Tall, David and Thomas, Michael (1991) Encouraging versatile thinking in algebra using the computer. Educational Studies in Mathematics, Vol.22 (No.2). pp. 125-147. doi:10.1007/BF00555720 ISSN 0013-1954.

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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 non-examples of a concept, in this case equivalent and non-equivalent expressions. We call such a piece of software ageneric organizer because if offers examples and non-examples 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 ( -2013)
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:	0013-1954
Official Date:	1991
Dates:	Date Event 1991 Published
Volume:	Vol.22
Number:	No.2
Page Range:	pp. 125-147
DOI:	10.1007/BF00555720
Status:	Peer Reviewed
Access rights to Published version:	Open Access (Creative Commons)

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