Mathematics Achievement of Children in China and the United States

Stevenson, Harold W.; Lee, Shin-Ying; Chen, Chuansheng; Lummis, Max; Stigler, James W.; Liu, Fan; Ge, Fang

doi:10.2307/1130875

Cited by 189 publications

(98 citation statements)

References 2 publications

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“…Several studies found differences between East Asians' and North Americans' performance on simple arithmetic (see, e.g., Campbell & Xue, 2001;Chen & Uttal, 1988;Geary, 1996;Geary, BowThomas, Liu, & Siegler, 1996;Geary et al, 1997;Geary, Liu, & Bow-Thomas, 1992;Geary, Salthouse, Chen, & Liu, 1996;LeFevre & Liu, 1997;Penner-Wilger, LethSteensen, & LeFevre, 2002;Stevenson, Chen, & Lee, 1993;Stevenson et al, 1990;Stevenson, Lee, & Stigler, 1986). Because East Asians rely primarily on memory retrieval, their arithmetic performance is faster and less error prone than that of North Americans, who frequently use procedures.…”

Section: Individual Differencesmentioning

confidence: 99%

The influence of problem features and individual differences on strategic performance in simple arithmetic

2007

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454Strategic performance of adults on cognitive problems consists of two main components. To solve a cognitive problem, people first have to choose the most appropriate strategy to solve it (i.e., strategy selection). Next, they have to execute the chosen strategy with reasonable speed and accuracy (i.e., strategy efficiency). For a long time, researchers studying mental arithmetic assumed that adults used only memory retrieval to solve simple arithmetic problems such as 8 3 or 5 4 (see, e.g., Ashcraft, 1987Ashcraft, , 1992Ashcraft, , 1995Campbell, 1987aCampbell, , 1995Campbell & Oliphant, 1992;Lebiere & Anderson, 1998;McCloskey, 1992;Siegler, 1989;Widaman & Little, 1992). Fairly recently however, LeFevre and colleagues ; see also Baroody, 1994;Geary, Frensch, & Wiley, 1993;Geary & Wiley, 1991) showed that even skilled adults still make substantial use of procedures such as counting (e.g., 6 3 6 1 1 1) and transformation (e.g., 7 5 7 3 2) when solving simple arithmetic problems. It is clear that retrieval and nonretrieval (i.e., procedural) strategies differ in their efficiency, since retrieval is generally much faster (i.e., more efficient) than any procedural strategy. Although people may adopt other strategies to solve arithmetic problems (such as using a calculator), the present study investigated mental arithmetic and thus focused on the two broad kinds of strategy mentioned above-retrieval and procedural.Both strategy selection and strategy efficiency may depend on factors such as problem features (e.g., operation, problem size) and individual differences 1 (e.g., arithmetic skill, arithmetic practice). Although models have been proposed in which such experiential factors are the main determinants of mental representation, acquisition, and performance (see, e.g., Ashcraft, 1987;Campbell & Graham, 1985;Siegler, 1988;Siegler & Shipley, 1995), there are very few direct comparisons of the simple arithmetic performance of adults who differ in their mathematical education, arithmetic skill, or arithmetic practice (see also LeFevre & Liu, 1997). Moreover, up until now, no study has investigated the effects of these factors in strategy selection and strategy efficiency separately. The present study therefore examined the effects of features that differed across problems and across individuals on strategic performance of simple arithmetic. Problem FeaturesAlthough adults rely on both retrieval and procedural strategies for the entire domain of elementary arithmetic (i.e., the four basic operations; see, e.g., Campbell & Xue, 2001), they adjust their strategy selection according to the operation involved. In solving subtraction and division problems, for example, adults rely more heavily on procedural strategies than they do when solving either addition or multiplication problems, for which retrieval strategies are predominantly used (Campbell & Xue, 2001;Seyler, Kirk, & Ashcraft, 2003). Furthermore, adults use direct retrieval to solve multiplication problems even more frequently than they do to solve addition prob...

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Section: Individual Differencesmentioning

confidence: 99%

The influence of problem features and individual differences on strategic performance in simple arithmetic

2007

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“…Relative to American children, children in East Asian nations receive much more exposure to basic arithmetic and, in fact, to nearly all other mathematical domains (Geary, 1994;Stevenson et al, 1990a;Stevenson & Stigler, 1992). Moreover, the exposure of East Asian children to basic arithmetic facts is likely to be more extensive, at least in terms of repeated and long-term (i.e.…”

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confidence: 99%

The Problem-size Effect in Mental Addition: Developmental and Cross-national Trends

Geary¹

1996

Mathematical Cognition

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Across two experiments, the magnitude of the problem-size effect in mental addition was examined for kindergarten and elementary school children, as well as adults, from mainland China and the United States. In North American samples, the problem-size effect represents the finding that arithmetic problems consisting of larger-valued numbers (e.g. 8+7) take longer to solve and are more error prone than are problems consisting of smaller-valued numbers (e.g. 2+3). This standard finding was found for the kindergarten, elementary school, and adult samples from the United States. For the Chinese children, the problem size effect was evident in kindergarten and at the beginning of first grade. However, the effect had disappeared at the end of first grade and had reversed (i.e. largervalued addition problems were solved more quickly than smaller-valued problems) by the end of third grade. However, the standard problem-size effect "reappeared" for the Chinese adults. The results are interpreted in terms of theoretical models of the nature of the memory representation for arithmetic facts and in terms of the mechanisms that govern the development of these representations.In the nearly 25 years since Groen and Parkman's (1972) seminal study of the mental processes underlying the solution of simple addition problems, cognitive arithmetic has emerged as a vibrant area of research. Scientists in this area have mapped the cognitive processes and neurological correlates that govern the mental solution of simple and complex arithmetic problems and have extended these basic findings to more applied issues, such as mathematical anxiety and mathematical disabilities

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“…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.…”

Section: Introductionmentioning

confidence: 86%

“…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?…”

Section: Introductionmentioning

confidence: 99%

Development of numerical estimation in Chinese preschool children

Chen

Pan

et al. 2013

Journal of Experimental Child Psychology

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a b s t r a c tAlthough much is known about the development of mental representations of numbers, it is not clear how early children begin to represent numbers on a linear scale. The current study aimed to examine the development of numerical estimation of Chinese preschoolers. In total, 160 children of three age groups (51 3-and 4-year-olds, 50 5-year-olds, and 59 6-year-olds) were administered the numerical estimation task on three types of number lines (Arabic numbers, dots, and objects). All three age groups took the test on the 0-10 number lines, and the oldest group also took it on the 0-100 and 0-1000 Arabic number lines. Results showed that (a) linear representation of numbers increased with age, (b) representation of numbers was consistent across the three types of tasks, (c) Chinese participants generally showed earlier onset of various landmarks of attaining linear representations (e.g., linearity of various number ranges, accuracy, intercepts) than did their Western counterparts, as reported in previous studies, and (d) the estimates of older Chinese preschoolers on the 0-100 and 0-1000 symbolic number lines fitted the two-linear and linear models better than alternative models such as the one-cycle, two-cycle, and logarithmic models. These results extend the small but accumulating literature on the earlier development of number cognition among Chinese preschoolers compared with their Western counterparts, suggesting the importance of cultural factors in the development of early number cognition.

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Mathematics Achievement of Children in China and the United States

Cited by 189 publications

References 2 publications

The influence of problem features and individual differences on strategic performance in simple arithmetic

The influence of problem features and individual differences on strategic performance in simple arithmetic

The Problem-size Effect in Mental Addition: Developmental and Cross-national Trends

Development of numerical estimation in Chinese preschool children

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