a new stimulus to any

member of an existing equivalence class, the new stimulus

will become equivalent to all other class members without any

further instruction (McDonagh et al, 1984; Sidman & Tailby,

1982). Each time a new member is added to an established

class, an expanding number of untaught relations emerges. As

a result, teaching efficiency increases as stimulus classes

are increased in size.

Data from a number of studies allows for the conclusion

that equivalence class membership can be expanded to include

a large number of members. Wetherby et al. (1983) taught 5-

year-old normally functioning children to develop equivalence

classes that consisted of three abstract visual stimuli, and









then expanded the classes to include an additional member.

Using purely visual stimuli, Lazar et al. (1984) demonstrated

expansion of equivalence class membership to five. Through

gradual class expansion, McDonagh et al. (1984) taught a

participant with mental retardation to develop a class of

equivalent stimuli that consisted of seven coin relations.

Larger classes can be formed by linking relations

between two existing smaller stimulus equivalence classes

(Sidman et al., 1985). Sidman et al. merged six small

stimulus classes into three larger classes by directly

training three linking conditional relations. The result was

three 6-member classes of equivalent stimuli. Saunders,

Saunders, Kirby, and Spradlin (1988) taught participants with

mental retardation to link two 4-member stimulus classes,

resulting in the emergence of two 8-member classes of

abstract visual stimuli. Saunders, Wachter, and Spradlin

(1988) taught participants to develop two 9-member

equivalence classes. Each class consisted of eight abstract

visual stimuli and one auditory stimulus. A total of 112

untaught relations emerged as a result of their

systematically designed instruction.

Saunders, Saunders, Kirby, and Spradlin (1988) and

Saunders, Wachter, and Spradlin (1988) noted that as more

members are added to an equivalence class, the relations

within that class may become more stable, new members may be

added more easily, and all members are more likely to be









maintained. Because there are more opportunities to

reinforce relations within a large equivalence class, a large

network of linked relationships makes the relations within a

class less susceptible to disturbance from extraneous

variables. Relations between members of a small equivalence

class may be weakened, and chances for recovery of lost

stimulus control are fewer because there are fewer

opportunities from which a weakened conditional relation can

be derived again.

Long Term Maintenance of Equivalence Classes

Data from follow-up tests allow for the determination

that equivalence relations are often maintained for

substantial periods of time. An example of a remarkably

stable performance is provided by Saunders et al. (1990).

Saunders and colleagues collected follow-up data on the

performances of a participant from a previous study

(Saunders, Wachter, & Spradlin, 1988). Saunders, Wachter,

and Spradlin (1988) taught the participant to develop two

nine-member equivalence classes; each class consisted of

eight abstract visual stimuli and a nonsense auditory

stimuli. A total of 112 conditional relations had emerged.

Both the taught and emerged relations remained stable for up

to 5 months in extinction. Saunders et al. (1990) tested the

previously learned relations 2 years (770 days) and nearly 3

years (1092 days) after the initial training. During both

follow-up test sessions, the participant performed both the









taught and the emerged relations with 100% accuracy. The

relations had remained stable despite the absence of exposure

to the arbitrary stimuli and without differential feedback

during testing.

Other studies have provided additional evidence that

equivalence relations are maintained for long periods of time

(Joyce et al., in press; Joyce & Wolking, 1989; Mackay &

Ratti, 1990). One year following training of spatial

positions on a modified recognition span test board, 1 of 3

participants achieved the maximum score possible on a

recognition span test (Mackay & Ratti, 1990). When given

instructions to orally name the positions, the other 2

participants in this study achieved the maximum score on the

recognition span test 1 month following stimulus equivalence

instruction. Joyce et al. (in press) conducted a follow-up

assessment 69 days after equivalence instruction that

involved relations between Spanish and English words. Both

participants in this study maintained or increased accuracy

of performances on the follow-up probe. Joyce and Wolking

(1989) also reported high accuracy of reading skills on a

maintenance probe that was conducted two weeks following

instruction. Both Joyce and Wolking and Joyce et al. noted

that performances on some relations had actually increased on

follow-up tests.









Ferro (1990) taught 2 students with limited English

skills to develop equivalence relations consisting of Spanish

and English words. Maintenance probes were conducted 2 weeks

and 4 weeks following instruction. Although a few relations

were maintained at high levels of accuracy, many of the

performances decreased in accuracy. Saunders, Wachter, and

Spradlin (1988) noted that repeated testing on maintenance

probes resulted in the reemergence of skills and brought the

accuracy of responding back to post-assessment levels. Ferro

conducted only one test session on the 2- and 4-week

maintenance probes. It is possible that if Ferro had

conducted repeated maintenance probes, accuracy may have

returned to initial post-assessment levels.

In summary, stimulus equivalence instruction results in

a network of efficiently derived skills that have more

meaning, are easily generalized, and are well retained.

Through a carefully arranged instructional sequence that is

based on the stimulus equivalence model, educators may tap

unsuspected behavioral capacities in learners of all

abilities. Studies that have used the stimulus equivalence

model to teach functional academic skills are reviewed in the

next section.

Using the Stimulus Equivalence Model to Teach Academic Skills

The majority of stimulus equivalence investigations have

been conducted in laboratory settings and have been directed

toward the analysis of complex stimulus control in concept









formation and language development. Despite the experimental

focus, a number of stimulus equivalence investigations have

resulted in potentially functional academic skills, and

researchers have suggested that the equivalence model can be

used as the basis of an efficient technology for teaching

functional academic skills. Stimulus equivalence experiments

have been conducted in the academic areas of vocabulary and

reading comprehension, spelling, money skills, pre-arithmetic

skills, and foreign language vocabulary development.

Vocabulary and Reading Comprehension

Several applications of the stimulus equivalence

paradigm have demonstrated the utility of the model for

teaching vocabulary and reading comprehension skills (Hollis

et al., 1986; Joyce & Wolking, 1989; Osborne & Gatch, 1989;

Sidman, 1971; Sidman & Cresson, 1973; Sidman et al., 1974).

Sidman (1971) defined three components of reading: oral

reading, reading comprehension, and auditory-receptive

reading. According to Sidman's definition, oral reading

requires a student to orally name a word when shown the

printed word. Oral reading may or may not involve reading

comprehension. Reading comprehension is a purely visual task

that involves relations between printed words and pictures.

