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Title: A diagrammatic view of the equals sign: arithmetical equivalence as a means, not an end
Authors: Jones, Ian
Keywords: Equals sign
Arithmetic
Diagrammatic activity
Issue Date: 2008
Publisher: Routledge (© British Society for Research into Learning Mathematics)
Citation: JONES, I., 2008. A diagrammatic view of the equals sign: arithmetical equivalence as a means, not an end. Research in Mathematics Education, 10 (2), pp. 151-165.
Abstract: It is recommended in the mathematics education literature that pupils be presented with equality statements that can be assessed for numerical balance by attending to notational structure rather than computation. I describe an alternative, diagrammatic approach in which pupils do not assess statements but instead use them to make substitutions of notation. I report on two trials of a computer-based task conducted with pairs of pupils and highlight two findings. First, the pupils found it useful to articulate the distinct substitutive effects of commutative (‘swap’, ‘switch’) and partitional (‘split’, ‘separate’) statements when working on the task. Secondly, the pupils did not notice that some of the statements presented were in fact false, which suggests their substituting activities were independent of numerical equivalence conceptions. This demonstrates that making substitutions offers task designers a mathematical utility for equality statements that is distinct from, but complementary to, assessing numerical balance.
Description: This article was published in the journal, Research in Mathematics Education [Routledge/Taylor & Francis © British Society for Research into Learning Mathematics] and the original publication is available at http://www.tandfonline.com/loi/rrme20
Version: Accepted for publication
DOI: 10.1080/14794800802233688
URI: https://dspace.lboro.ac.uk/2134/8588
Publisher Link: http://dx.doi.org/10.1080/14794800802233688
ISSN: 1479-4802
1754-0178
Appears in Collections:Published Articles (Mathematics Education Centre)

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