Page 1
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
Page 2
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
2
Page 3
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
3
Page 4
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
4
Page 5
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
5
Page 6
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
6
Page 7
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
7
Page 8
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
8
Page 9
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
9
Page 10
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
10
Page 11
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
11
Page 12
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
12
Page 13
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
13
Page 14
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
14
Page 15
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
15
Page 16
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
16
Page 17
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
17
Page 18
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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,
18
Page 19
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
19
Page 20
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 21
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 22
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 23
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 24
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 25
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 26
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 27
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 28
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 29
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
29
Page 30
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 31
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 32
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 33
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 34
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 35
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 36
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 37
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 38
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 39
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
station. During most sessions, the classroom was full of students engaged in academic
activities.
Apparatus and Data Recording
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
Page 40
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 41
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 42
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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.
Interobserver Agreement (IOA)
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
42
Page 43
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 44
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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%).
44
Page 45
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 46
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 47
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
47
Page 48
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 49
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
49
Page 50
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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.
Apparatus and Data Recording
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.
Interobserver Agreement (IOA)
50
Page 51
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 52
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 53
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 54
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 55
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 56
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 57
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
57
Page 58
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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).
58
Page 59
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
59
Page 60
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
60
Page 61
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
61
Page 62
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 63
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
63
Page 64
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
64
Page 65
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 66
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 67
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 68
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 69
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 70
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 71
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 72
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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).
72
Page 73
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 74
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 75
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 76
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
References
Adcock, A., Merwin, R., Wilson, K., Drake, C., Tucker, C., & Elliott, C. (2010). The
problem is not learning: Facilitated acquisition of stimulus equivalence classes
among low-achieving college students. The Psychological Record, 60, 43-56.
Retrieved from http://thepsychologicalrecord.siu.edu/
Arntzen, E., Grondahl, T., & Eilifsen, C. (2010). The effects of different training
structures in the establishment of conditional discriminations and the subsequent
performance on the tests for stimulus equivalence. The Psychological Record, 60,
437-462. Retrieved from http://thepsychologicalrecord.siu.edu/
Arntzen, E., Halstadtro, L., Bjerke, E., & Halstadtro, M. (2010). Training and testing
music skills in a boy with autism using a matching-to-sample format. Behavioral
Interventions, 25, 129-143. doi: 10.1002/bin.301
Arntzen, E., Halstadtro, L., Bjerke, E., Wittner, K. J., & Kristiansen, A. (2014). On the
sequential and concurrent presentation of trials establishing prerequisites for
emergent relations. The Behavior Analyst Today, 14, 23-30. Retrieved from
http://www.ejoba.org/
Artntzen, E., & Holth, P. (2000). Differential probabilities of equivalence outcome in
individual subjects as a function of training structure. The Psychological Record,
50, 603-628. Retrieved from http://thepsychologicalrecord.siu.edu/
Arntzen, E., & Vaidya, M. (2008). The effect of baseline training structure on
equivalence class formation in children. Experimental Analysis of Human Behavior
Bulletin, 29, 1–8. Retrieved from http://www.eahb.org/
Augustson, K. G., & Dougher, M. J. (1991). Teaching conditional discrimination to
76
Page 77
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
young children: Some methodological successes and failures. Experimental
Analysis of Human Behavior Bulletin, 9, 21-24. Retrieved from
http://www.eahb.org/
Barnes, D. (1994). Stimulus equivalence and relational frame theory. Psychological
Record, 44, 91-125. Retrieved from http://thepsychologicalrecord.siu.edu/
Barnes, D., McCullough, P. D., & Keenan, M. (1990). Equivalence class formation in
non-hearing impaired children and hearing impaired children. Analysis of Verbal
Behavior, 8, 19-30. Retrieved from http://www.abainternational.org/journals/the-
analysis-of-verbal-behavior.aspx/
Bloom, B., Englehart, M.. Furst, E., Hill, W., & Krathwohl, D. (1956). Taxonomy of
educational objectives: The classification of educational goals. Handbook I:
Cognitive domain. New York, Toronto: Longmans, Green.
