Multiple routes to solution of single-digit multiplication problems.

Researchers have assumed that adults solve simple arithmetic problems by retrieving answers from a network of stored facts. In 2 studies, undergraduates described their solutions of single-digit multiplication problems. They reported direct retrieval on approximately 80% of trials, but also reported rules (e.g., anything times 0 is 0), repeated addition (e.g., 2 × 4 = 4 + 4), number series (e.g., 3 × 5 = 5, 10, 15), and derived facts (e.g., 6 × 7 = [6 × 6] + 6). Participants were slower to retrieve problems that were most likely to be solved by nonretrieval procedures and faster to retrieve problems that were usually solved by retrieval. These results indicate that direct-retrieval models are incomplete accounts of adults' performance and support a continuing influence of learning and experience on the mental representation of simple multiplication problems.