Proceedings of the Annual Meeting of the Cognitive Science Society

Learning about fractions is a critical step on the path to high school mathematics, yet many children never masterbasic knowledge such as fraction arithmetic procedures. To better understand these difficulties, the present study describes acomputational model of fraction arithmetic problem solving. The model demonstrates that the majority of empirically observederrors over all four arithmetic operations can be explained by only two error-generating mechanisms – overgeneralization andrepair. Further, by assuming probabilistic selection of solution procedures using associative strengths learned from experience,the model predicts two other empirical phenomena: (1) variation in error rates and relative frequencies of specific errorsas a function of problem features, and (2) variable strategy selection within and between problems and individuals. Beyondproviding a formal account of errors, the model was used to simulate the effects of variation of instructional parameters, leadingto novel predictions regarding potentially effective instructional designs.