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01-05-2008 | Original Article

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

Auteurs: Ineke Imbo, André Vandierendonck

Gepubliceerd in: Psychological Research | Uitgave 3/2008

Abstract

Adult’s simple-arithmetic strategy use depends on problem-related characteristics, such as problem size and operation, and on individual-difference variables, such as working-memory span. The current study investigates (a) whether the effects of problem size, operation, and working-memory span on children’s simple-arithmetic strategy use are equal to those observed in adults, and (b) how these effects emerge and change across age. To this end, simple-arithmetic performance measures and a working-memory span measure were obtained from 8-year-old, 10-year-old, and 12-year-old children. Results showed that the problem-size effect in children results from the same strategic performance differences as in adults (i.e., size-related differences in strategy selection, retrieval efficiency, and procedural efficiency). Operation-related effects in children were equal to those observed in adults as well, with more frequent retrieval use on multiplication, more efficient strategy execution in addition, and more pronounced changes in multiplication. Finally, the advantage of having a large working-memory span was also present in children. The differences and similarities across children’s and adult’s strategic performance and the relevance of arithmetic models are discussed.

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Many different labels have been used to denote what we call here ‘procedural’ strategies. Examples are “reconstructive strategies”, “algorithmic strategies”, “back-up strategies”, “the usage of manipulatives”, et cetera. In the current study, we consistently use the term ‘procedural’ strategies, to refer to (mostly time-consuming) strategies in which the solution is obtained in a sequence of operations.

Since (a) not all children used both retrieval and procedural strategies, and (b) only RTs of the correctly solved problems were analyzed, for some children empty cells occurred in the ANOVAs on latencies. We replaced these empty cells for each child with the correct RT of the corresponding cell [i.e., the mean RT (over participants) of the grade x problem size x operation cell].

As age-related differences were substantially smaller in accuracy data than in latency data (cfr. ANOVA results), regression analyses were performed on latency data only.

In the regression analyses, problem size was determined by the correct answer of the problem (i.e., sizes from 5 to 17 for addition problems and sizes from 6 to 72 for multiplication problems). Thus, whereas a dichotomous measure of problem size was used in the analyses of variance, a continuous measure of problem size was used in the regression analyses. Operation was in the regression analyses coded by a dummy variable with value 1 for addition problems and value -1 for multiplication problems.

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Titel: Effects of problem size, operation, and working-memory span on simple-arithmetic strategies: differences between children and adults?
Auteurs: Ineke Imbo
André Vandierendonck
Publicatiedatum: 01-05-2008
Uitgeverij: Springer-Verlag
Gepubliceerd in: Psychological Research / Uitgave 3/2008
Print ISSN: 0340-0727
Elektronisch ISSN: 1430-2772
DOI: https://doi.org/10.1007/s00426-007-0112-8

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