RME2008_preprint[1].pdf (282.99 kB)
Download file

A diagrammatic view of the equals sign: arithmetical equivalence as a means, not an end

Download (282.99 kB)
journal contribution
posted on 07.07.2011, 11:15 authored by Ian Jones
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.

History

School

  • Science

Department

  • Mathematics Education Centre

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.

Publisher

Routledge (© British Society for Research into Learning Mathematics)

Version

AM (Accepted Manuscript)

Publication date

2008

Notes

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

ISSN

1479-4802;1754-0178

Language

en

Usage metrics

Categories

Exports