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Running head: STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING

Arbitrary Conditional Discriminations and Stimulus Equivalence

With Young Children Within the Classroom Setting

Emily C. Leonard

Dissertation

Presented in Partial Fulfillment of the Requirements for the Degree of Doctor of

Philosophy in the Graduate School of Social Work of Simmons College

August 17, 2015

Dissertation Committee: Approved By:

Dr. Gretchen Dittrich ________________________Dr. Harry Mackay Dr. Russell W. MaguireDr. Russell W. Maguire Advisor, Department Chair

Graduate School of Social Work

© 2015, Emily C. Leonard

STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING

Abstract

The current series of experiments investigated the formation of equivalence classes with

young children in classroom settings. Nine visual stimuli were divided into three groups

(A, B, and C) each containing three stimuli (A1, A2, A3, B1, B2, B3, C1, C2, C3). All

participants were pretested on all possible stimulus-stimulus relations. Then conditional

discrimination training was used to teach a few stimulus-stimulus relations (i.e., the AB

and AC relations). Following training, participants were posttested on all stimulus-

stimulus relations to determine if untrained relations emerged indicating the formation of

equivalence classes. Experiment 1 demonstrated the emergence of stimulus-stimulus

relations consistent with stimulus equivalence among stimuli from the third-grade science

curriculum of a boy with autism. Experiment 2 was a systematic replication of

Experiment 1 with six third-graders. Finally, Experiment 3 replicated the findings of

Experiment 2 with kindergarten students. Results indicated the emergence of match-to-

sample performances, suggesting that these methods could be applied both as an efficient

primary teaching technique and as a remediation technique for young children in the

classroom setting.

KEYWORDS: stimulus equivalence, conditional discrimination training, match-to-

sample, elementary education, science, equivalences

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Arbitrary Conditional Discriminations and Stimulus Equivalence

With Young Children Within the Classroom Setting

Numerous human behaviors emerge without direct reinforcement (Sidman, 1994).

Researchers have studied language development (Donahoe & Palmer, 2004; Fields,

Verhave, & Fath, 1984; Hayes, Blackledge, & Barnes-Holmes, 2001; Jenkins & Palmero,

1964; Lazar & Kotlarchyk, 1986; Sidman, 1971; Sidman & Willson-Morris, 1974;

Skinner, 1957) and concept formation (Bush, Sidman, & de Rose, 1989; Katz & Wright,

2006; Lawson, & Kalish, 2009; Lazar, 1977) trying to account for emergent

performances. However, Sidman’s (1987) analysis of stimulus equivalence may provide

the most parsimonious account of how such untrained performances are established. The

following provides an overview of related empirical studies and introduces key

vocabulary and basic notions as they relate to stimulus equivalence.

Stimulus substitutability and emergent behavior

Sidman first described stimulus equivalence in his 1971 study. The direct focus of

the study was on prerequisite skills required for the emergence of reading comprehension

(Sidman, 1994). However, the outcome demonstrated untrained responding, which

required further investigation (Sidman, 1971). The participant in the study was a 17-year-

old male with developmental disabilities who had a dense history with match-to-sample

(MTS) procedures involving pictures, colors and printed numbers but had not learned to

match these stimuli to their printed names. In Sidman’s experiment, MTS performances

with 20 pictures and the corresponding printed and dictated names were assessed using

tasks in which a sample stimulus and eight comparison stimuli were presented on each

trial. One comparison was correct, as it corresponded to the sample, while the other seven

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comparisons did not and were incorrect. Selection of the correct comparison was

reinforced whereas selection of incorrect comparison was followed by the presentation of

the next trial. Pretest results showed that he matched the pictures and printed words to

one another but only matched the pictures and not the words to their dictated names.

Furthermore, he did not match the printed words to the corresponding pictures, and

therefore, was described as lacking reading comprehension (Sidman, 1971).

The participant was also tested on oral naming tasks in which he was to respond

vocally with the name of the picture or printed word displayed. He named the pictures but

not the printed words. The differential reinforcement for responding was delivered as in

the matching tasks (Sidman, 1971).

After the baseline evaluations were completed training was given to establish

highly accurate matching of the printed words to their dictated counterparts. Results from

posttraining tests then suggested that the corresponding words and pictures had become

mutually substitutable members of classes (i.e., members of each class were equivalent to

one another). Specifically, when presented with the spoken word, the participant in

Sidman’s (1971) study selected the correct picture from an array of picture comparisons

(i.e. discriminative stimuli), thus demonstrating auditory to visual matching with pictures

at the start of the study. He then was trained to select textual comparison stimuli

conditionally upon the presentation of the same auditory samples. As a result, the textual

and picture stimuli became mutually substitutable and functioned as both conditional and

discriminative stimuli in matching tasks (Dube, MacIlvane, Maguire, Mackay &

Stoddard, 1989). This was especially noteworthy since neither the textual nor picture

stimuli had functioned as sample stimuli during training. It should be noted that all

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possible tests for mutual substitutability could not be performed because the procedures

did not readily allow matching with auditory stimuli presented simultaneously as

comparisons instead of successively across trials as samples.

The results from Sidman’s (1971) study generated new questions about emergent

relations and equivalence. From the experiment, Sidman was unable to determine if the

trained relations were required to be cross-modal, (e.g., auditory and visual), or whether

emergent matching would occur if all stimuli were visual. In addition, since the

participant also demonstrated emergent oral naming performance (i.e., provided the vocal

name for the printed words and selected the printed words when the auditory names were

dictated), Sidman was unable to determine if naming facilitated the emergence of text to

picture matching. Even though the participant did not name stimuli aloud during visual-

visual matching tasks, such responding could occur covertly (Sidman, 1971).

Set theory and overview of stimulus equivalence

When describing the results from the first experiment, Sidman (1971) initially

referred to each conditional relation as a separate equivalence relation (e.g., of dictated

words to pictures and of dictated to printed words). He later revised the description of

equivalence to include all of the ordered pairs of stimuli established by the contingencies

used in training (Sidman, 1994). The stimuli from both the baseline and emergent

relations are included in the classes formed. Sidman and colleagues (1982) also clarified

that although the development of if-then relations between the sample and comparison

stimuli are an outcome of conditional discrimination training, it should not be assumed

that the sample and comparison have become mutually substitutable or equivalent.

Specific tests for the properties of equivalence are required to confirm that the

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conditional discrimination procedure resulted in new MTS performances that were not

trained directly (Sidman et al., 1982). These tests for equivalence include evaluations of

the properties of reflexivity, symmetry, and transitivity (Sidman & Tailby, 1982).

Sidman and Tailby (1982) adapted definitions of equivalence relations from

mathematical set theory to parsimoniously describe the development of untrained

stimulus control in emergent stimulus-stimulus relations. Mathematical set theory

(Gellert, Kustner, Hellwich & Kastner, 1977) states that relations among events that

demonstrate the properties of reflexivity, symmetry, and transitivity are equivalence

relations (Sidman & Tailby 1982). When these properties describe the relations among

samples and comparisons of MTS tasks, it is possible to infer that these stimuli are

members of a class (Sidman & Tailby 1982). The property of reflexivity requires the

demonstration that each stimulus is related to itself (Gellert et al., 1977), for example,

through tests for identity match to sample (IDMTS). Symmetry refers to the matching

performance showing untrained functional sample-comparison reversibility (Dube, Green

& Serna, 1993). Symmetry is demonstrated if matching of one relation (AB) is trained

and performance on the sample-comparison reversal task (BA) emerges. Finally, the

property of transitivity refers to novel conditional and discriminative control as the result

of previous training (Dube, et al., 1989; Sidman et al., 1982). Transitivity requires three

groups of physically dissimilar stimuli (e.g., arbitrarily called sets A, B, and C). If AB

and BC matching are trained, testing AC matching can demonstrate transitivity (Dube, et

al., 1993). The AC matching performance emerges even though AC and CA conditional

discriminations have never been explicitly taught (Sidman & Tailby, 1982).

Training and class formation

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The stimulus equivalence paradigm provides an efficient and effective method for

teaching complex academic skills (Critchfield & Fienup, 2010; Sidman, 1994). To

illustrate specifically, consider the English and Spanish printed words for cat and a

picture of a cat, the English and Spanish words for fish and a picture of a fish, and the

English and Spanish words for a monkey and a picture of a monkey. This example would

require training that establishes three stimulus classes, one each for cat (Class 1), fish

(Class 2) and monkey (Class 3). Each class consists of three visually dissimilar stimuli.

For example, for Class 1, one stimulus, designated A1, would be English text (e.g.,

CAT), another (B1) would be Spanish text (e.g., GATO), and a third (C1) would be a

picture of a cat. Additional English and Spanish textual stimuli, FISH (A2) and PEZ (B2)

respectively, and a corresponding picture (C2) provide members of Class 2, and so on.

These stimuli are then used in training conditional discriminations, often through

MTS procedures. The training can be conducted in a variety of ways, one of which is

described as follows: to teach an English-speaking student to match the Spanish printed

words (Group B) as well as the English printed words (Group A) with corresponding

pictures (Group C), the student may be trained first to match the Spanish printed words to

the English printed words (AB relations), and then match the pictures to the

corresponding Spanish printed words (BC relations). In each trial, a sample stimulus and

three comparison stimuli are presented. Only one of the comparison stimuli is correct.

The correct comparison belongs in the same potential class as the sample and is assigned

by the experimenter. Responses to the correct comparison are reinforced and responses to

either of the two incorrect comparisons are not. For example, if CAT (A1) is presented as

the sample, with comparisons GATO (B1), PEZ (B2) and MONO (B3), responses to

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GATO are reinforced. The sample-comparison relation CAT-GATO thus is trained

directly. This is repeated for all AB relations (A1-B1, A2-B2, A3-B3) (Maguire, Stromer,

& Mackay, 1995; Sidman & Tailby, 1982).

After AB relations are taught, a second set of three stimulus-stimulus relations are

trained. If BC relations are trained, then the participants are presented with GATO (B1)

and a comparison array of Group C stimuli, a picture of a cat, a fish and a monkey.

Selecting the picture of a cat (C1) in the presence of sample GATO (B1) is reinforced.

When PEZ (B2) is presented as a sample, a response to a picture of a fish (C2) is

reinforced, and finally, when sample MONO (B3) is presented, the selection of a picture

of a monkey (C3), rather than a picture of a cat (C1) or fish (C2), is reinforced. Just as

with training AB relations, the reinforcement contingencies establish the conditional

relations B1-C1, B2-C2 and B3-C3. Following the training of all English-to-Spanish text

(AB) relations (A1-B1, A2-B2, and A3-B3) and the training of all Spanish-text-to-picture

(BC) relations (B1-C1, B2-C2 and B3-C3), MTS tasks are used to evaluate if untrained

conditional discriminations emerge (Maguire et al., 1995; Sidman et al., 1982).

The untrained relations tested include IDMTS relations (A1-A1, A2-A2, A3-A3,

B1-B1, B2-B2, B3-B3, C1-C1, C2-C2, and C3-C3). These relations document reflexivity

(Sidman & Tailby, 1982). For example, with CAT (A1) presented as sample and CAT

(A1), FISH (A2), and MONKEY (A3) as the comparisons the selection of comparison

stimulus CAT (A1) from the array would demonstrate reflexivity.

Symmetry is also evaluated following the training of the baseline conditional

discriminations. In these tests, the stimuli previously presented as samples are presented

as comparisons. For example, the English textual stimuli (Group A) presented as samples

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for AB training are presented as comparisons on trials with the Group B stimuli (Spanish

text) as samples. Thus, the text GATO (B1) would be presented as the sample on a

symmetry test, and CAT, FISH, and MONKEY (Group A) would be comparisons.

Selecting CAT would be a correct response since CAT and GATO are both stimuli from

class 1. The emergence of the conditional relations B1-A1, B2-A2, B3-A3, C1-B1, C2-

B2, AND C3-B3 on test trials would demonstrate symmetry of all the trained relations.

Finally, the English text (Group A) and pictures (Group C), which had previously

only been presented in conditional discriminations with stimuli from Group B, would be

used in MTS tasks to determine if novel conditional discriminations emerged between

Group A and Group C stimuli. English textual stimuli (Group A) would be presented as

the samples and corresponding picture stimuli (Group C) would serve as comparisons.

The emergence of the conditional relations A1-C1, A2-C2, A3-C3 on test trials would

demonstrate transitivity. When all three properties (i.e. reflexivity, symmetry, and

transitivity) are demonstrated, the stimuli are said to be members of an equivalence class,

because the stimuli have become mutually substitutable (Sidman, 2000; Sidman et al.,

1982; Sidman & Tailby, 1982).

Class formation

Once an equivalence class is demonstrated, the effect of a contingency applied to

one member must also appear with respect to other members of the class without

additional training (Goldiamond, 1962). For example, after stimuli are demonstrated to be

members of an equivalence class (e.g., stimuli A1, B1 and C1 from the previous

example), the participant could be trained to match an additional stimulus, D1, (e.g., the

French text) to the A1 stimulus. Since the stimulus A1 is a member of an equivalence

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class, responding to stimulus D1 would then be controlled also by other stimuli within the

class (e.g., B1 and C1). These stimuli are now members of a stimulus class. The stimulus

class thus consists of different discriminative stimuli that occasion the same response.

Through differential reinforcement contingencies stimuli within and outside of a class

develop differential control of behavior (Goldiamond, 1962).

Trained relations and training paradigms

In theory, the minimum number of stimulus-stimulus relations that require direct

training for all stimuli to form an equivalence relation is N-1 (Critchfield & Fienup,

2008). The term N represents the number of stimuli within a class. Therefore, in a class

with three stimuli (N=3) the number of relations requiring direct training (N-1) would be

two (3-1=2). Specifically, for a class with three stimuli, A1-B1-C1, two stimulus pairs

A1-B1 and B1-C1 would be trained and the remaining two-term relations should emerge

(Fields et al., 1984). These remaining two-term relations should emerge because all the

stimuli were indirectly related through training (Critchfield & Fienup, 2008; Fields et al.,

1984). As class size expands, the number of relations that must be trained increases. As a

result of training a greater number of relations, the number of potential emergent relations

increases as well. In a five-member class, four relations would be trained (i.e. A1-B1, B1-

C1, C1-D1, D1-E1) and stimulus relations should emerge. For example, the transitive

relation B1-E1 should emerge due to the shared training that the stimuli B1 and E1 have

with stimuli C1 and D1, respectively (Fields et al., 1984).

The number of trained relations relates directly to the size of the potential

stimulus classes, but the order in which they were trained can vary (Arntzen, Grondahl, &

Eilifsen, 2010; Critchfield & Fienup, 2008). For example, the case presented with English

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and Spanish textual stimuli utilized a linear training model, in which the AB and then the

BC relations were trained. Match-to-sample procedures are frequently used for training

with this linear model or either a one-to-many (OTM) or a many-to-one (MTO) training

paradigm (Arntzen, Halstadtro, Bjerk, & Halstadtro, 2010; Saunders, Saunders, Williams,

& Spradlin, 1993). The OTM training paradigm presents sample stimuli from the same

group (e.g., Group A) for both trained relations and comparisons from the remaining

stimulus groups (Group B and Group C). For example, in Sidman’s (1971) original study,

the participant demonstrated auditory to picture matching (AB) when he entered the study

and was taught auditory to visual textual relations (AC). The emergent relations

demonstrated were between the B and C stimuli (i.e., BC and CB matching in a three-

member class (Sidman, 1971). Whereas the MTO training presents samples from

multiple stimulus groups (i.e. groups B and C) while only presenting comparisons from

group A. Research has explored a variety of paradigms to determine if the emergent

relations are affected by which stimulus-stimulus relations are trained (Arntzen, Grondahl

et al., 2010).

