Neighborhood consistency and memory for number facts

Verguts and Fias (Memory & Cognition 33:1-16, 2005a) proposed a new model of memory for simple multiplication facts (2 x 3 = 6; 8 x 7 =56) in which learning and performance is governed by the consistency of a problem's correct product with neighboring products in the times table. In the present study, to directly investigate effects of neighborhood consistency, participants memorized a set of 16 novel "pound" arithmetic equations. The pound arithmetic table included eight tie equations with repeated operands (e.g., 4 # 4 = 29) and eight nontie equations (e.g., 5 # 4 = 39). In the consistent problem set, tie and nontie answers in adjacent columns and rows shared a common decade or unit value. In the inconsistent problem set, neighboring tie and nontie problems did not share a common decade or unit. Across 14 study-test blocks, memorization of the pound arithmetic table presented a robust effect of neighborhood consistency, with the rate of learning nearly doubling that of the inconsistent condition. An analysis of error types showed that consistency fostered the development of a categorical structure based on problem operands and that tie problems were encoded as a distinct subcategory of problems. There was also a substantial learning advantage for tie problems relative to nonties both with consistent and inconsistent neighbors. The results indicate that neighborhood consistency can have a major impact on memory for number facts.