Boelens, H., Van Den Broek, M., & Van Klarenbosch, T. (2000). Symmetric matching to
sample in 2-year-old children. The Psychological Record, 50, 293-304. Retrieved
from http://thepsychologicalrecord.siu.edu/
Bush, K. M., Sidman M., & de Rose, T. (1989). Contextual control of emergent
equivalence relations. Journal of the Experimental Analysis of Behavior, 51(1), 29-
45. doi: 10.1901/jeab.1989.51-29
Carrigan, P. F., & Sidman, M. (1992). Conditional discrimination and equivalence
relations: A theoretical analysis of control by negative stimuli. Journal of
Experimental Analysis of Behavior, 58, 183-204. doi:10.1901/jeab.1992.58-183
Cautilli, J. D., Hancock, M. A., Thomas, C. A., & Tillman, C. (2002). Behavior therapy
and autism: Issues in diagnosis and treatment. Behavior Analyst Today, 3, 230–242.
77
Page 78
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
Retrieved from http://baojournal.com/BAT%20Journal/BAT-Journals-2009.html/
Connell, J. E., & Witt, J. C. (2004). Applications of computer-based instruction: using
specialized software to aid letter-name and letter-sound recognition. Journal of
Applied Behavior Analysis, 37, 67-71. doi:10.1901/jaba.2004.37-67
Cowley, B. J., Green, G., & Braunling-McMorrow, D. (1992). Using stimulus
equivalence procedures to teach name-face matching to adults with brain injuries.
Journal of Applied Behavior Analysis, 25, 461–475. doi:10.1901/jaba.1992.25-461
Critchfield, T.S. (2014). Online equivalence-based instruction about statistical inference
using written explanation instead of match-to-sample training. Journal of Applied
Behavior Analysis, 47, 606-611. doi: 10.1002/jaba.150
Critchfield, T.S., & Fienup, D.M. (2008). Stimulus equivalence. In S.F. Davis &
W.F. Buskist (Eds.), 21st Century Psychology (pp. 360-372). Thousand Oaks, CA:
Sage.
Critchfield, T. S., & Fienup, D. M. (2010). Using stimulus equivalence technology to
teach statistical inference in a group setting. Journal of Applied Behavior Analysis,
43, 763-768. doi: 10.1901/jaba.2010.43-763
de Rose, J. C., de Souza, D. G., & Hanna, E. S. (1996). Teaching reading and spelling:
Exclusion and stimulus equivalence. Journal of Applied Behavior Analysis, 29, 451-
469. doi: 10.1901/jaba.1996.29-451
de Rose, J. C., Hidalgo, M., & Vasconcellos, M. (2013). Controlling relations in baseline
conditional discriminations as determinants of stimulus equivalence. The
Psychological Record, 63(1), 85-98. doi:10.11133/j.tpr.2013.63.1.007
Devany, J. M., Hayes, S. C., & Nelson, R. O. (1986). Equivalence-class formation in
78
Page 79
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
language-able and language-disabled children. Journal of the Experimental Analysis
of Behavior, 46, 243-257. doi:10.1901/jeab.1986.46-243
Donahoe, J. W., & Palmer, D. C. (2004). Learning and complex behavior. Richmond,
MA: Ledgetop.
Dube, W.V., Green, G., & Serna, R. W. (1993). Auditory successive conditional
discrimination and auditory stimulus equivalence classes. Journal of the
Experimental Analysis of Behavior, 59, 103-114. doi: 10.1901/jeab.1993.59-103
Dube, W. V., & McIlvane, W. J. (1999). Reduction of stimulus overselectivity with
nonverbal differential observing responses. Journal of Applied Behavior Analysis,
32, 25-33. doi: 10.1901/jaba.1999.32-25
Dube, W.V., McIlvane, W. J., Maguire, R.W., Mackay, H. A., & Stoddard, L. T. (1989).
