Equivalence Class Formation Research Articles

Vocalizing phonologically correct non-word stimuli during equivalence class formation

ABSTRACTSome attempts were made in an evolving set of four small experiments to track the formation of stimulus equivalence relations where these appeared to emerge during testing, after initial training of AB and BC base relations. In this simple linear training structure, it was postulated that some kind of access would be needed, on CA equivalence tests, to the absent nodal B stimuli, which provided the links between the base pairs. The roles of “recognition” and “recall” of stimuli were examined in a number of ways during training, during testing and after testing, including the use of a simplified form of protocol analysis made possible using phonologically correct non-words as stimuli, designed to be low in meaning but readily able to be pronounced aloud. Some interesting individual differences came to light, which, it is argued, deserve further exploration with other and more complex training structures using some of the methods described.

Training order and structural location of meaningful stimuli: effects on equivalence class formation.

In the present study, equivalence class formation was influenced by the temporal point of inclusion of a meaningful stimulus when baseline relations were serially or sequentially trained, and much less so by the location of the meaningful stimulus in the nodal structure of the class. In Experiment 1, participants attempted to form three 3-node, 5-member classes (A→B→C→D→E) under the simultaneous protocol. After serially training the baseline relations AB, BC, CD, and DE, in that order, the emergence of all emergent relations was tested concurrently. In the A-as-PIC condition, A was meaningful stimulus and B to E were meaningless stimulus, and 60 % of the participants formed classes. In addition, classes were formed by 40 %, 70 %, 40 %, and 20 % of the participants in the B-as-PIC, C-as-PIC, D-as-PIC, and E-as-PIC groups, respectively. Thus, the likelihood of class formation could have been influenced by the location of a meaningful stimulus in the class structure and/or by its order of introduction during training. In Experiment 2, we controlled for any effect of order of introduction by the concurrent training of all of the baseline relations. Regardless of the location of the meaningful stimulus, 0-20 % of participants formed classes. Thus, the temporal order of introducing a meaningful stimulus was the primary modulator of the class-enhancing property of meaningful stimuli, and not the location of the meaningful stimulus in the class structure.

EFFECTS OF VERBAL-LABELED RESPONSES ON STIMULUS CLASS FORMATION IN A COMPOUND STIMULUS PROCEDURE

Evidence suggests that humans form stimulus classes when they learn the baseline relations in a compound stimulus format with two response options. When two 3-member stimulus classes are trained with these procedures, the training contingencies establish the possibility of evoking any of the response options for the within-class transitive compound stimuli; this is described as an ambiguous set of training trajectories. We argue that verbal labels on the response options help human participants surpass the ambiguous training. Here, six adults were assigned to one experimental condition with verbal labels on the response options, other six participants served the second experimental condition with color patches on the response options. Five out of six participants responding with verbal labels responded correctly to symmetry and transitivity tests. Only one participant responding with colors responded correctly to those tests. We discuss a possible role of verbal mediation during equivalence class formation in these procedures.

Emergence of Topographical Responding Following Equivalence-Based Neuroanatomy Instruction

Equivalence-based instruction (EBI) has been utilized to teach a number of college-level academic concepts. The majority of these studies measured effectiveness with selection-based responding (i.e., multiple-choice questions). Recently, researchers have begun examining effectiveness using topographical responding, or responding to open-ended questions. In the current study, participants learned neuroanatomy concepts through section-based EBI, and we measured the effects of instruction on both selection-based and topographical responding. Following equivalence class formation, participants responded with higher accuracy to both selection-based and topographical questions compared to baseline. Furthermore, participants demonstrated higher levels of accuracy with selection-based questions than topographical questions. As a measure of social validity, topographical responding was assessed by a neuroscience professor who was naive to the study. Results demonstrated a typical grade distribution for topographical responding. Implications and future directions for EBI studies evaluating topographical responding are discussed.

Enhanced equivalence class formation by the delay and relational functions of meaningful stimuli

Undergraduates in six groups of 10 attempted to form three 3-node 5-member equivalence classes (A → B → C → D → E) under the simultaneous protocol. In five of six groups, all stimuli were abstract shapes; in the PIC group, C stimuli were pictures with the remainder being abstract shapes. Before class formation, participants in the Identity-S and Identity-D groups were given preliminary training to form identity conditional discriminations with the C stimuli using simultaneous and 6 s delayed matching-to-sample procedures, respectively. In the Arbitrary-S and Arbitrary-D groups, before class formation, arbitrary conditional discriminations were formed between C and X stimuli using simultaneous and 6 s delayed matching-to-sample procedures, respectively. With no preliminary training, classes in the PIC and ABS groups were formed by 80% and 0% of participants, respectively. After preliminary training, class formation (yield) increased with delay, regardless of relational type. For each of the two delays, yield was slightly greater after forming arbitrary- instead of identity-relations. Yield was greatest, however, when a class contained a meaningful stimulus (PIC). During failed class formation, probes produced experimenter-defined relations, participant-defined relations, and unsystematic responding; delay, but not the relation type in preliminary training influenced relational and indeterminate responding. These results suggest how meaningful stimuli enhance equivalence class formation.

