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Encouraging versatile thinking in algebra using the computer
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Tall, David and Thomas, Michael. (1991) Encouraging versatile thinking in algebra using the computer. Educational Studies in Mathematics, Vol.22 (No.2). pp. 125147. ISSN 00131954

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Official URL: http://dx.doi.org/10.1007/BF00555720
Abstract
In this article we formulate and analyse some of the obstacles to understanding the notion of a variable, and the use and meaning of algebraic notation, and report empirical evidence to support the hypothesis that an approach using the computer will be more successful in overcoming these obstacles. The computer approach is formulated within a wider framework ofversatile thinking in which global, holistic processing complements local, sequential processing. This is done through a combination of programming in BASIC, physical activities which simulate computer storage and manipulation of variables, and specific software which evaluates expressions in standard mathematical notation. The software is designed to enable the user to explore examples and nonexamples of a concept, in this case equivalent and nonequivalent expressions. We call such a piece of software ageneric organizer because if offers examples and nonexamples which may be seen not just in specific terms, but as typical, or generic, examples of the algebraic processes, assisting the pupil in the difficult task of abstracting the more general concept which they represent. Empirical evidence from several related studies shows that such an approach significantly improves the understanding of higher order concepts in algebra, and that any initial loss in manipulative facility through lack of practice is more than made up at a later stage.
Item Type:  Journal Article 

Subjects:  L Education > LB Theory and practice of education Q Science > QA Mathematics 
Divisions:  Faculty of Social Sciences > Institute of Education 
Library of Congress Subject Headings (LCSH):  Algebra, Signs and symbols, Computers  Study and teaching, Variables (Mathematics) 
Journal or Publication Title:  Educational Studies in Mathematics 
Publisher:  Springer Netherlands 
ISSN:  00131954 
Official Date:  1991 
Volume:  Vol.22 
Number:  No.2 
Page Range:  pp. 125147 
Identification Number:  10.1007/BF00555720 
Status:  Peer Reviewed 
Access rights to Published version:  Open Access 
References:  Bogen J.E. 1969: ”The Other Side of the Brain: 2. An Appositional Mind”, Bulletin of the LosAngeles 
URI:  http://wrap.warwick.ac.uk/id/eprint/508 
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