The association between numerical magnitude processing and mental versus algorithmic multi-digit subtraction in children

Linsen, Sarah; Verschaffel, Lieven; Reynvoet, Bert; Smedt, Bert De

doi:10.1016/j.learninstruc.2014.09.003

Cited by 33 publications

(18 citation statements)

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“…This latter advanced counting strategy requires a determination on the larger number and therefore draws on the comparison of numerical magnitudes. Similar comparison processes might play a role in more advanced mental calculation strategies, such as the flexible use of strategies in multi-digit subtraction (Linsen et al, 2015). The use of more advanced counting strategies further fosters the memorization of problem-answer associations in long-term memory, i.e., the development of arithmetic facts and these appear to be stored in long-term memory in a meaningful way that is according to their magnitude (e.g., Robinson, Menchetti, & Torgesen, 2002).…”

Section: Discussionmentioning

confidence: 99%

Symbolic magnitude processing in elementary school children: A group administered paper-and-pencil measure (SYMP Test)

2016

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The ability to compare symbolic numerical magnitudes correlates with children's concurrent and future mathematics achievement. We developed and evaluated a quick timed paper-and-pencil measure that can easily be used, for example in large-scale research, in which children have to cross out the numerically larger of two Arabic one-and two-digit numbers (SYMP Test). We investigated performance on this test in 1,588 primary school children (Grades 1-6) and examined in each grade its associations with mathematics achievement. The SYMP Test had satisfactory test-retest reliability. The SYMP Test showed significant and stable correlations with mathematics achievement for both one-digit and two-digit comparison, across all grades. This replicates the previously observed association between symbolic numerical magnitude processing and mathematics achievement, but extends it by showing that the association is observed in all grades in primary education and occurs for single-as well as multi-digit processing. Children with mathematical learning difficulties performed significantly lower on one-digit comparison and two-digit comparison in all grades. This all suggests satisfactory construct and criterionrelated validity of the SYMP Test, which can be used in research, when performing large-scale (intervention) studies, and by practitioners, as screening measure to identify children at risk for mathematical difficulties or dyscalculia.

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Section: Discussionmentioning

confidence: 99%

Symbolic magnitude processing in elementary school children: A group administered paper-and-pencil measure (SYMP Test)

2016

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“…Consequently, our results might reflect the previously demonstrated link between proficient symbolic numerical magnitude processing skills and successful arithmetic fact retrieval [ 9 ], [ 10 ], [ 38 ]. The link between symbolic numerical magnitude processing and multi-digit arithmetic might be less straightforward, depending on the type of procedure that is used to perform the calculation [ 39 ].…”

Section: Discussionmentioning

confidence: 99%

Symbolic Numerical Magnitude Processing Is as Important to Arithmetic as Phonological Awareness Is to Reading

et al. 2016

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In this article, we tested, using a 1-year longitudinal design, whether symbolic numerical magnitude processing or children’s numerical representation of Arabic digits, is as important to arithmetic as phonological awareness is to reading. Children completed measures of symbolic comparison, phonological awareness, arithmetic, reading at the start of third grade and the latter two were retested at the start of fourth grade. Cross-sectional and longitudinal correlations indicated that symbolic comparison was a powerful domain-specific predictor of arithmetic and that phonological awareness was a unique predictor of reading. Crucially, the strength of these independent associations was not significantly different. This indicates that symbolic numerical magnitude processing is as important to arithmetic development as phonological awareness is to reading and suggests that symbolic numerical magnitude processing is a good candidate for screening children at risk for developing mathematical difficulties.

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“…Peters, Smedt, Torbeyns, Verschaffel & Ghesqui ere, 2014). In contrast, written arithmetic merely requires learners to combine the two addends digit by digit by following a standard algorithm, and there is no need for mentally representing the magnitudes of the addends and the sum (Linsen, Verschaffel, Reynvoet & Smedt, 2015). Curriculumbased measures typically include a broad variety of mathematical skills, not all of which depend on numerical magnitude processing (Schneider et al, 2009).…”

Section: Implications Of the Findingsmentioning

confidence: 99%

Associations of non‐symbolic and symbolic numerical magnitude processing with mathematical competence: a meta‐analysis

Schneider

Beeres

Coban

et al. 2016

Developmental Science

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Many studies have investigated the association between numerical magnitude processing skills, as assessed by the numerical magnitude comparison task, and broader mathematical competence, e.g. counting, arithmetic, or algebra. Most correlations were positive but varied considerably in their strengths. It remains unclear whether and to what extent the strength of these associations differs systematically between non-symbolic and symbolic magnitude comparison tasks and whether age, magnitude comparison measures or mathematical competence measures are additional moderators. We investigated these questions by means of a meta-analysis. The literature search yielded 45 articles reporting 284 effect sizes found with 17,201 participants. Effect sizes were combined by means of a two-level random-effects regression model. The effect size was significantly higher for the symbolic (r = .302, 95% CI [.243, .361]) than for the non-symbolic (r = .241, 95% CI [.198, .284]) magnitude comparison task and decreased very slightly with age. The correlation was higher for solution rates and Weber fractions than for alternative measures of comparison proficiency. It was higher for mathematical competencies that rely more heavily on the processing of magnitudes (i.e. mental arithmetic and early mathematical abilities) than for others. The results support the view that magnitude processing is reliably associated with mathematical competence over the lifespan in a wide range of tasks, measures and mathematical subdomains. The association is stronger for symbolic than for non-symbolic numerical magnitude processing. So symbolic magnitude processing might be a more eligible candidate to be targeted by diagnostic screening instruments and interventions for school-aged children and for adults.

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The association between numerical magnitude processing and mental versus algorithmic multi-digit subtraction in children

Cited by 33 publications

References 36 publications

Symbolic magnitude processing in elementary school children: A group administered paper-and-pencil measure (SYMP Test)

Symbolic magnitude processing in elementary school children: A group administered paper-and-pencil measure (SYMP Test)

Symbolic Numerical Magnitude Processing Is as Important to Arithmetic as Phonological Awareness Is to Reading

Associations of non‐symbolic and symbolic numerical magnitude processing with mathematical competence: a meta‐analysis

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