For example, Arntzen, Grondahl, and colleagues (2010), trained 12 participants,

eight college-aged individuals, two adults and two children, with three sets of

experimental stimuli, one set for each of the different paradigms. Participants were split

into three groups to control for the sequence in which paradigms were presented (e.g.,

One group was trained with a linear sequence, then an OTM and finally an MTO

paradigm). For each training paradigm there were new sets of stimuli. The results

indicated that the OTM paradigm was slightly more effective than the MTO. The

difference between the OTM and MTO training paradigms became more pronounced as

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the class size increased (Arntzen, Grondahl et al., 2010). These findings were not

consistent with studies involving younger participants. When children were trained on

conditional discriminations, research suggested that the MTO arrangement was more

effective that the OTM (Arntzen & Vaidya, 2008; Saunders et al., 1993; Saunders &

Green, 1999; Saunders & McEntee, 2004). Arntzen, Grondahl, and colleagues (2010),

suggested that the discrepancy might be due to the fact that often only two comparisons

were presented to children in MTS tasks (Saunders et al., 1993; Saunders & Green, 1999;

Saunders & McEntee, 2004). This discrepancy is significant to the present studies, which

include young children. The number of comparisons presented in an array is, therefore,

an important experimental variable and will be further discussed.

Presentation of comparisons

In Sidman’s (1971) initial experiment, one correct comparison stimulus was

presented along with seven incorrect comparisons. However, as experiments became

more complex, an array of eight comparisons was not always feasible, and the number of

comparisons presented was reduced (Sidman, 1987). Sidman (1987) suggested that the

simpler presentation of the two-choice comparison array might be an optimal

arrangement for studying individuals with cognitive delays. However, presenting only

two comparisons during training increases the probability of false positives during testing

(Carrigan & Sidman, 1992; Sidman, 1987). Thus stimuli other than the correct

comparisons may come to control responding (Fields, et al., 1984).

In a two-choice array, one comparison stimulus (S+) is designated correct and

discriminative for reinforcement and the other (S-) is not. Notably, however, when the

same two stimuli are always presented as comparisons together it is possible that the

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selection of the correct comparison is the byproduct of the participant excluding

(responding away from) the S- rather than selecting the S+. In other words, that training

may result in S- control developing rather than discriminative control by the correct

comparison (Carrigan & Sidman, 1992; Fields, et al., 1984; Sidman, 1987). Such an

outcome is undesirable: both forms of stimulus control are important in developing

repertoires.

Further, with a two-choice array, the probability of selecting the correct

comparison by chance (and producing a reinforcer) is greater than the probability of

selecting the correct comparison by chance in a three-choice array (Fields et al., 1984).

False positives, therefore, have a greater probability of occurring when fewer

comparisons are presented in an array. As the number of comparisons in the array

increases, however, probability of false positives occurring decreases (Sidman, 1987).

Therefore, the configuration of the comparison array must be considered an important

aspect of the training procedure. Including more than two comparisons increases the

probability of developing the forms of stimulus control important for performance of

conditional discriminations.

In a related matter, Fields and colleagues (1984) suggested that in order to rule

out false positives and adequately assess for transitive stimulus control, the frequency of

presentation of both the correct and incorrect comparison must be controlled during

training. The stimuli that serve as correct or incorrect comparisons vary across trials and

each stimulus acquires discriminative control according to its history as S+ or S-. Fields

and colleagues (1984) caution that discriminative control may result from repeated and

unequal presentations as S+ and S-, a factor that may interfere with development of

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conditional control of comparison selection by the samples.

To determine the extent to which responding is controlled by the frequency of

correct and incorrect comparison presentations (discriminative control), Fields and

colleagues (1984) suggested calculating the valence for the presentation of each stimulus

as both a correct and incorrect comparison. Valence is a derived measure used to express

the extent to which each comparison is presented as a functional S+ and S- (Fields et al.,

1984). Valence is calculated by subtracting the number of incorrect comparison

presentations from the number of times the stimulus is presented as a correct comparison

(Fields et al., 1984). For example, in training with a two-choice array of comparisons, if

stimulus A1 were presented six times as the correct comparison and six times as the

incorrect comparison, the valence would be zero (+6-6=0), a desirable feature. However,

if A1 were presented four times as the correct comparison and six times as the incorrect

comparison the valence would be +2 (+6-4=+2) and if A1 were presented six times as the

correct comparison and only four times as the incorrect comparison the valence would be

-2 (+4-6=-2) (Fields, et al., 1984).

Fields and colleagues (1984) described three possible valence trial-types. The first

valence type is the strong comparison configuration in which the stimulus appears as an

incorrect comparison a greater number of times than a correct comparison. Valences in a

strong configuration suggest possible bias toward incorrect responses since opportunities

to respond to that particular stimulus as an incorrect comparison were greater than

opportunities to respond to the stimulus as a correct comparison. Therefore, responses to

the stimulus as correct comparison during testing would indicate strong transitive

stimulus control (Fields et al., 1984). Another valence type described is an inadequate

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configuration in which the valence of the correct comparison was greater than the valence

of the incorrect comparison producing a negative valence. Responses made to the correct

comparison within that type of inadequate configuration thus would not provide

sufficient evidence to demonstrate transitive stimulus control but might simply reflect its

particular history with respect to reinforcement. Correct responding during transitive tests

could be the result of exclusion or an artifact from the arrangement of comparisons,

rather than transitive stimulus control (Fields et al., 1984). Balancing the presentation of

comparisons throughout training decreases the likelihood of false positives in transitive

tests (Fields et al., 1984). The last valence type is a neutral comparison configuration in

which the presentations of each stimulus as correct and incorrect were equal. Responses

during tests for transitivity with a neutral configuration are unlikely to develop bias due

to the reinforcement history of comparison stimuli displayed. Selection of the correct

comparison would suggest transitive stimulus control (Fields et al., 1984). Therefore,

comparison presentation with a neutral valence would ensure transitive control is

demonstrated rather than an experimental artifact.

Fields and colleagues (1984) also suggested testing for transitive relations by

presenting novel incorrect stimuli. Novel stimuli would be stimuli the participant had not

encountered during training and could be substituted for another comparison in test

arrays. Responses to the correct comparison would suggest transitive stimulus control and

provide evidence that the stimulus control was not specific to the context supplied by

previous incorrect comparisons (Fields et al., 1984).

Fields and colleagues (2009) provide an example of incorporating novel

comparisons into testing. They conducted training and testing sessions using a two-choice

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array of comparisons in which the discriminative stimulus was always presented with the

same incorrect comparison. However, participants responded reliably with class-

consistent responses during trials in which two additional negative comparisons were

presented. This indicated that the participants’ responses were controlled by the

experimenter-defined sample and discriminative stimulus rather than by the S-, as

discussed by Sidman (1987) and Fields and colleagues (1984).

Presentation of MTS tasks

Regardless of the particular training paradigm employed or size of the comparison

array, MTS procedures have frequently been used in stimulus equivalence research

(Sidman & Tailby, 1982). Match-to-sample tasks are used to both train conditional

discriminations and to test for emergent conditional discriminations. These tasks can be

presented in a range of formats, via computer or as manual activities. For example,

Arntzen, Halstadtro, and colleagues (2010) used a MTS computer program to teach a 16-

year-old with autism conditional discriminations involving piano cords. The participant

was trained and tested with four different sets of stimuli. Each set contained four

physically dissimilar groups of visual representations of major or minor chords. Group A

consisted of chord names written in Norwegian, Group B were the corresponding chords

depicted as dots on piano keys, Group C depicted chords as notes on a music staff and

Group D consisted of chords written in Vietnamese. Two of the sets contained stimuli

related to major chords and two sets minor chords (Arntzen, Halstadtro et al., 2010).

Arntzen, Halstadtro and colleagues (2010) used both an OTM paradigm and an

MTO paradigm for training. Two sets (one major chord set and one minor set) were

trained with each of the paradigms. During OTM training, AB relations were trained first

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followed by AC relations, and then intermixed trials. Whereas during MTO training AB

relations were trained followed by CB relations, and then intermixed trials. After three

three-member classes were established, both the number of classes and of class members

were expanded by the addition of stimulus Set D. That is, the participant was then trained

and tested with four three-member classes followed by four four-member classes. With

the OTM training, AD relations were added, and with the MTO training, the DB relations

were added (Arntzen, Halstadtro et al., 2010).

Arntzen, Halstadtro and colleagues (2010) tested for emergent relations, and the

results demonstrated emergent performances consistent with stimulus equivalence

following OTM training for all sets. Tests for emergent relations following MTO training

demonstrated performances consistent with equivalence for all sets except the four four-

member classes with minor chords (Arntzen, Halstadtro et al., 2010). These findings

suggested that computer-based procedures provided effective training. Specifically, the

authors suggested that computer-based instruction provided reliable presentations and

scoring during MTS procedures (Arntzen, Halstadtro et al., 2010).

Computerized instruction has been used in numerous other studies and offers the

primary advantage of having the software manage stimulus presentations, timing, and

data collection (e.g., Arntzen, Grondahl et al., 2010; Arntzen, Halstadtro, Bjerke, Wittner,

& Kristiansen, 2014; Critchfield, 2014; Haegele, McComas, Dixon, & Burns, 2011;

Lynch & Cuvo, 1995; Stromer & Mackay, 1992; Walker & Rehfeldt, 2012). Haegele and

colleagues (2011) for example, analyzed the effects of computerized MTS procedures

compared to language immersion instruction on second language learning. Students in the

experimental group left the native language classroom and received computer-based

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language instruction for 15 minutes each day. The control group received two hours of

language immersion instruction in the classroom each day. The computerized group was

trained to match both number names written in the participants’ native language and

digits to the corresponding auditory English numbers. Results indicated the emergence of

stimulus-stimulus relations consistent with equivalence classes for all students who

received the computerized intervention. Students in the control group failed to

demonstrate class formation, and showed minimal improvement between the pretest and

posttest (Haegele et al., 2011). The results suggested that computerized training provided

effective instruction that resulted in the desired equivalence relations (Haegele et al.,

2011).

Walker and Rehfeldt (2012) and Critchfield (2014) extended computerized

instruction to an online course-delivery system. Results from both studies indicated that

the online format was effective in producing equivalence classes for college academic

content. Furthermore, Critchfield demonstrated that MTS procedures could be replaced

with verbal explanations, which reduced the instructional time required. The online

instructional system also allowed students to participate in training from a variety

different of environments (e.g. living spaces, coffee shops, or campus student centers)

(Critchfield, 2014). The flexibility of such an online instructional system could allow

effective training to reach a greater number of individuals without requiring them to

travel to an educational institution.

Training involving manual manipulation of stimuli (e.g., stimuli presented in a

three-ring binder, multiple choice questionnaire, or presented on cards), has also been

used effectively in training conditional discriminations (e.g, de Rose, de Souza, & Hanna,

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1996; Devany, Hayes, & Nelson, 1986; LeBlanc, Miguel, Cummings, Goldsmith, & Carr,

2003; Miguel, Yang, Finn, & Ahearn, 2009; Walker, Rehfeldt, & Ninness, 2010). For

example, LeBlanc and colleagues (2003) implemented a MTS procedure and presented

materials manually using a three-ring binder. Students responded by removing the

selected comparison from a Velcro sheet and handing it to the experimenter. In

posttesting both participants demonstrated successful three-member class-formation for

stimuli related to United States geography (LeBlanc et al., 2003).

Stimulus equivalence has attracted researchers because the emergence of new

MTS performances follows training of only a few conditional discriminations (Sidman,

1994). The emergence of equivalence relations is of particular interest not only because

of the efficiency and effectiveness of the procedures involved, but also because increased

understanding of the variables that are relevant may help to account for complex human

behavior, including verbal behavior and creativity (Barnes, 1994; Hayes et al., 2001;

Sidman, 1971; Sidman, 1994; Sidman & Tailby, 1982).

Variety of stimuli

Many stimulus equivalence studies have demonstrated emergent performances

indicating classes of equivalent stimuli following conditional discrimination training with

stimuli from academic areas, such as math (Hall, DeBernadis, & Reiss, 2006; Leader, &

Barnes-Holmes, 2001; Lynch & Cuvo, 1995), reading (deRose et al., 1996; Lane &

Critchfield, 1998; Mackay, 1985; Melchiori, de Souza, & deRose, 2000; Sidman, 1971),

spelling and letter names (Stromer, Mackay, & Stoddard, 1992), coin identification

(Keintz, Miguel, Kao, & Finn, 2011), languages (Siguroardottir, Mackay, & Green, 2012)

and tree and plant identification (Arntzen et al., 2014). The formation of equivalence

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classes has also been demonstrated with stimuli in the areas of facial recognition

(Cowley, Green, & Braunling-McMorrow, 1992), and use of daily schedules (Miguel et

al., 2009). Emergent stimulus-stimulus relations indicating classes of equivalent stimuli

have been demonstrated with a wide range of stimuli suggesting the applied value of

studying emergent relations within educational settings (e.g., Arntzen, Halstadtro et al.,

2010; Cowley et al., 1992; deRose et al., 1996; Hall et al., 2006; Keintz et al., 2011; Lane

& Critchfield, 1998; Leader & Barnes-Holmes, 2001; LeBlanc et al., 2003; Lynch &

Cuvo, 1995; Mackay, 1985; Melchiori et al., 2000; Miguel, Petursdottir, Carr, & Michael,

2008; Miguel et al., 2009; Sidman, 1971; Stromer et al., 1992).

Studies of equivalence relations also extend beyond specific academic stimuli,

and may provide explanations for verbal behavior (Shahan & Chase, 2002), creativity,

(Shahan & Chase; 2002, McVeigh & Keenan, 2009), and other complex behaviors (e.g.,

Adcock et al., 2010; Critchfield, 2014; McVeigh & Keenan, 2009). Shahan and Chase

(2002) argued that equivalence describes the occurrence of accurate responding to

untrained relation for both verbal and novel behavior. Parts of speech (e.g., nouns,

adjectives, verbs) can form equivalence classes and become equivalent in regards to

position within a sentence (Shahan & Chase, 2002). For example, adjectives could be

taught to be interchangeable in accord with their position in relation to a noun in the

sentence. Equivalence classes could also form among members of a category (e.g.,

colors, shapes, sizes) (Shahan & Chase, 2002). Lowe, Horne, and Hughes (2005)

extended the research on functional equivalence classes by teaching children to emit the

vocal response “zog” or “vek” in the presences of specific stimuli (i.e., tacts).

Specifically, each vocal response was taught in the presence of three particular arbitrary

20


stimuli. The children were then taught to wave or clap to one of the three arbitrary stimuli

from each class. Following training, transfer of function tests demonstrated class

formation. The clapping or waving response emerged for the two remaining arbitrary

stimuli that controlled the same vocal response (Lowe et al., 2005).

