Classroom applications of stimulus equivalence technology

We review basic concepts and methods of stimulus equivalence research and suggest applications in teaching rudimentary language arts skills in the classroom. We describe methods of establishing equivalence-based networks of matching-to-sample, writing, and naming performances. The methods may be used as a supplement to classroom instruction to assess whether standard curriculum-based approaches establish such integrated networks. Methods derived from equivalence research may be useful for remediation when traditional teaching approaches fail. Recent research suggests that direct focus on spelling performances may be required if entire networks of language arts skills are to be acquired. In addition, the equivalence relations themselves may require concentrated teaching in some children.     

Stability of functional equivalence and stimulus equivalence: effects of baseline reversals

Functional equivalence and stimulus equivalence classes were established, reversed, and tested for stability with college students. Functional stimulus classes were established using a task in which students were trained to say nonsense words in the presence of arbitrarily assigned sets of symbols. Computer-controlled speech-recognition technology was used to record and analyze students' vocal responses for accuracy. After the establishment of stimulus classes was demonstrated with a transfer-of-function test, the effects of reversing selected baseline simple discriminations were assessed during an additional transfer-of-function test and a follow-up test that occurred several weeks later. With the same students, stimulus equivalence classes were established and demonstrated with computerized matching-to-sample procedures. The effects of reversing selected baseline conditional discriminations also were assessed during a postreversal equivalence test and a follow-up test. Both functional stimulus classes and stimulus equivalence were sensitive to contingency reversals, but the reversals with stimulus equivalence closses affected stimulus class organization whereas reversals with functional stimulus classes did not. Follow-up performances were largely consistent with the original baseline contingencies. The similarities and differences between stimulus equivalence and functional equivalence are related to the specific contingencies that select responding in the presence of the stimuli that form the classes.     

Reading, equivalence, and recombination of units: a replication with students with different learning histories

First graders, preschoolers, special education students, and adults received a reading program in which they learned to match printed to dictated words and to construct (copy) printed words. The students not only learned to match the training words but also learned to read them. In addition, most of the students learned to read new words that involved recombinations of the syllables of the training words. The results replicate and extend the generality of a prior analysis of a reading program based on stimulus equivalence and recombination of units.     

Speed analyses of stimulus equivalence.

The functional substitutability of stimuli in equivalence classes was examined through analyses of the speed of college students'' accurate responding. After training subjects to respond to 18 conditional relations, subjects'' accuracy and speed of accurate responding were compared across trial types (baseline, symmetry, transitivity, and combined transitivity and symmetry) and nodal distance (one- through five-node transitive and combined transitive and symmetric relations). Differences in accuracy across nodal distance and trial type were significant only on the first tests of equivalence, whereas differences in speed were significant even after extended testing. Response speed was inversely related to the number of nodes on which the tested relations were based. Significant differences in response speed were also found across trial types, except between transitivity and combined trials. To determine the generality of these comparisons, three groups of subjects were included: An instructed group was given an instruction that specified the interchangeability of stimuli related through training; a queried group was queried about the basis for test-trial responding: and a standard group was neither instructed nor queried. There were no significant differences among groups. These results suggest the use of response speed and response accuracy to measure the strength of matching relations.     

Transfer of contextual stimulus function via equivalence class development

In a conditional discrimination, 6 college students arranged six Cyrillic letters into groups of three based upon which of two additional Cyrillic letters (contextual stimuli) was present. All subjects demonstrated symmetry and transitivity within each class of equivalent stimuli. In a second conditional discrimination, two more Cyrillic letters were related to each contextual stimulus. Testing of symmetrical and transitive relations between the original contextual stimulus and the two new ones confirmed the development of two three-member classes of contextual stimuli. Subsequent tests demonstrated that the new contextual stimuli controlled the previously trained sample-comparison relations for all subjects.     

Delayed constructed-response identity matching improves the spelling performance of students with mental retardation

We assessed the effects of a computerized matching-to-sample procedure on the spelling performances of three students with mental retardation. Initially, the students could 1) match pictures and printed words to one another, and 2) match pictures and printed words to spoken words. However, they could not construct words to either pictures or spoken words (e.g., touch, in order, the letters s->h->o->e given the spoken-word sample Shoe). Word constructions then improved markedly after exposure to delayed constructed-response identity matching (e.g., touch the letters s->h->o->e given the printed-word sample shoe). One subject's oral and written spelling also improved. The results extend previous research by showing multiple positive effects of a computerized spelling intervention. These effects may have occurred in part because of the formation of stimulus classes among pictures, printed words, and spoken words.     

