Introduction

Verschaffel, Lieven; Bryant, Peter; Torbeyns, Joke

doi:10.1007/s10649-012-9381-2

Cited by 14 publications

(5 citation statements)

References 31 publications

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“…Second, while our findings showed that children with better numerical magnitude processing ability performed better on both types of subtraction items, the role of numerical magnitude processing ability seemed to be more important in the IA-items, as indicated by the partial correlation analyses in which we controlled for the performance on the DS-items and vice versa, and by the direct comparison of these correlations. This could be explained by the fact that the flexible use of the indirect addition strategy requires a good understanding of the numerical magnitudes in the problem and their mutual relation (Baroody et al, 2009;Verschaffel et al, 2012). For example, the flexible use of the indirect addition strategy requires an appropriate estimation of the difference between minuend and subtrahend, on which children with better numerical magnitude ability may perform better.…”

Section: Discussionmentioning

confidence: 99%

“…Answer: 2", leads to a faster and less error-prone answer than the direct subtraction strategy "81 -70 = 11 and 11 -9 = 2" (De Smedt, Torbeyns, Stassens, Ghesquière, & Verschaffel, 2010;Peters, De Smedt, Torbeyns, Ghesquière, & Verschaffel, 2012;Torbeyns, De Smedt, Ghesquière, & Verschaffel, 2009b;Verschaffel et al, 2007;Woods, Resnick, & Groen, 1975). The meaningful and flexible use of this strategy requires a good understanding of the numerical magnitudes in the problem and their mutual relation (Baroody, Torbeyns, & Verschaffel, 2009;Verschaffel, Bryant, & Torbeyns, 2012), and, more particularly, an appropriate estimation of the difference between minuend and subtrahend.…”

Section: Mental Multi-digit Subtractionmentioning

confidence: 99%

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The association between children's numerical magnitude processing and mental multi-digit subtraction

et al. 2014

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Children apply various strategies to mentally solve multi-digit subtraction problems and the efficient use of some of them may depend more or less on numerical magnitude processing. For example, the indirect addition strategy (solving 72-67 as "how much do I have to add up to 67 to get 72?"), which is particularly efficient when the two given numbers are close to each other, requires to determine the proximity of these two numbers, a process that may depend on numerical magnitude processing. In the present study, children completed a numerical magnitude comparison task and a number line estimation task, both in a symbolic and nonsymbolic format, to measure their numerical magnitude processing. We administered a multi-digit subtraction task, in which half of the items were specifically designed to elicit indirect addition. Partial correlational analyses, controlling for intellectual ability and motor speed, revealed significant associations between numerical magnitude processing and mental multi-digit subtraction. Additional analyses indicated that numerical magnitude processing was particularly important for those items for which the use of indirect addition is expected to be most efficient. Although this association was observed for both symbolic and nonsymbolic tasks, the strongest associations were found for the symbolic format, and they seemed to be more prominent on numerical magnitude comparison than on number line estimation.

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Section: Discussionmentioning

confidence: 99%

Section: Mental Multi-digit Subtractionmentioning

confidence: 99%

The association between children's numerical magnitude processing and mental multi-digit subtraction

et al. 2014

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“…With this strategy, one can solve 81 − 79 very efficiently by determining how much needs to be added to 79 to make 81 (e.g., 79 + 1 = 80, 80 + 1 = 81, so the answer is 1 + 1 = 2). The use of the complementary addition Running head: SUBTRACTION BY ADDITION IN CHILDREN WITH MLD 4 operation on such problems can thus considerably facilitate the calculation process by reducing computational effort and increasing solution efficiency, i.e., fewer and/or smaller calculation steps, which lead faster to a correct answer (e.g., Heinze, Marschick, & Lipowsky, 2009;Verschaffel, Bryant, & Torbeyns, 2012). In contrast, for problems with a relatively small subtrahend compared to the difference, such as 81 − 2, the subtraction by addition strategy does not lead to fewer and/or smaller calculation steps.…”

Section: Introductionmentioning

confidence: 99%

Subtraction by addition in children with mathematical learning disabilities

Peters¹,

Smedt²,

Torbeyns³

et al. 2014

Learning and Instruction

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In the last decades, strategy variability and flexibility have become major aims in mathematics education. For children with mathematical learning disabilities (MLD), it is unclear whether the same goals can and should be set. Some researchers and policy makers advise to teach MLD children only one solution strategy, others advocate stimulating the flexible use of various strategies, as for typically developing children. To contribute to this debate, we investigated the use of the subtraction by addition strategy to mentally solve twodigit subtractions in children with MLD. We used non-verbal research methods to infer strategy use patterns, and found that MLD childrensimilar to their typically developing peersswitch between the traditionally taught direct subtraction strategy and subtraction by addition, based on the relative size of the subtrahend. These findings challenge typical special education classroom practices, which only focus on the routine mastery of the direct subtraction strategy.

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“…4. In the literature, such differences in solution strategies are associated with the long-term development of mathematical proficiency (Kilpatrick, Swafford, & Findel, 2001), and more specifically with the flexible/ adaptive use of the inverse relationship between addition and subtraction (Verschaffel, Bryant, & Torbeyns, 2012). Recent theoretical insights and empirical findings focus on the complexity, ambiguity, and longitudinal character of the constitution and use of this relationship over time.…”

Section: Paradigm Casementioning

confidence: 99%

Shortcomings of Mathematics Education Reform in The Netherlands: A Paradigm Case?

Gravemeijer

Bruin-Muurling

Kraemer³

et al. 2016

Mathematical Thinking and Learning

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This article offers a reflection on the findings of three PhD studies, in the domains of, respectively, subtraction under 100, fractions, and algebra, which independently of each other showed that Dutch students' proficiency fell short of what might be expected of reform in mathematics education aiming at conceptual understanding. In all three cases, the disappointing results appeared to be caused by a deviation from the original intentions of the reform, resulting from the textbooks' focus on individual tasks. It is suggested that this "task propensity", together with a lack of attention for more advanced conceptual mathematical goals, constitutes a general barrier for mathematics education reform. This observation transcends the realm of textbooks, since more advanced conceptual mathematical understandings are underexposed as curriculum goals. It is argued that to foster successful reform, a conscious effort is needed to counteract task propensity and promote more advanced conceptual mathematical understandings as curriculum goals.

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Introduction

Cited by 14 publications

References 31 publications

The association between children's numerical magnitude processing and mental multi-digit subtraction

The association between children's numerical magnitude processing and mental multi-digit subtraction

Subtraction by addition in children with mathematical learning disabilities

Shortcomings of Mathematics Education Reform in The Netherlands: A Paradigm Case?

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