Arbitrary conditional discriminative functions of meaningful stimuli and enhanced equivalence class formation

Equivalence class formation by college students was influenced through the prior acquisition of conditional discriminative functions by one of the abstract stimuli (C) in the to-be-formed classes. Participants in the GR-0, GR-1, and GR-5 groups attempted to form classes under the simultaneous protocol, after mastering 0, 1, or 5 conditional relations between C and other abstract stimuli (V, W, X, Y, Z) that were not included in the to-be-formed classes (ABCDE). Participants in the GR-many group attempted to form classes that contained four abstract stimuli and one meaningful picture as the C stimulus. In the GR-0, GR-1, GR-5, and GR-many groups, classes were formed by 17, 25, 58, and 67% of participants, respectively. Thus, likelihood of class formation was enhanced by the prior formation of five C-based conditional relations (the GR-5 vs. GR-0 condition), or the inclusion of a meaningful stimulus as a class member (the GR-many vs. GR-0 condition). The GR-5 and GR-many conditions produced very similar yields, indicating that class formation was enhanced to a similar degree by including a meaningful stimulus or an abstract stimulus that had become a member of five conditional relations prior to equivalence class formation. Finally, the low and high yields produced by the GR-1 and GR-5 conditions showed that the class enhancement effect of the GR-5 condition was due to the number of conditional relations established during preliminary training and not to the sheer amount of reinforcement provided while learning these conditional relations. Class enhancement produced by meaningful stimuli, then, can be attributed to their acquired conditional discriminative functions as well as their discriminative, connotative, and denotative properties.

Emergência de leitura recombinativa em crianças com paralisia cerebral

O ensino de discriminações silábicas tem sido adotado como um dos procedimentos para aquisição de leitura recombinativa. O objetivo deste estudo foi verificar os efeitos de um ensino de discriminação condicional auditiva e visual sobre a aquisição de leitura recombinativa por três crianças com paralisia cerebral, com idades entre oito e doze anos. A partir de três palavras de ensino, todas dissílabas, foram realizadas etapas de ensino de discriminações auditivas, visuais, auditivas-visuais e visuais-auditivas de sílabas e ensino de rima, aliteração, subtração e adição silábica. Um participante leu com compreensão cinco palavras novas, e os outros dois participantes, quatro. Os dados sugerem que o ensino ocasionou a formação de classes de equivalência demonstradas por indivíduos com comunicação diminuída. Estudos posteriores devem investigar variáveis de procedimentos de ensino mais relevantes, que usem procedimentos adicionais para evitar controle restrito, reexposição aos testes de leitura das palavras recombinadas e testes de manutenção do desempenho.

Transfer-of-Function and Novel Emergent Relations Using Simple Discrimination Training Procedures

The present study investigated whether simple discrimination procedures produce emergent relations that are consistent with functional and equivalence classes. In Experiment 1, 4 normally capable adults were exposed to simple successive discrimination reversal training. Responses to the S+ (A1, B1, and C1) but not S− (A2, B2, and C2) were reinforced. The participants were then exposed to repeated-reversal training, followed by tests of emergent equivalence relations. In Experiment 2, 4 additional adults were exposed to a simple successive discrimination training procedure using differential responses. Response 1 (R1) was reinforced only when emitted in the presence of A1, B1, or C1 (A1-R1, B1-R1, or C1-R1). Response 2 (R2) was reinforced only in the presence of A2, B2, or C2 (A2-R2, B2-R2, or C2-R2). A new response was then trained in the presence of 1 member of each class (A1-R3, A2-R4). A transfer-of-function test was then conducted to verify whether the new responses would be emitted in the presence of B1, B2, C1, and C2. In both experiments, emergent conditional relations were tested using a go/no-go procedure with compound stimuli. In Experiment 1, all of the participants showed functional classes, and 3 showed patterns that are consistent with the formation of equivalence classes. In Experiment 2, all 4 participants showed patterns that are consistent with functional and equivalence class formation. In these experiments, simple discrimination training generated a range of emergent stimulus relations that mirrored those that are indicative of equivalence class formation.

