Do we spend too much time thinking when it comes to elementary math?
Jamie I.D. Campbell, PhD, and Qilin Xue, of the University of Saskatchewan, sought to find out by conducting a study of the mental processing of elementary arithmetic by Canadian and Chinese students. Their goal was to determine whether there are differences in how the students solved the problems: Did they solve them using direct memory retrieval or by using a procedural strategy?
In addition to looking at the source of these observed differences in arithmetic performance of North American and Chinese adults, the authors also looked at the problem-size effect--whether difficulty increases as problem size increases--to determine its sources in addition, multiplication, subtraction and division.
The college-age groups included non-Asian Canadians, Chinese Canadians (those of Chinese descent who completed elementary and secondary school in Canada), and Asian Chinese (those who completed elementary and secondary education in China). The authors tested the students on simple and complex multi-step mental arithmetic, having them report their solution strategies.
In simple arithmetic, the Asian-Chinese and Chinese-Canadian groups significantly outperformed the non-Asian Canadians. In complex arithmetic, however, the Asian Chinese performed considerably better than both groups of Canadians.
The Asian-Chinese students also reported much less calculator use during early math education compared to the two Canadian groups.
The results show that the differences for simple arithmetic are not related to formal education, but to extracurricular, culture-specific factors; if education was the source of the differences between the groups, then the two Chinese groups educated in separate places would not have performed better than the non-Asian Canadian group, the researchers concluded.
Though the results confirm the importance of procedural knowledge and strategies in skilled adults' elementary math performance, the authors found the poorer performance of non-Asian Canadians on simple arithmetic was due to greater use of slow procedural strategies and slower retrieval processes, especially for larger problems. Retrieval use varied across operations. All groups relied primarily on retrieval for multiplication, and Chinese adults relied almost solely on retrieval for addition and multiplication (the rate was lower for subtraction and division as well as for larger problems).
Campbell suggests that for complex arithmetic, "the Asian-Chinese students' better performance relative to both Canadian groups could be related to the latters' greater reliance on calculators. Extensive calculator use in early education might restrict the level of expertise achieved in working memory skills for complex arithmetic."
The study, "Cognitive arithmetic across cultures," appears in the June issue of APA's Journal of Experimental Psychology: General. (Vol. 33, No. 2).
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