In a second experiment, Lowe and colleagues (2005) expanded stimulus classes

by training the manual response (e.g. wave or clap) to new stimuli. Tests were then

conducted to determine whether the new stimuli had entered into the stimulus classes

with the initial three arbitrary stimuli. The results demonstrated that the new stimuli had

entered into the previously established classes zog and vek. (Lowe et al., 2005). The

research by Lowe and colleagues (2005) has also been extended to more complex

responses, such as drawing (McVeigh & Keenan, 2009). Several other studies have

suggested that stimulus equivalence may partially account for creativity, but do not

elaborate or provide data to support this claim (Runco, 2007; Winston & Baker, 1985).

Variety of participants

In addition to studying a wide range of stimuli, stimulus equivalence studies have

also included a wide range of participants. Many of the studies evaluated emergent

relations in participants with autism (Arntzen, Halstadtro et al., 2010; Arntzen, et al.,

2014; Eikeseth & Smith, 1992; Green, 2001; Keintz et al., 2011; LeBlanc et al., 2003;

Maguire, Stromer, Mackay, & Demis, 1994; Miguel et al., 2009). Other studies

investigated whether or not equivalence can be demonstrated among participants with

brain injury (Cowley et al., 1992), developmental disabilities (Arntzen, Grondahl et al.,

2010; Hall et al., 2006; Lane & Critchfield, 1998; Stromer & Mackay, 1992), hearing

impairment (Barnes, McCullagh, & Keenan, 1990), and visual impairment (Toussaint &

21


Tiger, 2010). Studies have also included participants recommended by a teacher for low

academic performance (de Rose et al., 1996; Lynch & Cuvo, 1995). Finally, a small

number of studies included typically developing individuals (Augustson & Dougher,

1991; Devany et al., 1986; Eilifsen & Arntzen, 2009; Joyce, Joyce, & Wellington, 1993:

Lynch & Cuvo, 1995; Miguel et al., 2008; Pilgrim, Jackson, & Galizio, 2000).

One study involving typically developing students investigated emergent

stimulus-stimulus relations with fractions and decimals (Lynch & Cuvo, 1995). Fifth and

sixth grade students were selected because their math teacher identified them as having

difficulty with fraction-decimal relations. A computer was used for training and data

collection. All sessions occurred outside of the students’ classroom and were scheduled

based on the students’ availability. Students were trained to match printed fraction ratios

to corresponding picture representations (AB relations), and the picture representations to

the corresponding printed decimals (BC relations). All participants demonstrated

performances indicating the formation of equivalence classes. The results from Lynch

and Cuvo (1995) supported the previously demonstrated emergence of many relations

after training only a few and extended previous findings by using novel mathematical

stimuli.

The literature on stimulus equivalence also spans a broad age-range of

participants. Multiple studies trained adults (Cowley et al., 1992; Melchiori et al., 2000;

Eilifsen & Arntzen, 2009; Sidman, Wynne, Maguire, & Barnes, 1989; Siguroardottir et

al., 2012) or elementary-aged students (e.g., de Rose et al., 1996; de Rose, Hidalgo, &

Vasoncellos, 2013; Keintz et al., 2011; LeBlanc et al., 2003; Lynch & Cuvo, 1995;

Melchiori et al., 2000; Miguel et al., 2009; Pilgrim et al., 2000; Stromer & Mackay,

22


1992). The participants in the study conducted by Melchiori and colleagues (2000) were

described as preschoolers, however in the United States they would have been

elementary-aged. A smaller number of studies investigated the emergence of novel

conditional discriminations in even younger children (e.g., Arntzen & Holth, 2000;

Auguston & Dougher, 1991; Boelens, Van Den Broek, & Van Klarenbosch, 2000;

Devany et al., 1986; Egli, Joseph, & Thompson, 1997; Haegele et al., 2011; Joyce et al.,

1993; Pilgrim et al., 2000). With some younger learners additional instruction may be

required if the desired arbitrary conditional discriminations were not demonstrated

following training procedures (Pilgrim et al., 2000).

Stimulus equivalence research in the classroom

Even with the breadth of research in stimulus equivalence, including participants

across different ages and types of disability (Cowley et al., 1992; Fields et al., 2009; Lane

& Critchfield, 1998; Leblanc et al., 2003; Lynch & Cuvo, 1995; Pilgrim et al., 2000;

Smeets & Barnes-Holmes, 2005), using different training paradigms (Arntzen, Grondahl

et al., 2010; Saunders et al., 1993), and a wide variety of academic stimuli (Arntzen,

Halstadtro et al., 2010; Arntzen et al., 2014; Cowley et al., 1992; Keintz et al., 2011;

Leblanc et al., 2003; Lynch & Cuvo, 1995; Miguel et al., 2009; Stromer & Mackay,

1992), the stimulus equivalence paradigm has yet to be integrated into general education

instruction within the classroom or at school-wide level, in spite of direct efforts to

facilitate such integration (Stromer et al., 1992).

Fields and colleagues (2009) discussed the benefit of integrating teaching

procedures that produced emergent stimulus-stimulus relations indicating classes of

equivalent stimuli into standard educational practices. The researchers identified that

23


college students often struggled to master concepts in statistics and that there were

numerous benefits to being able to interpret data. Therefore, college students were trained

initially to match line graphs of statistical interactions with the written textual

descriptions of the interactions (AB). This was followed by tests for the symmetrical

relations (BA). Once established, the students were taught to match the textual

descriptions with the textual names of the interactions (BC), and then tested on the

symmetrical relations (CB). After the maintenance of both symmetrical relations was

assured, transitive relations (AC and CA) were tested. The results demonstrated the

emergence of three three-member equivalence classes. The classes were then expanded

by training CD relations, in which the technical definitions of the line graph interaction

(D) were added. The training of three stimulus-stimulus relations resulted in the

emergence of 12 new relations (Fields et al., 2009).

Fields and colleagues (2009) then demonstrated the additional importance of

creating equivalence classes by administering paper-and-pencil tests that assessed for

generalization. Students who were exposed to the training program that resulted in the

formation of four equivalence classes scored an average of 37% higher on the paper-and-

pencil posttest than students in the control group, who received no additional training

between pretest and posttest. Since the stimuli presented on the posttest differed both in

form and content from those used during training, these results demonstrated the

generalized, productive nature of the performance acquired. It was considered likely that

participants would apply the complex relational discriminations to new examples in real-

world settings (Fields et al., 2009).

24


Sidman (1994) discussed the disconnection between educational research and

pedagogy. The failure to integrate teaching techniques used in stimulus equivalence

studies into classroom teaching may limit the learning potential of students (Sidman,

1994). The present body of stimulus equivalence research still has not integrated

procedures with in general education curriculum. Teaching techniques that result in the

formation of equivalence classes are not used with elementary students in general

education classrooms, nor has published research to date evaluated whether MTS training

can be utilized within the classroom as a method for curriculum modification for students

with special education needs (Cautilli, Hancock, Thomas, & Tillman, 2002). Sidman

(1994) suggested the lack of integration of conditional discrimination training techniques

and curriculum planning to allow for emergent relations in mainstream education

represented a failure in communication between research and pedagogy. The lack of

applied stimulus equivalence research in the classroom today suggests that lack in

communication continues (Cautilli et al., 2002).

In the process of reviewing the literature, articles including stimulus equivalence

research at the elementary education level in which instruction occurs simultaneously in

the classroom with multiple students were not found. Nor were articles including

stimulus equivalence research with science curriculum stimuli found. Arntzen and

colleagues (2014) conducted a study with botanical stimuli related to trees and plants and

successfully demonstrated emergent stimulus-stimulus relations that indicated the

formation of equivalence classes. It may be noted however that these stimuli were

selected based on the participant’s interested and were not related to the general

education curriculum. As a result, teaching with a MTS procedure within the stimulus

25


equivalence paradigm and testing for emergent relations and class formation has yet to

make its way into the classroom setting.

Therefore, the purpose of the present series of experiments was to expand the

literature on conditional discrimination training and stimulus equivalence to include the

general education classroom setting and science curriculum. Specifically, these studies

evaluated the effectiveness of teaching with MTS procedures within the classroom

environment with young children, and then tested for emergent relations required to

indicate the formation of equivalence classes among science curriculum stimuli.

General Method

Overview of Experiments

Experiment 1 (Third-Grade). The purpose of this study was to demonstrate

emergence of novel stimulus-stimulus relations consistent with stimulus equivalence as a

result of using conditional discrimination training as a remedial technique with a third-

grade student with Attention Deficit Hyperactivity Disorder (ADHD), Dyslexia, and an

autism spectrum disorder (ASD). The participant, who had not learned the relations

between printed names of animal skull pictures and their relations to the animals’ diets,

was trained using a sequential OTM procedure. First the participant was trained to match

photographs of animal skulls (B) to the corresponding scientific printed word samples

(A). Then the participant was taught to match brief printed descriptions of the animals’

diet (C) to the corresponding same scientific printed words (A). All possible stimulus-

stimulus relations were tested.

26


Experiment 2 (Third-Grade). Experiment 2 was a systematic replication of

Experiment 1 with procedural improvements and new participants. Six neurotypical

third-grade students were taught using an internet-based survey program, Qualtrics®.

Experiment 3 (Kindergarten). The third experiment replicated Experiment 2

systematically with five kindergarten-aged children within the classroom setting.

Setting

All training and testing sessions occurred in each student’s general education

classroom. The number of sessions completed each day varied depending on the time

available in the general education schedule. Each session was always completed in its

entirety.

Stimuli

As shown in Table 1, all stimuli were visual and formed three groups (A, B, and

C), each group contained three stimuli. Group A (Carnivore, Herbivore, Omnivore) and

Group C (Eats Meat, Eats Plants, Eats Both) were textual stimuli (Arial font, 64 point).

Group B contained three pictures of skull profiles. All pictures had a black background

and were equal in size, however sizes varied across experiments. The particular display

formats (e.g., comparison stimulus locations) differed across experiments and are

described later.

Procedure

Student assent was obtained before pretesting began. Each student was told that a

parent said they were allowed to play a matching game at school and asked if s/he would

like to play the game. If the student replied in the affirmative, the student was told that

s/he was allowed to request to stop a session at any point.

27


The first trial of each session was displayed on the screen to start the session. The

student was instructed to select a comparison stimulus from the array.

Pretests. Pretests assessed MTS performance with all possible stimulus-stimulus

pairs. The results were analyzed for each participant to determine which relations were to

be used in training and further testing to assess possible symmetric and transitive

properties of the stimulus control established. Pretests were conducted in extinction

conditions without any prompts. Responses on each trial initiated a brief inter-trial

interval that was followed by the presentation of the next trial.

Identity-match-to-sample performance (e.g., matching A1 to A1, B1 to B1 and so

on) was assessed first. Performance with all stimuli was evaluated in one session. All A

relations, followed by all B relations and then all C relations were tested for a total of 54

IDMTS trials as listed in Appendix A. Pretests also assessed all possible arbitrary MTS

relations that were to serve later as training relations and in tests for emergence of

symmetry, transitivity, and equivalence. Trials of AB and AC relations are listed in

Appendix B as examples. Each pretest session included 18 trials for a particular type of

relation. Each stimulus in a group was presented as the sample six times and the

configurations of comparisons were balanced to ensure equal but unsystematic

appearance of each stimulus in each position.

Individualization of training. For all participants, the goal was to demonstrate

three three-member equivalence classes between physically dissimilar stimuli from

Group A, Group B, and Group C. Pretest results were used to determine the particular

training given to each participant. Three pretest patterns emerged. Table 2 presents

28


relations demonstrated on pretests, relations selected for training, and potential emergent

symmetrical and transitive relations.

Differential reinforcement training. Training sessions contained intermixed

trials of three stimulus-stimulus relations (e.g., A1-B1, A2-B2, A3-B3). The array of

comparisons was balanced to ensure equal occurrence of correct comparisons. The

position of these stimuli in the array changed unsystematically across trials. Appendix B

presents an example of the arrangement of comparisons for trials involving relations AB

and AC. The sample and comparisons were presented simultaneously (as illustrated in

Figure 1) and remained on the screen throughout the trial. Differential reinforcement was

provided following each trial. Trials were considered correct when the student selected

the comparison that was a member of the same class as the sample. Trials were

considered incorrect when the comparison selected was from a different stimulus class

than the sample. Feedback related to performance accuracy followed correct trials. The

occurrence of incorrect trials resulted in different consequences across experiments and is

described subsequently in each experiment. The student was required to reach 100%

mastery in the training phase to move on to posttesting. If mastery was not attained, the

training session was repeated.

Posttests. Posttesting repeated the pretest conditions for all arbitrary relations and

was conducted in extinction conditions. No additional prompts were given and each

incorrect response merely presented the stimuli for the next trial with no additional

consequence.

Experiment 1: Method

Participant

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The participant, Nolan, was a nine-year-old, male in the third-grade. He was

diagnosed with ASD, dyslexia, and ADHD, for which he took stimulant medication.

Nolan had reading glasses, but did not wear them regularly at school (nor during this

study). At school he shared the support of a paraprofessional in the classroom with one

other student, and received special education instruction for math and literacy in a

separate setting. Additionally, Nolan received four hours of specialized reading

instruction each week from a trained special educator, outside of the general education

classroom. Nolan was selected for this study because his performance on an end-of-unit

test in the science curriculum suggested that he did not understand the classification of

carnivores, herbivores, and omnivores, and the skulls that corresponded to each.

However, he read the words Herbivore, Carnivore, and Omnivore and other text

displayed as stimuli. He had experience with a touch-pad on a laptop, and required no

instruction regarding the use of a mouse. However, Nolan had no prior experience with

MTS instruction or using PowerPoint® in slide show mode. In addition to obtaining

consent from Nolan’s parents, his special education coordinator was consulted to ensure

sessions could occur within the student’s schedule.

Setting

Occasionally, training or testing was conducted at a small worktable in the hall

just outside the classroom, when a workspace was not available within the classroom.

Apparatus and Data Recording

Nolan completed all testing and training on an Apple® 13” MacBook® using

PowerPoint® presentation software. Each PowerPoint® slide displayed four stimuli. All

stimuli appeared equidistant from each other and from the center of the slide. One

30


stimulus appeared in each quadrant of the slide (Figure 1). The sample stimulus always

appeared in the top left quadrant and was outlined by a red frame. The three comparison

stimuli appeared in the other three quadrants and were outlined by blue frames. Data

were recorded using paper and pencil. The data sheets were printed copies of all the trials

presented to the student. The recorder circled on paper the stimulus that corresponded to

the stimulus the student selected on the computer.

Stimuli

Table 1 displays the stimuli used. All stimuli were consistent with the description

provided in the General Procedure section of this manuscript, except all textual stimuli

presented in Group A and Group C were Arial font (60 point), and stimulus C3 was Eats

Meat and Plants instead of Eats Both. The pictures presented in Group B were 3.17

inches in height by 4.67 inches in width.

Procedure

Only specific differences from the general procedure are described below. All

data collected in Experiment 1 were analyzed retrospectively.

