Development of efficient arithmetic computation.

Kaye, Daniel B.; deWinstanley, Patricia A.; Chen, Qi; Bonnefil, Virginia

doi:10.1037/0022-0663.81.4.467

Cited by 36 publications

(25 citation statements)

References 17 publications

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“…According to , arithmetic skill can be viewed on a continuum from novice to expert, with high-skill subjects retrieving arithmetic facts more frequently and more efficiently than lowskill subjects (see also Ashcraft, Donley, Halas, & Vakali, 1992;Kaye, 1986;Kaye, deWinstanley, Chen, & Bonnefil, 1989;LeFevre & Kulak, 1994); these effects were observed in the present study as well. Indeed, regression analyses showed that arithmetic skill was the only individual trait that was highly predictive both of use of a retrieval strategy and of strategy efficiency in both addition and multiplication problems.…”

Section: Arithmetic Skillsupporting

confidence: 74%

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: Arithmetic Skillsupporting

confidence: 74%

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

2007

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“…Because errors and latencies rose under such a load, Hitch and colleagues concluded that children's counting processes involve inner speech. The dual-task method was further used by Kaye, deWinstanley, Chen, and BonneWl (1989). In their study, second, fourth, and sixth graders veriWed simple addition problems while their working memories were loaded by means of a probe detection task.…”

Section: The Role Of Working Memory In Children's Arithmetic Strategymentioning

confidence: 99%

“…A third and Wnal shortcoming is that very few studies have investigated the role of working memory in normally achieving children (but see Adams & Hitch, 1997;Ashcraft & Fierman, 1982;Bull & Scerif, 2001;Geary, Bow-Thomas, Liu, & Siegler, 1996;Hecht, Torgesen, Wagner, & Rashotte, 2001;Kaye et al, 1989). Because we believe that it is important to know how the interaction between working memory and arithmetic performance progresses in normal development, the current study tested children without mathematical disabilities.…”

Section: The Role Of Working Memory In Children's Arithmetic Strategymentioning

confidence: 99%

The development of strategy use in elementary school children: Working memory and individual differences

Imbo¹,

Vandierendonck²

2007

Journal of Experimental Child Psychology

197

172

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The current study tested the development of working memory involvement in children's arithmetic strategy selection and strategy eYciency. To this end, an experiment in which the dual-task method and the choice/no-choice method were combined was administered to 10-to 12-year-olds. Working memory was needed in retrieval, transformation, and counting strategies, but the ratio between available working memory resources and arithmetic task demands changed across development. More frequent retrieval use, more eYcient memory retrieval, and more eYcient counting processes reduced the working memory requirements. Strategy eYciency and strategy selection were also modiWed by individual diVerences such as processing speed, arithmetic skill, gender, and math anxiety. Short-term memory capacity, in contrast, was not related to children's strategy selection or strategy eYciency.

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“…It is also possible that some processes involved in verification (e.g., decision processes associated with pressing a button) were sped up as a result of additional time spent on computation processes. Kaye, deWinstanley, Chen, and Bonnefil (1989) reported evidence suggesting that raw latencies do not reflect how availability of memory resources contributes to verification during the solving of two-term additions (e.g., 34 + 56). Lack of available memory resources affected the computational phase in children and affected processes associated with comparison and decision stages in adults.…”

Section: -Accepted By Previous Editorial Teammentioning

confidence: 99%

Counting on working memory in simple arithmetic when counting is used for problem solving

2002

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Development of efficient arithmetic computation.

Cited by 36 publications

References 17 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 development of strategy use in elementary school children: Working memory and individual differences

Counting on working memory in simple arithmetic when counting is used for problem solving

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