Synopsis of
Campbell, J. I. D., & Xue, Q. (2001). Cognitive arithmetic across cultures. Journal of Experimental Psychology: General,130, 299-315.
Synopsis by Jamie Campbell
August 15, 2001
Summary.
We examined arithmetic skills in three groups of students studying at the University of Saskatchewan in 1997: Asian Chinese students who learned their basic arithmetics skills in China, and two Canadian-educated groups; Canadian Chinese students whose ancestry was Asian and non-Asian Canadian students. We tested very simple arithmetic problems like 2 + 2, 3 x 6, 7 - 5, 56 / 8, etc., and also more complex arithmetic; e.g., adding three two-digit numbers, long division, etc. Finally, we asked our participants to indicate how much they used calculators during primary and secondary school. For simple arithmetic, the two Chinese groups performed equally well, but both were slightly faster than the non-Asian Canadians. This difference was due to the non-Asian Canadians' slower rote memory for arithmetic facts, and also greater use of slower solution strategies such as counting, transformation, etc. For complex arithmetic, the pattern across groups was different. Here, the Asian Chinese group substantially out performed both Canadian groups. The Asian Chinese students also reported much less calculator use during early math education. As less calculator use predicted better performance on the complex arithmetic, the Asian Chinese students' better performance on complex arithmetic might arise in part from less reliance on calculators. Reliance on calculators could restrict the level of expertise achieved in long-term and short-term memory skills for mental arithmetic. The Asian Chinese advantage on complex arithmetic could also be related to better understanding of the conceptual structures that support arithmetic procedures.
Method overview.
Canadian university students either of Chinese or non-Asian origin and Chinese university students educated in China solved all simple arithmetic problems in the four basic operations (e.g., 3 + 4, 7 - 3, 3 × 4, 12 ÷ 3) and reported their solution strategies (retrieving the answer from memory vs. use of a computational procedure such as counting or transformation). The simple arithmetic problems were displayed one at a time on a computer screen. Prior to this, participants completed a test of several hundred complex pencil and paper arithmetic problems (e.g., 84 + 57 + 32, 937 ÷ 8, 84- 47, 67 x 8). Finally, we asked participants to estimate their calculator use during elementary and secondary school (1-never, 2-rarely, 3-sometimes, 4-often, 5-always). There were 12 males and 12 females in each of the three groups, for a total of 72 participants. Testing occurred in the spring of 1997 at the University of Saskatchewan, Canada.
Findings.
re: group differences in complex arithmetic...
For complex arithmetic, the Asian Chinese students correctly completed 58% more problems than the non-Asian Canadian students and 33% more than the Chinese Canadian students. Thus, the Asian Chinese students substantially outperformed both Canadian groups on the complex arithmetic task. The relatively smaller 19% advantage for Chinese Canadians compared to non-Asian Canadians was only marginally reliable statistically.
re: group differences in simple arithmetic...
In contrast, for simple arithmetic, the Asian Chinese and Chinese Canadians were practically equivalent and both performed better than non-Asian Canadians. Specifically, non-Asian Canadians were 24% slower than the Asian Chinese students and 21% slower than the Chinese Canadians. The advantage for the two Chinese groups was observed for all four basic arithmetic operations.
The average time in seconds to correctly answer simple arithmetic problems was 1.1, 0.9, and 0.9 seconds for the non-Asian Canadians, Chinese Canadians, and Asian Chinese respectively. Thus, whereas the simple arithmetic deficit presented by the non-Asian Canadian students appears quite large when expressed as a percentage difference (i.e., about 22% slower than the Chinese groups), in absolute terms all three groups were fast and did not differ greatly. There were no overall group differences in error rates.
Although memory retrieval is the dominant strategy for simple arithmetic, the results indicated that procedural strategies (e.g. counting, decomposition) played an important role in performance of simple arithmetic for all three groups. Chinese Canadians reported procedure use at rates very similar to the Asian Chinese (13% and 15%, respectively), whereas non-Asian Canadians reported substantially more procedure use (28%).