Recombinative reading derived from pseudoword instruction in a miniature linguistic system

A miniature linguistic system was used to study acquisition of recombinative symbolic behavior. Three studies evaluated the teaching conditions of conditional discriminations with printed and spoken pseudowords that could potentially generate recombinative reading. Fifty-four college students across all studies learned to match 12 printed pseudowords to 12 spoken pseudowords. Some also matched pictures to the same spoken words. Each two-syllable pseudoword was formed by symbols from an arbitrarily created alphabet composed of four vowels and four consonants. Letters had univocal correspondence with phonemes. Recombinative receptive reading, comprehensive reading, and textual responding to pseudowords were periodically assessed. Experiment 1 (n = 20) showed that recombinative reading increased as the number of trained words composed of the same symbols increased. Experiment 2 (n = 14) showed that overtraining the same two words did not produce recombinative reading for most participants. Experiment 3 (n = 20), in which training with pictures was omitted, showed that elemental control by within-syllable units can develop even when the trained pseudowords are meaningless (not related to pictures). The present results support the utility of the miniature linguistic system methodology for identifying and controlling environmental determinants of rudimentary reading skills.     

Formation of new stimulus equivalence classes by exclusion

This study presents three experiments that aimed to show the formation of stimulus equivalence relations among stimuli that had been previously related only by exclusion. In Experiment 1, participants were trained on baseline conditional discriminations to establish two 3‐member equivalence classes. Then, they were exposed to exclusion trials, without feedback, in which undefined stimuli had to be matched by rejecting the defined baseline stimuli. Finally, participants responded to test trials evaluating the emergence of symmetry and transitivity among the undefined stimuli from the exclusion trials. For half of the participants, the stimuli related by exclusion were introduced as S‐ stimuli in the baseline trials, whereas for the other half they were not. Further, half of the participants were assessed for emergent relations with stimuli from all the classes, whereas the other half was assessed for emergent relations with only the stimuli related by exclusion. In Experiment 2, the S‐ comparisons in the emergent relations test trials with stimuli only related by exclusion were stimuli from a null class. In Experiment 3, the number of exclusion trials was doubled. Across experiments, most participants showed emergence of equivalence relations among the stimuli related by exclusion. Some conditions of stimulus control associated with exclusion learning and the emergence of equivalence relations are discussed.     

The development of derived stimulus relations through training in arbitrary-matching sequences

Five-year-old children were taught three-stage sequences of arbitrary matching: A-C, B-C, A-D; A-C, B-D, B-C; or A-C, A-D, B-C. Each stage refers to a sample-comparison relation between stimuli. Unreinforced test probes revealed untrained arbitrary matches (B-D, A-D, and B-D, respectively), derivable by substitution of stimuli with a common sample or comparison function. Additional probes revealed further untrained sample-comparison relations derivable by substitution and identity, including the commuted relations D-B, D-A, and D-B, respectively. These processes may have relevance to conceptual and verbal behavior.     

The transfer of contextual control over equivalence classes through equivalence classes: a possible model of social stereotyping.

In Experiment 1, subjects acquired conditional equivalence classes controlled by three male and three female names as contextual stimuli. When equivalence relations were tested using new names not used in training (three male and three female), contextual control remained intact. Thus, generalized control of the composition of conditional equivalence classes by characteristically gender-identified names was shown. A basic analysis of this finding was tested in Experiment 2. Contextual equivalence classes were established using as contextual stimuli nonrepresentational visual figures that were members of additional pretrained three-member equivalence classes. When other stimuli in the pretrained equivalence classes were used as contextual stimuli, the conditional equivalence classes remained intact. Control subjects showed that this effect depended on the equivalence relations established in pretraining. The results show that contextual control over equivalence classes can transfer through equivalence classes. The implications of this phenomenon for social stereotyping are discussed.     