Efeito do treino de composição (cópia) na aprendizagem do conceito de proporção

This experiment investigated the effect of training conditional relations between pictorial and numerical fractional stimuli, with and without composition training, upon the learning of the proportion concept. It was evaluated the formation of equivalence classes, expansion of classes formed, generalization to new situations, and pencil and paper problem solving with fractional stimuli. The participants were 20 students of the sixth grade of Elementary School. The QEG and TCQEC groups were exposed to training and testing of conditional relations, but the last group was exposed, additionally, to a fractional composition training before the conditional relations training; two control groups were exposed only to the initial and final tests. The results indicated the formation of equivalence classes, but did not show effects of the composition training.

Enhancement of equivalence class formation by pretraining discriminative functions.

The present experiment showed that a simple discriminative function acquired by an abstract stimulus through simultaneous and/or successive discrimination training enhanced the formation of an equivalence class of which that stimulus was a member. College students attempted to form three equivalence classes composed of three nodes and five members (A→B→C→D→E), using the simultaneous protocol. In the PIC group, the C stimuli were pictures and the A, B, D, and E stimuli were abstract shapes. In the ABS group, all of the stimuli were abstract shapes. In the SIM + SUCC (simultaneous and successive) group, simple discriminations were formed with the C stimuli through both simultaneous and successive discrimination training before class formation. Finally, in the SIM-only and SUCC-only groups, prior to class formation, simple discriminations were established for the C stimuli with a simultaneous procedure and a successive procedure, respectively. Equivalence classes were formed by 80% and 70% of the participants in the PIC and SIM + SUCC groups respectively, by 30% in the SUCC-only group, and by 10% apiece in the ABS and SIM-only groups. Thus, pretraining of combined simultaneous and successive discriminations enhanced class formation, as did the inclusion of a meaningful stimulus in a class. The isolated effect of forming successive discriminations was more influential than that of forming simultaneous discriminations. The establishment of both discriminations together produced an enhancement greater than the sum of the two procedures alone. Finally, a sorting test documented the maintenance of the classes formed during the simultaneous protocol. These results also provide a stimulus control-function account of the class-enhancing effects of meaningful stimuli.

Equivalence Class Formation in Accuracy or Speed Conditions: Immediate Emergence, Adduction, and Retention

Six pairs of participants were matched from a pool of 26 participants based on their performance in pretraining for conditional discrimination. One participant from each pair completed either a speed or an accuracy condition in the conditional discrimination training by using an linear series (LS) structure to establish potentially three, 3-member classes. Initially, the speed participants completed the training with a titrating limited hold (LH) on the comparison stimuli. The accuracy participants were yoked to the trial number of the speed participants with whom they were matched. In Phase 2, the speed participants completed matching to sample (MTS) training with a fixed 1,000-ms LH, and the accuracy participants were not yoked. In Phase 3, the probabilities of the programmed consequences were gradually reduced to 0 %. Phase 4 introduced tests for baseline and emergent relations and adduction. In Phase 5, a 2-week retention test was administered. The results indicated that 1 of 6 speed participants, compared with 3 of 6 accuracy participants, responded according to stimulus equivalence in the initial testing, whereas accuracy in the adduction test was nearly equal for all participants. In a 2-week retention test, no accuracy participants and two speed participants responded according to stimulus equivalence, whereas accuracy in the adduction test was equal between the participants. In the second retention test, 1 of 3 speed participants responded in accord with stimulus equivalence. All speed participants had a higher number of errors during the baseline trials and completed a higher number of acquisition trials. Inverse reaction time (InvRT) to comparisons did not vary as a function of trial type.

Two Discriminative Functions of Meaningful Stimuli That Enhance Equivalence Class Formation