Because it is a purely visual task, a student may be capable

of reading comprehension (e.g., matching words to pictures)

without being able to read the words orally. Auditory-

receptive reading requires a student to select a printed word









when its corresponding word is dictated. Like oral reading,

auditory-receptive reading may or may not involve

comprehension of either the printed word or the spoken word.

Auditory comprehension occurs only when the visual and

auditory stimuli are related by equivalence.

Tests for equivalence are needed to verify that

comprehension has taken place in oral reading and auditory-

receptive reading. Confirmation of an equivalence class

shows that the stimuli within the class have the same

meaning. The stimulus equivalence model that Sidman (1971)

and Sidman and Cresson (1973) used to teach receptive reading

of 20 words to persons with severe mental retardation and to

confirm reading comprehension is described at the beginning

of this chapter and illustrated in Figure 2-1.

Sidman et al. (1974) taught the same list of 20 words to

an institutionalized adolescent who had Down's syndrome. The

purpose of the experiment was to explore the role of verbal

mediation in the formation of stimulus classes. Instead of

teaching dictated names to printed words (AC) as did Sidman

(1971), the participant was taught to match printed words to

pictures (BC). In a second experiment, a second participant

learned a similar sequence of cross-modal and visual-visual

relations, except the stimuli were upper- and lower-case

alphabet letters rather than words and pictures. In both

experiments the conditional relations emerged before the

participants were able to name the stimuli. Based on their









findings, Sidman et al. concluded that emergent relations

were not mediated by naming (productive mediation), but were

enhanced by training the receptive (AB) relations (receptive

mediation).

Joyce and Wolking (1989) also used the model illustrated

in Figure 2-1 to teach reading skills to preschool children

with normal intelligence. A set of ten 4-letter words was

taught in the same sequence that Sidman (1971) used.

Pretests demonstrated that the children were able to match

pictures to dictated names (AB), and to orally name pictures

(BD). The children were taught to match printed words to

dictated words (AC). Without further training, the children

were able to match pictures to printed words (CB), printed

words to pictures (BC), and they were able to orally name the

printed words (CD).

Two studies (Hollis et al, 1986; Osborne & Gatch, 1989)

generalized the use of Sidman's (1971) stimulus equivalence

paradigm to preschool children who had severe and profound

hearing impairments. Hollis et al. taught 4 children two

lists of words: an "easy" list that consisted of six words

that were easily discriminated through speechreading (e.g.,

dog and bed), and a "difficult" list that consisted of six

words that were not easily discriminated through

speechreading (e.g., plane and plate). The model was the

same as the model illustrated in Figure 2-1 except that

lipreading replaced the dictated word component (A).









Pretests showed that children were able to orally name words

that they lipread. The children were trained on the BC

relations (matching printed words to pictures).

Posttest data enabled the conclusion to be drawn that

stimulus properties specified by the equivalence model are

applicable to vocabulary and reading instruction with deaf

children. All remaining relations (AB, AC, CB, and CD)

emerged without instruction. Although receptive tasks are

sensitive to receptive discrimination problems, it was

demonstrated that lipreading, a visual modality, can be

substituted for speech, an auditory modality. On the "easy"

list, mean performance across all six (emerged and taught)

relations was 99% correct, with a 90% increase in performance

from baseline. On the "difficult" list, mean performance

across all six relations was only 88% correct, with a 75%

increase in performance from baseline. The authors indicated

that most errors made involved lipreading.

Osborne and Gatch (1989) replicated Sidman's (1971)

procedures with two hearing-impaired preschool-aged children.

As shown in Figure 2-3, dictated words (A) were replaced with

manual signs. The children were taught to match pictures to

manual signs (AB) and printed words to manual signs (AC). On

posttests, the BC (matching printed words to pictures) and CB

(matching pictures to printed words) relations emerged with

97%-100% accuracy. On maintenance probes 1 week and 1 month










B E

Finger-
Picture ... spelled
Word



Manual
A Sign



Prited Produce
SF dHanual
Word Sign

C D




Figure 2-3. Stimulus Equivalence instructional model used
by Osborne and Gatch, 1989.

Note. Solid lines represent taught relations. Dotted lines
represent relations that emerged.









after posttesting, one child was tested on matching pictures

to fingerspelled words (EB) and producing a manual

performed these emergent relations at 100% and 95% accuracy

respectively.

Spelling

Mackay (1985) added anagram naming, an expressive

performance, to Sidman's paradigm. Mackay taught 3 teenage

boys with mental retardation to form equivalence classes

consisting of dictated color names (A), six color patches

(B), printed color names (C), oral color naming (D), and

anagram construction of the color words (E). Pretests

enabled the investigator to demonstrate that the participants

were already able to match color patches to dictated color

names (AB) and to orally name the colors (BD). In response

to color patches, the participants learned to construct color

names (BE) by selecting appropriate 6x6 mm letter cards from

a letter pool and placing the letters in sequence on a

program card. A fading procedure was used to teach the

participants to construct (spell) the color words. After

learning to construct words when given the color patches, the

following skills, which were not present before training

emerged: the participants were able to orally name printed

color words (CD), they were able to match color patches to

their printed color names when the printed names were used as

both the sample (CB) and the comparison stimuli (BC), and

when given dictated color names as samples, they were able to









match them with the printed name (AC) and to create the color

anagram (AE). Mackay and Sidman (1984) also demonstrated

stimulus class formation using matching-to-sample and a

constructed response procedure that required a participant to

print number words in response to the printed numbers.

Teaching the participant to write number words in response to

printed numerals established equivalence relations that

included dictated numbers, printed number names, printed

numerals, oral naming of printed number names and printed

numerals, and the participant's printed number words.

The constructed response and fading procedures used in

the spelling experiments allow for the conclusion that the

formation of equivalence relations is not restricted to a

particular teaching procedure. If equivalence relations are

a significant factor in concept development, then the

establishment of equivalence classes must be generalizable

across a variety of naturally occurring and explicitly

contrived teaching methods (Mackay & Sidman, 1984). By using

simple and easily assembled instructional materials, Mackay

(1985) demonstrated that methods employed in the laboratory

are applicable for teaching and assessing elementary reading

skills. Furthermore, training in matching-to-sample and

anagram naming may have implications for providing a usable

method of communication to people who have severe

deficiencies in receptive and productive language.