The transfer of specific and general consequential functions through simple and conditional equivalence relations

The purpose of this study was to examine the transfer of consequential (reinforcement and punishment) functions through equivalence relations. In Experiment 1, 9 subjects acquired three three-member equivalence classes through matching-to-sample training using arbitrary visual forms. Comparison stimuli were then given conditioned reinforcement or punishment functions by pairing them with verbal feedback during a sorting task. For 8 of the 9 subjects, trained consequential functions transferred through their respective equivalence classes without additional training. In Experiment 2, transfer of function was initially tested before equivalence testing per se. Three of 4 subjects showed the transfer without a formal equivalence test. In Experiment 3, 3 subjects were given training that gave rise to six new three-member conditional equivalence classes. For 2 of the subjects, the same stimulus could have either a reinforcement or punishment function on the basis of contextual cues that defined its class membership. Experiment 4 assessed whether equivalence training had established general or specific consequential functions primarily by adding novel stimuli in the transfer test. Subjects treated even novel feedback stimuli in the transfer test as consequences, but the direction of consequential effects depended upon the transfer of specific consequential functions through equivalence relations.     

Six-member stimulus classes generated by conditional-discrimination procedures

In conditional-discrimination procedures with three sets of stimuli, A, B, and C, three stimuli per set (A1A2A3, B1B2B3, and C1C2C3), subjects (children and adults) learned to select Set-B and Set-C comparisons conditionally upon Set-A samples (A1B1, A1C1, A2B2, A2C2, A3B3, A3C3). If the conditional-discrimination procedures also generated equivalence relations, three 3-member stimulus classes would be demonstrable, A1B1C1, A2B2C2, and A3B3C3. In addition to these three sets, the present experiments used three other sets of stimuli--D, E, and F. The subjects learned to select Set-E and Set-F comparisons conditionally upon Set-D samples (D1E1, D1F1, D2E2, D2F2, D3E3, D3F3). This established a second group of three 3-member stimulus classes, D1E1F1, D2E2F2, and D3E3F3. In all, two groups of three 3-member classes were established by teaching subjects 12 conditional discriminations. The two groups of 3-member classes were then combined (successfully for 5 of 8 subjects) into a single group of three 6-member classes by teaching the subjects three more conditional relations (E1C1, E2C2, and E3C3). With three other children, enlarging the classes one member at a time also produced 6-member classes. As a consequence of class formation, 60 untrained conditional relations emerged from 15 that had been explicitly taught. Six of the subjects also proved capable of naming the stimuli consistently in accord with their class membership, but two subjects demonstrated class formation even in the absence of consistent naming.     

Speed contingencies, number of stimulus presentations, and the nodality effect in equivalence class formation.

Two experiments compared performances on conditional discrimination tasks using single-participant designs with and without speed contingencies. Experiment 1 was a systematic replication of Spencer and Chase (1996). Experiment 2 presented equal numbers of training and testing trials. In each experiment, 2 female undergraduates participated. Each formed three five-member and three seven-member equivalence classes in Experiments 1 and 2, respectively. Response speed was an inverse function of nodal number and relational type in Experiment 1, but only of relational type (i.e., baseline, symmetry, transitivity, and equivalence) in Experiment 2, with and without the speed contingency. Accuracy tended to peak without the speed contingency in both experiments. Adding the speed contingency increased response speeds in both experiments, more so in Experiment 2 with a lower limited hold for I participant. The results of Experiment 2 cast doubt on previous reports of the nodality effect and on the notion of "relatedness" among class members, and they support a reinforcement-contingency, rather than a structural, account of equivalence class formation.     

Conditional discrimination and equivalence relations: A theoretical analysis of control by negative stimuli

A detailed analysis is presented of the ways in which control by the negative stimulus in two-comparison conditional discriminations may be expected to affect the outcome of tests for the properties of equivalence relations. Control by the negative stimulus should produce the following results: (a) no observable effect on symmetry tests; (b) reflexivity test results should look like “oddity” rather than “identity”; and (c) transitivity tests that involve an odd number of nodes should yield results that are 100% opposite to tests that involve an even number of nodes. The analysis also considers the effects of variation in the type of comparison-stimulus control between and within baseline conditional discriminations. Methods are suggested for experimentally regulating the type of control, and for verifying the predictions that the analysis generates. If suggested experiments continue to support the analysis, investigators who use two-comparison conditional discriminations to study equivalence relations will either have to control explicitly whether the positive or the negative comparison governs their subjects' choices, or they will have to abandon two comparisons and use three or more comparisons instead.     