Pretests. Two pretests were conducted. Nolan was first pretested according to the

pretest procedures described in the General Procedure section of this manuscript and then

retested on only arbitrary MTS relations (Table 3). At the completion of each pretest,

Nolan selected a tangible reward from the classroom prize jar.

Training. Nolan’s training occurred in two phases. The first phase involved a

fading procedure (Ellis, Ludlow, & Walls 1978; Etzel & LeBlanc, 1979), and the second

phase used only differential reinforcement (as described in the General Procedure section

of this manuscript). During both phases, clicking on the correct comparison produced a

31


feedback slide that included an audio chime accompanied by the text You’re Right on the

computer screen for 3s. The stimulus display for the next trial then appeared. An

incorrect response terminated the trial and immediately produced the display for the next

trial.

Fading. This training involved both text-to-picture (AB) and text-to-text (AC)

relations (Figure 2). Trials for both the AB and AC relations were presented in the same

session. Eighteen AB trials were presented first, followed by 18 AC trials. During fading,

the sample and three comparisons were presented and the two S- comparison stimuli

were dissolved (Microsoft® Powerpoint® feature) over 3s thus leaving only the sample

and the correct comparison on the screen. Clicking on the correct comparison was

reinforced by presentation of the feedback slide whereas clicking anywhere outside of the

stimulus resulted in initiation of the next trial. The criterion for advancing to the

differential reinforcement phase was completing three consecutive sessions with 100%

accuracy.

Differential reinforcement. Training of AB relations (18 trials per session) was

conducted first. The mastery criterion was accuracy of 100% across three consecutive

sessions. Nolan then selected a prize from the classroom prize jar and differential

reinforcement training for the AC relations (18 trials per session) began. The criterion for

AC training was 100% accuracy across three consecutive sessions.

Posttesting. Four posttest sessions were presented in the following order:

transitive relations (BC & CB), symmetrical relations (CA & BA), trained relations (AB

and AC), and tests for reflexivity (AA, BB, & CC). When all sessions were complete,

Nolan selected a final prize from the classroom prize jar.

32


Interobserver Agreement (IOA)

Interobserver agreement was calculated for all posttest sessions but was not

collected during pretesting or training sessions. Therefore, IOA was calculated for 16%

of all trials presented (i.e., 14% of all sessions). To collected IOA data, the second

observer sat behind the student and scored responses on a data sheet identical to the sheet

used by the primary observer. The total number of agreements across the two observers

were totaled, then divided by the total number of trials observed that session, and finally

multiplied by 100 to calculate a percentage of agreement. IOA was 100% for all posttest

sessions.

Results

The results demonstrated the emergence of all identity and arbitrary MTS

performances as well as the maintenance of trained stimulus-stimulus relations. During

Pretest 1, Nolan matched all identical stimuli with 100% accuracy. The results for

arbitrary matching in Pretest 1 and Pretest 2 (Table 4) showed performances suggesting

that Nolan had not acquired stimulus-stimulus relations consistent with the three classes

illustrated in Table 1. Accuracy for Pretest 1 and Pretest 2 was consistently below 55.5%

for all relations (Table 4).

Nolan’s matching performances were consistent with acquisition of all AB (text-

picture) and AC (text-text) relations during Phase 1 of training in which the fading was

incorporated. However, such performance was not maintained during Phase 2 of training

(differential reinforcement only) when trials involving the AB relations (A1-B1, A2-B2,

& A3-B3) were intermixed and trained before the training of AC relations (A1-C1, A2-

C2, & A3-C3) began. The results for the differential reinforcement training are depicted

33


in Figure 3. Nolan’s performance on all AB trials was below 33% accuracy, like his

pretest performance, but accuracy rapidly increased across the first three sessions.

Training the AB relations to criterion took six sessions.

Thirteen sessions were required to meet the training criteria for the AC relations.

The pattern of acquisition differed across the three relations. Notably, performance on

trials with the A3-C3 relation showed high levels of accuracy across all thirteen sessions

(Figure 4). In contrast, Nolan’s performances on A1-C1 and A2-C2 trials began below

20% accuracy, but improved rapidly, although inconsistently across ten sessions.

During posttests (Figure 5), Nolan’s performance demonstrated a high degree of

accuracy, greater than 94%, across all relations. In addition, he responded with 100%

accuracy for all IDMTS during posttests. Nolan’s performance on all matching tasks

during the posttest suggested that three classes of equivalent stimuli had formed.

Results for a six-month maintenance test are presented in Figure 6. First, it is

noteworthy that performance with all Class 3 (omnivore) stimuli remained above 83%

accuracy, whereas performance with the stimuli from Classes 1 and 2 were inconsistent

(Figure 6). This suggests potential confounds in the Class 3 stimuli. Performance was

well maintained, remaining above 93% accuracy, on the trained AB relations and their

symmetric counterparts (BA). In contrast, performance on trials for the trained relations,

AC (50%), was not maintained, while a high level of performance occurred on CA (94%)

trials that typically would be considered to reflect symmetry of the trained set.

Performance on trials that assessed transitive relations (BC and CB) was not well

maintained with accuracy below 62% on both relations.

Discussion

34


Experiment 1 was conducted in Nolan’s general education classroom after he

failed to master the science concepts (i.e., carnivore, herbivore, and omnivore) from

general education instruction. The MTS training procedure in this study modified the

presentation of the science content. During the fading procedure, Nolan’s accuracy was

consistent, with no errors across three sessions. However, when the fading procedure was

replaced by differential reinforcement (Phase 2), Nolan’s performance returned to pretest

levels. The discrepancy between the fading procedure and the start of the differential

reinforcement procedure suggests that the fading procedure did not establish the intended

conditional stimulus control. Differential reinforcement resulted in the emergence of all

stimulus-stimulus relations.

As a result of teaching two sets of stimulus-stimulus relations (AB and AC) with

differential reinforcement, Nolan demonstrated the emergence of the symmetrical

relations BA and CA, and the transitive relations BC and CB. These results add to

previous stimulus equivalence research by demonstrating that the MTS procedure was

effective in producing emergent relations required to demonstrate equivalence classes

among stimuli used in third-grade science education.

It was surprising that Nolan made many errors on trials with the AB and AC

relations (Figure 3) following the training with the fading procedure. During the fading

procedure, Nolan was 100% accurate across three sessions. The fading procedure did not

transfer stimulus control to the discriminative stimulus as demonstrated by Touchette and

Howard (1984). Touchette and Howard (1984) utilized a delayed prompting procedure in

which the delay duration was systematically increased across correct trials. In this

procedure, participants could respond to the discriminative stimulus even before the S-

35


stimuli had faded out. Touchette and Howard (1984) found that participants reliably

responded before the prompt, suggesting that discriminative stimulus control had

developed. This transfer of stimulus control was not demonstrated in the current study.

This discrepancy most likely results from one of two procedural differences. First, the

current study used a conditional discrimination procedure in which the sample and

correct comparison changed from trial to trial. In contrast, Touchette and Howard (1984)

provided the same verbal instruction, and the correct comparison remained the same

across multiple trials. Second, in the current study, a fading phase was followed

immediately by differential reinforcement alone.

During training of the AB relations, the student reached mastery in six training

sessions. Training for the AC relations took twice as many sessions (thirteen total), as

depicted in Figure 3. It is possible that the AB relations were learned more rapidly

because they were presented immediately after the three errorless learning phases. In

contrast, there was a longer delay between the errorless training phase and the differential

reinforcement phase for the AC relations. This delay may have reduced any positive

effects apparent from the errorless training of AC relations.

Another possible explanation for the fewer number of AB training trials could be

in differences between the B and C comparison stimuli. The AB training required

discriminations between pictures whereas AC training required textual discriminations. It

may be noted that there were irrelevant stimulus features (e.g., skull direction) in the

photographs (Group B) that may have facilitated acquisition of the discriminations

between these stimuli. In contrast, the textual stimuli may be considered compound

stimuli, with each letter serving as an element of the stimulus (Touchette & Maguire,

36


1986). As the number of elements (e.g., text length) increases, the difficulty of

discrimination may increase as well (Touchette & Maguire, 1986).

With respect to the analysis of errors in the AC differential reinforcement

training, recall that accuracy on trials with the A3-C3 relation was 100% accurate across

the first three sessions (Figure 4). This surprisingly accurate performance suggested

presence of an artifact relevant to Class 3 (omnivore). Notably, the text presented as

stimulus C3 Eats Meat and Plants is two words longer than the text for the C1 (Eats

Meat) and C2 (Eats Plants) stimuli. The length of the text thus provided a cue. This

additional cue made it easy to discriminate and thus quickly came to control selections

among the comparisons (Figure 4). The existence of a possible confound in the omnivore

class was further supported by the high degree of accuracy on all relations in the

omnivore class at the 6-month follow up.

Regardless of the errors that occurred during training, the results from Experiment

1 suggested that the MTS procedures provided a method for teaching aspects of general

education science curriculum. If MTS can be used as a remedial method in the way

demonstrated, perhaps it also can be used as an effective primary instructional strategy.

Experiment 2 was designed to evaluate whether the MTS procedure employed in

Experiment 1 would establish the same equivalence classes in multiple students, thus

ensuring acquisition of class formation for the science content of the regular curriculum.

Experiment 2: Method

Participants

The option to participate in the study was extended to 46 third-grade students. A

total of 13 students returned consent forms signed by parents/guardians. Four participants

37


demonstrated 100% accuracy for all stimulus-stimulus relations and one participant’s

pretest scores yielded a combination of relations at 100% accuracy, suggesting the classes

had already been formed. Therefore, those five students did not participate further.

Additionally, one student was not included due to participation in special education

services, and training for another was discontinued after she shared that a friend had told

her the answers. Therefore, six participants qualified for the study based on their pretest

scores. The participants were eight-year-old and nine-year-old students from third-grade

classrooms in a public school.

Sarah was 8.5 years old, Scott and Saeed were 9 years old, and Sam, Suzanne, and

Sasha were 9.5 years old. All students received the general third-grade education

available in their classrooms. Sam also received reading support because reading

assessments indicated his reading was below grade level. Sam spoke only Russian at

home and his teacher reported that he frequently needed teacher support with English

vocabulary. Sarah’s academics were all at grade level, but her teacher reported she

performed inconsistently in the classroom. Saeed’s, Suzanne’s, Scott’s, and Sasha’s

reading and mathematical skills were slightly above grade level. None of the participants

had prior experience using MTS for instruction or experience using Qualtric®.

Setting

All training and testing occurred in a third-grade classroom which was not the

participants’ primary classroom. All sessions were conducted on Apple® iMac®

computers that were placed on a table in the rear of the classroom. Two computers were

available, thus allowing two participants to work simultaneously. The computers faced

away from each other to ensure the one student could not view the screen of the other

38


station. During most sessions, the classroom was full of students engaged in academic

activities.


Students completed all testing and training on an iMac® desktop computer using

the Internet survey program Qualtrics®. This survey program was designed to present a

series of questions to individuals and then analyze their responses. The questions

presented were in the form of MTS tasks. Each MTS presentation of four stimuli was

displayed on a new screen. As illustrated in Figure 7, the sample stimulus always

appeared above the comparisons on the left side of the screen. Nothing occurred if the

student clicked on the sample stimulus. The three comparison stimuli appeared below the

sample in a horizontal row. The students were verbally instructed to select a comparison

by either clicking on the actual comparison (text or picture) from the array or by clicking

on the circle below a comparison. Selecting a comparison filled in the circle below the

stimuli. The student could click on more than one comparison during a trial. Each new

click filled in the corresponding circle below the new stimuli. Only one of the stimuli

could be selected at a time. A selection was recorded by the computer only when the

participant clicked on the arrow button in the bottom left corner of the screen. No data

were collected regarding the additional clicks on the comparisons. In the event that the

student clicked the arrow button before selecting a comparison, the program displayed a

message that a selection was required. The program calculated the percentage of correct

selections, which was presented at the end of each session, and also displayed which

comparison the participant selected on each trial. The student had the opportunity to

39


review the feedback on each trial, but was not instructed to do so. The experimenter then

scored each trial by hand to determine the percent correct for each stimulus class.

Stimuli

The classes of stimuli are presented in Table 5. The potential difficulties with the

B3 and C3 stimuli identified in Experiment 1 were corrected in Experiment 2 by

removing the potentially irrelevant stimulus features. The B3 skull photograph was

rotated to face in the same direction as the B1 and B2 skull photographs. All photographs

were 1.92 inches in height by 2.75 inches wide. The text in C3 was changed from Eats

Meat and Plants to Eats Both to ensure that text length was equal across all Group C

stimuli.

Procedure

In addition to the changes made in the B3 and C3 stimuli from Experiment 1 to

Experiment 2, and elimination of the fading procedure, two other procedural changes

were made in Experiment 2 in attempt to make procedures easier for use in the traditional

classroom. First, the differential reinforcement procedure was modified. In addition, the

mastery criterion was lowered to a single session with 100% accuracy.

Pretests. The pretest included 108 trials that evaluated arbitrary MTS relations.

The order in which stimulus-stimulus relations were pretested is shown in Table 6. At the

completion of the pretest, a screen appeared that thanked the student for completing the

survey.

Differential reinforcement training. During training sessions, differential

reinforcement was provided following each trial. Figures 8 and 9 show the feedback

displays that were used. As with pretesting, the participant could click on multiple

40


comparisons within a trial, but selection was only scored when followed by a click on the

arrow in the bottom left corner. Clicking on the correct comparison and then clicking on

the arrow produced the array of comparisons stacked vertically below the sample. A

green check mark was next to the comparison the student had selected (Figure 8). The

stimulus that had been presented on the left during the trial appeared on the top of the

array on the feedback display, the center comparison remained in the middle, and the

comparison from the right appeared on the bottom. If an incorrect comparison was

selected, followed by a click on the arrow button, the feedback display that followed the

selection also presented the vertical array of comparisons, but a red x was next to the

comparison the student had selected (Figure 9). The student was required to click on the

arrow at the bottom left in the feedback slide to advance to the next MTS trial. When

each training session was completed a screen appeared that thanked the student for taking

the survey.

Three different training sequences were used with different participants based on

their pretest performances: training of only the AB relations, training of both the AB and

AC relations, and training of the CA and CB relations. Specific rationales will be

presented with the results. Training of only the AB relation consisted of 18 trials. In the

AB and AC training, 18 AB trials were presented to the student immediately followed by

the AC trials (18 trials), for a total of 36 trials per training session. In the CA and CB

training, 18 CA trials were presented to the student immediately followed by the 18 CB

trials for a total of 36 trials per training session.

Posttesting. As with pretesting, a click on any comparison selected that

comparison. Selection was indicated by a filled in circle below the comparison. The

41


participant could click on multiple comparisons during the trial, but only one comparison

was selected at a time. The response was recorded when the student clicked on the arrow

button at the bottom of the screen (Figure 7). The next trial then began. The sequence of

trials in the posttest was identical to the sequence used in pretesting. When the entire

posttesting session was complete, a screen appeared thanking the student for taking the

survey.


The observer independently scored the students’ responses. IOA was calculated

for 33% of pretest, training, and posttest trials for each participant. IOA was calculated

by totaling the number of agreements, dividing the total by the number of observed trials

and then multiplying by 100 to achieve a percentage. Interobserver agreement was 99.7%

across the two observers and matched the scoring by Qualtrics® (100% agreement).