Two experiments explored how order of training, familiar pictures, and abstract stimuli that acquired discriminative functions influenced equivalence class formation. In Experiment 1, three 3-node, 5-member equivalence classes (A → B → C → D → E) were established using a variation of the simultaneous protocol that involved the serialized training of the AB, BC, CD, and DE baseline relations in that order, after which the emergence of all derived relations was tested on a concurrent basis. Classes were formed by 70 % of participants when the A-stimuli were familiar pictures and were members of the first-trained AB relations, while the B-E stimuli were abstract shapes. Classes were formed by 40 % of participants when the E-stimuli were familiar pictures and were members of the last-trained DE relations, while the A-D stimuli were abstract shapes. In two matching conditions, abstract stimuli that had acquired discriminative functions (SDs) prior to class formation were substituted for the A and E stimuli, and classes were formed by 20 % of participants in each condition. Further, greater enhancement effects were obtained using pictures than abstract stimuli that have acquired discriminative functions when these stimuli were the A members of the classes, while very little differences in yield were observed when they were the E members of the classes. Thus, likelihood of class formation could have been influenced by the position of a meaningful stimulus or an SD in the structure of a class (i.e., A or E) and/or their order of introduction during training (first or last). For more than 92 % of the participants (37 of 40), a final sorting task produced the same outcomes as the derived relations tests. Experiment 2 isolated the effects of these variables by the concurrent establishment of the baselines with the A stimuli as pictures or as SDs. No participants formed classes in either condition. Thus, class enhancement by a meaningful stimulus depended on its inclusion in the first trained baseline relation and not its placement in the class structure.

Discriminative functions and over-training as class-enhancing determinants of meaningful stimuli.

Likelihood of equivalence class formation (yield) was influenced by pre-class formation of simultaneous and successive discriminations, their mastery criteria, and overtraining of the successive discriminations. Each undergraduate in seven groups attempted to form two 3-node, 5-member equivalence classes (ABCDE). In the pictorial (PIC) group, meaningless nonsense syllables were used as the A, B, D, and E stimuli and meaningful pictures as the C stimuli. Nonsense syllables only were used in the other groups. The abstract (ABS) or 0-0-0 group involved no pre-class training. In the 84-0-0, 84-5-0 and 84-20-0 groups, simultaneous discriminations were trained among C stimuli to a mastery criterion of 84 trials, followed by successive discriminations trained to mastery criteria of 0, 5, and 20 trials, respectively. In the 84-20-0, 84-20-100, and 84-20-500 groups, simultaneous and successive discriminations were trained as noted, followed by overtraining with 0, 100, 500 successive-discrimination trials, respectively. The ABS group produced a 6% yield with the 84-0-0, 84-5-0, and 84-20-0 groups producing further modest increments. Overtraining produced a linear increase in yield, reaching 85% after 500 overtraining trials, a yield matching that produced by classes containing pictures as C stimuli (PIC). Thus, acquired discriminative functions and the overtraining of at least one function can account for class enhancement by meaningful stimuli.

Identity and Delay Functions of Meaningful Stimuli: Enhanced Equivalence Class Formation

The inclusion of a meaningful stimulus in a set of abstract stimuli enhances the likelihood of forming an equivalence class with the set. Class enhancement effects can be due to the discriminative, conditional discriminative, and class-based behavioral functions served by the meaningful stimulus. This experiment determined whether acquisition of an identity conditional discriminative function by an abstract stimulus enhances the formation of an equivalence class of which it is a member along with other abstract stimuli. Forty adults attempted to form 3 three-node five-member equivalence classes (A → B → C → D → E) using the simultaneous protocol. In the PIC group, the C stimuli were pictures and the A, B, D, and E stimuli were abstract shapes. In the ABS group, all of the stimuli were abstract shapes. In the Id-S-MTS (identity simultaneous matching-to-sample) and Id-6sD-MTS (identity 6 s delayed matching-to-sample) groups, prior to class formation, identity conditional discriminations were formed with the C stimuli using simultaneous or 6 s delayed matching-to-sample procedures, respectively. Classes were formed by 80 and 60 % of participants in the PIC and delayed identity groups, and by 0 and 10 % of participants with no prior training (ABS group) or after forming identity relations on a simultaneous basis. These outcomes were confirmed with post class formation sorting tests. Thus, a portion of the class enhancing effects of meaningful stimuli can be attributed to their presumed delayed identity conditional discriminative function. Adventitious coding or mediating behavior during identity training might have influenced acquisition of baseline relations and likelihood of class formation.

Stimulus Sorting: A Quick and Sensitive Index of Equivalence Class Formation

Fifty college students were given standard matching-to-sample-based training and testing to form three 5-member equivalence classes that had linear series training structures (A→B→C→D→E). A matching to sample (MTS) based derived-relations test was used to assess the emergence of the classes. Thereafter, 15 cards, each of which contained one of the 15 stimuli in the classes, were given to the participants who were asked to sort them into piles of “related” cards. There was a very high concordance between measures of equivalence-class formation produced by relation tests and sorting tests. In some cases, sorting tests appeared to be more sensitive to tracking class formation than the MTS-based derived-relations tests. In addition, sorting tests were administered in a fraction of the time needed to administer an MTS-based derived-relations test to document class formation. Finally, sorting test data were very easy to interpret, especially when findings other than experimenter-defined class formation was produced. Therefore, sorting may be a viable alternative for tracking equivalence class formation.

