Cognitive change as strategy change

Torbeyns, Joke; Arnaud, Laurence; Lemaire, Patrick; Verschaffel, Lieven

doi:10.1017/cbo9780511489938.007

Cited by 9 publications

(8 citation statements)

References 42 publications

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“…Unfortunately, the choice/no-choice method is not without its methodological problems. As discussed in detail by Torbeyns, Arnaud, Lemaire, and Verschaffel (2004) and by Torbeyns, Verschaffel, and Ghesquière (2004), the sound application of the choice/no-choice method requires the researcher to design one ADAPTIVE EXPERTISE 20-100 461 no-choice condition for each of the strategies observed in the choice condition. Consequently, in most studies, the choice condition will necessarily be a restricted-choice condition allowing the participants to choose among only a small number of strategies, as opposed to a completely free-choice condition.…”

Section: Discussionmentioning

confidence: 99%

The Development of Children's Adaptive Expertise in the Number Domain 20 to 100

Torbeyns

Verschaffel²,

Ghesquière³

2006

Cognition and Instruction

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Section: Discussionmentioning

confidence: 99%

The Development of Children's Adaptive Expertise in the Number Domain 20 to 100

Torbeyns

Verschaffel²,

Ghesquière³

2006

Cognition and Instruction

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“…Even when an initial strategy is successful, continued experience with a problem can lead to more efficient strategies for arriving at correct solutions. This type of strategy change reflects a restructuring of the representation of the problem, a fundamentally different way of approaching the problem, rather than a quantitative improvement in the existing strategy (Dixon & Kelley, 2006Siegler, 2005Siegler, , 2006Torbeyns, Arnaud, Lemaire, & Verschaffel, 2004). For example, the solver may suddenly adopt a more abstract representation of the problem or a more efficient route to the solution.…”

Section: Emergent Structure In Problem Solvingmentioning

confidence: 99%

The Self-Organization of Insight: Entropy and Power Laws in Problem Solving

Stephen¹,

Dixon²

2009

The Journal of Problem Solving

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Explaining emergent structure remains a challenge for all areas of cognitive science, and problem solving is no exception. The modern study of insight has drawn attention to the issue of emergent cognitive structure in problem solving research. We propose that the explanation of insight is beyond the scope of conventional approaches to cognitive science in terms of symbolic representation. Cognition may be better described in terms of an open, nonlinear dynamical system. By this reasoning, insight would be the self-organization of novel structure. Self-organization is a well-studied phenomenon of dynamical systems theory, associated with specific trends in entropy and power-law behavior. We present work using nonlinear dynamics to capture these trends in entropy and power-law behavior and thus to predict the self-organization of novel cognitive structure in a problem-solving task. Future explorations of problem solving will benefit from considerations of the continuous nonlinear interactions among action, cognition, and the environment.

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“…Recent theoretical and empirical studies on children's strategy choices on cognitive tasks (Cary & Reder 2003;Payne, Bettman, & Johnson 1993;Siegler 1996;Torbeyns, Arnaud, Lemaire, & Verschaffel 2004) showed that children do not merely fit their strategy choices to task but also to subject characteristics: They tend to select the strategy that leads fastest to an accurate answer to the item, taking into account also their individual strategy performance characteristics (which are not necessarily the same as each strategy's assumed efficiency on each item on the basis of researchers' rational task analysis). The frequent forced practice of the standard sequential strategy may have resulted in fluent application of this strategy on all types of additions and subtractions up to 100 and to a considerably less fluent performance of other strategies, such as the compensation and indirect addition strategy, that these older and mathematically higher achieving students discovered by themselves but practiced much less frequently.…”

Section: Use Of Self-invented Shortcut Strategiesmentioning

confidence: 99%

Acquisition and use of shortcut strategies by traditionally schooled children

et al. 2008

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This study aimed at analysing traditionally taught children's acquisition and use of shortcut strategies in the number domain 20-100. One-hundred-ninety-five second, third, and fourth graders of different mathematical achievement levels participated in the study. They were administered two tasks, both consisting of a series of two-digit additions and subtractions that maximally elicit the use of the compensation 45 þ 29 ¼ ; 45 þ 30 À 1 ¼ 75 À 1 ¼ 74 ð Þ and indirect addition strategy (71 À 68 ¼ ; 68 þ 2 ¼ 70; 70 þ 1 ¼ 71, so the answer is 2+1 or 3). In the first task, children were instructed to solve all items as accurately and as fast as possible with their preferred strategy. The second task was to generate at least two different strategies for each item. Results demonstrated that children of all grades and all achievement levels hardly applied the compensation and indirect addition strategy in the first task. Children's strategy reports in the second task revealed that younger and lower achieving children did not apply these strategies because they did not (yet) discover these strategies. By contrast, older and higher achieving children appeared to have acquired these strategies by themselves. Results are interpreted in relation to cognitive psychological and socio-cultural perspectives on children's mathematics learning.

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Cognitive change as strategy change

Cited by 9 publications

References 42 publications

The Development of Children's Adaptive Expertise in the Number Domain 20 to 100

The Development of Children's Adaptive Expertise in the Number Domain 20 to 100

The Self-Organization of Insight: Entropy and Power Laws in Problem Solving

Acquisition and use of shortcut strategies by traditionally schooled children

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