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.

Strategies in subtraction problem solving in children

“…This difference between subtraction and addition has also been found in adults. LeFevre, De Stefano, Penner-Wilger, and Daley's (2006) participants reported retrieval on 82% of easy problems (minuend < 10) but on only 42% of hard problems, results echoing those reported by Campbell and Xue (2001), who observed retrieval on 73 and 42% of easy and hard problems, respectively. For sake of comparison, LeFevre, Sadesky, and Bisanz (1996) reported a retrieval rate of 71% in adults solving the 100 additions with operands from 0 to 9.…”

Effects of problem size, operation, and working-memory span on simple-arithmetic strategies: differences between children and adults?

“…According to Campbell and Xue (2001), there are three strategy-related sources of the problem-size eVect in adults: less frequent retrieval use for large than for small problems, lower retrieval eYciency for large than for small problems, and lower procedural eYciency for large than for small problems. In the current study, we investigated which of these sources determine the problem-size eVect in children.…”

“…Adult studies consistently show operation-related diVerences in both strategy selection and strategy eYciency (e.g., Campbell, 1995;Campbell & Xue, 2001;Hecht, 1999;Imbo, Vandierendonck, & Rosseel, 2007, in press). Generally, retrieval is used more frequently in multiplication than in addition, whereas both retrieval and procedural eYciencies are higher in addition than in multiplication.…”

Development of numerical estimation in Chinese preschool children

“…For example, Dehaene and colleagues (2008) found that their sample of American adults had linear representation of 0-10 symbolic numbers (in English and in Spanish, with the latter being a second language for the participants) and 1-10 dots, but not of 1-100 dots or 1-10 tones, both of which were logarithmically mapped. Third, although we expected similar developmental trends in Chinese children as in Western children, we expected that the shift from logarithmic to linear representation would occur earlier in Chinese children than has been found in American children because of the former's advantage in early mathematics (e.g., Campbell & Xue, 2001;Chen & Stevenson, 1995;Miller et al, 1995;Stevenson et al, 1990Stevenson et al, , 1993. This hypothesis was a downward extension of Siegler and Mu's (2008) findings from kindergarteners to preschoolers.…”

“…This lack of research on young children is especially relevant to Chinese children who begin preschool at 3 years of age and receive formal education about numbers. Previous studies have documented Chinese children's superior performance in mathematics across all age groups as compared with their Western counterparts (e.g., Campbell & Xue, 2001;Chen & Stevenson, 1995;Miller, Smith, Zhu, & Zhang, 1995;Stevenson, Chen, & Lee, 1993;Stevenson et al, 1990). Would Chinese 3-and 4-year-olds then have developed linear representations of numbers after a year or so of learning numbers in preschool?…”