Relaciones de equivalencia y estilo cognitivo: hallazgos de una relación no explorada

The formation of equivalence classes derived from exposure to conditional discrimination training is a widely demonstrated phenomenon in human research. However, low performance in equivalence tests and difficulties in the acquisition of relations among class members are not infrequent.The present study examined whether types of perceptual response to the experimental stimulus (the cognitive style of visual field sensitivity) are related to the variability observed in equivalence tests. The masked figures test (MFT) was used to determine the cognitive styles of 32 participants who were also exposed to equivalence tests after conditional discrimination training trials with a respondent matching-to-sample procedure. Observed frequencies, as reported in contingency tables,and correlation coefficients between performance in equivalence tests and MFT scores suggested a positive association between the cognitive style of visual field dependence-independence and the formation of equivalence classes.

Competing Arbitrary and Non-Arbitrary Relational Responding in Normally Developing Children and Children Diagnosed with Autism

The current study seeks to further investigate the previously reported disruptive effect of competing non-arbitrary stimulus relations on derived relational responding (Stewart et al. The Psychological Record, 52, 77–88, 2002; Kenny et al. The Psychological Record,2014). Initially, Experiment 1 utilised procedures adapted from the previous Stewart et al. (The Psychological Record, 52, 77–88, 2002) study, rendering them developmentally appropriate for a participant population of normally developing children. The results showed all participants demonstrated equivalence class formation when only black stimuli were used and maintained criterion levels of equivalence-consistent responding in the Colour Test condition, where a competing non-arbitrary colour relation was present. Experiment 2 exposed a cohort of children diagnosed with autism to identical training and testing procedures. While these participants also demonstrated equivalence class formation with stimuli only black in colour, five of the six participants showed significantly lower levels of equivalence-consistent responding in the Colour Test condition. These results are consistent with previously reported research findings that children with autism perform more poorly in tasks containing competing sources of stimulus control (Huizinga et al. Neuropsychologia, 44, 2017–2036. 2006; Baker et al. Clinical Neurospsychologist, 15(3), 309–313. 2001; Pennington et al. 1997). The results of Experiment 1 suggest possible procedures to undermine spurious sources of non-arbitrary stimulus control in normally developing children.

Variables affecting the emergence of untaught equivalence relations in children with and without autism

Objective: This study examined the formation of equivalence classes among children with ASD and typically developing children. Design: A single-subject AB and BA design was used. Methods: Two of the six equivalence relations were taught. Participants were then tested to determine whether the remaining four equivalence relations were acquired without teaching. Half of the children were taught naming responses first, then selecting responses. Half were taught in the reverse order. Results: Five out of 10 participants with ASD demonstrated the emergence of all four untaught relations. The remaining five participants showed variability. Nine of the 10 typically developing children demonstrated emergence of all untaught relations. Variation in teaching conditions had no significant effect on outcomes. Conclusions: Many children with ASD are capable of generalising to untaught equivalence relations. The results fail to support the claim that acquisition of naming responses is a pre-requisite for the emergence of untaught equivalence relations.

Controlling Relations in Stimulus Equivalence Classes of Preschool Children and Individuals with Down Syndrome.

We evaluated emergent stimulus-stimulus relations after two different training procedures. Participants were five typically developing preschool children and three individuals with Down Syndrome. Experiment 1 used two-comparison matching to sample (MTS) to establish AB and BC relations. Experiment 2 used two-comparison and blank-comparison MTS, each on 50% of training trials to establish AB and BC relations. In both experiments, tests for emergent relations (AC, CA) were conducted to assess equivalence class formation. In Experiment 2 subsequently, class expansion was assessed after CD training. All participants showed positive equivalence test outcomes. Seven showed class expansion. After class formation tests in both studies, probe tests were conducted for select and reject relations in baseline relations. Initial results were somewhat variable, but became more consistent after class expansion.

Simple and Conditional Discrimination and Specific Reinforcement in Teaching Reading: An Intervention Package.

This study evaluated an intervention package combining simple and conditional discrimination training and specific reinforcement for each stimulus class in teaching reading of simple words to individuals with intellectual disabilities. In conditional discrimination training, participants matched printed words and pictures to the recorded sounds made by the pictured objects and animals. Fourteen children and adolescents with intellectual disabilities were assigned to an experimental and a control group. The two groups' performance did not differ in the pretest. The experimental group demonstrated equivalence class formation and read the words that participated in the equivalence classes, whereas the control group did not.