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ERIC Number: EJ785270
Record Type: Journal
Publication Date: 2008-Jan
Pages: 16
Abstractor: Author
Reference Count: 0
ISBN: N/A
ISSN: ISSN-0013-1954
Procedural Embodiment and Magic in Linear Equations
de Lima, Rosana Nogueira; Tall, David
Educational Studies in Mathematics, v67 n1 p3-18 Jan 2008
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 3x + 2 = 8 by "undoing" the operations on the left, they do not find such equations easier to solve than 3x - 1 = 3 + x, 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.
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Publication Type: Journal Articles; Reports - Evaluative
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A