The Algebraic Calculator and Mathematics Education

This paper describes the recent development of hand-held algebraic calculators and evaluates their significance for secondary education. Sophisticated computer algebra systems (CAS) have been available to mathematicians for some years now but have been too powerful, too sophisticated and too expensive and have required too much access to powerful computers to have had much impact on teaching and learning elementary algebra and calculus. Unlike CAS, algebraic calculators have been developed to meet the needs mathematics students rather than those of mathematicians, scientists and engineers. Access to an algebraic calculator will allow students to deal with all of the symbolic manipulation demands of the conventional secondary school algebra and calculus curriculum. The implications of such access for the mathematics curriculum, teaching methods, assessment and the professional development of teachers are discussed in the paper. Alternative ways of regulating access to and controlling the use of algebraic calculators are discussed, together with the desirability of doing so. Parallels are drawn between the significance of the algebraic calculator for the secondary school and of the arithmetic calculator for the elementary school. Introduction The idea of using computer technology for symbolic manipulation purposes is not a new one. Useful and powerful software that could deal with the more routine aspects of algebra and calculus first appeared in the 1970's on mainframe computers and were available on microcomputer platforms by the late 1970's and early 1980's. Since then, such software has developed considerably in sophistication, usability and the range of capabilities. Indeed, from the outset of the Asian Technology Conference on Mathematics four years ago, computer algebra systems (CAS) such as Maple and Mathematica (among others) have featured prominently on the conference programs. For the most part, interest in CAS has been strongest among research mathematicians and senior undergraduates, as well as computer scientists interested in how such software is optimally designed. The same conference programs have included papers concerned with graphics calculators, arguably of increasing importance to mathematics education because of their potential accessibility to secondary school students as well as early undergraduates. (Kissane, 1995). It is now often stated that a graphics calculator is also a computer, albeit a relatively small, inexpensive and limited one. The present paper is an attempt to summarize how much the gap has closed between CAS and graphics calculators with the development of