Selection of procedures in mental addition: Reassessing the problem size effect in adults.

Abstract

Adults' solution times to simple addition problems typically increase with the sum of the problems (the problem size effect). Models of the solution process are based on the assumption that adults always directly retrieve answers to problems from an associative network. Accordingly, attempts to explain the problem size effect have focused either on structural explanations that relate latencies to numerical indices (e.g., the area of a tabular representation) or on explanations that are based on frequency of presentation or amount of practice. In this study, the authors have shown that the problem size effect in simple addition is mainly due to participants' selection of nonretrieval procedures on larger problems (i.e., problems with sums greater than 10). The implications of these results for extant models of addition performance are discussed. Twenty years of research on mental arithmetic has shown that problems involving larger numbers (e.g., 9 + 6) are solved more slowly than problems involving smaller numbers (e.g., 3 + 4). Surprisingly, in spite of the wealth of empirical data and the extensive theoretical development on mental arithmetic, the problem size effect has eluded satisfactory explanation (Ashcraft, 1992; McCloskey, Harley, & Sokol, 1991; Widaman & Little, 1992). The goal of the present research was to test an explanation of the problem size effect in adults that has been used to account for the arithmetic performance of children (Ashcraft, 1992; Siegler, 1987). We hypothesized that variability in the selection of procedures to solve simple addition problems has a major impact on solution latencies and may account for a substantial portion of the problem size effect.

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