Money Skills

In a series of experiments, McDonagh et al. (1984),

Stoddard et al. (1987), and Stoddard, Brown, Hulbert, Manoli,

and McIlvane (1989) used constructed response matching-to-

sample to teach monetary skills to individuals with mental

retardation. The value of these studies is that rather than

attempting to teach large numbers of individual monetary

combinations by rote, a relatively small number of critical

prerequisites are taught. As a result of a small number of

critical prerequisites being taught, new performances emerge

without explicit training (Stoddard et al, 1987). McDonagh

and colleagues taught a 28-year-old participant with moderate

mental retardation to form an equivalence class that

consisted of printed prices and coin combinations. Pretests

showed that the participant could: (a) name printed prices

up to 250; (b) name the coins, "penny," "nickel," "dime," and

"quarter"; (c) state the value of each coin, (d) match a coin

to its dictated and printed price; and (e) match identical

quantities of coins. Excluding identity matches, the

participant was not able to match any stimulus that contained

more than one coin.

The participant quickly learned to match five pennies to

the printed price "50." Posttests showed that the

participant had developed a three-member equivalence class









consisting of the printed price "5," a nickel, and five

pennies. Figure 2-4 provides a schematic representation of

the first portion of the experiment.

The next sequence of teaching and testing phases is

illustrated in Figure 2-5. Next, the participant was taught

to match 10 pennies to the printed price "l00." After the

10t:10 pennies relation was established, the participant was

immediately capable of matching a dime to 10 pennies,

demonstrating the transitive property. Finally, the

participant was taught to match stimuli consisting of 2

nickels and then 10 pennies to the printed price "5054."

Again, the participant was immediately capable of performing

the emergent relation of matching 10 pennies to 2 nickels.

Because the participant did not demonstrate mastery when

tested on the emergent relations represented by the sequence

numbers 10 through 18 in Figure 2-5, a constructed-response

matching-to-sample procedure was initiated. The constructed-

response matching-to-sample required the participant to

select from a pool of coins and prices, combinations of coins

and prices that corresponded to a displayed sample. Under

the constructed-response matching-to-sample instruction, the

new performances (labelled numbers 10-18 in Figure 2-5)

emerged rapidly to 94% to 100% correct.
































Figure 2-4. Schematic representation of the stimulus
equivalence class demonstrated by McDonagh et
al., 1984.

Note. Solid lines represent previously known and taught
conditional relations. Dotted lines represent relations that
emerged. Numbers designate the sequence of teaching and
testing.













//* 6: 13


i 5 Pennies .....
17 12 11 :0 5 Pennies : 18



g ..... I.... .I

Nickel




14 15 16

................. Nickel

...................................... 5 Pe es .........


Figure 2-5. Schematic representation of the teaching and
testing phases in the development of the
stimulus equivalence class demonstrated by
McDonagh et al., 1984.
Note. Solid lines represent previously known (line 4) and
taught conditional relations (lines 5, 7, and 8). Dotted
lines represent relations that emerged. Numbers designate
the sequence of teaching and testing.









Stoddard et al. (1989) taught 3 participants to develop

equivalences among printed prices, coins, and groups of coins

up to 50. Instruction included a combination of methods

that focus on producing new behavior without explicit

training: matching-to-sample instruction, exclusion, and

component-matching training. Data from two of the three case

studies allowed for the conclusion to be drawn that the speed

at which new monetary equivalences were acquired increased as

the participants' repertoires expanded. On that basis, it

was concluded that protracted training with basic relations

may be an efficient instructional strategy.

Pre-arithmetic Skills

Gast et al. (1979) taught numeration skills to children

with mental retardation and preschool aged children who had

normal intelligence. The purpose of the study was to

determine whether children with mental retardation and

normally functioning preschoolers show similar patterns of

emergence of untaught skills. Pretests showed that for the

numbers 1 to 6, all participants were able to recognize and

name the numerals. Further, all participants were able to

count sets of manipulatives when given the spoken number or

the printed numeral. None of the participants could perform

any task involving printed number words. The children were

taught the auditory-receptive task of matching printed number

words to dictated numbers. After training on the single

cross-modal relation, all children demonstrated improved









performance on the following tasks: matching numerals to

printed number words, matching printed words to numerals,

matching sets to printed number words and orally naming

printed number words. The data from this study allowed for

the determination to be drawn that there was no difference

between the performances of children with mental retardation

and preschool aged children with normal intelligence.

Foreign Language Vocabulary Development

Two studies demonstrated the formation of equivalence

classes that included Spanish words (Ferro, 1990; Joyce et

al., in press). Joyce and colleagues taught 2 adolescents

who had sustained traumatic brain injuries to form

equivalence classes consisting of dictated Spanish words,

printed English words, printed Spanish words, and pictures.

Pretests showed that the participants were able to orally

identify pictures (in English) and to read printed words in

English. One participant was taught to match pictures to

Spanish printed words. The 2nd participant was taught to

match Spanish printed words to pictures. Posttests enabled

the investigators to demonstrate the emergence of untaught

relations with 80% to 100% accuracy.

In two experiments, Ferro investigated the development

of equivalence classes. One class consisted of Spanish

words, English words, and pictures, and the other class

consisted of English words, word synonyms, and their parts of

speech. The participants were students with limited English









skills who had demonstrated learning difficulties in their

native countries. In the first experiment, the student could

match pictures to Spanish words. After instruction on

matching Spanish words to English words, the student was then

able to match English words to pictures. The new

performances were not attributed to the development of an

equivalence class, however, because there was an increase in

baseline scores. The increase in baseline scores allowed for

the conclusion that the student may have been learning some

of the relations outside of the experimental setting. In the

second experiment, 1 student demonstrated the formation of an

equivalence class that consisted of an English word, a

synonym, and their part of speech.

The results of these experiments (Ferro, 1990; Joyce et

al., in press) enabled the investigators to conclude that the

stimulus equivalence paradigm can be used to teach foreign

language vocabulary to students of varying abilities.

