A functional analytic approach to computer-interactive mathematics

The Relational Abilities Index+: Initial Validation of a Functionally Understood Proxy Measure for Intelligence

The Relational Abilities Index (RAI) has shown considerable utility as a functional proxy measurement of intellectual performance by providing a metric of an important skill set known as relational skills, which are proposed to underlie much of what we conceive of as intellectual behavior. The Relational Abilities Index+ (RAI+) assesses performance across an extended range of relational skills (Same/Opposite, More/Less, Same/Different, Before/After, and Analogy), and has been designed to provide a more comprehensive and nuanced assessment of relational skills. The current study aims to investigate the validity and utility of the RAI+ by assessing its degree of correlation with well-established assessments of intelligence (WASI), numeracy (WAIS: Arithmetic), and educational attainment (WIAT-T-II). Results indicate that the RAI+ displays considerable efficacy in predicting intellectual performance and numeracy, but not educational attainment.

An Evaluation of Two Stimulus Equivalence Training Sequences on the Emergence of Novel Intraverbals

Researchers have begun to investigate the emergence of novel intraverbals using equivalence-based instruction (EBI) in typically developing children (Carp & Petursdottir, 2012; Pérez-González, Herszlikowicz, & Williams, 2008). We sought to replicate and extend the previous research by investigating two stimulus equivalence training sequences (e.g., linear series-LS and one to many-OTM) in the emergence of novel intraverbals in a two-part study with college students. Experiment 1 was designed to partially replicate the previous research by training intraverbals using an LS arrangement and then testing for the emergence of novel intraverbals. Novel intraverbals did not emerge after baseline training alone for the majority of participants. Experiment 2 investigated whether a different training sequence (i.e., OTM) would result in the emergence of novel intraverbals. Novel intraverbals did emerge following baseline training alone for the majority of participants. Overall, these results suggest that training intraverbals in an OTM training sequence may establish conditional discriminations during training, which may make it a more advantageous sequence, in that following training, more novel intraverbals emerge.

Learning Skinner's Verbal Operants: Comparing an Online Stimulus Equivalence Procedure to an Assigned Reading

The purpose of the present study was to compare the effects of an online stimulus equivalence procedure to that of an assigned reading when learning Skinner's taxonomy of verbal behavior. Twenty-six graduate students participated via an online learning management system. One group was exposed to an online stimulus equivalence procedure (equivalence group) that was designed to teach relations among the names, antecedents, consequences, and examples of each elementary verbal operant. A comparison group (reading group) read a chapter from a popular textbook. Tests for the emergence of selection-based and topography-based intraverbal responses were then conducted, as were tests for generalization and maintenance. Overall, results suggest that the online equivalence procedure was not significantly more effective in promoting topography-based responses than the assigned reading. However, performance on selection-based tests was enhanced by the online equivalence procedure as was performance on topography-based tests when participants were required to provide operant names in response to consequences or examples. On average, the equivalence group performed at a level that was 10 percentage points (i.e., a full letter grade) above that of the reading group. The viability of the equivalence-based procedure is discussed in relation to the assigned reading.

An evaluation of the stimulus equivalence paradigm to teach single-subject design to distance education students via Blackboard

The purpose of the current study was to examine the degree to which instruction based on stimulus equivalence procedures could be used to teach single-subject design methodology to graduate-level professionals through a Web-based course management system known as Blackboard (see http://www.blackboard.com). Specifically, we used the stimulus equivalence paradigm to teach relations among the names, definitions, graphical representations of the designs, and two practical scenarios of when it would be appropriate to implement each design. Most participants demonstrated the emergence of untaught relations, and some participants showed generalization to novel vignettes and graphs. Relations largely were not maintained at follow-up but were retaught.