Results

Results for participants in Experiment 2 are displayed in Figures 10, 11, and 12.

All six students obtained 100% accuracy on trials for all IDMTS relations (AA, BB, CC);

therefore these relations were not retested in the posttesting phase. The pretest results for

arbitrary matching trials demonstrated three patterns of performance, and the relations to

be trained were selected based on these patterns. Figure 10 shows one pattern that was

shown by three students who demonstrated 100% accuracy on trials with the AC and CA

relations, and below 50% on all other relations. As illustrated in Figure 10, these students

received training that added only the AB relations to their pretest repertoires.

The second pattern (see Figure 11) occurred with one student, who scored below

50% on all relations. These results were similar to Nolan’s pretest scores from

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Experiment 1 and suggested that no stimulus classes existed. Therefore, the student was

trained with the same two relations trained in Experiment 1, AB and AC, (Figure 11).

Finally, one student responded with the greatest accuracy on pretest trials with

relations AC, CA, and CB. Relations CA and CB (Figure 12) were selected for training to

remain consistent with the OTM training design. Training two relations to mastery, which

were already performed with high accuracy, allowed for the potential emergence of

relations with lower accuracy.

The training sessions developed accurate responding for all six students. Five of

the six students required only two training sessions and the remaining student, Suzanne,

required four sessions to reach 100% accuracy. All students in Experiment 2 required

fewer training sessions than Nolan required in Experiment 1. Results are organized

according to the relations that were trained. All six participants demonstrated the

emergent stimulus-stimulus relations indicating the formation of three equivalence

classes.

AB Training Only.

Sarah, Sasha, and Saeed all demonstrated relations AC and CA on pretests, but

none of the remaining relations (Figure 10). They, therefore, were trained with only the

AB relation before tests that assessed symmetry (i.e., relation BA) and transitivity (i.e.,

relations BC and CB) were administered. This paradigm is depicted in Figure 13.

Sarah required two sessions of AB training. Posttesting then revealed consistent

responding with no errors across all six stimulus-stimulus relations. The performance on

trials with the AC and CA relations remained at 100% accuracy, as did performance on

43


the trained relation AB. Relations of symmetry (BA) and transitivity (BC and CB)

emerged.

Sasha’s performance on pretesting (middle panel of Figure 10) revealed the same

pattern as Sarah’s pretest performance. Sasha received only AB training sessions and

needed two sessions to reach mastery. Posttesting revealed that performance on AC, CA,

and AB trials was maintained and symmetry (BA) and transitivity (BC and CB) were

demonstrated.

Saeed’s performance on pretests (bottom panel of Figure 10) showed the same

pattern as Sarah and Sasha. Saeed required two sessions of AB training to reach mastery.

Posttesting revealed the emergence of symmetry (BA) and transitivity (BC and CB).

AB and AC Training.

Figure 11 shows results for Scott and Suzanne. Pretest results for Suzanne

(bottom panel) showed performance was below 50% accuracy for all relations. Therefore,

she received training to establish the AB and AC relations (Figure 14). After four training

sessions, Suzanne’s performance demonstrated 100% accuracy for all six stimulus-

stimulus relations (AB, BA, AC, CA, BC, and CB).

Scott’s performance on relations AC and CA was 100% accurate, thus resembling

the three students shown in Figure 10. However, he began training before the AB-only

training was created. Therefore, he was trained with both the AB and AC relations

(Figure 14). He required two training sessions to reach mastery.

Scott’s scores on the pretest (top panel of Figure 11) were below 39% accurate for

AB, BA, BC, and CB relations. During posttests, however, Scott maintained above 93%

accuracy on trained relations (AB and AC) and also on the CA trials (100%).

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Performance on tests for symmetry of the trained AB relations (i.e., BA) and transitivity

(BC) was 100% accurate. Two errors were made during CB test trials: C1-B1 and C3-B3.

CA and CB Training.

Sam’s pretest performance (Figure 12) demonstrated greater than 50% accuracy

for all relations except AB (39%). Accuracy on tests for the BA relation was 61% correct,

for AC and CA, accuracy was 89% and 72%, respectively, and accuracy was 56% and

94% for BC and CB, respectively. Sam required two sessions of CA and CB training

(Figure 15) to reach mastery. During posttesting Sam’s performance demonstrated

symmetry of the trained CB relations (BC). However, it is important to note his high

level of performance, 89% accuracy, on tests of the AC relations at pretesting. His

performance on the same trial types after training therefore was not an emergent

demonstration of symmetry. It is unclear where the AC performance had been acquired.

Posttesting also demonstrated transitivity (AB and BA) and both trained relations (CA

and CB) were 94% correct, both errors (C1-A1 and C1-B1) occurring on trials with

stimulus Class 1.

Discussion

The six participants demonstrated different degrees and patterns of accuracy on

pretests. These performances were therefore analyzed to determine training. The training

combinations were planned in order to enable emergence of the symmetrical and

transitive relations made possible by combination with the existing test performances of

each participant. Whenever possible, the relation with the greatest accuracy in pretesting

was trained.

45


The total number of training sessions that each participant required in Experiment

2 was less than Nolan required in Experiment 1. This suggested that the procedural

changes introduced in Experiment 2 may have increased the efficiency of training.

Specifically, the differential reinforcement in Experiment 2 was made more salient by

including feedback displays following incorrect and correct trials, (a red X and green

check, respectively, displayed beside the stimulus that had been selected). In Experiment

1, errors merely resulted in the presentation of the next trial. Additionally, Experiment 2

allowed students to click on multiple comparisons during a trial before submitting their

selection by clicking on the arrow bottom that also initiated the next trial. While these

clicks (and the appearance of a filled circle) were not recorded, it would be interesting to

analyze the number of clicks participants took before submitting the response. This may

provide evidence of response fluency.

It is also possible that the differences in individual learning histories between

Nolan in Experiment 1 and students in Experiment 2 contributed to the difference in the

extent of training required. Nolan, for example, had already been exposed to the stimuli

during regular education science lessons, and therefore may have had a longer history of

errors with the stimuli than the participants from Experiment 2. In Experiment 2, Sarah,

Sasha, Saeed, and Scott demonstrated mastery of the stimulus-stimulus relations AC and

CA during pretesting. Perhaps they were able to read all of the text presented and had

been previously taught the vocabulary of carnivore, herbivore, and omnivore. These

vocabulary words are within the typical reading level of third-grade students, and it is

possible that Sarah, Sasha, Saeed, and Scott had been taught the meaning of these

vocabulary words previously, and were able to read the text during this experiment.

46


Sam’s accuracy in pretesting was above 50% except for the AB relations, and

only Suzanne’s accuracy was at or below 50% for all stimulus-stimulus relations, which

was similar to Nolan’s results.

The number of training trials, and thereby time required, was reduced from

Experiment 1 to Experiment 2 in two ways. First, the criterion for mastery was reduced

from three consecutive sessions with 100% accuracy to a single session at 100%

accuracy. Training sessions, in which two sets of relations were differentially reinforced,

took approximately six to eight minutes to complete in Experiment 2. Second, the

errorless learning procedure used in Experiment 1 was eliminated from the procedure in

Experiment 2. The errorless learning procedure had been included in Experiment 1 to

increase the rate at which stimulus control developed between the sample and

corresponding correct comparison. Results from Experiment 1 suggested that the

stimulus control intended by the experimenter was not established with the fading

procedure. The results in Experiment 2 suggested that differential reinforcement was

sufficient to develop accurate responding for all students during training. Furthermore,

these performances served as baseline prerequisite performances that allowed

demonstration of emergent symmetry and transitivity. These two procedural changes

were effective in Experiment 2, and increased the efficiency of the procedures used in

Experiment 1.

During posttesting, the performances of all six participants indicated equivalence

class formation. For all participants, accuracy was at 89% or higher for all stimulus-

stimulus relations. For Suzanne, this is particularly noteworthy, since she had the lowest

levels of accuracy during pretesting, and required the greatest number of training

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sessions. Suzanne’s results suggest an extended number of training sessions due to errors

did not negatively affect class formation. For Saeed, Sam, and Sasha, all errors occurred

in tests of untrained stimulus-stimulus relations; however Scott made one error on a

trained relation, in addition to two errors in tests for transitive relations. Although very

few errors were made, further analysis of isolated errors would determine if posttesting

errors were consistent with errors that occurred during training trials. If errors were

consistent between training and posttesting, it might be expected that integrating a

differential observing response (Dube & McIlvane, 1999) into MTS training would result

in improved performance. Future research in the classroom setting should analyze how

the inclusion of a differential observing response alters the efficiency of the training

procedures. Identifying where specific errors occur will also help isolate stimulus features

that contribute to the development of stimulus control, and ways the training procedure

could be modified to increase efficiency.

It was important to demonstrate that the training procedure from Experiment 2 is

adequate for a broader range of students. Additionally, evidence was needed that MTS

training could be used to reliably produce emergent conditional discriminations

consistent with stimulus equivalence in the classroom. Experiment 3, therefore, was

designed to replicate the finding from Experiment 2, systematically, with a younger

general education population of Kindergarten students.

The testing and training sessions in Experiment 3 utilized Qualtrics®. However,

the students responded on an Apple® iPad® by touching the stimuli displayed on the

screen. Using the Apple® iPad® eliminated the use of a computer mouse, and also

allowed sessions to occur at any work station within the classroom, without requiring

48


students to move to the computer area. The use of the Apple® iPad® allowed for easy

integration into the regular classroom routine.

Experiment 3: Methods

Participants

Kindergarten students in public school classrooms were recruited for Experiment

3. The option to participate was extended to 65 students. Twenty-four students returned

informed consent forms signed by a parent or guardian and 23 of those students gave

assent for participation. These 23 students were then pretested to determine their IDMTS

skills. Students were required to demonstrate IDMTS performance with at least 98%

accuracy on a 54-trial test to be included. Ten kindergarteners were eliminated because

their accuracy on IDMTS was less than 98% correct. Of the remaining 13 participants,

five completed pretesting, training, and posttesting. Cathy and Aurora were six years old,

Amelia and Laura were 6.3 years old, and Alex was 6.9 years old. All five participants

were reported to have high academic skills. According to the school’s reading assessment

system, all five participants read beyond grade level for students in the Spring of

Kindergarten. The remaining eight participants were still in the training phase of

Experiment 3 when the school year ended; therefore the data from those eight

participants were not included in the current analysis.

None of the participants had prior experience with MTS instruction, iPads for

instruction in the classroom setting, or experience with Qualtrics®. All five participants

reported having used an iPad at home to play games.

Setting

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All sessions were conducted while the student was seated at a worktable in the

classroom. During training sessions, other kindergarten students were in the same room

participating in their traditional classroom routine. All training and testing sessions

included 36 total trials, except for the IDMTS test, which had 54 trials.


The Kindergarten students completed all testing and training on an Apple® iPad®

using Qualtrics® surveys. Students were instructed to select a comparison by touching it.

All other procedural arrangements were as described in Experiment 2.

Stimuli

The stimuli were identical to the stimuli used in Experiment 2.

Procedure

Pretests. Following the IDMTS tests, pretests of arbitrary MTS responding were

conducted in a series of three sessions, each consisting of 36 trials, that included trials

with only the particular relations listed in order in Table 7.

Differential reinforcement training. Pretest scores were analyzed in the same

manner described in Experiment 2. Two of the three patterns described in Experiment 2

emerged from pretest scores. Amelia showed mastery of the AC and CA relations was

trained with AB relations only (Figure 13), and the remaining four students who showed

low accuracy with all potential relations were trained with AB and AC relations (Figure

14).

Posttesting. The posttest procedures were identical to the arbitrary MTS pretests.

Table 7 shows the order in which relations were tested.


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The second observer scored each response independently of the first observer.

IOA was calculated for 33% of all pretests, training, and posttests for each participant.

The total number of agreements was divided by the total number of scored trials and then

multiplied by 100 to reach a percentage. Interobserver agreement was 99.9% across the

two observers and matched the scoring of Qualtrics® with 100% agreement.

Results

Pretesting for IDMTS

All Kindergarten students demonstrated IDMTS performance at or above 98%

accuracy. Results for Experiment 3 appear in Figures 16 and 17. Similar to the results

from Experiment 2, the pretest results demonstrated two patterns: AC and CA relations at

100% accuracy, and all other relations below 33% correct, or all six relations below 50%

accuracy. Students received training according to these patterns as was described in

Experiment 2. These training arrangements allowed for the potential emergence of

symmetrical and transitive relations. Results are organized according to the relations that

were trained. All five participants demonstrated emergent stimulus-stimulus relations

indicating the formation of three equivalences classes.

AB Training Only

Amelia’s results are depicted in Figure 16 and resemble Sarah’s, Sasha’s, Saeed’s,

and Scott’s pretest performances from Experiment 2. During pretesting, Amelia’s

arbitrary MTS for both the AC and CA relations was 100% correct. All other relations

were performed below 33% accuracy. Therefore, she was only trained with AB relations

to allow potential emergence of the transitive relations BC and CB. Amelia required two

sessions of training with AB relations to reach the criteria for mastery. These sessions

51


were conducted across two days. After reaching the mastery criterion, all posttesting was

conducted on the following day. Amelia’s posttest results demonstrated maintenance of

the AC and CA relations at 100% correct. Amelia’s performance was 100% accurate for

symmetry (BA), and transitivity (BC and CB). She made only one error on the trained

AB relation.

AB and AC Training

Figure 17 shows the results for the four participants who were trained on relations

AB and AC. Aurora’s and Laura’s pretest performances were below 45% accuracy on all

relations. Alex’s scores on pretests were less than 50% for all potential relations, except

AB (78%), and Cathy scored below 57% correct for all relations. Therefore, the pretests

of these participants indicated that training AB and AC relations would allow for

emergence of potential symmetrical (BA and CA) and transitive (BC and CB) relations.

Aurora’s results appear in the top panel of Figure 17. She responded with the

greatest accuracy when the stimuli from Group C (AC and BC) were presented as

comparisons. Aurora required seven training sessions of the AB and AC relations. These

sessions were conducted across seven days. After the mastery criterion was

demonstrated, posttesting began on the same day. The three posttests were delivered over

two days. Aurora made no errors on trained relations during posttesting, and

demonstrated all symmetrical (BA and CA) and transitive (BC and CB) relations.

Laura’s results appear in the panel second from the top of Figure 17. Laura

required five training sessions of the AB and AC relations. These sessions were

conducted within 19 days. After reaching the mastery criterion, posttesting began the

same day. The three posttests were delivered across two days. Laura made no errors on

52


trained relations during posttesting, and reliably demonstrated all symmetrical and

transitive relations.

Alex’s results for arbitrary MTS appear in the panel second from the bottom in

Figure 17. Alex required four training sessions. These sessions were conducted over four

days. After reaching the mastery criterion, all three posttests were delivered the same day.

Alex made no errors on trained relations or symmetrical relations (BA and CA) on

posttesting. He made no errors on tests for the transitive relation BC, and only one error

on a trial assessing the transitive CB relation.

