Abstract
Fifteen participants unfamiliar with mathematical operations relative to reflections and vertical and horizontal shifts were exposed to an introductory lecture regarding the fundamentals of the rectangular coordinate system and the relationship between formulas and their graphed analogues. The lecture was followed immediately by computer-assisted instructions and matching-tosample procedures in which participants were e)(posed to computerposted rules regarding the relationship between particular types of formulas and their respective graphs. After participants demonstrated mutual entailment on formula-to-graph and graph-toformula functions, they were assessed for 36 novel relations on complex variations of the original training formulas and graphs. In Experiment 1, 5 of 15 participants demonstrated perfect or near perfect performance on all novel relationships. Experiment 2 was directed at the remaining 10 participants who failed to correctly identify all mathematical relationships assessed in Experiment 1. The error patterns for these 10 participants were classified with the help of an artificial neural network self-organizing map (SOM). Training in Experiment 2 was directed exclusively at the types of errors identified by the SOM. Following remedial training, all participants demonstrated a substantial reduction in errors compared to their performance in Experiment 1. Derived transfer of stimulus control using mathematical relations is discussed.
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BARNES-HOLMES, D., HAYES, S. C., DYMOND, S., & O’HORA, D. (2001). multiple stimulus relations and transformations of stimulus functions. In S. C. Hayes, D. BARNES-HOLMES, & B. Roche (Eds.), Relational frame theory: A post-Skinnerian account of human language and cognition (pp. 51–71). New York: Kluwer Academic/Plenum Publishers.
HAYES, S. C., BARNES-HOLMES, D., & ROCHE, B. (2003). Behavior analysis, relational frame theory, and the challenge of human language and cognition: A reply to the commentaries on relational frame theory: A post- Skinnerian account of human language and cognition. The Analysis of Verbal Behavior, 19, 39–54.
HAYES, S. C., BARNES-HOLMES, D., & ROCHE, B. (Eds.). (2001). Relational frame theory: A post-Skinnerian account of human language and cognition. New York: Kluwer Academic/Plenum Publishers.
HAYES, S. C., FOX, E., GIFFORD, E. V., WILSON, K. G., BARNES-HOLMES, D., & HEALY, O. (2001). Derived relational responding as learned behavior. In S. C. Hayes, D. Barnes-Holmes, & B. Roche (Eds.), Relational frame theory: A post-Skinnerian account of human language and cognition (pp. 21–49). New York: Kluwer Academic/Pienum Publishers.
KOHONEN, T. (2001). Self-organizing maps (3rd ed). Berlin, Germany: Springer-Verlag.
LEADER, G., & BARNES-HOLMES, D. (2001). Establishing fractional-decimal equivalence using a respondent-type training procedure. The Psychological Record, 51, 151–166.
LYNCH, D. O., & CUVO, A. J. (1995). Stimulus equivalence instruction of fraction-decimal relations. Journal of Applied Behavior Analysis, 28, 115–126.
NINNESS, H. A. O., & NINNESS, S. K. (1998). Superstitious math performance: Interactions between rule-governed and scheduled contingencies. The Psychological Record, 48, 45–62.
NINNESS, H. A. C., & NINNESS, S. K. (1999). Contingencies of superstition: Fallacious rules and irrelevant responding during second-order schedules of reinforcement. The Psychological Record, 49, 221–243.
NINNESS, H. A. O., MCCULLER, G., & OZENNE, L. (2000). School and behavioral psychology: Research in human-computer interactions, functional assessment and treatment. Norwell, MA: Kluwer Academic Publishers.
NINNESS, C., RUMPH, R., MCCULLER, G., BRADFIELD, A., HARRISON, O., VASQUEZ, E., & NINNESS, S., (2003, May). Artificial neural network analysis of derived relational frames. Paper presented at the Association for Behavior Analysis 29th Annual Convention, San Francisco, CA.
SMEETS, P. M., BARNES-HOLMES, Y, AKPINAR, D., & BARNES-HOLMES, D. (2003). Reversal of equivalence relations. The Psychological Record, 53, 91–120.
STEELE, D. L., & HAYES, S. C. (1991). Stimulus equivalence and arbitrarily applicable relational responding. Journal of the Experimental Analysis of Behavior, 56, 519–555.
STEWART, I., BARNES-HOLMES, D., ROCHE, B., & SMEETS, P. M. (2001). Generating derived relational networks via the abstraction of common physical properties: A possible model of analogical reasoning. The Psychological Record, 51, 381–408.
STEWART, I., BARNES-HOLMES, D., ROCHE, B., & SMEETS, P. M. (2002). A functional-analytic model of analogy: A relational frame analysis. Journal of the Experimental Analysis of Behavior, 78, 375–396.
WULFERT, E., & HAYES, S. C. (1988). The transfer of conditional sequencing through conditional equivalence classes. Journal of the Experimental Analysis of Behavior, 66, 267–281.
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Ninness, C., Rumph, R., McCuller, G. et al. A Relational Frame and Artificial Neural Network Approach to Computer-Interactive Mathematics. Psychol Rec 55, 135–153 (2005). https://doi.org/10.1007/BF03395503
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DOI: https://doi.org/10.1007/BF03395503