Furthermore, both of of the studies used a HyperCard computer

environment to control stimulus presentation. The computer-

based instruction minimized the intervention required by the

experimenters, provided a reliable method of stimulus

control, and provided easy storage and retrieval of data.

Variables that Influence Equivalence Class Development

Humans develop equivalence relations at varying rates;

some participants fail to demonstrate equivalence even after

protracted training (Sidman & Tailby, 1982; Spradlin &









Saunders, 1986). A number of variables that may influence

equivalence class formation have been identified. The number

of nodes that separate stimuli, testing sequences, and

stimulus modality are variables that may influence

equivalence class formation. A better understanding of these

variables could lead to procedures that expedite equivalence

class development.

Nodality

The number of nodes involved in training is a structural

variable that may influence the development of equivalence

classes. Fields, Verhave, and Fath (1984) used the term

"node" to refer to stimuli that are linked by training to at

least two other stimuli in a class. For example, a four-

member equivalence class (A, B, C, D) may be established by

relating three stimuli (B, C, and D) to a single stimulus or

node (A). This four-member class, illustrated in Figure 2-6,

contains one node (A). Another possible way that the four-

member class (A, B, C, D) may be established is by relating A

to B, B to C, and C to D. In this second example, also

illustrated in Figure 2-6, there are two nodes (B and C).

Fields, Verhave, and Fath (1984) and Fields and Verhave

(1987) proposed that the number of nodes in an equivalence

relation may inversely influence stimulus control.

Specifically, the more nodes a relation has, the less control

the stimuli in the relation will have. Lazar, Davis-Lang,

and Sanchez (1984) and Sidman, Kirk, and Willson-Morris













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(1985) observed that for some participants, multi-nodal

relations require more trials to emerge than do single-node

relations.

Fields et al. (1990) investigated the influence of the

number of nodes on the establishment of four-member

equivalence classes. Seven female college students were

taught two 4-member classes of nonsense visual symbols. Each

four-member class (A, B, C, D) was formed by training AB ,BC,

and CD relations. After training, all emergent relations

were tested without informative feedback. For 6 of the 7

students, the one-node relations (e.g., AC) exerted more

control than the two-node relations (e.g., AD). With

repeated testing, however, the difference between the one-and

two-node relations decreased. The accuracy of responding for

the two-node relations increased and eventually reached the

100% level that had been previously established and

maintained with the single-node relations.

Data from Fields et al., (1990) support and extend

previous observations regarding two variables that influence

equivalence class formation: nodality and the number of test

trial presentations. These data enabled the investigators to

conclude that the control exerted by an emergent relation is

inversely related to the number of nodes that separate the

two stimuli that comprise the derived relation. Thus, a

single-node relation is more likely to emerge in fewer test

trials than a multiple-node relation. Conversely, the number









of test trial presentations is directly related stimulus

control. After repeated test trial presentations, a

multiple-node relation may develop to high levels of

accuracy.

Testing Sequence

The role of testing and test sequence in stimulus

equivalence development is still not clearly understood.

When equivalence relations fail to emerge, certain testing

sequences may help to enhance development. Lazar et al.

(1984), for example, reported that when a participant was

unable to perform untaught AB and BA relations, equivalence

was remedied by assessing the two relations in separate test

sessions. For another participant who failed to demonstrate

equivalence classes in the same study, separation of the

relations in testing did not result in positive tests for

equivalence. For this participant, taught relations that

were necessary for the unemerged performance were reviewed,

and with this review, accuracy levels began to increase.

For some students, testing for the three properties of

equivalence relations in their hierarchical sequence may

enhance equivalence class development (Lazar et al., 1984;

Stoddard & Mcllvane, 1986). Sidman and colleagues (1986)

reported that 3 participants failed combined tests for

symmetry and transitivity. When symmetry was tested

directly, 2 of the participants immediately demonstrated

evidence of the symmetric property for both sets of trained









relations. Furthermore, when the participants were

subsequently given a combined test, both participants

provided evidence of both symmetric and transitive

properties.

Stimulus Modality

Equivalence classes that include auditory stimuli (e.g.,

dictated names as samples) may develop more quickly than

classes consisting entirely of visual stimuli (Sidman et al,

1986). Sidman and colleagues compared learning produced by

cross-modal and purely visual conditional relations and found

that young adults with mental retardation developed

equivalences in fewer trials when classes included auditory

stimuli. Three of 4 participants with mental retardation

required repeated testing before the classes of visual

stimuli emerged, only 1 participant with mental retardation

required repeated testing for the cross-modal classes to

emerge. Two children without mental retardation showed no

difference in the number of test trials needed for the

development of equivalence classes through cross-modal

relations and purely visual relations.

In a replication of Sidman and colleague's (1986) study,

Green (1990) also found that some participants with mental

retardation formed equivalence classes more readily when one

relation was cross-modal than when the relations consisted of

only visual stimuli. Green taught 5 young adult females with

mild mental retardation to develop four equivalence classes.









Two classes consisted of three abstract visual stimuli, and

two classes consisted of one spoken nonsense syllable and two

abstract visual stimuli.

For 3 of the 5 participants, the number of trials

required to reach criterion in the cross-modal equivalence

classes differed greatly from the number needed in purely

visual classes. The 3 participants required more training to

acquire the visual conditional relations than were needed to

acquire the cross-modal conditional relations. Following

training on conditional relations in each class, all

participants eventually demonstrated equivalence in the two

visual and the two cross-modal classes. Two of the

participants required repeated testing and review before a

criterion of 100% correct was reached on equivalence tests in

the all-visual classes. In contrast, without review or

repeated testing, all of the participants demonstrated

equivalence almost immediately in the classes containing

cross-modal stimuli.

Data from these two studies (Green, 1990; Sidman et al.,

1986) allow for the conclusion that individuals with mental

retardation exhibit reliable differences in the rate of

formation of cross-modal and all-visual equivalence classes.

The difference is not always evident in the number of

teaching trials needed to reach criterion, but it is evident

in the number of repeated testing sessions needed before

stimulus equivalence is demonstrated. Sidman et al. did not









find performance differences in the development of cross

modal and all-visual equivalence classes in young children

who had normal intelligence. It is not known whether

performance differences will be observed in other

populations.