Evaluating the evidence base for relational frame theory: a citation analysis

Relational frame theory (RFT) is a contemporary behavior-analytic account of language and cognition. Since it was first outlined in 1985, RFT has generated considerable controversy and debate, and several claims have been made concerning its evidence base. The present study sought to evaluate the evidence base for RFT by undertaking a citation analysis and by categorizing all articles that cited RFT-related search terms. A total of 174 articles were identified between 1991 and 2008, 62 (36%) of which were empirical and 112 (64%) were nonempirical articles. Further analyses revealed that 42 (68%) of the empirical articles were classified as empirical RFT and 20 (32%) as empirical other, whereas 27 (24%) of the nonempirical articles were assigned to the nonempirical reviews category and 85 (76%) to the nonempirical conceptual category. In addition, the present findings show that the majority of empirical research on RFT has been conducted with typically developing adult populations, on the relational frame of sameness, and has tended to be published in either The Psychological Record or the Journal of the Experimental Analysis of Behavior. Overall, RFT has made a substantial contribution to the literature in a relatively short period of time.

Comparison of a stimulus equivalence protocol and traditional lecture for teaching single-subject designs

This study compared the effects of a computer-based stimulus equivalence protocol to a traditional lecture format in teaching single-subject experimental design concepts to undergraduate students. Participants were assigned to either an equivalence or a lecture group, and performance on a paper-and-pencil test that targeted relations among the names of experimental designs, design definitions, design graphs, and clinical vignettes was compared. Generalization of responding to novel graphs and novel clinical vignettes, as well as the emergence of a topography-based tact response after selection-based training, were evaluated for the equivalence group. Performance on the paper-and-pencil test following teaching was comparable for participants in the equivalence and lecture groups. All participants in the equivalence group showed generalization to novel graphs, and 6 participants showed generalization to novel clinical vignettes. Three of the 4 participants demonstrated the emergence of a topography-based tact response following training on the stimulus equivalence protocol.

Efficiently establishing concepts of inferential statistics and hypothesis decision making through contextually controlled equivalence classes

Computerized lessons that reflect stimulus equivalence principles were used to teach college students concepts related to inferential statistics and hypothesis decision making. Lesson 1 taught participants concepts related to inferential statistics, and Lesson 2 taught them to base hypothesis decisions on a scientific hypothesis and the direction of an effect. Lesson 3 taught the conditional influence of inferential statistics over decisions regarding the scientific and null hypotheses. Participants entered the study with low scores on the targeted skills and left the study demonstrating a high level of accuracy on these skills, which involved mastering more relations than were taught formally. This study illustrates the efficiency of equivalence-based instruction in establishing academic skills in sophisticated learners.

Transportability of equivalence-based programmed instruction: efficacy and efficiency in a college classroom

College students in a psychology research-methods course learned concepts related to inferential statistics and hypothesis decision making. One group received equivalence-based instruction on conditional discriminations that were expected to promote the emergence of many untaught, academically useful abilities (i.e., stimulus equivalence group). A negative control group received no instruction, and a positive (complete instruction) control group received instruction on all possible relations (those taught to, and emerging untaught in, the stimulus equivalence group). On posttests, the stimulus equivalence group performed as well as the positive control group (and both outperformed the negative control group), but those in the equivalence-based instruction condition achieved this outcome with significantly less training, thereby demonstrating the efficiency of equivalence-based instruction. Social validity measures indicated that participants found the instruction to be beneficial and as enjoyable as traditional teaching methods.

Toward a technology of derived stimulus relations: an analysis of articles published in the journal of applied behavior analysis, 1992-2009

Every article on stimulus equivalence or derived stimulus relations published in the Journal of Applied Behavior Analysis was evaluated in terms of characteristics that are relevant to the development of applied technologies: the type of participants, settings, procedure (automated vs. tabletop), stimuli, and stimulus sensory modality; types of relations targeted and emergent skills demonstrated by participants; and presence versus absence of evaluation of generalization and maintenance. In most respects, published reports suggested the possibility of applied technologies but left the difficult work of technology development to future investigations, suggestions for which are provided.

