MATHEMATICAL COGNITION AND THE PROBLEM SIZE EFFECT

We review a foundational finding in the area of mathematical cognition, the problem size effect, as it has been studied and modeled across the past 30 years. Early research on the effect indicated a substantial role for memory retrieval, as opposed to simple counting-based performance, leading to research on the nature of the memory representation supporting such retrieval, the emergence of memory retrieval in development, and the underlying source of the problem size effect. Three possible reasons for the problem size effect, one based on strength in memory, one on errors, and one on strategy-based responding, are considered, along with the role of working memory and the individual difference variable of math anxiety. A unifying theoretical framework is suggested, based on strength, that yields both error and strategy predictions that entail working memory effects. We conclude with remarks concerning the likelihood that the problem size effect is changing, probably due to educational factors, with clear consequences for both theories and for mathematical achievement.