Stimulus class formation and stimulus-reinforcer relations. . Journal of the
Experimental Analysis of Behavior, 51, 65-76. doi: 0.1901/jeab.1989.51-65
Ellis, W. D., Ludlow, B. L., & Walls, R. T. (1978). Learning, transfer, and retention of
errorless fading versus trial-and-error teaching. Psychological Reports, 43, 553-554.
doi: 10.2466/pr0.1978.43.2.553
Egli, M., Joseph, B., & Thompson, T. (1997). Transfer of social attributions in stimulus
equivalence classes by preschool children. Psychological Reports, 80, 3-21.
doi:10.2466/pr0.1997.80.1.3
Eilifsen, C., & Arntzen, E. (2009). On the role of trial types in tests for stimulus
equivalence. European Journal of Behavior Analysis, 10, 187–202. Retrieved from
http://www.ejoba.org/
Eikeseth, S., & Smith, T. (1992). The development of functional and equivalence
79
Page 80
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
classes in high-functioning autistic children: the role of naming. Journal of
Experimental Analysis of Behavior, 58, 123-133. doi: 10.1901/jeab.1992.58-123
Etzel, B. C., & LeBlanc, J. M. (1979). The simplest treatment alternative: The law of
parsimony applied to choosing appropriate instructional control and errorless-
learning procedures for the difficult-to-teach child. Journal of Autism and
Developmental Disorders, 9, 361-382. doi: 10.1007/BF01531445
Fields, L., Reeve, K. F., Adams, B., & Verhave, T. (1991). Stimulus generalization and
equivalence classes: a model for natural categories. Journal of the Experimental
Analysis of Behavior, 55, 305-312. doi: 10.1901/jeab.1991.55-305
Fields, L., Travis, R., Roy, D., Yadlovker, E., Aguiar-Rocha, L., & Sturmey, P. (2009).
Equivalence class formation: A method for teaching statistical interactions. Journal
of Applied Behavior Analysis, 42, 575-593. doi: 10.1901/jaba.2009.42-575
Fields, L., Verhave, T., & Fath, S. (1984). Stimulus equivalence and transitive associates:
A methodological analysis. Journal of Experimental Analysis of Behavior, 42, 143-
157. doi: 10.1901/jeab.1984.42-143
Fienup, D. M., & Critchfield, T. S. (2010). Efficiently establishing concepts of inferential
statistics and hypothesis decision making through contextually controlled
equivalence classes. Journal of Applied Behavior Analysis, 43, 437- 462.
doi:10.1901/jaba.2010.43-437
Fienup, D. M., & Critchfield, T. S. (2011). Transportability of equivalence-based
programmed instruction: efficacy and efficiency in a college classroom. Journal of
Applied Behavior Analysis, 44, 435-450. doi:10.1901/jaba.2011.44-435
Fienup, D. M., Covey, D. P., & Critchfield, T. S. (2010). Teaching brain-behavior
80
Page 81
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
relations economically with stimulus equivalence technology. Journal of Applied
Behavior Analysis, 43, 19-33. doi: 10.1901/jaba.2010.43-19
Gellert, W., Kustner, H., Hellwich, M., & Kastner, H. (1977). The VNR concise
encyclopedia of mathematics. New York: Van Nostrand Reinhold.
Goldiamond, I. (1962). Perception. In A. Bachrach (Eds.), Experimental foundations of
clinical psychology. (pp. 280-340). New York: Basic Books Inc.
Green, G. (1990). Differences in development of visual and auditory-visual equivalence
relations. American Journal of Mental Retardation, 95, 260-270. Retrieved from:
http://aaiddjournals.org/loi/ajmr.1
Green, G. (2001). Behavior analytic instruction for learners with autism: Advances in
stimulus control technology. Focus on Autism and Other Developmental
Disabilities, 16, 72-85. doi: 10.1177/108835760101600203
Guercio, J. M., Podolska-Schroeder, H. P., & Rehfeldt, R. A. (2004). Using stimulus
equivalence technology to teach emotion recognition to adults with acquired brain
injury. Brain Injury, 6, 593-601. doi: 10.1080/02699050310001646116
Haegele, K. M., McComas, J. J., Dixon, M., & Burns, M. K. (2011). Using a stimulus
equivalence paradigm to teach numerals, english words, and native american words
to preschool-age children. Journal Of Behavioral Education, 20, 283-296.
doi:10.1007/s10864-011-9134-9
Hall, S. S., Debernardis, G. M., & Reiss, A. L. (2006). The acquisition of stimulus
equivalence in individuals with fragile X syndrome. Journal of Intellectual
Disability Research, 50, 643 – 651. doi: 10.1111/j.1365-2788.2006.00814.x
Hayes, S. C., Blackledge, J. T., & Barnes- Holmes, D. (2001). Language and cognition:
81
Page 82
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
Constructing an alternative approach within the behavioral tradition. In S. C. Hayes,
D. Barnes-Holmes, & B. Roche (Eds.), Relational frame theory: A post-Skinnerian
account of human language and cognition (pp. 3–20). New York: Kluwer
Academic/Plenum.
