Group differences in adult simple arithmetic: Good retrievers, not-so-good retrievers, and perfectionists

Hecht, Steven A.

doi:10.3758/bf03193399

Cited by 19 publications

(20 citation statements)

References 49 publications

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“…A perfect distinction between computational and retrieval strategies was not achieved, but note that this reflects actual, common behavior: most people apply strategies flexibly, alternating between retrieval and computation even for very easy problems (Hecht, 2006;LeFevre et al, 1996;Siegler, 2007;Van der Ven et al, 2012).…”

Section: Discussionmentioning

confidence: 91%

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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Section: Discussionmentioning

confidence: 91%

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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show abstract

“…The novelty in the present research is that our results suggest that older participants do not resort to backup strategies for one-digit addition problems. Therefore, older adults seem to be good retrievers and do not behave as perfectionist individuals who prefer to backup retrieval with reconstructive strategies ( Hecht, 2006 ) .…”

Section: Discussionmentioning

confidence: 99%

The Use of the Operand-Recognition Paradigm for the Study of Mental Addition in Older Adults

Thévenot¹,

Castel²,

Danjon³

et al. 2012

The Journals of Gerontology Series B: Psychological Sciences an

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“…It is possible that some students will demonstrate substantially higher levels of procedural or conceptual knowledge when constrained to use these kinds of knowledge to solve the problems than a choice-allowed condition like that currently used (see e.g. Hecht, 2006, Siegler, 1988 for a related case with whole number simple arithmetic).…”

Section: Methodsmentioning

confidence: 99%

Patterns of strengths and weaknesses in children’s knowledge about fractions

Hecht

Vagi

2012

Journal of Experimental Child Psychology

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The purpose of this study was to explore individual patterns of strengths and weaknesses in children’s mathematical knowledge about common fractions. Tasks that primarily measure either conceptual or procedural aspects of mathematical knowledge were assessed with the same children in their fourth and fifth grade years (n = 181; 56% female). Procedural knowledge was regressed on levels of conceptual knowledge, and vice versa, to obtain residual scores. Residual scores capture variability in each kind of math knowledge that is not shared with the other type of knowledge. Cluster analysis using residuals indicated four distinct knowledge profiles in fourth graders: a) higher than expected conceptual knowledge and relatively lower procedural knowledge, b) relatively lower conceptual knowledge and higher procedural knowledge, c) lower concepts but expected levels of procedural knowledge, and d) relatively higher than expected levels of both procedural and conceptual knowledge. In fifth grade, another cluster emerged that showed lower procedures but expected levels of conceptual knowledge. In general, students with relatively lower than expected conceptual knowledge showed poorer accuracy on measures used to form the clusters and also word problem set-ups and estimation of sums. Implications for explaining seemingly conflicting results from prior work across studies were discussed.

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Group differences in adult simple arithmetic: Good retrievers, not-so-good retrievers, and perfectionists

Cited by 19 publications

References 49 publications

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

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

The Use of the Operand-Recognition Paradigm for the Study of Mental Addition in Older Adults

Patterns of strengths and weaknesses in children’s knowledge about fractions

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