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

Torbeyns, Joke; Verschaffel, Lieven; Ghesquière, Pol

doi:10.1207/s1532690xci2404_2

Cited by 53 publications

(53 citation statements)

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“…The finding that children with higher mathematical achievement levels used shortcut strategies more often than their lower achieving peers supports this idea. Moreover, they add to the body of literature questioning the desirability and feasibility of striving for adaptivity and flexibility for low mathematics achievers (e.g., Fagginger Auer et al 2016a; Torbeyns et al 2006), although there are studies showing promising results (e.g., Peltenburg et al 2012). Several scholars argue that low mathematics achievers might benefit from instruction in a single strategy instead of multiple strategies ( Further research into the levels of flexibility and adaptivity low mathematical achievers can obtain in different domains and under different (instructional) conditions are necessary, to provide insights into the feasibility of fostering flexibility and adaptivity for students of all levels of mathematical competence.…”

Section: Discussionmentioning

confidence: 99%

“…Second, to which extents do the student factors gender and general mathematics achievement level affect the likelihood to use shortcut strategies? We hypothesized that boys are more inclined to use shortcut strategies than girls (e.g., Blöte et al 2001;, and that students with higher mathematics achievement level are more likely to use shortcut strategies than students with lower level achievement (Heinze et al 2009;Torbeyns et al 2006). Third, to what extent does stimulating the use of shortcut strategies by providing an explicit instruction to "have a close look at the numbers and use a clever strategy" increase shortcut strategy use?…”

Section: Current Studymentioning

confidence: 99%

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Dutch sixth graders’ use of shortcut strategies in solving multidigit arithmetic problems

Hickendorff

2017

Eur J Psychol Educ

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Strategy flexibility, adaptivity, and the use of clever shortcut strategies are of major importance in current primary school mathematics education worldwide. However, empirical results show that primary school students use such shortcut strategies rather infrequently. The aims of the present study were to analyze the extent to which Dutch sixth graders (12-year-olds) use shortcut strategies in solving multidigit addition, subtraction, multiplication, and division problems, to what extent student factors and task instructions affected this frequency of shortcut strategy use, and to what extent the strategies differed in performance. A sample of 648 sixth graders from 23 Dutch primary schools completed a paper-and-pencil task of 12 multidigit arithmetic problems, designed to elicit specific shortcut strategies such as compensation. Based on the students' written work, strategies were classified into whether a shortcut strategy was used or not. Results showed that the frequency of shortcut strategies ranged between 6 and 21% across problem types, and that boys and high mathematics achievers were more inclined to use shortcut strategies. An explicit instruction to look for a shortcut strategy increased the frequency of these strategies in the addition and multiplication problems, but not in the subtraction and division problems. Finally, the use of shortcut strategies did not yield higher performance than using standard strategies. All in all, spontaneous as well as stimulated use of shortcut strategies by Dutch sixth graders was not very common.

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Section: Discussionmentioning

confidence: 99%

Section: Current Studymentioning

confidence: 99%

Dutch sixth graders’ use of shortcut strategies in solving multidigit arithmetic problems

Hickendorff

2017

Eur J Psychol Educ

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“…Its roots can be found in the seminal work of Krutetskii (1976) and Wertheimer (1959), and for years it has been considered an important element of adaptive expertise (Baroody & Dowker, 2003;Hatano & Inagaki, 1986). More recently, it has received significant attention from European researchers, who have been interested in children's flexibility with arithmetic (Blöte, Klein, & Beishuizen, 2000;Blöte, Van der Burg, & Klein, 2001;Klein, Beishuizen, & Treffers, 1998;Torbeyns, Verschaffel, & Ghesquiere, 2006;Verschaffel, Luwel, Torbeyns, & Van Dooren, 2007). Perhaps because of these varying interests, definitions of flexibility have also varied.…”

Section: Exploring the Development Of Flexibility In Struggling Algebmentioning

confidence: 99%

Understanding the Development of Flexibility in Struggling Algebra Students

Newton

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Lynch

2010

Mathematical Thinking and Learning

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The ability to flexibly solve problems is considered an important outcome for school mathematics and is the focus of this paper. The paper describes the impact of a three-week summer course for students who struggle with algebra. During the course, students regularly compared and contrasted worked examples of algebra problems in order to promote flexible use of solution strategies. Assessments were designed to capture both knowledge and use of multiple strategies. The students were interviewed in order to understand their rationales for choosing particular strategies, as well as their attitudes toward instruction that emphasized multiple strategies. Findings suggest that students gained both knowledge of and appreciation for multiple strategies, but they did not always use alternate strategies. Familiarity, understandability, efficiency, and form of the problem were all considerations for strategy choice. Practical and theoretical implications are discussed.

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“…Complex Mulken, 1997; Blöte, Klein, & Beishuizen, 2000;Lucangeli, Tressoldi, Bendotti, Bonanomi, & Siegel, 2003;Torbeyns, Verschaffel, & Ghesquière, 2006; reviewed by Varol & Farran, 2007).…”

mentioning

confidence: 99%

Cultural differences in complex addition: Efficient Chinese versus adaptive Belgians and Canadians.

Imbo

LeFevre

2009

Journal of Experimental Psychology: Learning, Memory, and Cogni

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In the present study, the authors tested the effects of working-memory load on math problem solving in 3 different cultures: Flemish-speaking Belgians, English-speaking Canadians, and Chinese-speaking Chinese currently living in Canada. Participants solved complex addition problems (e.g., 58 ϩ 76) in no-load and working-memory load conditions, in which either the central executive or the phonological loop was loaded. The authors used the choice/no-choice method to obtain unbiased measures of strategy selection and strategy efficiency. The Chinese participants were faster than the Belgians, who were faster and more accurate than the Canadians. The Chinese also required fewer working-memory resources than did the Belgians and Canadians. However, the Chinese chose less adaptively from the available strategies than did the Belgians and Canadians. These cultural differences in math problem solving are likely the result of different instructional approaches during elementary school (practice and training in Asian countries vs. exploration and flexibility in non-Asian countries), differences in the number language, and informal cultural norms and standards. The relevance of being adaptive is discussed as well as the implications of the results in regards to the strategy choice and discovery simulation model of strategy selection (J. Shrager & R. S. Siegler, 1998).

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

Cited by 53 publications

References 24 publications

Dutch sixth graders’ use of shortcut strategies in solving multidigit arithmetic problems

Dutch sixth graders’ use of shortcut strategies in solving multidigit arithmetic problems

Understanding the Development of Flexibility in Struggling Algebra Students

Cultural differences in complex addition: Efficient Chinese versus adaptive Belgians and Canadians.

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