Summary

Stimulus equivalence research findings enable the

conclusion to be drawn that there is much untapped potential

in the stimulus equivalence model for the instruction of

children with mild disabilities. Stimulus equivalence

instruction results in emergence of untaught skills, skill

generalization, and long-term maintenance of skills. The

efficient emergence of untaught skills and skill

generalization and maintenance are advantages that may prove

to be especially beneficial to students who have learning

deficits.

To benefit fully from the stimulus equivalence model,

further research is needed to define variables that determine

the success, failure, and expediency of equivalence class

development. Research is also needed to determine which

functional academic skills can be taught most efficiently

through stimulus equivalence instruction.

The present study addresses these two research needs.

First, the study investigates the effect of stimulus modality







64

on learning. Second, the study demonstrates the

effectiveness of the application of the stimulus equivalence

model for teaching time-telling skills.















CHAPTER III

METHOD

The training and testing procedures described in this

chapter were designed to teach students with mild

disabilities to develop equivalence classes in an academic

subject area. The research method in this investigation was

designed to determine whether equivalence class development

does occur and to determine the effects of stimulus modality

on equivalence class development. The research methodology

including descriptions of the subjects, setting, apparatus,

stimuli, variables under investigation, measurement of the

variables, and the experimental design and procedures follow.

Subjects

Seven students participated in this study. The students

were elementary school students who received special

education resource services in a varying exceptionalities

classroom located in Alachua County. Student

characteristics, including sex, race, age, grade, special

education classification, intelligence quotient, and

achievement test scores for math and reading, are summarized

in Table 3-1.

To participate in the study, each student was required

to meet the following criteria: (a) the student met state















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identification criteria for Specific Learning Disabilities,

Educable Mentally Handicapped, or Emotionally Handicapped;

(b) the student received mathematics instruction in a special

education classroom; (c) the student functioned below grade

level in mathematics; (d) the student's current

individualized educational program (I.E.P.) goals included

the measurement of time; (e) the student was capable of

generalized identity matching and (f) the student scored 50%

or less on a computer-based time-telling test.

Permission for this study was obtained from the Alachua

County School Administration, the University of Florida

Institutional Review Board, and the students' parents.

Copies of all permission forms are in Appendix A.

Setting

All sessions were conducted during regular school hours

in the student's special education resource classroom. The

student sat at a table facing a Macintosh SE computer

equipped with a mouse. The table and computer were located

in the corner of the classroom. A tall bookshelf separated

the student from ongoing classroom activities. An Apple IIe

computer was next to the Macintosh. When students in the

class came to use the Apple IIe computer, a partition was

placed between the participant and the student using the

other computer. Other participants, who were present in the

classroom and working on ongoing classroom activities, were

not able to see the computer screen as each student worked at









the Macintosh computer. The experimenter was present during

each session and was positioned behind and slightly to the

side of the student. Only one student worked at the computer

at a time. During sessions, the special education resource

teacher, students, classroom volunteers, and the experimenter

were present in the classroom.

Apparatus

All training and testing sessions were conducted using

an Apple Macintosh SE computer with a 20 MB hard drive and 4

MB internal memory and a mouse attachment. All visual

stimuli were displayed on the computer's 11.5 cm x 17 cm

monochrome monitor. Using the mouse attachment to control

cursor location, students responded to stimuli by placing a

hand-shaped cursor and clicking (depressing) the mouse

button. All auditory stimuli were delivered through the

computer's internal speaker.

Across all phases of the experiments, stimulus

presentation and data collection and storage was controlled

by specially designed HyperCard stacks (instructional

computer programs). The HyperCard stacks were modeled after

an instructional program designed by Ferro (1990), but

modified and programmed by the experimenter.

Stimuli

Clock times were represented by three forms of visual

stimuli: clock times printed in digits (e.g., 3:15), clock

times printed in words (e.g., quarter after three), and









analog clock faces. Clock times printed in digits and words

appeared on the screen in 24 point, boldface, Geneva text

style. The analog clock faces were drawn using HyperCard's

graphics capabilities. The clock faces were round, 2.8 cm in

diameter, with digits in 10 point, boldface, Geneva text

style.

Auditory stimuli included mechanically voiced clock

times and a 2-second series of tones. The mechanically

voiced clock times were digitized using a Macintosh II si

computer, incorporated into the HyperCard stacks, and voiced

by the computer. The mechanically voiced clock time, which

was cued on the computer screen with a visual loud-speaker

icon, sounded similar to a tape recording of the

experimenter's voice. A student received a 2-second series

of six auditory tones as a consequence for making a correct

response. The series of tones was programmed to use

HyperCard's prerecorded sounds.

Figure 3-1 illustrates the positions of sample and

comparison stimuli on the computer screen. Visual stimuli

were centered within transparent rectangular (4.7 x 1.6 cm)

fields. Training and testing trials began with the

presentation of a sample stimulus followed by three

comparison stimuli. The presentation order of the sample

stimuli and the position on the computer screen of the

comparison stimuli were determined randomly by the computer

program.



















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Under the all-visual condition, the sample stimulus

(clock time printed in words) appeared in the center of the

computer screen. The comparison stimuli remained hidden

until the student placed the cursor on the sample stimulus

and clicked the mouse. When the sample stimulus was

selected, a "beep" sounded through the computer's speaker and

comparison stimuli appeared in three of the six transparent

comparison buttons. Comparison stimuli were displayed in a

triangular arrangement with the sample stimulus in the center

of the triangle. Throughout the sequence of trials,

comparison arrangements alternated between Comparison View 1

and Comparison View 2 as illustrated in Figure 3-1.

The trial continued when the student selected a correct

or incorrect comparison stimulus by clicking on the stimulus.

During training, if a correct comparison was selected, the

student received the 2-second series of auditory tones, 1

point was added to the student's score that appeared in a

rectangular (8 x 11 mm) box in the upper right corner of the

screen, and then the computer screen was cleared in

preparation for the next trial. If an incorrect comparison

was selected, the two incorrect comparisons disappeared from

the screen, and an arrow cued the student to select the

correct comparison. At this point, mouse clicks anywhere on

the computer screen except the correct comparison had no

programmed consequences. When the student selected the cued









correct comparison, the student did not receive the 2-second

series of auditory tones for the selection, but the screen

was cleared in preparation for the next trial.

