Stability and change in children’s division strategies

Robinson, Katherine M.; Arbuthnott, Katherine D.; Rose, D T; McCarron, Michelle; Globa, Carin A.; Phonexay, Sylvia D.

doi:10.1016/j.jecp.2005.09.002

Cited by 45 publications

(57 citation statements)

References 37 publications

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“…Simple additions involving large numbers are more difficult than additions of smaller numbers, an effect that was replicated for subtractions, multiplications, and divisions [19]. However, the present study showed that the number of processing steps in the algorithm explicitly taught in French classrooms is a better predictor of the difficulty of divisions than the number of digits or the magnitude of the numbers involved in the problems.…”

Section: The Number Of Processing Stepscontrasting

confidence: 59%

“…While some authors suggest that multiplication (e.g., 6 x 8=48) and division (e.g., 48/6=8) facts are stored and retrieved as independent representations [13,14], others proposed that multiplication could be used as a check after direct retrieval of the quotient [15][16][17]. For children, the results of the sole longitudinal study in 8 year old children were more in line with the idea of a shared memory network for multiplication and division facts [18], and in accordance with this idea, Robinson et al [19] observed that multiplication is the predominant strategy to solve simple division between Grade 5 and 7. The impact of multiplicative facts knowledge would be magnified in long division, because most of the long divisions need multiple and successive retrievals.…”

Section: Introductionmentioning

confidence: 74%

“…This classification relies on the number of digits in the divisor and in the quotient. However, studies in the solving of other arithmetic operations including simple divisions [19] showed that the magnitude of operands is a determinant factor. This was not the case here.…”

Section: The Characteristics Of Operationsmentioning

confidence: 99%

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Why is It so Hard to Solve Long Divisions for 10-Year-Old Children?

Camos¹,

Baumer²

2015

Int J Sch Cog Psychol

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Although division is considered as the most difficult arithmetic operation to solve, it is also the less studied. The aim of the present study was to explore the contribution of some cognitive abilities (knowledge of multiplicative facts, attentional and spatial capacities) of 10-year-old children to their achievement in solving long divisions, and to define the factors that make long divisions difficult. Although the size of the operands predicted performance, the number of processing steps required to perform each division was the best predictor of achievement. Moreover, increased attention capacity and better knowledge in multiplicative facts favoured division solving, whereas spatial capacity did not contribute for unique variance. Finally, the decrease in performance when solution requires more processing steps was stronger in children with lower attentional capacity.

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Section: The Number Of Processing Stepscontrasting

confidence: 59%

Section: Introductionmentioning

confidence: 74%

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Why is It so Hard to Solve Long Divisions for 10-Year-Old Children?

Camos¹,

Baumer²

2015

Int J Sch Cog Psychol

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“…The current study focuses on the first three of these aspects, on the domain of multidigit arithmetic. In the domain of elementary or simple arithmetic, strategy use has been studied extensively: in elementary addition and subtraction (e.g., Carr & Jessup, 1997;Carr & Davis, 2001;Torbeyns, Verschaffel, & Ghesquière, 2004, 2005, in elementary multiplication (e.g., Anghileri, 1989;Imbo & Vandierendonck, 2007;Lemaire & Siegler, 1995;Mabbott & Bisanz, 2003;Mulligan & Mitchelmore, 1997;Sherin & Fuson, 2005;Siegler, 1988b), and in elementary division (e.g., Robinson et al, 2006). By contrast, research on solution strategies in complex or multidigit arithmetic problems is less extensive, but there is a growing body of studies in multidigit addition and subtraction (e.g., Beishuizen, 1993;Beishuizen, Van Putten, & Van Mulken, 1997;Blöte al., 2001;Torbeyns, Verschaffel, & Ghesquière, 2006) and in multidigit multiplication and division (e.g., Ambrose, Baek, & Carpenter, 2003;Buijs, 2008;Hickendorff, Heiser, Van Putten, & Verhelst, 2009;Hickendorff & Van Putten, 2012;Hickendorff, Van Putten, Verhelst, & Heiser, 2010;Van Putten, Van den Brom-Snijders, & Beishuizen, 2005).…”

