Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education

Verschaffel, Lieven; Luwel, Koen; Torbeyns, Joke; Dooren, Wim Van

doi:10.1007/bf03174765

Cited by 218 publications

(220 citation statements)

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“…Strategy adaptivity is seen as an important characteristic in most reform-based approaches to mathematical education (Verschaffel, Greer, & De Corte, 2007;Verschaffel, et al, 2009). It has been argued that one has to look at adaptivity as a function of problem, context, and subject characteristics.…”

Section: Implications Of the Present Studymentioning

confidence: 99%

“…This strategic variability implies that one always has to choose a strategy from his/her strategic repertoire when solving a particular problem. Several studies have demonstrated that problem, subject, and/or environmental characteristics bear an influence on participants' strategy choices (Siegler, 1996;Verschaffel, Luwel, Torbeyns, & Van Dooren, 2009). …”

Section: Introductionmentioning

confidence: 99%

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The Effect of Single Versus Repeated Previous Strategy Use on Individuals' Subsequent Strategy Choice

Schillemans¹,

Luwel

Ceulemans³

et al. 2012

PSYCHOL BELG

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Previous research has shown that participants' strategy choices can be influenced by the previously-used strategy. This perseveration effect has been demonstrated both after a repeated use of the previous strategy (e.g., Schillemans, Luwel, Bulté, Onghena, & Verschaffel, 2009), but also after a single use of the previous strategy (Lemaire & Lecacheur, 2010). In the present study, we tested whether this perseveration effect would be stronger after a repeated than after a single previous strategy application. We were able to replicate the perseveration effect but we did not find evidence for an influence of the number of previous strategy applications on the strength of this effect. An additional cluster analysis revealed that only about one third of the participants was susceptible for the perseveration effect. The theoretical, methodological, and educational implications of these results are discussed.

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Section: Implications Of the Present Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Effect of Single Versus Repeated Previous Strategy Use on Individuals' Subsequent Strategy Choice

Schillemans¹,

Luwel

Ceulemans³

et al. 2012

PSYCHOL BELG

Self Cite

View full text Add to dashboard Cite

show abstract

“…Greater procedural flexibility is also associated with increased understanding of underlying concepts (see Schneider, Rittle-Johnson, & Star, 2011;Verschaffel et al, 2009). When students do not know or use multiple solution strategies, they attend to, or mentally represent, less information about the problem.…”

mentioning

confidence: 99%

“…In contrast, when students are exposed to new problem-solving strategies, they attend to features of the problems that are important for executing these strategies, which helps to support understanding of the underlying concepts (Alibali, Phillips, & Fischer, 2009;McNeil & Alibali, 2004). Numerous studies have demonstrated that knowledge of a variety of solution strategies is associated with deeper conceptual understanding of how these strategies are used (see Baroody, 2003;Heinze, Star, & Verschaffel, 2009;Schneider et al, 2011;Siegler, 1994;Verschaffel et al, 2009).…”

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confidence: 99%

Inducing mental set constrains procedural flexibility and conceptual understanding in mathematics

DeCaro

2016

Mem Cogn

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An important goal in mathematics is to flexibly use and apply multiple, efficient procedures to solve problems and to understand why these procedures work. One factor that may limit individuals' ability to notice and flexibly apply strategies is the mental set induced by the problem context. Undergraduate (N = 41, Experiment 1) and fifth-and sixthgrade students (N = 87, Experiment 2) solved mathematical equivalence problems in one of two set-inducing conditions. Participants in the complex-first condition solved problems without a repeated addend on both sides of the equal sign (e.g., 7 + 5 + 9 = 3 + _), which required multistep strategies. Then these students solved problems with a repeated addend (e.g., 7 + 5 + 9 = 7 + _), for which a shortcut strategy could be readily used (i.e., adding 5 + 9). Participants in the shortcutfirst condition solved the same problem set but began with the shortcut problems. Consistent with laboratory studies of mental set, participants in the complex-first condition were less likely to use the more efficient shortcut strategy when possible. In addition, these participants were less likely to demonstrate procedural flexibility and conceptual understanding on a subsequent assessment of mathematical equivalence knowledge. These findings suggest that certain problem-solving contexts can help or hinder both flexibility in strategy use and deeper conceptual thinking about the problems.

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“…That is, does the solver have sufficient metacognitive competence to control his or her decision making? Interestingly, while clearly agreeing with the need for self-regulatory competence, De Corte et al argue for metaknowledge, which embraces both meta-cognition and meta-volition, or understanding how one's motivation and mathematics-related affect influence problem solving engagement (De Corte 1995, De Corte et al 2000Verschaffel, Luwel, Torbeyns & Van Dooren 2009). Finally, successful problem solvers see the problem as worth solving, are prepared to give it the time it requires and believe they have the competence to solve it (Schoenfeld 1992(Schoenfeld , 2004; they have an appropriately productive mathematical worldview (b 1985b), derived experientially, that not only shapes the mathematical knowledge and strategies they bring to bear on a problem but also the manner in which they exploit them (Schoenfeld 2010a).…”

Section: Problem Solving From the Solver's Perspectivementioning

confidence: 99%

Analysing the relationship between the problem-solving-related beliefs, competence and teaching of three Cypriot primary teachers

Andrews

Xenofontos

2014

J Math Teacher Educ

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In this paper we analyse the problem solving-related beliefs, competence and classroom practice of three Cypriot upper-primary teachers. Data derived from semi-structured interviews focused on teachers' beliefs about the nature of mathematical problems, problem solving, and their competence as both problem solvers and teachers of problem solving; clinical interviews during which teachers solved a context-free geometrical problem; and observations of a lesson during which teachers introduced the same geometrical problem to their grade 6 students. Analyses, which were structured by a framework derived from key problem solving literature, indicated firstly, that the framework was an effective tool, being sensitive to variation both within and across the data from the three teachers, and secondly that all three teachers, in largely explicable ways, exhibited both consistency and inconsistency in the ways in which their beliefs, competence and practice interacted. Some implications for further research are discussed.

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Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education

Cited by 218 publications

References 53 publications

The Effect of Single Versus Repeated Previous Strategy Use on Individuals' Subsequent Strategy Choice

The Effect of Single Versus Repeated Previous Strategy Use on Individuals' Subsequent Strategy Choice

Inducing mental set constrains procedural flexibility and conceptual understanding in mathematics

Analysing the relationship between the problem-solving-related beliefs, competence and teaching of three Cypriot primary teachers

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