Cathy’s arbitrary MTS results appear in the bottom panel of Figure 17. Her

accuracy was greatest for the AC matching (56% correct). Cathy required 14 sessions of

AB and AC training, the greatest number of training sessions across all Kindergarten

participants. These sessions were conducted within 28 days. After the mastery criterion

was met, posttesting began the same day. The three posttests were delivered across two

days. In posttesting, symmetry (CA and BA) and transitivity (BC and CB) were

demonstrated. She made one error on the trained relation AB.

Discussion

All participants demonstrated the formation of classes of equivalent stimuli.

These results replicate previous stimulus equivalence research that taught a few relations

and resulted in the emergence of multiple conditional discriminations without additional

teaching (Mackay, 1985; Stromer et al., 1992).

The AC and CA matching tasks involved text-to-text arbitrary relations. For

example, when the word Carnivore was presented as the sample, Amelia reliably selected

the text Eats Meat from the array of Group C stimuli. Her accuracy was 100% with tests

53


for symmetry (CA), in which Group C stimuli were presented as samples and Group A

stimuli served as the comparisons. Therefore, Amelia’s pretest results suggest that she

had a learning history with these textual stimuli. Perhaps she was able to read all of the

text presented and had been previously taught the vocabulary of carnivore, herbivore, and

omnivore. Although these words are beyond the typical reading level of kindergarten

students, these words are displayed in the school’s preschool classroom during a unit of

study on dinosaurs. Therefore, it is possible that Amelia had been taught the meaning of

these vocabulary words previously, and was able to read the text during Experiment 3.

Further information could be gathered from Kindergarten participants during pretesting

and posttesting to determine if students read the text, created new names for the text, or

engaged in other covert verbal behavior that was not observed within Experiment 3.

With regard to training, all Kindergarten students reached 100% accuracy within

two to 14 training sessions (Figure 18). Kindergartners required a greater number of

training sessions than third-graders (Figure 18). This supports results from previous

studies that suggested that young children have difficulty acquiring arbitrary matching

(Pilgrim et al., 2000). Additionally, the accuracy of all Kindergarteners was lower in

pretesting, Suzanne, in Experiment 2, also demonstrated similar low accuracy in

pretesting, and she required more training sessions to reach mastery than third-graders

who demonstrated greater accuracy on pretests. Training on AB relations took

approximately five minutes per session (18 trials) to complete and training with both AB

and AC relations (36 trials) required eight minutes. The time per session is similar to the

amount of time third-graders required to complete training sessions of the same length.

Even with the greater number of training sessions required by all Kindergarten students,

54


the results from Experiment 3 replicate the emergence of equivalence classes for all

participants.

Experiment 3 extends Experiment 2 by demonstrating the MTS procedures were

sufficient for training the younger Kindergarten students. The results also demonstrate the

formation of classes of equivalent stimuli with younger children, utilizing a three-choice

array of comparisons. The results from previous research with young children, under the

age of six years, typically used a two-choice array (Melchiori et al., 2000; Pilgrim,

Chambers, & Galizio, 1995; Pilgrim et al., 2000; Smeets, & Barnes-Holmes, 2005;

Smeets, Barnes-Holmes & Cullinan, 2000). Lazar, Davis-Lang, and Sanchez (1984)

intermixed the presentation of trials containing arrays of two and three comparisons, and

very few studies with young children have presented three-choice arrays throughout all

training and testing (Smeets & Barnes-Holmes, 1995). Arntzen, Grondahl and colleagues

(2010) discussed the possibility of a two-choice array resulting in the S- control discussed

earlier. Employing a three- or four-choice array of comparisons increases the probability

that appropriate sample S+ stimulus control will develop (Fields et al., 1984).

General Discussion

Experiments 1, 2, and 3 extend the existing research by successfully

demonstrating emergent stimulus-stimulus indicating the formation of equivalence

classes following training in the general education classroom. All three experiments used

an MTS procedure to train and test stimulus-stimulus relations and determine if untrained

relations emerged. The results demonstrated responding consistent with equivalence with

three physically dissimilar stimulus sets. Each stimulus equivalence class contained a

55


scientific word (carnivore, herbivore and omnivore), corresponding skull picture and

description of the mammal’s diet.

Curriculum modification

In the retrospective analysis of data collected for Experiment 1, the MTS

procedure was used as a curriculum modification to train the student to match the pictures

to the corresponding terms (Carnivore, Herbivore, or Omnivore; AB), and to match the

text describing the animal’s diet to the same terms (AC). Training resulted in the

emergence of all symmetric (CA and BA) and transitive relations (BC and CB), thus

indicating the formation of equivalence classes. These results replicated Sidman’s (1971)

findings, but used all visual stimuli. There are few studies that used applied stimuli that

are all visual. Arntzen, Halstadtro, and colleagues (2010) used all visual stimuli to teach

piano chords, and Lynch and Cuvo (1995) presented visual stimuli to teach fractions and

decimals. Leblanc and colleagues (2003) presented all visual stimuli to teach United

States geography, but their training procedure included verbal prompts that were specific

to the stimulus-stimulus relations presented.

The participant in Experiment 1, Nolan, had several diagnosed learning

disabilities, including autism, and required instructional modifications. Results from

Experiment 1 support Lynch and Cuvo’s (1995) findings that suggested MTS procedures

may provide a viable modification to academic instruction, and resulted in the emergence

of stimulus-stimulus relations suggesting the formation of equivalence classes. Results

from Experiment 1 also support findings in which participants with learning disabilities

demonstrated matching performances on novel stimulus-stimulus relations indicating

equivalence class formation following the direct training of only a few of the relations

56


involved (Lane & Critchfield, 1998; Keintz et al., 2011; Leblanc et al., 2003; Miguel et

al., 2009; Stromer & Mackay, 1992).

The results from Experiment 1 suggest high social significance. Nolan accessed

modified instruction for the science curriculum within his general education classroom,

and learned the relations among the pictures, labels, and additional text that demonstrated

acquisition of the same science conceptual content as his peers. The training procedures,

materials, and time required to complete training and testing sessions were flexible

enough to be conducted without adjusting Nolan’s typical schedule. Also, Nolan often

asked for the opportunity to work on training sessions, which suggested that the MTS

tasks on the computer were a preferred activity.

Extending into the general education classroom

Results from Experiment 1 support the findings that MTS procedures can be

integrated into the general education environment to teach students with learning

disabilities in a least restrictive environment (Arntzen, Halstadtro et al., 2010; Keintz et

al., 2011; LeBlanc et al., 2003; Miguel et al., 2009). There is limited stimulus

equivalence research (e.g., Lynch & Cuvo, 1995) published from studies conducted in the

general education classroom at the elementary education level. Even in the study

conducted by Lynch and Cuvo (1995), all training and testing was conducted outside of

the students’ classroom as part of a math intervention. To date, there are no published

stimulus equivalence studies in which typically developing elementary-aged children

were trained and tested within their usual classroom.

The purpose of Experiments 1, 2, and 3 was to demonstrate that MTS procedures

could be incorporated within the classroom as an efficient instructional method that

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results in the formation of equivalence classes. Therefore, procedural changes were made

from Experiment 1 to Experiments 2 and 3 to make the procedures easier to integrate into

the general education classroom. The use of PowerPoint® in Experiment 1 to present

MTS tasks required the presence of a teacher to collect data for all sessions. When IOA

was collected, two teachers were needed to observe during the session. Requiring the

presence of a teacher may restrict the opportunities for the procedures to be carried out,

and may limit the convenience of the teaching method in some settings. In the study

investigating emergent reading comprehension, Sidman (1971) noted that the

prerequisites identified in the 1971 study held great practical value, since both auditory-

visual relations (i.e., matching dictated names with pictures, and dictated names with

printed words) could be trained without a teacher present.

Reading programs, perhaps computer-based, could present auditory sample

stimuli and the corresponding visual comparisons. Similarly, students could be trained

with all visual stimuli without the presence of a teacher. Skinner (1968) outlined a similar

method of instruction while describing teaching machines. Before the technology of

computers was developed, Skinner (1968) identified ways an automated system of

instruction could improve the contingencies learning in classroom. Computer-based

instruction allows for immediate reinforcement of correct responses for each student,

thereby allowing the opportunity to complete a greater number of trials and move through

the curriculum at his or her own pace (Skinner, 1968). Computer-based instruction

therefore could reach more learners, and teachers could perform other important

instructional tasks (Sidman, 1971; Skinner, 1968).

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After switching from PowerPoint® to Qualtrics® for Experiments 2 and 3, the

presence of a teacher became unnecessary. The use of Qualtrics® enabled the

presentation of stimuli, the collection of response data, and the delivery of contingent

differential reinforcement during training without requiring a teacher to be present. The

automation of the procedures eliminated the need for an observer, and thereby increased

the availability and flexibility of the teaching method. For these reasons too, several

students could participate simultaneously within the general education classroom while

the teacher provided instruction to other students.

In addition to the change in the software used, other more detailed procedural

changes also were made. The results from Experiment 1 indicated that the stimulus

fading procedure did not establish the desired stimulus control of comparison selections

by sample stimuli, but that the reinforcement procedure was effective. Therefore, the

stimulus fading procedure was eliminated. The presentation of a feedback display

following incorrect trials was added to provide clear differential reinforcement during

training. Students were also able to click on multiple comparisons during the trial before

submitting their final selection by clicking on the arrow button. Future studies should

collect data on extra clicks to provide information regarding what stimuli students

responded. These data would show if the option to click on multiple comparisons

benefited performance by providing a procedure that allowed correction. The final

procedural change was the elimination of back-up reinforcers delivered contingent on

completing sessions, which allowed the use of reinforcement for participating students

without additional rewards that non-participating students did not have the opportunity to

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earn. Furthermore, removing selections of the back-up reinforcer from the prize jar

eliminated the need for additional resources in the classroom.

Experiments 2 and 3 extended existing research by demonstrating that the

procedures used for pretesting, training, and posttesting can be conducted in a general

education classroom environment. Additionally, the results showed that training can be

given simultaneously for several students in the classroom. Training sessions consisting

of 36 trials took approximately six minutes in Experiment 2, and eight minutes in

Experiment 3. The brevity of the sessions in Experiments 2 and 3 made it easy for

students to complete MTS tasks at various points in their school day without disrupting

the classroom schedule. When possible, students were given the opportunity to complete

multiple sessions. The teachers of the classrooms in which these sessions occurred

continued to deliver instruction to other students within the classroom. In the

Kindergarten classrooms, the sessions often fit naturally into working in stations that

existed in the daily schedule.

Extending to science curriculum

Using stimuli selected from science curriculum in the current three experiments

extended the literature by demonstrating emergent stimulus-stimulus relations indicating

classes of equivalent with elementary science stimuli. While previous stimulus

equivalence research has employed a range of academic stimuli, including math (Hall et

al., 2006; Leader & Barnes-Holmes, 2001; Lynch & Cuvo, 1995), reading (de Rose et al.,

1996; Lane & Critchfield, 1998; Melchiori et al., 2000; Sidman, 1971), and spelling of

color and numeral names (Mackay, 1985; Mackay, Kotlarchyk, & Stromer, 1997;

Stromer et al., 1992), research to date has not included science stimuli used at an

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elementary education level. The results from Experiments 1, 2, and 3 provided evidence

that stimulus equivalence research can and should expand to include an even wider range

of academic stimuli. Further research could look at utilizing conditional discrimination

training and various training paradigms for emergent equivalence classes with a broad

range of elementary science curriculum topics. Topics, such as weather, rock formations,

or the skeletal system, all require mastery of class-formation, even at the level of

vocabulary acquisition resembling the present studies.

Although stimulus equivalence research has yet to extend to science-related

stimuli and class formation within the elementary education curriculum, there are several

studies in which stimulus equivalence was studied in the context of college math and

science courses (Critchfield & Fienup, 2010; Fields et al., 2009; Fienup & Critchfield,

2010; Fienup & Critchfield, 2011; Fienup, Covey, & Critchfield, 2010; Ninness et al.,

2006; Ninness et al., 2009; Ninness et al., 2005; Walker & Rehfeldt, 2012; Walker et al.,

2010). For example, Walker and Rehfeldt (2012) presented stimuli related to single

subject research designs through the Blackboard® course server to eleven graduate

students who were enrolled in an online course on behavioral assessment and

observation. Students were taught the name-to-definition (AB) relations and the name-to-

graph (AC) relations. All eleven students accurately demonstrated symmetry by matching

graphs to corresponding names (CA); however, only half of the students demonstrated

the remaining potential emergent relations. The results suggest the need for further

research in using derived relations in teaching technology used with graduate science

concepts and computerized distance learning (Walker & Rehfeldt, 2012). Nevertheless,

the three experiments in the current study expanded the literature regarding the utilization

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of computer training (e.g., Connell & Witt, 2004; Fienup et al., 2010; Lovett, Rehfeldt,

Garcia, & Dunning, 2011; Lynch & Cuvo, 1995; Oliveira, Goyo, & Pear, 2012; Stromer

& Mackay, 1992; Walker & Rehfeldt, 2012; Walker et al., 2010) for applied science

concepts to a younger educational population.

Individualized training

The results from Experiment 1, 2, and 3 demonstrated that the procedures used

were efficient, since students demonstrated a greater number of derived relations than the

number of relations directly trained. For all students, nine stimulus-stimulus relations

were possible (i.e., AA, BB, CC, AB, BA, AC, CA, BC, and CB) per class. Participants

in all three experiments were taught specific conditional discriminations that allowed for

potential symmetrical and transitive relations to emerge. The relations trained depended

on the errors demonstrated during each participant’s pretest. Sarah, Sasha, Saeed, and

Amelia made no errors on the AC and CA relations during pretesting. All the stimuli in

these relations were text. Therefore it is likely that the accurate performance

demonstrated with relations AC and CA indicated that students had been taught

previously the vocabulary of carnivore, herbivore, and omnivore. For these students, two

of the nine stimulus-stimulus relations already existed in their repertoire. Training only

AB relations allowed for testing of the symmetrical relation BA, and transitive relations

BC and CB. Sarah, Sasha, Saeed, and Amelia demonstrated six emergent relations in

posttesting (BA, BC, CB, AA, BB, and CC).

Scott’s pretest results followed a similar pattern, and he should have been trained

with only AB relations; however his training with both AB and AC relations began

before a training procedure for AB-only was created. Although the AC training was

62


unnecessary, the training maintained the performance, and his results were similar to

participants who received the AB-only training.

AB and AC training also was delivered to seven students (i.e., Nolan, Scott,

Suzanne, Aurora, Laura, Alex, and Cathy). During their pretests, performances were low

in accuracy across all relations. Training the AB and AC relations allowed for testing of

symmetrical relations BA and CA, as well as transitive relations BC and CB. The seven

students, along with Sam, who received training for the CA and CB relations, were

trained with two stimulus-stimulus relations. Training two stimulus-stimulus relations

(six total stimulus-stimulus pairs) resulted in the demonstration of a total of seven

emergent relations. Students trained with AB and AC relations demonstrated the

emergent BA, CA, BC, CB, AA, BB, and CC relations. The student (Sam) was trained

with CA and CB relations and demonstrated AC, BC, AB, BA, AA, BB, and CC

relations. These results supported Stromer and colleagues’ (1992) statement that efficient

instruction is a trademark feature of the principles of stimulus equivalence.