Horne, P. J., & Lowe, F. C. (1996). On the origins of naming and other symbolic
behavior. Experimental Analysis of Behavior, 65, 185-241. doi:
10.1901/jeab.1996.65-185
Horne, P. J., Lowe, F. C., & Randle, V. R. (2004). Naming and categorization in young
children: II. Listener behavior training. Journal of Experimental Analysis of
Behavior, 81, 267-288. doi: 10.1901/jeab.2004.81-267
Imam, A. A., & Blanche, J. V. (2013). Effects of a CARO on stimulus equivalence
formation: A systematic replication. Psychological Record, 63, 141-156. Retrieved
from http://thepsychologicalrecord.siu.edu/
Jenkins, J. J., & Palmero, D. S. (1964). Mediation processes and the acquisition of
linguistic structure. In U. Bellugi & R. Brown (Eds.), The acquisition of language.
Monographs of the Society for Research in Child Development, Serial No. 92, 29,
No. 1, 141-169.
Joyce, B. G., Joyce, J. H., & Wellington, B. (1993). Using stimulus equivalence
procedures to teach relationships between english and spanish words. Education &
Treatment Of Children, 16, 48-65. Retrieved from socINDEX with full text.
Katz, J.S., & Wright, A. A. (2006). Same/different abstract-concept learning by pigeons.
Journal Of Experimental Psychology: Animal Behavior Processes, 32, 80-86. doi:
10.1037/0097-7403.32.1.80
82
Page 83
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
Keintz, K. S., Miguel, C. F., Kao, B., & Finn, H. E. (2011). Using conditional
discrimination training to produce emergent relations between coins and their
values in children with autism. Journal of Applied Behavior Analysis, 44, 909-913.
doi: 10.1901/jaba.2011.44-909
Lane, S. D., & Critchfield, T. S. (1998). Classification of vowels and consonants by
individuals with moderate mental retardation: Development of arbitrary relations
via match-to-sample training with compound stimuli. Journal of Applied Behavior
Analysis, 31, 21-41. doi: 10.1901/jaba.1998.31-21
Lawson, C. A., & Kalish, C. W. (2009). Sample selection and inductive
generalization. Memory & Cognition (Pre-2011), 37, 596-607. Retrieved from
http://ezproxy.simmons.edu:2048/login?url=http://search.proquest.com/docview/
217444588?accountid=13870
Lazar, R. (1977). Extending sequence-class membership with matching to sample.
Journal of the Experimental Analysis of Behavior, 27, 381–392. doi:
10.1901/jeab.1977.27-381
Lazar, R. M., Davis-Lang, D., & Sanchez, L. (1984). The formation of visual stimulus
equivalences in children. Journal of Experimental Analysis of Behavior, 41, 251-
266. doi:10.1901/jeab.1984.41-251
Lazar, R. M., & Kotlarchyk, B. J. (1986). Second-order control of sequence-class
equivalences in children. Behavioral Processes, 13, 205–215. doi: 10.1016/0376-
6357(86)90084-7
Leader, G., & Barnes-Holmes, D. (2001). Establishing fraction-decimal equivalence
using a respondent-type training procedure. Psychological Record, 51, 151-165.
83
Page 84
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
Retrieved from http://thepsychologicalrecord.siu.edu/
LeBlanc, L. A., Miguel, C. F., Cummings, A. R., Goldsmith, T. R., & Carr, J. E. (2003).
The effects of three stimulus-equivalence testing conditions on emergent us
geography relations of children diagnosed with autism. Behavioral Interventions,
18, 279-289. doi: 10.1002/bin.144
Longano, J. M., & Greer, R. D. (2015). Is the source of naming multiple conditioned
reinforcers for observing responses? The Analysis of Verbal Behavior. 31, 96-117.
doi: 10.1007/s40616-014-0022-y
Lovett, S., Rehfeldt, R. A., Garcia, Y., & Dunning, J. (2011). Comparison of a stimulus
equivalence protocol and traditional lecture for teaching single-subject designs.