Under the cross-modal condition, the sample auditory

stimulus was cued by a visual loud-speaker icon that appeared

in the center of the computer screen. When the student

selected the loud-speaker icon, the computer voiced the

auditory stimulus (mechanically voiced clock time) and three

comparison (visual) stimuli were displayed on the computer

screen in the manner described above. During training, as in

the all-visual condition, if a positive comparison was

selected, the student received a 2-second series of auditory

tones and 1 point was added to the student's score in the

upper right corner of the screen. The computer screen was

then cleared in preparation for the next trial. If an

incorrect comparison was selected, an arrow cued the student

to select the correct comparison.

During tests for untrained relations, no programmed

consequences were provided for responding to comparison

stimuli. Prior to testing, students were informed that they

were to be tested and that they would not receive the series

of tones for correct responses. A testing trial was the same

as a training trial except there were no programmed

consequences for correct or incorrect responding. When a

student responded to a correct or incorrect comparison

stimulus, the computer screen was automatically cleared in









preparation for the next test trial. When a testing session

was completed, the student's score (number correct) was shown

on the computer screen.

Variables Under Investigation

Independent Variable

The modality of stimulus presentation was the

independent variable in this investigation. Training and

testing for stimulus equivalence occurred in two ways: (a) a

condition in which all stimuli were visual and (b) a cross-

modal condition in which sample stimuli were auditory and

comparison stimuli were visual. The all-visual condition

incorporated into training and testing three forms of visual

stimuli (printed digits, printed words, and analog clock

faces). The cross-modal condition incorporated an auditory

stimulus (digitized mechanically voiced clock times) and only

two forms of visual stimuli (printed digits and analog clock

faces). Each student was taught classes of clock times under

both conditions.

Dependent Variable

The dependent variables are measures of correct

matching-to-sample items on conditional and equivalence

relations. Three measures were used: percent of correct

responses, number of training and testing sessions to

criterion, and item error analysis. Following each session

in both the teaching and testing phases, the percent of

correct responses was calculated for each independent









variable. In addition, the number of training and testing

sessions needed to reach a criterion of 91.6% correct in

Experiment 1 and 87.5% correct in Experiment 2 on equivalence

tests for each independent variable was calculated.

Matching-to-sample instruction sometimes results in the

development of equivalence classes different than those

intended by the experimenter (Saunders & Green, 1992). In

the event that an equivalence class failed to emerge in

either of the experimental treatments, an exhaustive analysis

of response data was conducted. An item error analysis,

including an analysis of the incorrect comparisons selected

and the position of the selections, was conducted to

determine whether there were any consistent patterns among

error responses.

Measurement

Independent variable. Procedural reliability for the

independent variable was evaluated through an extensive

preview of the HyperCard training and testing stacks prior to

experimental application. The sequence of presentation of

the sample and comparison stimuli was randomly determined by

a computer program. The program kept data on the sequence

and position of all stimuli during training and testing

sessions. Reliability of the HyperCard stacks in presenting

training and testing trials and collecting response data was

demonstrated in a pilot study with 3 students.









Dependent Variable. Data needed to determine the

percent of correct responses and item error analysis was

collected each session. The HyperCard stacks were programmed

to collect response data including the comparison selections

made by the student, the screen placement of each selection,

and response latency for each trial. The response data was

presented in tabular form in a section of the HyperCard stack

that was not accessible to the student. A printout of the

response data was printed after each session.

The percent of correct responses was calculated for each

condition each session. The percent of correct responses was

obtained by dividing the number of correct responses (within

a condition) by the total number of correct plus incorrect

responses (within the condition). The percent of correct

responses for each condition was displayed graphically. The

graphic representation was analyzed visually to determine

whether patterns of responding varied according to treatment.

Charted data were analyzed for differences in level of

correct responding and direction and degree of trend for each

treatment in each experimental phase.

In Experiments 1 and 2, when a criterion of 91.6% (one

error in 12 trials and 87.5% correct (one error in eight

trials) respectively was established on equivalence tests,

the total number of training and testing trials needed to

reach criterion was calculated for each condition. One trial

consisted of the presentation of a sample stimulus followed









by the student's response to one of the comparison stimuli.

For each experiment, the number of trials within each

condition remained constant across sessions. In Experiment 1

there were 56 trials in each training session and 48 trials

in each testing session. In Experiment 2 there were 56

trials in each training session and 32 trials in each testing

session.

Error responses and response position data were

collected for each trial. The error responses and response

position data were analyzed to determine whether a student

demonstrated response or position bias.

Experimental Design

The primary purpose of this investigation was to

determine the effects of all-visual and cross-modality

stimuli on the development of equivalence classes. The

experimental design of this study was a single subject

alternating treatments design within a withdrawal strategy

(Barlow & Hayes, 1979). The design's rationale is based on

discrimination learning principles: if the same behavior is

treated differently in the presence of different stimuli,

then the behavior will exhibit different characteristics in

the presence of those stimuli (Tawney & Gast, 1984). Based

on this rationale, the alternating treatments design is

characterized by the rapid alternation of two or more

distinct independent variable conditions. Stimulus

discrimination allows the student to determine which









intervention is in effect. The combination of stimulus

discrimination and rapid alternation of interventions permits

the direct comparison of the independent variables (Barlow &

Hayes, 1979; Sulzer-Azaroff & Mayer, 1991).

The alternating treatments design was chosen as the most

appropriate for this investigation because of the following

reasons:

1. The design permits the effects of two or more

independent variables to be compared.

2. Differential effects may emerge rapidly in the

alternating treatments design, thus, it provides an

efficient method for comparing two treatments.

3. The design minimizes the extent to which the

experiment's results are confounded by sequence effects.

4. The rapid alternation of interventions in the

alternating treatment design controls for threats of

maturation and history.

5. The design is appropriate for studying dependent

variables whose rates are unlikely to be reversed

following protracted presentations of the independent

variable (Sulzer-Azaroff & Mayer, 1991; Tawney & Gast,

1984).

Experimental Procedures

All students experienced the same general procedures,

however, additional training and testing sessions were

necessary for some students and were prescribed according to









individual performances. Two experiments were conducted.

