Can models of learning in non-mathematical domains explain knowledge transfer in arithmetic?

This paper considers whether approaches to learning and memory developed in non-mathematical cognitive domains can explain when and how mathematical learning will transfer from practice problems to novel problems. Studies in non-mathematical cognition suggest that different practice experiences lead learners to acquire different memory models of the practiced facts, which in turn produce different patterns of transfer to novel queries. In experiments with adults and children, we show that the same factors strongly influence learning and transfer in arithmetic, with different practice experiences producing equally good learning of studied problems but remarkably different patterns of transfer to novel problems. The results suggest that the struggles faced by children learning math may partly arise from the kinds of practice to which they are exposed, and also that it may be useful to view mathematical knowledge as being supported by the same learning and memory processes that underpin non-mathematical knowledge.