Journal of Applied Behavior Analysis, 44, 819-833. doi: 10.1901/jaba.2011.44-819
Lowe, C.F., Horne, P.J., & Hughes, C.J. (2005). Naming and categorization in young
children: III. vocal tact training and transfer of function. Journal of the
Experimental Analysis of Behavior, 83, 47-65. doi: 10.1901/jeab.2005.31-04
Lynch, D. C., & Cuvo, A. J. (1995). Stimulus equivalence instruction of fraction-decimal
relations. Journal of Applied Behavior Analysis, 28, 115-126.
doi:10.1901/jaba.1995.28-115
McIlvane, W.J., & Dube, W.V. (1990). Do stimulus classes exist before they are tested?
Analysis of Verbal Behavior, 8, 13-17. Retrieved from:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2748603/
McVeigh, B., & Keenan, M.(2009). Multiple functions in equivalence classes. The
Psychological Record, 59, 93-118. Retrieved from
http://thepsychologicalrecord.siu.edu/
84
Page 85
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
Mackay, H. A. (1985). Stimulus equivalence in rudimentary reading and spelling.
Analysis and Intervention of Developmental Disabilities, 5, 373-387. doi:
10.1016/0270-4684(85)90006-0
Mackay, H., Kotlarchyk. B., & Stromer, R. (1997). Stimulus classes, stimulus sequences,
and generative behavior. In E. M. Pinkston & D.M. Baer (Eds). Environment and
behavior. Boulder, CO: Westview Press.
Maguire, R. W., Stromer R., & Mackay, H. A. (1995). Delayed matching to complex
samples and the formation of stimulus classes in children. Psychological Reports,
77, 1059-1076. doi:10.2466/pr0.1995.77.3f.1059
Maguire, R. W., Stromer, R., Mackay, H. A., & Demis, C. A. (1994). Matching to
complex samples in adults with autism and young children. Journal of Autism and
Developmental Disabilities, 24, 753– 772. doi: 10.1901/jaba.2010.43-131
Melchiori, L. E., de Souza, D. G., & de Rose, J. C. (2000). Reading, equivalence, and
recombination of units: A replication with students with different learning histories.
Journal of Applied Behavior Analysis, 33, 97-100. doi: 10.1901/jaba.2000.33-97
Microsoft® Powerpoint® for Macs(Version 14.3.1) [Software and presentation program].
(2011). Available from http://www.microsoft.com/
Miguel, C. F., Petursdottir, A. I., Carr, J. E., & Michael, J. (2008). The role of naming in
stimulus categorization by preschool children. Journal of Experimental Analysis of
Behavior, 89, 383-405. doi: 10.1901/jeab.2008-89-383
Miguel, C. F., Yang, H. G., Finn, H. E., & Ahearn, W. H. (2009). Establishing derived
textual control in activity schedules with children with autism. Journal of Applied
Behavior Analysis, 42, 703-709. doi: 10.1901/jaba.2009.42-703
85
Page 86
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
Ninness, C., Barnes-Holmes, D., Rumph, R., McCuller, G., Ford, A. M., Payne, R., et al.
(2006). Transformations of mathematical and stimulus functions. Journal of
Applied Behavior Analysis, 39, 299-321. doi: 10.1901/jaba.2006.139-05
Ninness, C., Dixon, M., Barnes-Holmes, D., Rehfeldt, R. A., Rumph, R., McCuller, G., et
al. (2009). Constructing and deriving reciprocal trigonometric relations: A
functional analytic approach. Journal of Applied Behavior Analysis, 42, 191–208.
doi: 10.1901/jaba.2009.42-191
Ninness, C., Rumph, R., McCuller, G., Harrison, C., Ford, A. M., & Ninness, S. K.
(2005). A functional analytic approach to computer-interactive mathematics.
