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Teaching using contextualised and decontextualised representations: examining the case of differential calculus through a comparative judgement technique

journal contribution
posted on 07.01.2020 by Marie-Josée Bisson, Camilla Gilmore, Matthew Inglis, Ian Jones
An ongoing debate concerns whether novel mathematical concepts are better learned using contextualised or decontextualised representations. A barrier to resolving this debate, and therefore to progress in the discipline, has been the paucity of validated methods of measuring students’ understanding of mathematical concepts. We developed an innovative and efficient method for measuring, in experimental settings, students’ understanding of any mathematical concept using comparative judgement. We demonstrate the method by applying it to the comparison of learning outcomes from two teaching conditions. Participants (260 15-16 year olds across six schools) were introduced to differential calculus using contextualised or decontextualised representations. We then assessed participants’ comparative conceptual understanding of derivatives. We found evidence that contextualised and decontextualised representations were equally effective at promoting student learning in this context. The assessment method yielded valid and reliable results, suggesting that it offers a robust and efficient approach for the problem of assessing conceptual understanding in experimental or other comparative settings

Funding

Nuffield Foundation grant

Royal Society Dorothy Hodgkin Research Fellowship

Royal Society Worshipful Company of Actuaries Research Fellowship

History

School

  • Science

Department

  • Mathematics Education Centre

Published in

Research in Mathematics Education

Pages

1 - 20

Publisher

Taylor and Francis

Version

AM (Accepted Manuscript)

Rights holder

© British Society for Research into Learning Mathematics

Publisher statement

This is an Accepted Manuscript of an article published by Taylor & Francis in Research in Mathematics Education on 18 Dec 2019, available online: https://doi.org/10.1080/14794802.2019.1692060.

Acceptance date

04/11/2019

Publication date

2019-12-18

Copyright date

2019

ISSN

1479-4802

eISSN

1754-0178

Language

en

Depositor

Dr Ian Jones . Deposit date: 2 January 2020

Exports