Using stimulus equivalence technology to teach statistical inference in a group setting

Computerized lessons employing stimulus equivalence technology, used previously under laboratory conditions to teach inferential statistics concepts to college students, were employed in a group setting for the first time. Students showed the same directly taught and emergent learning gains as in laboratory studies. A brief paper-and-pencil examination, suitable for classroom use, captured effects demonstrated previously through laboratory tests. The results support the extension of the lessons to more naturalistic settings.     

Orthographic learning in children with isolated and combined reading and spelling deficits

Dissociations between reading and spelling problems are likely to be associated with different underlying cognitive deficits, and with different deficits in orthographic learning. In order to understand these differences, the current study examined orthographic learning using a printed-word learning paradigm. Children (4th grade) with isolated reading, isolated spelling and combined reading and spelling problems were compared to children with age appropriate reading and spelling skills on their performance during learning novel words and symbols (non-verbal control condition), and during immediate and delayed reading and spelling recall tasks. No group differences occurred in the non-verbal control condition. In the verbal condition, initial learning was intact in all groups, but differences occurred during recall tasks. Children with reading fluency deficits showed slower reading times, while children with spelling deficits were less accurate, both in reading and spelling recall. Children with isolated spelling problems showed no difficulties in immediate spelling recall, but had problems in remembering the spellings 2 hours later. The results suggest that different orthographic learning deficits underlie reading fluency and spelling problems: Children with isolated reading fluency deficits have no difficulties in building-up orthographic representations, but access to these representations is slowed down while children with isolated spelling deficits have problems in storing precise orthographic representations in long-term memory.     

Contextual control of stimulus generalization and stimulus equivalence in hierarchical categorization

The purpose of this study was to determine whether hierarchical categorization would result from a combination of contextually controlled conditional discrimination training, stimulus generalization, and stimulus equivalence. First, differential selection responses to a specific stimulus feature were brought under contextual control. This contextual control was hierarchical in that stimuli at the top of the hierarchy all evoked one response, whereas those at the bottom each evoked different responses. The evocative functions of these stimuli generalized in predictable ways along a dimension of physical similarity. Then, these functions were indirectly acquired by a set of nonsense syllables that were related via transitivity relations to the originally trained stimuli. These nonsense syllables effectively served as names for the different stimulus classes within each level of the hierarchy.     

Evidence of precurrent responses expanding equivalence classes in a delayed matching-to-sample task

Delayed matching to sample (DMTS) increases the probability of equivalence class formation. Precurrent responses can mediate the retention interval in DMTS trials and control the selection of comparisons. In human participants, precurrent responses usually consist of naming the experimental stimuli based on their similarities to meaningful stimuli with preexperimental history. We tested whether precurrents expand classes by serving as nodes between experimental and meaningful stimuli. A DMTS (2 s) was used throughout the entire experiment. Eleven undergraduates learned A1B1 and A2B2 relations and then were submitted to ArC trials that required them to answer math problems presented during the DMTS interval: when the sample was A1, the problems resulted in 12 and C1 was correct; when the sample was A2, they resulted in 9 and C2 was correct. Response-as-node tests assessed whether participants would relate B1 and C1 to the printed number 12 and B2 and C2 to the printed number 9. Ten participants responded accordingly to this pattern, showing that the responses to the problems expanded the classes. Parity tests using the words “even” and “odd” further confirmed this hypothesis. These results contribute to understanding why DMTS enhances equivalence performances. Implications of using this procedure in stimulus-equivalence studies are discussed.     

Effects of delayed constructed-response identity matching on spelling of dictated words

We studied the effects of delayed constructed-response identity matching on spelling with 6 first graders with histories of school failure. After training, the children learned to spell words to dictation and their cursive writing improved. These results replicate studies showing that delayed constructed-response matching establishes spelling. For 2 children, spelling of generalization words--words formed by recombining the syllables of training words--also improved. These results extend studies that have shown recombinative generalization in reading and spelling.