Journal of Applied Behavior Analysis, 38, 1-22. doi: 10.1901/jaba.2005.2-04
Oliveira, M., Goyos, C., & Pear, J. (2012). A pilot investigation comparing instructional
packages for mts training: "Manual alone" vs. "manual-plus-computer-aided
personalized system of instruction". Behavior Analyst Today, 13, 20-26. Retrieved
from: http://baojournal.com/
Pilgrim, C., Chambers, L., & Galizio, M. (1995). Reversal of baseline relations and
stimulus equivalence: II. Children. Journal of Experimental Analysis of Behavior,
63, 239-254. doi: 10.1901/jeab.1995.63-239
Pilgrim, C., Jackson, J., & Galizio, M. (2000). Acquisition of arbitrary conditional
discriminations by young normally developing children. Journal of the
Experimental Analysis of Behavior, 73, 177–193. doi: 10.1901/jeab.2000.73-177
Petursdottir, A. I., & HafliDadottir, R. D. (2009). A comparison of four strategies for
teaching a small foreign-language vocabulary. Journal of Applied Behavior
Analysis, 42, 685-690 doi: 10.1901/jaba.2009.42-685
86
Page 87
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
Qualtrics. (2014). Qualtrics: online survey technology [Online surveys]. Unpublished
instrument. Retrieved from http://www.qualtrics.com/
Rehfeldt, R. A. (2011). Toward a technology of derived stimulus relations: An analysis of
articles published in JABA, 1992–2009. Journal of Applied Behavior Analysis, 44,
109–119. doi: 0.1901/jaba.2011.44-109
Runco, M. A. (2007). A hierarchical framework for the study of creativity. New Horizons
in Education, 55, 1-9. Retrieved from ERIC.
Saunders, R. R., & Green, G. (1999). A discrimination analysis of training structure
effects on stimulus equivalence outcomes. Journal of the Experimental Analysis of
Behavior, 72, 117–137. doi: 10.1901/ jeab.1999.72-117
Saunders, K. J., Saunders, R. R., Spradlin, J. E., & Williams, D. C. (1993). An interaction
of instructions and training design on stimulus class formation: Extending the
analysis of equivalence. The Psychological Record, 43, 725-744. Retrieved from
http://thepsychologicalrecord.siu.edu/
Saunders, R. R., & McEntee, J. E. (2004). Increasing the probability of stimulus
equivalence with adults with mild mental retardation. The Psychological Record,
54, 423–435. Retrieved from http://thepsychologicalrecord.siu.edu/
Shahan, T. A., & Chase, P. N. (2002). Novelty, stimulus control, and operant variability.
The Behavior Analyst, 25, 175-190. Retrieved from
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2731615/
Sidman, M. (1971). Reading and auditory-visual equivalences. Journal of Speech and
Hearing Research, 14, 5-13. Retrieved from http://jslhr.pubs.asha.org/
Sidman, M. (1987). Two choices are not enough. Behavior Analysis, 22, 11-18. Retrieved
87
Page 88
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
from http://www.equivalence.net/pdf/Sidman_1987.pdf
Sidman, M. (1994). Equivalence relations: A research story. Boston: Authors’
Cooperative.
Sidman, M. (2000). Equivalence relations and the reinforcement contingency. Journal of
the Experimental Analysis of Behavior, 74, 127-146. doi: 10.1901/jeab.2000.74-127
Sidman, M., Willson-Morris, M., & Kirk, B. (1986). Matching-to-sample procedures and
the role of naming. Analysis and Intervention in Developmental Disabilities 6, 1-19.
doi:10.1016/0270-4684(86)90003-0
Sidman, M., Rauzin, R., Lazar, R., Cunningham, S., Tailby, W., & Carrigan, P. (1982). A
search for symmetry in the conditional discriminations of rhesus monkeys, baboons,
and children. The Experimental Analysis of Behavior, 37, 23-44. doi:
10.1901/jeab.1982.37-23
Sidman, M., & Tailby, W. (1982). Conditional discrimination vs. matching to sample: An
expansion of the testing paradigm. Journal of the Experimental Analysis of
Behavior, 37, 5–22. doi: 10.1901/jeab.1982.37-5
Sidman, M., & Willson-Morris, M. (1974). Testing for reading comprehension: a brief
report on stimulus control. Journal of Applied Behavior Analysis, 7, 327-332. doi:
10.1901/jaba.1974.7-327
Siguroardottir, Z. G., Green, G., & Saunders, R. R. (1990). Equivalence classes generated
by sequence training. Journal of the Experimental Analysis of Behavior, 53, 47-63.
doi: 10.1901/jeab.1990.53-47
Siguroardottir, Z. G., Mackay, H. A., & Green, G. (2012). Stimulus equivalence,
generalization, and contextual stimulus control in verbal classes. The Analysis of
88
Page 89
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
Verbal Behavior, 28, 3-29. Retrieved from
http://www.abainternational.org/journals/the-analysis-of-verbal-behavior.aspx/
Skinner, B. F. (1968). The science of learning and the art of teaching. In J. Vargas (Eds.),
Technology of teaching (pp. 9-28). New York: Appleton-Century-Crofts.
