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Iconicity in mathematical notation: commutativity and symmetry

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journal contribution
posted on 04.12.2020, 14:31 by Theresa WegeTheresa Wege, Sophie Batchelor, Matthew InglisMatthew Inglis, Honali Mistry, Dirk Schlimm
Mathematical notation includes a vast array of signs. Most mathematical signs appear to be symbolic, in the sense that their meaning is arbitrarily related to their visual appearance. We explored the hypothesis that mathematical signs with iconic aspects – those which visually resemble in some way the concepts they represent – offer a cognitive advantage over those which are purely symbolic. An early formulation of this hypothesis was made by Christine Ladd in 1883 who suggested that symmetrical signs should be used to convey commutative relations, because they visually resemble the mathematical concept they represent. Two controlled experiments provide the first empirical test of, and evidence for, Ladd’s hypothesis. In Experiment 1 we find that participants are more likely to attribute commutativity to operations denoted by symmetric signs. In Experiment 2 we further show that using symmetric signs as notation for commutative operations can increase mathematical performance.

Funding

Social Sciences and Humanities Research Council of Canada (SSHRC)

Research England, via a grant to the Centre for Mathematical Cognition

Loughborough University Summer Research Project Bursary

History

School

  • Science

Department

  • Mathematics Education Centre

Published in

Journal of Numerical Cognition

Volume

6

Issue

3

Pages

378 - 392

Publisher

PsychOpen

Version

VoR (Version of Record)

Rights holder

© The Authors

Publisher statement

This is an Open Access Article. It is published by PsychOpen under the Creative Commons Attribution 4.0 International Licence (CC BY). Full details of this licence are available at: https://creativecommons.org/licenses/by/4.0/

Acceptance date

16/09/2020

Publication date

2020-12-03

Copyright date

2020

ISSN

2363-8761

Language

en

Depositor

Ms Theresa Wege. Deposit date: 28 September 2020

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