Twelve equivalence classes were trained in Experiment 1, and

sets of four equivalence classes were trained in

Experiment 2. Systematic within-subject replications were

conducted for 4 students in Experiment 2.

Equivalence Classes

Figure 3-2 illustrates the stimulus sets that composed

the all-visual and cross-modal equivalence classes in

Experiments 1 and 2. Each all-visual equivalence class

consisted of a clock time printed in words (Word), a printed

digital clock time (Digit), and an analog clock face (Clock).

Each cross-modal stimulus equivalence class contained a

mechanically voiced clock time (Spoken), a printed digital

clock time (Digit), and an analog clock face (Clock). For

ease of presentation, conditional and equivalence relations

are represented by a code for the sample stimulus and its

designated correct comparison. For example, "Word->Digit"

denotes the conditional relation in which the digital clock

time comparison is matched to the sample clock time printed

in words (i.e., "1:05" is matched to "five after one"). The

code "Spoken->Digit" denotes the conditional relation between

the voiced stimuli "five after six" and the digital

representation "6:05".

Reading Fluency

Before initial training sessions were conducted in

Experiments 1 and 2, each student was required to read







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fluently all words that would be presented as stimuli in the

clock times printed in words. Reading fluency was required

to ensure that a student could perform the reading tool

movement necessary to make Word->Digit and Word->Clock

matches. Daily reading performances were charted and

monitored using precision teaching methods. Daily reading

instruction was provided until the student was able to read

the stimulus words at a rate of 50 words per minute with 100%

accuracy. Weekly follow-up timings were conducted to ensure

that the reading rate was maintained at a minimum of 50 words

per minute.

Experiment 1

Experiment 1 Baseline. In Experiment 1, each student

was trained in a total of 12 equivalence classes. Students

were tested on the emergent relations Digit->Clock, and

Clock->Digit for all 12 equivalence classes. The dotted

lines in Figure 3-2 represent emergent relations, that is,

the relations that were tested, but never taught or

reinforced. The baseline phase served as the final criterion

for participant selection; for inclusion in the study, each

student was required to perform at or below 50% correct on

the emergent relations within each condition of the

independent variable. Equivalence tests were repeated across

sessions until responding was stable under both conditions.

Test sessions consisted of 12 trials for each of the

four relations tested. A total of 48 trials were presented









during each testing session in Experiment 1. The order of

the relations tested was alternated for each testing session.

For example, the all-visual Clock->Digit and Digit->Clock

relations were presented first on one session, and on the

next session the cross-modal Clock->Digit and Digit->Clock

relations were presented first.

Experiment 1 Training. Training for both the all-

visual and cross-modal conditions began in the same session.

The solid lines in Figure 3-2 represent the conditional

relations that the students were taught during the training

phase of the experiment. The order of condition presentation

was alternated each session. Half of the sessions began with

all-visual training followed by cross-modal training; the

other half began with cross-modal training followed by all-

visual training. The equivalence classes trained in

Experiment 1 are provided in Table 3-2. In the all-visual

condition, students selected digital clock time and analog

clock face comparisons conditionally upon the presentation of

printed time word samples (Word->Digit and Word->Clock). In

the cross-modal condition, students selected the digital

clock time and analog clock face comparisons conditionally

upon the presentation of clock times mechanically voiced

through the computer (Spoken->Digit and Spoken->Clock).

Training sessions consisted of 56 trials, with 14 trials for

each conditional discrimination taught. Training continued in





























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both conditions until a visual analysis of the data showed

that the rate of learning had leveled or until a criterion of

100% correct was reached in one of the conditions.

Experiment 1 Return to Baseline. Equivalence tests

for both conditions were administered when a visual analysis

of the data showed that learning had leveled or following a

training session in which a criterion score of 100% correct

was obtained during training for either of the experimental

conditions. Equivalence tests were repeated until responding

was stable or deteriorating under both conditions. Rather

than testing separately for evidence of symmetry and

transitivity, simultaneous equivalence tests (Sidman &

Tailby, 1982) were conducted. Testing for the property of

symmetry was possible in the all-visual condition, but not in

the cross-modal

condition. Because the mechanically voiced stimuli in the

cross-modal condition were auditory, it was not possible to

present them simultaneously as comparisons. Symmetry of the

Spoken->Digit and Spoken->Clock conditional relations could

not be determined by testing the Digit->Spoken and

Clock->Spoken relations. Simultaneous equivalence testing

allowed the number of testing trials to remain equal across

conditions.

Experiment 2

Testing and training procedures remained as they were in

Experiment 1 except sets of 4 rather than 12 equivalence









relations were trained in Experiment 2. The equivalence

classes trained in Experiment 2 are provided in Table 3-3.

Experiment 2 Return to baseline. Equivalence tests

for both conditions were administered after a training

session in which a criterion score of 100% correct was

obtained for either of the experimental conditions.

Equivalence tests were repeated until responding was stable

under both conditions. Training was resumed for any

condition in which the student did not obtain a criterion

score of 87.5% correct (1 error in 8 trials) on equivalence

testing.

Experiment 2 Additional training. Additional training

was provided for any condition in which the student did not

obtain a criterion score of 87.5% correct on equivalence

testing. If criterion was not reached in only one condition,

then training was continued for only the condition in which

criterion was not reached. Training in this phase followed

the same procedures as described above for two conditions,

except there was no alternation of conditions if only one

condition remained to be trained. Training continued until a

criterion of 100% correct was reached.

Experiment 2 Return to baseline. Equivalence tests

for both conditions were administered following the

additional training phase. Equivalence tests were repeated

until a criterion score of 87.5% correct was demonstrated or















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until it was clear that the criterion score would not be

reached. When a criterion score of 87.5% correct was not

demonstrated, additional training and testing phases were

conducted.

Experiment 2 Maintenance probes. Four of the 6

students were given equivalence tests for both conditions 2

weeks and 4 weeks after the final training session. Two

additional students were retested at only 2 weeks after the

final training session. The remaining student was not

available for follow-up testing. Testing procedures were

followed as they were in baseline. No consequences for

responding was provided; students were praised for their

participation at the end of each session.