Skinner, B. F. (1957). Verbal behavior. New York: Appleton-Century-Crofts.
Smeets, P. M., & Barnes-Holmes, D. (1995). Auditory-visual and visual-visual
equivalence relations in children. Psychological Record, 55, 483-503. Retrieved
from http://thepsychologicalrecord.siu.edu/
Smeets, P. M., & Barnes-Holmes, D. (2005). Establishing equivalence classes in
preschool children with one-to-many and many-to-one training protocols.
Behavioural Processes, 69, 281-293. doi:10.1016/j.beproc.2004.12.009
Smeets, P.M., Barnes-Holmes, D., & Cullinan, V. (2000). Establishing equivalence
classes with match-to-sample format and simultaneous-discrimination format
conditional discrimination tasks. Psychological Record, 50, 721-744. Retrieved
from http://thepsychologicalrecord.siu.edu/
Stromer, R., & Mackay, H. A. (1992). Spelling and emergent picture-printed word
relations established with delayed identity matching to complex samples. Journal of
Applied Behavior Analysis, 25, 893-904. doi: 10.1901/jaba.1992.25-893
Stromer, R., Mackay, H. A., & Remington, B. (1996). Naming, the formation of stimulus
classes, and applied behavior analysis. Journal Of Applied Behavior Analysis, 29,
409-431. doi:10.1901/jaba.1996.29-409
Stromer, R., Mackay, H. A., & Stoddard, L. T. (1992). Classroom applications of
stimulus equivalence technology. Journal of Behavioral Education, 2, 225-256. doi:
89
Page 90
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
10.1007/BF00948817
Touchette, P.E., & Howard, J.S. (1984). Errorless learning: Reinforcement contingencies
and stimulus control transfer in delayed prompting. Journal of Applied Behavior
Analysis, 17, 175-188. doi: 10.1901/jaba.1984.17-175
Touchette, P. E., & Maguire, R. W. (1986). Stimulus control following discrimination of
compound stimuli by autistic children. Paper presented at the Association for
Behavior Analysis, Milwaukee, WI.
Toussaint, K. A., & Tiger, J. H. (2010). Teaching early braille literacy skills within a
stimulus equivalence paradigm to children with degenerative visual impairments.
Journal of Applied Behavior Analysis, 43, 181-194. doi:10.1901/jaba.2010.43-181
Walker, B. D., & Rehfeldt, R. A. (2012). An evaluation of the stimulus equivalence
paradigm to teach single-subject design to distance education students via
Blackboard. Journal of Applied Behavior Analysis, 45, 329-344.
doi:10.1901/jaba.2012.45-329
Walker, B. D., Rehfeldt, R. A., & Ninness, C. (2010). Using the stimulus equivalence
paradigm to teach course material in an undergraduate rehabilitation course. Jounal
of Applied Behavior Analysis, 43, 615-633. doi: 10.1901/jaba.2010.43-615.
Winston, A. S., & Baker, J.E. (1985). Behavior analytic studies of creativity: A critical
review. The Behavior Analyst, 8, 191-205. Retrieved from
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2741825/
Microsoft, Encarta, MSN, and Windows are either registered trademarks or
trademarks of Microsoft Corporation in the United States and/or other
countries.
90
Page 91
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 92
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 93
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 94
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 95
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 96
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 97
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 98
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 99
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 100
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 101
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 102
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 103
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 104
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 105
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 106
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 107
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING 107
Page 108
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 109
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 110
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 111
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 112
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 113
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 114
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 115
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
Page 116
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
116
Page 117
STIMULUS EQUIVALENCE IN THE CLASSROOM SETTING
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
117