Microgenetic patterns of children’s multiplication learning: Confirming the overlapping waves model by latent growth modeling

Ven, Sanne H. G. van der; Boom, Jan; Kroesbergen, Evelyn H.; Leseman, Paul

doi:10.1016/j.jecp.2012.02.001

Cited by 52 publications

(34 citation statements)

References 31 publications

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“…Spatial working memory was as expected found to be related to children's visual-spatial encoding [visual processing being an important component of figural tasks (Laski & Siegler, 2014;Rasmussen & Bisanz, 2005;Van der Ven, Boom, Kroesbergen, & Leseman, 2012)], although this was not associated with improvement on the tasks. In contrast, verbal workingmemory positively influenced both children's initial ability and rate of change but only in relation to full construction (accuracy) of the tasks (see also Siegler, 2006).…”

Section: Discussionmentioning

confidence: 55%

Progression paths in children’s problem solving: The influence of dynamic testing, initial variability, and working memory

Resing

Bakker

Pronk

et al. 2017

Journal of Experimental Child Psychology

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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Progression paths in children's problem solving:The influence of dynamic testing, initial variability and working-memory AbstractThe current study investigated developmental trajectories of analogical reasoning performance of 104 7-to-8-year-old children. We employed a microgenetic research method and multilevel analysis to examine the influence of several background variables and experimental treatment on the children's developmental trajectories. Our participants were divided into two treatment groups: repeated practice alone and repeated practice with training. Each child received an initial working-memory assessment, and was subsequently asked to solve figural analogies on each of several sessions. We examined children's analogical problem-solving behavior and their subsequent verbal accounts of their employed solving processes. We also investigated the influence of verbal and visual-spatial working-memory capacity and initial variability in strategyuse on analogical reasoning development. Results indicated that children in both treatment groups improved but gains were greater for those who had received training. Training also reduced the influence of children's initial variability in the use of analogical strategies with the degree of improvement in reasoning largely unrelated to working memory capacity. Findings from this study demonstrate the value of a microgenetic research method and the use of multilevel analysis to examine inter-and intra-individual change in problem-solving processes.

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Section: Discussionmentioning

confidence: 55%

Progression paths in children’s problem solving: The influence of dynamic testing, initial variability, and working memory

Resing

Bakker

Pronk

et al. 2017

Journal of Experimental Child Psychology

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show abstract

“…In computational efficiency models it is assumed that various computational strategies are used to solve multiplication problems (Imbo, Duverne, & Lemaire, 2007;Imbo & Vandierendonck, 2008;Lemaire & Siegler, 1995;Mabbott & Bisanz, 2003;Siegler, 1988;Van der Ven et al, 2012;Wu et al, 2008). Some problems require more and more difficult steps than others (LeFevre et al, 1996).…”

Section: Solving Single-digit Multiplication Problems: Effects Theormentioning

confidence: 99%

Learning multiplication: An integrated analysis of the multiplication ability of primary school children and the difficulty of single digit and multidigit multiplication problems

Ven

Straatemeier

Jansen

et al. 2015

Learning and Individual Differences

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a b s t r a c tIn this study the mental multiplication ability of primary school children and the difficulty structure of all single digit and 469 multidigit multiplication problems, each solved tens of thousands of times in a web-based practice program, were investigated. Child analyses indicated three groups: single digit problem solvers, multidigit problem solvers, and high performers. Within-grade ability differences were very large. In the item analyses, previously identified effects in single digit multiplication, such as the problem size effect and the tie effect, were replicated in one integrated analysis. Data from two tasks were contrasted: one in which children used predominantly computational strategies, and one in which they are expected to rely mostly on retrieval. In both tasks we found most support for the computational efficiency model. Finally, exploratory analyses on the difficulty of multidigit problems suggest that children rely on the base 10 structure of our number system.

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“…Verbal reports can also help identify difficulties encountered during problem-solving and help determine ways to alleviate these difficulties. Moreover, verbal reports are highly suitable for investigating individual differences in arithmetic strategy use (e.g., Imbo & Vandierendonck, 2008a,b;Mabbott & Bisanz, 2003;Van der Ven, Boom, Kroesbergen, & Leseman, 2012). In this respect, verbal reports can be superior to other commonly used measures, namely latency and accuracy data.…”

Section: Identifying Strategy Use Through Verbal Reportsmentioning

confidence: 99%

Third graders’ verbal reports of multiplication strategy use: How valid are they?

Reed¹,

Stevenson²,

Broens-Paffen³

et al. 2015

Learning and Individual Differences

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Microgenetic patterns of children’s multiplication learning: Confirming the overlapping waves model by latent growth modeling

Abstract: Microgenetic patterns of children's multiplication learning: Confirming the overlapping waves model by latent growth modeling van der Ven, S.H.G.; Boom, J.; Kroesbergen, E.H.; Leseman, P.P.M.

Cited by 52 publications

References 31 publications

Progression paths in children’s problem solving: The influence of dynamic testing, initial variability, and working memory

Progression paths in children’s problem solving: The influence of dynamic testing, initial variability, and working memory

Learning multiplication: An integrated analysis of the multiplication ability of primary school children and the difficulty of single digit and multidigit multiplication problems

Third graders’ verbal reports of multiplication strategy use: How valid are they?

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