A multidimensional scaling approach to mental multiplication

Abstract

Adults consistently make errors in solving simple multiplication problems. These errors have been explained with reference to the interference between similar problems. In this paper, we apply multidimensional scaling (MDS) to the domain of multiplication problems, to uncover their underlying similarity structure. A tree-sorting task was used to obtain perceived dissimilarity ratings. The derived representation shows greater similarity between problems containing larger operands and suggests that tie problems (e.g., 7 × 7) hold special status. A version of the generalized context model (Nosofsky, 1986) was used to explore the derived MDS solution. The similarity of multiplication problems made an important contribution to producing a model consistent with human performance, as did the frequency with which such problems arise in textbooks, suggesting that both factors may be involved in the explanation of errors.