Nogueira de Lima , Rosana and Tall, David. (2008) Procedural embodiment and magic in linear equations. Educational Studies in Mathematics, Vol. 6 (No. 1). pp. 3-18. ISSN 0013-1954

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Abstract

How do students think about algebra? Here we consider a theoretical framework which builds from natural human functioning in terms of embodiment – perceiving the world, acting on it and reflecting on the effect of the actions – to shift to the use of symbolism to solve linear equations. In the main, the students involved in this study do not encapsulate algebraic expressions from process to object, they do not solve ‘evaluation equations’ such as by ‘undoing’ the operations on the left, they do not find such equations easier to solve than , and they do not use general principles of ‘do the same thing to both sides.’ Instead they build their own ways of working based on the embodied actions they perform on the symbols, mentally picking them up and moving them around, with the added ‘magic’ of rules such as ‘change sides, change signs.’ We consider the need for a theoretical framework that includes both embodiment and process-object encapsulation of symbolism and the need for communication of theoretical insights to address the practical problems of teachers and students.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics L Education > L Education (General)
Divisions:	Faculty of Social Sciences > Institute of Education
Library of Congress Subject Headings (LCSH):	Equations, Mathematics -- Study and teaching, Mathematical notation
Journal or Publication Title:	Educational Studies in Mathematics
Publisher:	Springer Netherlands
ISSN:	0013-1954
Date:	January 2008
Volume:	Vol. 6
Number:	No. 1
Page Range:	pp. 3-18
Identification Number:	10.1007/s10649-007-9086-0
Status:	Peer Reviewed
Access rights to Published version:	Restricted or Subscription Access
Funder:	Brazil. Coordenação do Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brazil. Ministério da Educação
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URI:	http://wrap.warwick.ac.uk/id/eprint/479

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