Replication of Experiment 2

Replications of Experiment 2 provided systematic

intrasubject replication. All experimental conditions

remained the same as Experiment 2 except four new equivalence

classes were trained in each replication. The equivalence

classes trained in the replications of Experiment 2 are

provided in Table 3-3. A complete replication, including 2-

week and 4-week maintenance probes, was conducted with 2

students. An additional replication was conducted with a

third student, except only one maintenance probe was given at

2 weeks after the final training session.















CHAPTER IV

RESULTS

The major purpose of this study was to investigate the

effects of stimulus modality on equivalence class

development. Two experiments were conducted with 7 students

participating in each experiment. In Experiment 1

participants were taught conditional relations for six all-

visual and six cross-modal equivalence classes. In

Experiment 2 participants were taught conditional relations

for two all-visual and two cross-modal equivalence classes.

To determine the long-term stability of equivalence

relations, 2-week and 4-week follow-up equivalence tests were

conducted in Experiment 2. Also in Experiment 2, within-

subject replications were conducted with 4 students.

The results of Experiments 1 and 2 for each student are

described first; second, the four research questions posed in

Chapter 1 are addressed.

Student 1

Student 1 was a 6 year 9 month old male in the first

grade. His special education identification was Emotionally

Handicapped. Psychological reports indicated that Student 1

had an attention deficit disorder with hyperactivity (ADD-H).









Student 1 received special education resource services for

math, reading, and language arts for 2 1/2 hours each day.

Experiment 1

For all 7 students, six all-visual and six cross-modal

equivalence classes were trained in Experiment 1. The all-

visual classes included relations for the clock times 11:05,

6:05, 5:20, 8:20, 10:55, and 2:55. The cross-modal classes

included relations for the clock times 3:10, 12:10, 7:30,

9:30, 1:50, and 4:50. For Student 1, Experiment 1 consisted

of a baseline condition, a training condition, and a return

to baseline. Results of Experiment 1 are presented in Figure

4-1.

Experiment 1 -- Baseline. Student 1 was given a series

of two equivalence tests. Low baseline scores indicated that

the student had not previously formed equivalence relations

for any of the tested relations. The student was unable to

make correct Digit->Clock or Clock->Digit matches for either

experimental condition. The student did score 50% correct on

cross-modal Digit->Clock and Clock->Digit relations, but an

analysis of responses showed that the correct responses were

distributed across relations with no consistently correct

responding between members of any one class.

Experiment 1 -- Training. Training of the all-visual

Word->Digit and Word->Clock relations and the cross-modal

Spoken->Digit and Spoken->Clock relations was conducted for

15 sessions. Analysis of the learning rates after the 15th









session revealed that there was no increase in learning for

the all-visual condition and that the learning rate for the

cross-modal condition was increasing, but at an

unsatisfactorily slow rate. Because the learning rates were

low, training was terminated.

Experiment 1 -- Return to baseline. A series of three

equivalence tests were administered following the final

training session. Performances on the equivalence tests did

not reach the criterion level. With the exception of an

increase to 58.3% correct on the cross-modal Digit->Clock

relations at the second test session, scores on all tested

relations clustered at or below pre-training baseline levels.

The post-training baseline scores provide evidence to

conclude that Student 1 formed no equivalence relations in

Experiment 1.

Experiment 2

Experiment 2 consisted of an initial study with two

replications. For the purposes of analysis and discussion

with Student 1 and following students, initial investigations

in Experiment 2 are referred to as Phase 1 and subsequent

replications as Phase 2 and 3 respectively. For each phase

in Experiment 2, two all-visual and two cross-modal

equivalence classes were trained. The clock times trained in

each phase varied across students.

Phase 1 -- Baseline. For Student 1, the all-visual

classes trained in Phase 1 included relations for the clock









times 10:55 and 2:55. The cross-modal classes included

relations for the clock times 3:10 and 12:10. Phase 1

consisted of a baseline condition, a training condition, a

return to baseline, and 2-week and 4-week maintenance probes.

Results of Phase 1 are presented in Figure 4-2.

Two equivalence tests were administered in Phase 1.

Student 1 matched few of the all-visual and cross-modal

relations presented during baseline equivalence tests. As

indicated by the low baseline scores, the student had not

previously formed equivalence relations for any of the tested

relations.

Phase 1 -- Training. Although learning rates for both

the all-visual and the cross-modal conditions accelerated

rapidly, the correct responding in the all-visual condition

was at a higher level than that of the cross-modal condition.

After five training sessions, Student 1 obtained a criterion

score of 100% correct on the all-visual Word->Digit and

Word->Clock relations. Responding for the cross-modal

condition was not up to criterion, but had increased from

62.5% on the first training session to 87.5% on the fifth

session.

Phase 1 -- Return to baseline. A series of four

equivalence tests were administered beginning on the session

following the session in which the criterion score was

reached in the all-visual condition. On the first

administration of equivalence tests, performance on emergent









relations allowed for the conclusion that equivalence

relations had developed for the cross-modal classes 3:10 and

12:10. The all-visual equivalence class, 10:55, also

emerged, but the 2:55 class did not. An analysis of

student's comparison choices made on the all-visual

Digit->Clock relations showed that when the student chose

incorrect comparisons for the 2:55 relations, the choice that

was made was consistently the 3:10 clock. On the third

administration of equivalence tests, all cross-modal and all-

visual relations had emerged to criterion levels (87.5%),

allowing for the conclusion that Student 1 formed equivalence

classes for all relations trained in Phase 1.

Phase 1 -- Maintenance. Maintenance probes were

conducted 2 weeks and 4 weeks after the final training

session. On the 2-week administration of equivalence tests,

Student 1 continued to respond at or above the criterion

level (87.5%) for both the all-visual and the cross-modal

conditions. On the 4-week probe, responding on the all-

visual relations maintained at the 100% level. Responding on

the cross-modal relations decreased slightly to 87.5% on the

Clock->Digit relations and to 75% on the Digit->Clock

relations. An analysis of errors revealed that Student 1

demonstrated no consistent patterns of incorrect choices.

Phase 2 -- Baseline. For Student 1, the all-visual

classes trained in Phase 2 included relations for the clock

times 6:05 and 11:05. The cross-modal classes included