A relational frame and artificial neural network approach to computer-interactive mathematics

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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-to-sample procedures in which participants were exposed to computer-posted rules regarding the relationship between particular types of formulas and their respective graphs. After participants demonstrated mutual entailment on formula-to-graph and graph-to-formula 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.

Original Citation

Ninness, C., Rumph, R., McCuller, G., Vasquez III, E., Harrison, C., Ford, A.M., Capt, A., Ninness, S.K., Bradfield, A. (2005). A relational frame and artificial neural network approach to computer-interactive mathematics. Psychological Record, 55(1), 135-153.