Sam’s pretesting demonstrated CA, AC, and CB relations each with greater than

70% accuracy. He received training on CB and CA relations to establish these

performances and determine if increasing these performances to 100% accuracy would

also increase accuracy on the remaining untrained relations. Training CB and CA

relations allowed for testing of the emergent symmetrical relation BC. Although accuracy

increased on the symmetrical relation AC after training, this performance may not be

emergent because its accuracy was at 89% correct during pretesting. Tests for transitive

relations BA and AB were also conducted.

Differential reinforcement

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Regardless of the stimulus-stimulus pairs trained via the procedural variations that

involved differential reinforcement, every student met mastery criterion, suggesting that

the procedures were effective. Notably, the procedure used in all experiments required

students to select a comparison before advancing to the next trial. Requiring the selection

of a comparison is supported by the findings of Imam and Blanche (2013), which found

that procedures with a Cannot Answer Response Option (CARO) decreased response

accuracy and the number of emergent relations that develop. In all three experiments in

the current study, comparison selection was required, and not selecting a comparison was

not an option in the procedure.

In Experiment 1, once a comparison was selected the next trial was presented. In

Experiments 2 and 3, the comparison was selected, but the participant then had to click

on the arrow displayed before a consequence (reinforcement delivery or punishment) was

delivered. The differential reinforcement was especially noteworthy in Experiments 2 and

3, in which the only contingent reinforcement or punishment delivered was a green check

or red X, respectively, paired with the stimulus selected. The green check was displayed

contingent on the selection of the comparison from the same class as the presented

sample. The red X was contingent on the selection of a comparison that was not in the

same class as the sample. The results from Experiments 2 and 3 suggested that the

conditioned reinforcer of the green check mark appearing next to the correct response and

conditioned punisher of the red X appearing next to the incorrect response served as

effective differential consequences of responding as evidenced by the increased accuracy

in performance on trained relations and decrease in errors. All participants, even the

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Kindergarten students, developed accurate performance with trained relations, and

demonstrated emergent symmetrical and transitive relations among stimuli.

Results from Experiments 1, 2, and 3 support the large body of stimulus

equivalence research that suggests the provision of curriculum materials within a

stimulus equivalence paradigm may provide an efficient teaching methodology. This

methodology could be applied as a curriculum modification, as demonstrated in

Experiment 1, or as the primary instructional method, used in Experiments 2 and 3.

Teaching could be designed to teach directly the fewest relations needed to establish

stimulus classes efficiently. Class formation, therefore, could be taught economically,

within the classroom, and could potentially decrease the amount of time special education

students spend separated from typical peers. Computer-based training, such as the

procedures described in Experiments 2 and 3, has several advantages. Immediate

feedback is provided to each student for both correct and incorrect responses. A high

level of experimental control can be maintained while remaining practical in the

classroom setting. Computerized MTS instruction requires minimal teacher training, and

the possibility of experimenter cuing affecting responses is less likely than manual,

tabletop procedures (Oliveira et al., 2012). Finally, training procedures could also be used

to allow all students to move through curriculum at their own pace (Oliveira et al., 2012;

Skinner, 1968). This would ensure each student achieves the criteria for mastery before

moving on to new skills, and would allow students to progress through academic content

at their own pace (Skinner, 1968).

Limitations

65


There are several limitations in Experiments 1, 2 and 3. Experiment 1 presents

results for only a single participant. Therefore, future studies are needed to examine

additional situations in which procedures from Experiment 1 can be utilized as

curriculum modifications both for students with learning disability and for neurotypical

students. Additionally, errors made by participants during training should be analyzed to

identify ways in which training procedures could be made even more efficient.

Another limitation in the three experiments was that only visual stimuli pertaining

to science curriculum were utilized. To provide evidence that procedures are effective

and efficient for general education science instruction in the classroom, a wide variety of

stimuli should be used in future studies. Future research should demonstrate that MTS

procedures result in the formation of equivalence classes with a wide range of stimulus

modalities, including classes containing all textual stimuli and auditory stimuli. Sidman

and colleagues (1986) suggested that classes that included an auditory name often formed

more rapidly than classes with only visual stimuli. Similarly, Green (1990) compared

auditory-visual matching procedures to visual-visual matching procedures across five

participants. Green (1990) reported that for three of the five participants, equivalence

relations emerged more rapidly following auditory-visual training. Furthermore, when a

sorting task was administered, all the participants immediately grouped stimuli into

classes based on the auditory-visual training, whereas only two of the participants

demonstrated immediate sorting following visual-visual training procedures (Green,

1990).

Smeets and Barnes-Holmes (1995) reported findings similar to those of Green

(1990) and Sidman and colleagues (1986). Smeets and Barnes-Holmes (1995) trained 16

66


children with both auditory-visual and visual-visual MTS procedures. During auditory-

visual MTS training, participants were trained to select abstract visual comparisons when

presented with a corresponding auditory sample, (i.e., “la”, “voo” or “kee”). During the

visual-visual MTS training, novel abstract visual stimuli were presented as samples and

novel abstract visual stimuli were presented as comparisons. The results were consistent

with those of Green (1990), and indicated that training with auditory samples was the

more effective procedure for yielding classes of equivalent stimuli (Smeets & Barnes-

Holmes, 1995). The authors noted that auditory-visual equivalence relations were almost

always demonstrated on the first test, where as visual-visual equivalence relations were

not demonstrated unless retesting or retraining occurred (Smeets & Barnes-Homes,

1995). Such results suggest the possibility that using auditory samples could increase the

efficiency of the procedures presented in Experiments 1, 2, and 3 even further.

Future research with auditory stimuli

Studies that use an auditory sample stimuli would expand the current literature on

stimulus equivalence and allow for the testing of a naming response (Cowley & Green,

1992; Guercio, Podolska-Schoeder, & Rehfeldt, 2004; Keintz et al., 2011; Lazar et al.,

1984; Sidman, 1971; Siguroardottir, Green, & Saunders, 1990; Stromer, Mackay, &

Remington, 1996). For example, Keintz and colleagues (2011) taught six-year-old boys

with autism the three sets of stimulus-stimulus relations AB, BC, and DC, where A

stimuli were the auditory names of coins, and B (actual coins) and C (printed price of

coins) stimuli were visual. First, students were taught to match the coin to the auditory

sample of the dictated coin name (AB). Then the coin was presented as the sample, and

students were taught to select the corresponding printed price (BC). Finally, the boys

67


were taught to select the printed price when the price was dictated as an auditory sample

(DC). Following training, both students named the coin when presented with the coin

(BE) (Keintz et al., 2011). However, naming does not always occur following auditory-

visual training (Horne, Lowe, & Randle, 2004; Keintz et al., 2011; Petursdottir &

HafliDadottir, 2009). In the study by Keintz and colleagues (2011), only one of the boys

accurately named the price when shown the printed price, named the coin when the price

was dictated, and named the price when the coin name was dictated.

The potential emergence of oral naming is a topic that requires much additional

research and procedure development. Longano and Greer (2014) conducted a study to

examine the effects of a procedure for conditioning reinforcement for observing

responses on the emergence of naming. The results of the study suggested that visual and

auditory stimuli may need to function jointly as reinforcers for naming to emerge. The

procedures used by Longano and Greer, successfully increased naming responses.

Investigating the likelihood of such performance is important. Since classroom

instruction often involves auditory stimuli, procedures that result in the production of

naming may provide more opportunities for MTS procedures in the classroom. This may

be of particular importance for individuals with developmental disabilities, as it may

allow for greater inclusion in the general education classroom (Longano and Greer,

2014).

Although it was not a primary purpose of these studies to observe and measure

naming responses during MTS tasks, anecdotal notes were made during Experiment 3

regarding a student’s spontaneous verbal behavior. Aurora stated verbally that she could

read the Group C stimuli (C1: Eats Meat, C2: Eats Plants, C3: Eats Both). During

68


training of the AC relations, Aurora said she did not know what the A3 (Omnivore) text

said and that she decided to call it “oatmeal”. She added, “I don’t know why oatmeal eats

both, but it does, and I get it right.” Her overt verbal behavior suggested that she had been

naming covertly, as suggested by Horne and Lowe (1996). Aurora was the only

participant from any of the three experiments who spoke about names she had given to

stimuli. Therefore, it is impossible to determine, on the basis of their observable

behavior, if the other participants created and used names for stimuli.

Some researchers argue that naming responses, which involve both speaker and

listener repertoires, are required for successful performances indicating equivalence

classes (Horne & Lowe, 1996). Horne and Lowe (1996) proposed that participants

engage in naming and other verbal behavior during MTS tasks. They argued that the lack

emergent performances indicating the formation equivalence classes with nonverbal

organisms supports the argument that verbal behavior is required (Horne & Lowe, 1996).

Student-generated names for samples have not reliably facilitated mastery of

arbitrary matching in experimental conditions (Pilgrim et al., 2000). The preschoolers

who participated in the study by Pilgrim and colleagues’ (2000), often required specific

instructions or experimenter-assigned names for sample stimuli in order for arbitrary

matching to meet the mastery criterion. The students in Experiment 3 were of comparable

age to students in the study by Pilgrim and colleagues. The procedures in Experiment 3

did not include instructions or assigned names, and all Kindergarteners demonstrated the

necessary emergent stimulus-stimulus relations to indicate classes of equivalent stimuli

had formed. The results from Experiment 3 suggested that the procedures sufficed to

69


establish the prerequisites for equivalence in Kindergarteners without directly teaching a

naming response.

Generality, generalization and maintenance

Other potential limitations in Experiments 2 and 3 could be the lack of assessment

for performance generality. Fienup and colleagues (2010) described the limitation of

assessing only selection-based responding, which applies to the present studies as well.

The selection-based procedure utilized confines responding to a multiple-choice format.

However, functional responding beyond the experimental setting frequently requires

topography-based responding other than the naming and spelling performances discussed

above (e.g., writing an essay or report). Topography-based responding was not assessed

in the present experiments, thus limiting the assessment of procedural generality. It has

yet to be demonstrated whether responses established with selection-based methods

would produce topography-based repertoires as well (Fienup et al., 2010)

Another limitation of the current study is the lack of assessment for generalization

to stimuli beyond those used in training. Testing for generalization to novel stimuli could

provide valuable information regarding the utility of procedures in the education setting.

Rehfeldt (2011) suggested that examining generalization performances is one of the most

important aspects of an assessment of whether the study’s procedures and findings can

transfer. Procedures that result in emergent performances with a variety of tasks have

great educational value (Rehfeldt, 2011).

Stimulus generalization was assessed in Experiment 1 with Nolan. Following

training, Nolan was presented with a three-dimensional carnivore skull. The skull was not

an identical match to the animal presented in the photograph (B3), but the general shape

70


of the skull, snout, eye sockets, and teeth were similar to the features of the picture.

Nolan correctly identified the stimulus from Groups A and C that matched the skull.

Although this task does not thoroughly assess generalization, since it did not present

three-dimensional skulls for herbivores or omnivores, it does suggest that novel variants

of stimuli can enter, or be confirmed as members of, extant stimulus classes through

stimulus generalization. These results are consistent with the results of experimental

analyses of generalization (e.g., Fields, Reeve, Adams, & Verhave, (1991).

However, the results the stimulus generalization task in Experiment 1 differ from

those of Walker and Rehfeldt (2012). Walker and Rehfeldt (2012) tested for stimulus

generalization by including posttraining tests with novel stimuli. Graduate level students

were taught to match the definition of a graph to the name of the graph (AB), a visual of

the graph to the name of the graph (AC), and a written scenario to the definition (DB).

When presented with novel stimuli (e.g., variants of the visual graphs or variants of the

scenarios), participants failed to demonstrate reliable matching performances on

emergent (CA, DA, and DB) relations (Walker & Rehfeldt, 2012). The failure to

demonstrate stimulus generalization indicated that participants may have been responding

to irrelevant stimulus features of the highly complex stimuli used (Walker & Rehfeldt,

2012). If only specific features of a complex stimulus control responding, then

responding cannot be expected to maintain when those specific features are no longer

present in novel stimuli presented on test trials (Walker & Rehfeldt, 2012).

A final limitation to the current study is the lack of assessment for the

maintenance of equivalence relations over time. Some experiments showed that matching

performances may become less accurate over time. Walker and Rehfeldt (2012)

71


conducted maintenance probes of emergent relations (BA, CA, DA, and DB) 16 weeks

after training AB, AC, and BD relations. The relations tested for maintenance were the

same relations previously tested for emergence. In immediate posttraining tests,

symmetrical relations (BA) were demonstrated by six of the 11 participants, and all 11

participants demonstrated symmetrical relations (CA). Emergent relations (DB) were

demonstrated by 5 of the 11 participants, and DA relations were demonstrated by 7 of the

11 participants. However, when maintenance was assessed for seven participants 16

weeks later, none of the participants maintained the BA or DB relations, only two

participants maintained the CA relations and one participant maintained the DA relations

(Walker & Rehfeldt, 2012). The results from the 16-week follow-up indicated that the

emergent relations were not durable over time (Walker & Rehfeldt, 2012).

Nolan, in Experiment 1, was tested for six-month maintenance. Overall,

performance on the maintenance tests was inconsistent, except for trained relation AB

and the symmetric BA relations, which remained accurate. The results indicated that

matching performances on all trials including a stimulus from Class 3 (omnivore) were

the only performances that remained accurate. As previously discussed, the text presented

as stimulus C3 (Eats Meat and Plants) is two words longer that the text the for stimuli C1

(Eats Meat) and C2 (Eats Plants), and the skull presented as the B3 stimulus had the

snout oriented to the right whereas the skulls presented as the B1 and B2 stimuli were

oriented to the left. The text length and the skull direction may have provided

idiosyncratic cues that came to control selections and continued to do so during tests for

maintenance. The variability shown by Nolan is consistent with the findings reported by

Walker and Rehfeldt (2012).

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Neither generalization nor maintenance was evaluated in Experiment 2 or 3.

Given the results from Walker & Rehfeldt (2012), and Nolan’s decline in accuracy in

several stimulus-stimulus relations in maintenance testing, further research is needed.

Maintenance tests should be conducted with all participants to determine which relations

maintain over time, and how procedures might be altered to increase the probability of

lasting equivalence relations.

Extending stimulus equivalence beyond MTS

Sidman (1994) suggested that the emergence of new behavior without direct

training is a feature of creativity. Consideration for the emergence of stimulus-stimulus

relations suggestive of equivalence class formation may partially explain the emergence

of untaught behavior that, in more general terms, is said to be the result of the creative

process. Sidman suggested that arranging contingencies within the experimental

paradigm that establishes the prerequisites of equivalence might allow researchers to

predict creativity under specific circumstances. However, McIlvane and Dube, (1990)

introduced a caution with respect to the role of testing: different test conditions might

produce different forms of novel behavior. Testing itself may exert control over

responding (McIlvane & Dube, 1990). Sidman (1994) acknowledged that reading

comprehension and creativity are likely more complex than just equivalence relations.

However, he suggested that an increased understanding about equivalence might lead to

better understanding about novel performances and creativity (Sidman, 1994). Similarly,

a better understanding of the affects of testing on emergent behavior is needed.

Another important aspect of additional research that is needed will involve

investigating equivalence class formation with tasks that do not involve MTS procedures.