The non-Asian Canadians' relatively poor simple arithmetic performance resulted both from greater use of slow procedural strategies and also slower retrieval processes. The non-Asian Canadians, however, presented equivalent or perhaps slightly better efficiency when using procedural strategies for simple arithmetic, perhaps because they were more practiced at using such strategies. Nonetheless, the non-Asian Canadian's overall greater use of procedures, which are generally less efficient than retrieval, contributed to their slower performance of simple arithmetic.
re: group differences in calculator use...
Use of calculators was reportedly rare in elementary school for all groups, but especially for the Asian Chinese students; 83% reported never using a calculator in elementary school compared to 44% for the Canadian students. Eighty-one percent of the Canadian students reported using a calculator at least sometimes in secondary school; 48% reported using a calculator often or always. In contrast, only 25% of the Asian Chinese sample reported using a calculator at least sometimes in secondary school, and 46% reported never using a calculator in secondary school. In summary, calculator use was relatively rare for the Asian Chinese students prior to university, but Chinese Canadians and non-Asian Canadians were more likely to begin using a calculator in elementary school and reliance on calculators was substantial by the time they were in secondary school.
Less use of calculators was associated with better performance of the complex arithmetic task. As the Asian Chinese students reported less calculator use prior to university relative to both Canadian groups it is likely that the Asian Chinese students had more practice performing relatively complex arithmetic without the aid of a calculator. This would promote better working memory skills for complex arithmetic procedures such as carrying, borrowing, and place keeping. The Asian Chinese advantage on complex arithmetic could also be related to better understanding of the conceptual structures that support arithmetic procedures.
As the two Canadian groups reported equivalent calculator use, the simple arithmetic advantage for the Chinese Canadians relative to non-Asian Canadians apparently is unrelated to calculator use. More generally, calculator use was not predictive of simple arithmetic performance, indicating that greater calculator use is not necessarily associated with weaker elementary arithmetic skills.
Conclusions.
The experiment suggests that cross-cultural differences in young adults' simple arithmetic skill are not necessarily attributable to cross-national differences in formal education. Asian Chinese and Chinese Canadians, despite receiving their formal math education in China and Canada, respectively, were practically equivalent in all aspects of simple arithmetic.
In contrast, Chinese Canadians and non-Asian Canadians, who both received formal mathematics education in Canada, presented different levels of performance. The better simple arithmetic performance of Chinese Canadians relative to non-Asian Canadians suggests that extracurricular cultural-specific factors, rather than cross-national differences in formal education, underlie differences in simple arithmetic performance observed between Chinese and North American adults.
The Asian Chinese outperformed both Canadian groups on the complex arithmetic, possibly because they relied less on calculators in elementary and secondary school than the Canadian students.
Previous research (e.g., by Prof. Harold Stevenson and his colleagues) has also identified a variety of extracurricular cultural differences between North Americans and East Asians that likely contribute to differences in mathematical development and achievement (e.g., parents and peers holding high academic standards, believing that effort mediates success, pursuing extracurricular instruction or practice, having positive attitudes about achievement).
Other research (e.g., by Prof. David Geary and his colleagues) has found that differences between East Asian and North American samples are still found when IQ is controlled, and are observed for arithmetic but not necessarily for non-mathematical measures of cognitive or academic performance. This research has also found that the arithmetic competencies of older Chinese and American adults (60 to 80 years old) do not differ. These findings suggest that the cross-cultural differences in simple arithmetic performance observed in children and young adults is a recent development, and reinforces the conclusion that the achievement gap is to due cultural (i.e., educational and other social influences) rather than biological or linguistic factors.
Finally, the results indicate that procedural strategies constitute a major part of educated adults' repertoire of simple arithmetic skills. Indeed, exclusive reliance on retrieval for simple arithmetic probably is a rare achievement. Even the Asian Chinese, whose educational and cultural experiences apparently provide an especially strong foundation for simple arithmetic, did not report having memorized all the basic number facts. The findings confirm the central importance of procedural knowledge in skilled adults' performance of elementary mathematics.