Computational and reasoning abilities in arithmetic: Cross-generational change in China and the United States

Geary, David C.; Hamson, Carmen O.; Chen, Guopeng; Fan, Liu; Hoard, Mary K.; Salthouse, Timothy A.

doi:10.3758/bf03210805

Cited by 46 publications

(38 citation statements)

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“…Consistent with this pattern is the finding of comparable performance of younger and older American adults, and sometimes an advantage for older adults, on tests of computational arithmetic (Geary, Salthouse, et al 1996). In contrast, younger adults in mainland China consistently outperform their older peers on the same tests (Geary et al, 1997;Geary, Salthouse, et al, 1996). The overall pattern suggests that older American adults have had considerably more experience with computational arithmetic than younger American adults and that if they were equated on experience, then younger adults would outperform older adults on arithmetic tests in the United States, as in China.…”

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confidence: 63%

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Numerical Cognition: Age-Related Differences in the Speed of Executing Biologically Primary and Biologically Secondary Processes

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1998

Experimental Aging Research

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confidence: 63%

“…Conceptually, the goal was to do so in a way that tested our hypothesis that these cognitive arithmetic ndings are due to a schooling-related cross-generational decline in arithmetical competencies in the United States (Geary et al, 1997).…”

Section: Hypothesismentioning

confidence: 99%

Numerical Cognition: Age-Related Differences in the Speed of Executing Biologically Primary and Biologically Secondary Processes

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1998

Experimental Aging Research

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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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“…Other quite surprising results have been found concerning the arithmetic abilities of normal educated adults. Geary, Salthouse, Chen, and Fan (1996) and Geary et al (1997) showed declines in mental arithmetic performance across successive North-American generations. Comparable results were obtained by Mulhern and Wylie (2004), who showed that performance levels of…”

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confidence: 99%

Practice effects on strategy selection and strategy efficiency in simple mental arithmetic

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Vandierendonck

2007

Psychological Research

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Two experiments were conducted to investigate the eVects of practice on strategy selection and strategy eYciency in mental arithmetic. Participants had to solve simple addition or multiplication problems, after having received 0, 3, or 6 practice sessions (Experiment 1), and before and after having received 3 practice sessions (Experiment 2). Strategy selection was measured by means of trial-by-trial strategy reports, whereas strategy eYciency was measured by means of response latencies. Results showed signiWcant practice eVects on retrieval frequency, procedural frequency, retrieval eYciency, and procedural eYciency. However, practice eVects on strategy eYciency appeared to be both strategy-speciWc (i.e., only for procedural strategies) and operation-speciWc (i.e., only for multiplication problems). Implications of the present results for mathematic cognition and its modeling are discussed.

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Computational and reasoning abilities in arithmetic: Cross-generational change in China and the United States

Cited by 46 publications

References 10 publications

Numerical Cognition: Age-Related Differences in the Speed of Executing Biologically Primary and Biologically Secondary Processes

Numerical Cognition: Age-Related Differences in the Speed of Executing Biologically Primary and Biologically Secondary Processes

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

Practice effects on strategy selection and strategy efficiency in simple mental arithmetic

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