73


Teaching matching relations reliably results in the emergence of untrained relations in the

context of MTS: within these tasks stimuli are interchangeable. Researching mutually

substitutable relations only in the context of MTS procedures limits the potential for

understanding more general roles that stimulus equivalence may play in the occurrence of

complex behavior.

An important direction for such potential research is discussed by Fienup and

colleagues (2010). They used computer-based instruction to teach college students four

equivalence classes with stimuli relevant to neuroanatomy and brain function. The stimuli

included names and locations of various brain lobes, brief statements of psychological

functions and problems associated with each lobe region (e.g., frontal lobe, involved in

movement, involved in higher cognitive functions, damage causes impulsiveness,

respectively). All four students demonstrated performances consistent with equivalence

class formation following training. In the discussion of results, Fienup and colleagues

acknowledged the important role of contextual control in understanding the relevance of

stimulus equivalence in an account of the complex relational discriminations observed.

Performances indicating the formation of equivalence classes required students to treat

stimuli as interchangeable within the instructional context of the MTS procedures used.

However, this interchangeability may not be observed in performances outside that

instructional context. For example, there are a great many situations in which frontal lobe

and damage causes impulsiveness would not be treated as matching or interchangeable

stimuli or described as belonging (going) together. With regard to the present studies, the

children matched, for example, a picture of the skull of an herbivore with the words

Herbivore and Eats Plants. Thus, the text Herbivore may be said to belong (go) with (or

74


substitute for) Eats Plants in a MTS lesson, but not in many other everyday contexts. The

stimuli may function as equivalent within the specific teaching conditions provided, but

these stimuli are not absolutely interchangeable (Fienup et al., 2010). Research should

investigate conditions needed to produce novel verbal behavior when presented with

stimuli from various classes, such as those of the current experiments. For example, it

would be important to examine procedures that result in a student saying “That’s the skull

of an animal that eats plants” (i.e., a relevant property) when presented with an actual

skull. A response of this type, in which a complex response emerges following the

training of an MTS response, demonstrates a higher level of understanding (Bloom,

Engelhart, Furst, Hill, & Krathwohl, 1956) Moreover, procedures that develop responses,

such as “a horse is an herbivore because it eats plants”, would demonstrate synthesis of a

learned MTS response. Applied and synthesized responses go beyond simple selection-

based responses and have applied value as they demonstrate more complex response in

contexts outside of training conditions (Bloom et al., 1956). Investigating conditions that

promote occurrence of such verbal behavior is an important next step; particularly since

novel verbal responses (both oral and written) are used for assessment within the

mainstream classroom.

The results from the three experiments described here show one avenue for how

one might integrate stimulus equivalence into classroom instruction. Research should

continue to study efficient procedures that not only produce emergent stimulus-stimulus

relations indicative of the formation of equivalence classes, but also expand to analyze

verbal behavior and a range of response topographies beyond those involved in MTS

tasks.

75


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90


Table 1.

Stimuli Used in Experiment 1.

Class Stimuli A Stimuli B Stimuli C

1 Carnivore Eats Meat

2 Herbivore Eats Plants

3 Omnivore Eats Meat and Plants

Note: The physically dissimilar stimuli appear in vertical columns of Group A, Group B,

and Group C. The three classes are depicted in the horizontal rows and include one

stimulus from each of the groups.

91


Table 2

Individualized Training

Pretest ResultsRelations Trained

Potential Symmetric Relations

Potential Transitive Relations

Pattern 1

AC and CA at 100% accuracy, all other relations below 50% accuracy

AB only BA BC and CB

Pattern 2

All relations below 50% accuracy or only AB and AC relations above 50 % accuracy

AB and AC BA and CA BC and CB

Pattern 3

CA, CB, and AC relations greater than 75% accuracy, all other relations below 75% accuracy

CA and CB AC and BC AB and BA

92


Table 3

Alphanumeric Designations of Arbitrary Relations in Experiment 1, 2, & 3.

Stimulus relations Class1 Class2 Class3AB A1-B1 A2-B2 A3-B3BC B1-C1 B2-C2 B3-C3CA C1-A1 C2-A2 C3-A3BA B1-A1 B2-A2 B3-A3AC A1-C1 A2-C2 A3-C3CB C1-B1 C2-B2 C3-B3

Note: The first stimulus (A1) represents the sample and second represents the S+

comparison.

93


Table 4

Pretest results from Pretest 1 and Pretest 2 in Experiment 1.

Stimulus-Stimulus Relation

Pretest 1 Pretest2

A1-B1 16.6 50A2-B2 33.3 33.3A3-B3 16.6 16.6A1-C1 16.6 16.6A2-C2 16.6 0A3-C3 50 50B1-A1 33.3 33.3B2-A2 50 50B3-A3 50 33.3C1-A1 33.3 33.3C2-A2 0 16.6C3-A3 33.3 16.6B1-C1 50 66.6B2-C2 66.6 33.3B3-C3 33.3 33.3C1-B1 50 66.6C2-B2 33.3 33.3C3-B3 83.3 33.3Note: Stimulus-stimulus relations are labeled in the left-most vertical column. Percents

correct for each relation are presented in the columns for Pretest 1 and Pretest 2.

94


Table 5

Stimuli Used in Experiments 2 and 3. Class Stimuli A Stimuli B Stimuli C

1 Carnivore Eats Meat

2 Herbivore Eats Plants

3 Omnivore Eats Both

Note: The physically dissimilar stimuli in vertical columns of Group A, Group B, and

Group C. The three classes are depicted in the horizontal rows and include one stimulus

from each of the groups.

95


Table 6

Sequence of Conditions for all Testing– Experiment 2________________________________________________________________________Pretest Posttest__ AB ABBC BCCA CABA CBAC BACB AC___ Note: A = text (Carnivore, Herbivore, Omnivore), B = picture, C = text (Eats Meat, Eats

Plants, Eats Both). Identity tests (AA, BB, CC) were conducted prior to pretesting.

96


Table 7

Sequence of Conditions –in Experiment 3 (AB & AC Training)

IDMTS Pretest1 Pretest2 Pretest3 Training Posttest1 Posttest2 Posttest3AA AB CB AC AB AB CB ACBB BC BA CA AC BC BA CACCNote: A = text (Carnivore, Herbivore, Omnivore), B = picture, C = text (Eats Meat, Eats

Plants, Eats Both). BA and CA represent posttests for symmetry, BC and CB represent

posttests for transitivity. AA, BB, and CC represent identity tests.

97


Figure 1. Example of trial as presented to Nolan in Experiment 1. The sample stimulus

was presented in the top left corner and was outlined in a red frame. The three

comparison stimuli were presented in the three remaining quadrants and were outlined in

blue.

98


Figure 2. The stimulus equivalence paradigm for Experiment 1. Group A contained

textual stimuli (e.g., Carnivore), Group B consisted of pictorial images of mammalian

skulls, and Group C included the textual stimuli specifying the mammal’s diet (e.g., eats

meat). Arrows point from sample to comparison stimuli. The solid arrows depict trained

relations (AB & AC). Broken arrows represented potential emergent relations (BA, CA,

BC, & CB).

99


Figure 3. Accuracy of Nolan’s responding in Experiment 1 for each specific stimulus-

stimulus relation (A1-B1, A2-B2, A3-B3, A1-C1, A2-C2, & A3-C3) throughout the

differential reinforcement training phases. The A-B phases began immediately after the

errorless training. The A-C training phase began once the student met the mastery criteria

for A-B training. The A-B training phase included a maintenance probe at session 14.

100


Figure 4. Responses during AC training sessions one through nine are presented in the

above matrices. The matrices display the comparisons selected by Nolan during the

presentation of samples A1, A2, and A3. The horizontal rows are labeled with the sample

stimuli and the vertical columns are labeled with the comparison stimuli. The top row of

matrices from left to right correspond to sessions one through three, sessions four through

six appear in the middle row, and sessions seven through nine appear across the bottom

row.

101


Figure 5. Results from Experiment 1. The graph displays Nolan’s percent correct

responding to all stimulus-stimulus relations in pretest 1, pretest 2, posttest, and 6-month

follow up phases. Pretesting and posttesting occurred within three-weeks of each other.

102


Figure 6. Percent correct for Nolan’s responding in Experiment 1 for each stimulus-

stimulus relation at the six-month follow up. Performance for each class (carnivore,

herbivore, and omnivore) is displayed separately.

103


Figure 7. Example of Qualtrics® screen presented for each MTS presentation in

Experiment 2 and Experiment 3. The sample stimulus, here Carnivore (stimulus A1), was

presented in the top left corner. The three comparison stimuli were presented horizontally

across the bottom. In this example the comparisons are, from left to right, the pictures of

animal skulls B1, B3, and B2.

104


Figure 8. Illustration of a reinforcement feedback display presented in Experiment 2 and

Experiment 3 following a correct selection of a comparison. A green checkmark appeared

next to the comparison selected by the student.

105


Figure 9. Illustration of the feedback display presented in Experiment 2 and Experiment

3 following the selection of an incorrect comparison. A red X is displayed next to the

comparison selected by the student.

106

STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING 107


Figure 10. Pretest and posttest results from Experiment 2 for participants Sarah, Sasha,

and Saeed, top to bottom respectively. These participants were trained with only AB

relations. Posttesting displays emergent symmetrical (BA) and transitive relations (CB

and BC).

Figure 11. Pretest and posttest results from Experiment 2 for participants trained with AB

and AC relations. Scott (top panel) was trained with AB and AC relations even though

the AC and CA relations were 100% in pretesting. Posttesting for Scott demonstrated

108


emergent symmetrical (BA) and transitive relations (CB and BC). Posttesting for

Suzanne (bottom panel) displayed emergent symmetrical (BA and CA) and transitive

relations (CB and BC).

Figure 12. Depicts pretest and posttest results for Sam from Experiment 2. Sam was

trained with CA and CB relations. Posttesting displayed emergent symmetrical (AC and

BC) and transitive (AB and BA) relations.

109


Figure 13. The stimulus equivalence paradigm for training only AB relations. This

paradigm was used in Experiments 2 and 3. Group A contained textual stimuli, Group B

included pictorial images of mammalian skulls, and Group C consisted of textual stimuli

specifying the mammal’s diet. The solid arrows represent trained relation (AB) and the

dashed arrows represented emergent relations (BA, BC, & CB). The AC and CA relations

existed in the student’s repertoire at pretesting.

110


Figure 14. The stimulus equivalence paradigm for training AB and AC relations. This

paradigm was used in Experiments 2 and 3. Group A contained textual stimuli, Group B

consisted of pictorial images of mammalian skulls, and Group C contained textual stimuli

specifying the mammal’s diet. The solid arrows depict trained relations (AB & AC) and

the dashed arrows represented emergent relations (BA, CA, BC, & CB).

111


Figure 15. The stimulus equivalence paradigm for Experiment 2 when relations CA and

CB were trained. Group A contained textual stimuli, group B consisted of pictorial

images of mammalian skulls, and C included textual stimuli specifying the mammal’s

diet. The solid arrows depict trained relations (CA & CB) and the dashed arrows

represented emergent relations (AC, BC, AB, & BA).

112


Figure 16. Depicts pretest and posttest results for Amelia, a kindergarten student, from

Experiment 3. Amelia was trained with only AB relations. Posttesting demonstrated the

emergent symmetrical (BA) and transitive (BC and CB) relations.

113


Figure 17. Pretest and posttest results from Experiment 3 for participants Aurora, Laura,

Alex and Cathy, top to bottom respectively. These participants were trained with AB and

AC relations. Posttesting displays emergent symmetrical (BA and CA) and transitive

relations (CB and BC).

114


Figure 18. Scatterplot depicting number of training sessions Kindergarten and third-grade

participants required to meet the criterion for mastery of 100%. Each point represents the

number of training sessions a participant completed. Multiple points at the same level

indicate that numerous students required the same

115


Appendix A

List of each trial presented during IDMTS showing balanced presentation of the sample

(Sa) stimulus and the equal presentation of all comparison stimuli in each position of the

array (L=left, C=center, R=right)

trial Sa L C R trial Sa L C R1 A1 A1 A3 A2 28 B2 B1 B3 B22 A3 A2 A3 A1 29 B1 B2 B1 B33 A2 A2 A1 A3 30 B2 B3 B1 B24 A3 A1 A2 A3 31 B1 B1 B2 B35 A1 A3 A1 A2 32 B3 B1 B3 B26 A3 A3 A2 A1 33 B1 B3 B2 B17 A1 A2 A3 A1 34 B2 B2 B3 B18 A2 A1 A2 A3 35 B3 B2 B1 B39 A3 A3 A1 A2 36 B2 B3 B2 B1

10 A2 A1 A3 A2 37 C1 C1 C3 C211 A1 A2 A1 A3 38 C3 C2 C3 C112 A2 A3 A1 A2 39 C2 C2 C1 C313 A1 A1 A2 A3 40 C3 C1 C2 C314 A3 A1 A3 A2 41 C1 C3 C1 C215 A1 A3 A2 A1 42 C3 C3 C2 C116 A2 A2 A3 A1 43 C1 C2 C3 C117 A3 A2 A1 A3 44 C2 C1 C2 C318 A2 A3 A2 A1 45 C3 C3 C1 C219 B1 B1 B3 B2 46 C2 C1 C3 C220 B3 B2 B3 B1 47 C1 C2 C1 C321 B2 B2 B1 B3 48 C2 C3 C1 C222 B3 B1 B2 B3 49 C1 C1 C2 C323 B1 B3 B1 B2 50 C3 C1 C3 C224 B3 B3 B2 B1 51 C1 C3 C2 C125 B1 B2 B3 B1 52 C2 C2 C3 C126 B2 B1 B2 B3 53 C3 C2 C1 C327 B3 B3 B1 B2 54 C2 C3 C2 C1

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Appendix B

List of each trial presented during arbitrary matching of AB and AC relations showing

balanced presentation of the sample (Sa) stimulus and the equal presentation of all

comparison stimuli in each position of the array (L=left, C=center, R=right). Bold print

represents the comparison that corresponds to the sample being presented in that trial.

trial Sa L C R trial Sa L C R1 A1 B1 B3 B2 19 A1 C1 C3 C22 A3 B2 B3 B1 20 A3 C2 C3 C13 A2 B2 B1 B3 21 A2 C2 C1 C34 A3 B1 B2 B3 22 A3 C1 C2 C35 A1 B3 B1 B2 23 A1 C3 C1 C26 A3 B3 B2 B1 24 A3 C3 C2 C17 A1 B2 B3 B1 25 A1 C2 C3 C18 A2 B1 B2 B3 26 A2 C1 C2 C39 A3 B3 B1 B2 27 A3 C3 C1 C210 A2 B1 B3 B2 28 A2 C1 C3 C211 A1 B2 B1 B3 29 A1 C2 C1 C312 A2 B3 B1 B2 30 A2 C3 C1 C213 A1 B1 B2 B3 31 A1 C1 C2 C314 A3 B1 B3 B2 32 A3 C1 C3 C215 A1 B3 B2 B1 33 A1 C3 C2 C116 A2 B2 B3 B1 34 A2 C2 C3 C117 A3 B2 B1 B3 35 A3 C2 C1 C318 A2 B3 B2 B1 36 A2 C3 C2 C1

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