Subtraction by addition strategy use in children of varying mathematical achievement level: A choice/no-choice study
Author(s) / Creator(s)
Torbeyns, Joke
Peters, Greet
De Smedt, Bert
Ghesquière, Pol
Verschaffel, Lieven
Abstract / Description
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.
Keyword(s)
subtraction by addition multi-digit subtraction strategy flexibility model of strategy change choice/no-choice method mathematical achievement levelPersistent Identifier
Date of first publication
2018-06-07
Journal title
Journal of Numerical Cognition
Volume
4
Issue
1
Page numbers
215–234
Publisher
PsychOpen GOLD
Publication status
publishedVersion
Review status
peerReviewed
Is version of
Citation
Torbeyns, J., Peters, G., De Smedt, B., Ghesquière, P., & Verschaffel, L. (2018). Subtraction by addition strategy use in children of varying mathematical achievement level: A choice/no-choice study. Journal of Numerical Cognition, 4(1), 215–234. https://doi.org/10.5964/jnc.v4i1.77
-
jnc.v4i1.77.pdfAdobe PDF - 286.61KBMD5: 5f74b26e9f366b754fce3b84264c97aa
-
There are no other versions of this object.
-
Author(s) / Creator(s)Torbeyns, Joke
-
Author(s) / Creator(s)Peters, Greet
-
Author(s) / Creator(s)De Smedt, Bert
-
Author(s) / Creator(s)Ghesquière, Pol
-
Author(s) / Creator(s)Verschaffel, Lieven
-
PsychArchives acquisition timestamp2018-11-21T11:42:53Z
-
Made available on2018-11-21T11:42:53Z
-
Date of first publication2018-06-07
-
Abstract / DescriptionWe 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.en_US
-
Publication statuspublishedVersion
-
Review statuspeerReviewed
-
CitationTorbeyns, J., Peters, G., De Smedt, B., Ghesquière, P., & Verschaffel, L. (2018). Subtraction by addition strategy use in children of varying mathematical achievement level: A choice/no-choice study. Journal of Numerical Cognition, 4(1), 215–234. https://doi.org/10.5964/jnc.v4i1.77en_US
-
ISSN2363-8761
-
Persistent Identifierhttps://hdl.handle.net/20.500.12034/1284
-
Persistent Identifierhttps://doi.org/10.23668/psycharchives.1476
-
Language of contenteng
-
PublisherPsychOpen GOLD
-
Is version ofhttps://doi.org/10.5964/jnc.v4i1.77
-
Keyword(s)subtraction by additionen_US
-
Keyword(s)multi-digit subtractionen_US
-
Keyword(s)strategy flexibilityen_US
-
Keyword(s)model of strategy changeen_US
-
Keyword(s)choice/no-choice methoden_US
-
Keyword(s)mathematical achievement levelen_US
-
Dewey Decimal Classification number(s)150
-
TitleSubtraction by addition strategy use in children of varying mathematical achievement level: A choice/no-choice studyen_US
-
DRO typearticle
-
Issue1
-
Journal titleJournal of Numerical Cognition
-
Page numbers215–234
-
Volume4
-
Visible tag(s)Version of Record