Cognitive arithmetic across cultures.

Abstract

Canadian university students either of Chinese origin (CC) or non-Asian origin (NAC) and Chinese university students educated in Asia (AC) solved simple-arithmetic problems in the 4 basic operations (e.g., 3 + 4, 7 - 3, 3 X 4, 12 •*• 3) and reported their solution strategies. They also completed a standardized test of more complex multistep arithmetic. For complex arithmetic, ACs outperformed both CCs and NACs. For simple arithmetic, however, ACs and CCs were equal and both performed better than NACs. The superior simple-arithmetic skills of CCs relative to NACs implies that extracurricular culture-specific factors rather than differences in formal education explain the simple-arithmetic advantage for Chinese relative to non-Asian North American adults. NAC's relatively poor simple-arithmetic performance resulted both from less efficient retrieval skills and greater use of procedural strategies. Nonetheless, all 3 groups reported using procedures for the larger simple subtraction and division problems, confirming the importance of procedural knowledge in skilled adults' performance of elementary mathematics. Knowledge of elementary arithmetic (i.e., simple addition, multiplication, subtraction, and division) is a pervasive requirement of everyday modern life, providing the essential means for dealing with a widely diverse variety of numerical-problem-solving situations. Basic arithmetic also provides the foundation for the more advanced mathematical skills that are central to all modern scientific disciplines. Consequently, understanding this fundamental intellectual skill is an important goal for cognitive science (Ashcraft, 1995; Geary, 1994). In this study, Chinese adults educated in the People's Republic of China and Canadian adults educated in Canada, either of Chinese or non-Asian origin, solved simple arithmetic problems involving the four basic operations (e.g., 3 + 4, 7 - 3, 3 X 4, 12 -=- 3). Participants also reported their strategy (i.e., direct memory retrieval vs. procedural strategies) after each problem. The purpose was to address three important questions of current research in cognitive arithmetic. First, when adults solve simple-arithmetic problems, what is the relative balance of direct memory retrieval versus use of procedural strategies such as counting or transformation (e.g., 6 + 7 = 6 + 6+1 = 13)? Recent evidence suggests that even skilled adults make substantial use of procedures (e.g., LeFevre, Sadesky, & Bisanz, 1996), but no study has attempted to assess this for the entire domain of elementary arithmetic. Second, what determines the problem-size effect (PSE) in cognitive arithmetic? The PSE is the virtually ubiquitous phenomenon that the difficulty of simplearithmetic problems increases as problem size increases. The PSE has been recognized and studied systematically for over 75 years (e.g., Clapp, 1924), but our study was the first to estimate the