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Procedural embodiment and magic in linear equations
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Nogueira de Lima , Rosana and Tall, David. (2008) Procedural embodiment and magic in linear equations. Educational Studies in Mathematics, Vol. 6 (No. 1). pp. 318. ISSN 00131954

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Official URL: http://dx.doi.org/10.1007/s1064900790860
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 processobject 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 ( 2013) 
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:  00131954 
Official Date:  January 2008 
Volume:  Vol. 6 
Number:  No. 1 
Page Range:  pp. 318 
Identification Number:  10.1007/s1064900790860 
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 
References:  Anderson, C.: 1997, Persistent errors in indices: a cognitive perspective. PhD Thesis 
URI:  http://wrap.warwick.ac.uk/id/eprint/479 
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