Teaching brain-behavior relations economically with stimulus equivalence technology

Instructional interventions based on stimulus equivalence provide learners with the opportunity to acquire skills that are not directly taught, thereby improving the efficiency of instructional efforts. The present report describes a study in which equivalence-based instruction was used to teach college students facts regarding brain anatomy and function. The instruction involved creating two classes of stimuli that students understood as being related. Because the two classes shared a common member, they spontaneously merged, thereby increasing the yield of emergent relations. Overall, students mastered more than twice as many facts as were explicitly taught, thus demonstrating the potential of equivalence-based instruction to reduce the amount of student investment that is required to master advanced academic topics.

Using the stimulus equivalence paradigm to teach course material in an undergraduate rehabilitation course

In 2 experiments, we examined whether the stimulus equivalence instructional paradigm could be used to teach relations among names, definitions, causes, and common treatments for disabilities using a selection-based intraverbal training format. Participants were pre- and posttested on vocal intraverbal relations and were trained using multiple-choice worksheets in which selection-based intraverbal relations were taught and feedback was delivered until mastery. Most participants in Experiment 1 showed the emergence of vocal intraverbal relations, but responding did not generalize to final written intraverbal tests. Participants in Experiment 2 showed the emergence of not only vocal intraverbal relations but also written intraverbal relations on final tests. Results suggest that the stimulus equivalence paradigm can be effectively implemented using a selection-based intraverbal training format, the protocol may be an effective means of emphasizing important concepts in a college course, and emergent skills may generalize to novel response topographies.

Constructing and deriving reciprocal trigonometric relations: a functional analytic approach

Participants were pretrained and tested on mutually entailed trigonometric relations and combinatorially entailed relations as they pertained to positive and negative forms of sine, cosine, secant, and cosecant. Experiment 1 focused on training and testing transformations of these mathematical functions in terms of amplitude and frequency followed by tests of novel relations. Experiment 2 addressed training in accordance with frames of coordination (same as) and frames of opposition (reciprocal of) followed by more tests of novel relations. All assessments of derived and novel formula-to-graph relations, including reciprocal functions with diversified amplitude and frequency transformations, indicated that all 4 participants demonstrated substantial improvement in their ability to identify increasingly complex trigonometric formula-to-graph relations pertaining to same as and reciprocal of to establish mathematically complex repertoires.

Arbitrarily applicable comparative relations: experimental evidence for a relational operant

Arbitrarily applicable derived relational responding has been argued by relational frame theorists to be a form of operant behavior. The present study examined this idea with 4 female participants, ages 4 to 5 years old, who could not perform a series of problem-solving tasks involving arbitrary more than and less than relations. In a combined multiple baseline (across responses and participants) and multiple probe design (with trained and untrained stimuli), it was shown that reinforced multiple-exemplar training facilitated the development of arbitrary comparative relations, and that these skills generalized not just across stimuli but also across trial types. The sequence of training identified potential prerequisites in the development of comparative relations (e.g., nonarbitrary comparative relations). Taken as a whole, the present data, along with previous work by others in this area, suggest that relating arbitrary events comparatively is an operant. The implications of this conclusion for the analysis of complex behavior are discussed.

Transformations of mathematical and stimulus functions

Following a pretest, 8 participants who were unfamiliar with algebraic and trigonometric functions received a brief presentation on the rectangular coordinate system. Next, they participated in a computer-interactive matching-to-sample procedure that trained formula-to-formula and formula-to-graph relations. Then, they were exposed to 40 novel formula-to-graph tests and 10 novel graph-to-formula tests. Seven of the 8 participants showed substantial improvement in identifying formula-to-graph relations; however, in the test of novel graph-to-formula relations, participants tended to select equations in their factored form. Next, we manipulated contextual cues in the form of rules regarding mathematical preferences. First, we informed participants that standard forms of equations were preferred over factored forms. In a subsequent test of 10 additional novel graph-to-formula relations, participants shifted their selections to favor equations in their standard form. This preference reversed during 10 more tests when financial reward was made contingent on correct identification of formulas in factored form. Formula preferences and transformation of novel mathematical and stimulus functions are discussed.