Section: Solution Strategiesmentioning

confidence: 99%

The Effects of Presenting Multidigit Mathematics Problems in a Realistic Context on Sixth Graders' Problem Solving

Hickendorff

2013

Cognition and Instruction

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SOLVING MULTIDIGIT MATHEMATICS PROBLEMS 2The effects of presenting multidigit mathematics problems in a realistic context on sixth graders' problem solving Mathematics education and assessments increasingly involve arithmetic problems presented in context: a realistic situation that requires mathematical modeling. The present study's aim was to assess the effects of such typical school mathematics contexts on two aspects of problem solving, performance and strategy use, with a special focus on the role of students' language level. 685 sixth graders from the Netherlands solved a set of multidigit arithmetic problems on addition, subtraction, multiplication, and division. These problems were presented in two conditions: with and without a realistic context. Regarding performance, item response theory (IRT) models showed first that the same (latent) ability dimension was involved in solving both types of problems. Second, the presence of a context increased the difficulty level of the division problems, but not of the other operations. Regarding strategy use, results showed that strategy choice and strategy accuracy were not affected by the presence of a problem context. More importantly, the absence of context effects on performance and on strategy use held for different subgroups of students, with respect to gender, home language, and language achievement scores. In sum, the present findings suggest that at the end of primary school the presence of a typical context in a multidigit mathematics problem had no marked effects on students' multidigit arithmetic problem solving behavior.Keywords: word problems, mathematics education, solution strategy, multidimensional IRT, linear logistic test model (LLTM). SOLVING MULTIDIGIT MATHEMATICS PROBLEMS 3 IntroductionMathematics education has experienced a large international reform (e.g., Kilpatrick, Swafford, & Findell, 2001). A general characteristic of this reform is that instruction no longer focuses predominantly on decontextualized traditional mathematics skills, but that instead the process of solving realistic mathematics problems and doing mathematics are important educational goals (e.g., NationalCouncil of Teachers of Mathematics, 1989Mathematics, , 2000. Word problems or the broader category of contextual problems 1 -typically a mathematics structure in a realistic In the Netherlands, the reform is characterized by the principles of Realistic Mathematics Education (RME; Freudenthal, 1973Freudenthal, , 1991 Treffers, 1993). In RME, contextual problems (defined as a problem that is experientially real to students) are central: they are the starting point for instruction, which is based on the principle of progressive schematization or mathematization by guided reinvention (Gravemeijer & Doorman, 1999). That is, contextual problems are expected to elicit informal or naive solution strategies which are progressively abbreviated and schematized, in a process guided by the teacher. In the last decades, RME has become the dominant instructional approach in mathemati...

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“…Consequently, it is less demanding to increase multiplication eYciencies than to increase addition eYciencies. Strategy selection and strategy eYciency processes in other arithmetic operations (such as subtraction and division) have been investigated less frequently (but see Campbell & Xue, 2001;Imbo & Vandierendonck, 2007b, c;Robinson et al, 2006;Seyler et al, 2003) and are an issue for further research.…”

Section: Diverences Between Addition and Multiplicationmentioning

confidence: 99%

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

Imbo

Vandierendonck

2007

Psychological Research

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Adult's simple-arithmetic strategy use depends on problem-related characteristics, such as problem size and operation, and on individual-diVerence variables, such as working-memory span. The current study investigates (a) whether the eVects 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 eVects 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 eVect in children results from the same strategic performance diVerences as in adults (i.e., sizerelated diVerences in strategy selection, retrieval eYciency, and procedural eYciency). Operation-related eVects in children were equal to those observed in adults as well, with more frequent retrieval use on multiplication, more eYcient 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 diVerences and similarities across children's and adult's strategic performance and the relevance of arithmetic models are discussed.

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Stability and change in children’s division strategies

Cited by 45 publications

References 37 publications

Why is It so Hard to Solve Long Divisions for 10-Year-Old Children?

Why is It so Hard to Solve Long Divisions for 10-Year-Old Children?

The Effects of Presenting Multidigit Mathematics Problems in a Realistic Context on Sixth Graders' Problem Solving

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

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