Subtraction by addition in children with mathematical learning disabilities

Peters, Greet; Smedt, Bert De; Torbeyns, Joke; Verschaffel, Lieven; Ghesquière, Pol

doi:10.1016/j.learninstruc.2013.11.001

Cited by 16 publications

(21 citation statements)

References 33 publications

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“…Students fared better with terms related to addition (e.g., sum) than with terms related to subtraction (e.g., difference). This result corroborates previous research in which students perform better on addition tasks than subtraction tasks (Canobi, 2004) and use addition to solve subtraction problems (Peters, De Smedt, Torbeyns, Verschaffel, & Ghesquière, 2014).…”

Section: Discussionsupporting

confidence: 91%

An Investigation of the Mathematics-Vocabulary Knowledge of First-Grade Students

Powell

Nelson

2017

The Elementary School Journal

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Competency with mathematics requires use of numerals and symbols as well as an understanding and use of mathematics vocabulary (e.g., add, more, triangle). Currently, no measures exist in which the primary function is to gauge mathematics-vocabulary understanding. We created a 64-item mathematics-vocabulary measure for first grade and piloted the assessment with 104 first-grade students. We also administered standardized measures of general word knowledge and mathematics fluency to investigate the validity of the mathematics-vocabulary measure. Results indicated a wide variability in how first-grade students interpret mathematics-vocabulary terms but strong reliability for the mathematics-vocabulary measure.

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Section: Discussionsupporting

confidence: 91%

An Investigation of the Mathematics-Vocabulary Knowledge of First-Grade Students

Powell

Nelson

2017

The Elementary School Journal

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“…The results of the present study are in line with previous findings on low achievers' subtraction by addition strategy use (Peltenburg et al, 2012;Peters, De Smedt, Torbeyns, Ghesquière, & Verschaffel, 2014). They also complement and extend these findings by using a choice/no-choice method that systematically addresses this strategy's occurrence, frequency and efficiency and by applying a more complex definition of strategy flexibility as fitting strategy choices to both item and strategy performance characteristics.…”

Section: Subtraction By Addition 228supporting

confidence: 90%

Subtraction by addition strategy use in children of varying mathematical achievement level: A choice/no-choice study

et al. 2018

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We investigated the use of the subtraction by addition strategy, an important mental calculation strategy in children with different levels of mathematics achievement. In doing so we relied on Siegler’s cognitive psychological model of strategy change (Lemaire & Siegler, 1995), which defines strategy competencies in terms of four parameters (strategy repertoire, distribution, efficiency and selection), and the choice/no-choice method (Siegler & Lemaire, 1997), which is essentially characterized by offering items in two types of conditions (choice and no-choice). Participants were 63 11-12-year-olds with varied mathematics achievement levels. They solved multi-digit subtraction problems in the number domain up to 1,000 in one choice condition (choice between direct subtraction or subtraction by addition on each item) and two no-choice conditions (obligatory use of either direct subtraction or subtraction by addition on all items). We distinguished between two types of subtraction problems: problems with a small versus large difference between minuend and subtrahend. Although mathematics instruction only focused on applying direct subtraction, most children reported using subtraction by addition in the choice condition. Subtraction by addition was applied frequently and efficiently, particularly on small-difference problems. Children flexibly fitted their strategy choices to both numerical item characteristics and individual strategy speed characteristics. There were no differences in strategy use between the different mathematical achievement groups. These findings add to our theoretical understanding of children’s strategy acquisition and challenge current mathematics instruction practices that focus on direct subtraction for children of all levels of mathematics achievement.

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“…A good understanding of the numbers in terms of their magnitudes can be helpful for choosing an efficient calculation strategy (e.g. 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).…”

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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625

551

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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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Subtraction by addition in children with mathematical learning disabilities

Cited by 16 publications

References 33 publications

An Investigation of the Mathematics-Vocabulary Knowledge of First-Grade Students

An Investigation of the Mathematics-Vocabulary Knowledge of First-Grade Students

Subtraction by addition strategy use in children of varying mathematical achievement level: A choice/no-choice study

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

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