Cultural differences in complex addition: Efficient Chinese versus adaptive Belgians and Canadians

Ineke Imbo, Jo-Anne LeFevre
2009 Journal of Experimental Psychology. Learning, Memory and Cognition  
The present study tested the effects of working-memory load on math problem solving in three different cultures: Flemish-speaking Belgians, English-speaking Canadians, and Chinesespeaking Chinese currently living in Canada. They solved complex addition problems (e.g., 58 + 76) in no-load and working-memory load conditions, in which either the central executive or the phonological loop was loaded. The choice/no-choice method was used to obtain unbiased measures of strategy selection and strategy
more » ... efficiency. The Chinese participants were faster than the Belgians, who were faster and more accurate than the Canadians. The Chinese also required fewer working-memory resources than the Belgians and Canadians. However, the Chinese chose less adaptively from the available strategies than the Belgians and Canadians. These cultural differences in math problem solving are likely the result of different instructional approaches during elementary school (practice and training in Asian countries versus exploration and flexibility in non-Asian countries), differences in the number language, and informal cultural norms and standards. The relevance of being adaptive is discussed, as well as the implications of the results in regards to the SCADS model of strategy selection (Shrager & Siegler, 1998) . Cultural differences in complex addition: Efficient Chinese versus adaptive Belgians and Canadians Increased globalization in the 21 st century has made the world seem smaller and more homogeneous. However, large differences among cultures persist, despite extensive travel opportunities and cross-cultural interactions. Cultural differences occur not only in habits, norms and language but may also be expressed as differences in individuals' basic cognitive processes. In the present study, we examined the effects of culture on one aspect of cognition, namely mental arithmetic. More specifically, we tested whether cultural differences in early instructional approaches have an influence on adults' math performance. Our participants were from three different nationalities, cultures, and continents. Asian, European, and North American participants solved complex arithmetic problems and reported their solution strategy after each problem. The Asians had been educated in China (through high school); the Europeans had been educated in Belgium; and the North Americans had been educated in Canada. Educational approaches to mathematics differ greatly among these three cultures. In Asia, the focus is on training and automaticity: pupils are expected to be fast and accurate -whatever strategy they use. In North America and Europe, the focus is on exploration and flexibility, and less so on speed. The question is now whether these early educational approaches have a persistent influence on people's math performance in adulthood. The goal of the present study was to address two important empirical questions about cognitive arithmetic. First, is there any cultural variation in adults' strategic performance? And second, do people of various cultures use their working memory differently when solving math problems? Obviously, these research questions interact: variations in strategy choices and in levels of strategy efficiency may implicate a differential use of available working-memory resources. We also address a more theoretical question, that is, are current models of strategy Complex Arithmetic -4 selection such as the Strategy Choice And Discovery Simulation model (SCADS; Shrager & Siegler, 1998) able to account for cultural differences in strategic math performance? Strategic Performance According to Lemaire and Siegler (1995) , there are at least four dimensions of people's strategic performance. The first dimension is the repertoire or collection of strategies that people use. In complex addition, the strategy repertoire usually consists of left-to-right strategies and right-to-left strategies (e.g., Hitch, 1978; Green, Lemaire, & Dufau, 2007) . The right-to-left order of problem solving implies that participants start by adding the units, then the tens, and so on. For addition, the right-to-left algorithm is typically taught for written, paper-and-pencil solutions (Fuson, 1990) . The left-to-right order of problem solving implies that participants start by adding the leftmost digits and move rightwards until they reach the units. The left-to-right order is often taught as a strategy for solving arithmetic problems mentally (Beishuizen, 1993) . The second dimension of strategic performance is the relative frequency with which the different strategies are applied. In complex arithmetic, this relative frequency depends greatly on the presence of carries. Carry operations are needed when the sum of a category (e.g., the units or the tens) exceeds 10. For example, in the problem 25 + 37, the sum of the units is 12, and hence the value 10 has to be carried from the units to the tens. In a seminal study, Hitch (1978) observed that some participants used the right-to-left strategy when they had to perform a carry operation and the left-to-right strategy when no carry operation was required. These first two dimensions (strategy repertoire and strategy frequency) constitute the dimension "strategy selection", which refers to the strategies people choose in order to solve the presented problems. For at least the last 15 years, children in Belgium, Italy, and the Netherlands have been taught mental procedures for solving two-digit + two-digit addition problems that involve processing tens first and units second (Beishuizen, 1993; Beishuizen, Van Putten, & Van
doi:10.1037/a0017022 pmid:19857017 fatcat:hhkqqohgfresddjqzokyqd7zou