Using CAS to Enrich the Teaching and Learning of Mathematics

Abstract

Computer Algebra Systems (CAS) are powerful tools for both doing and learning mathematics. They may be used to perform algorithmic routines both quickly and correctly but harnessing this power in a manner which is effective for promoting learning is not trivial. Research undertaken with both secondary school and undergraduate students clearly indicates that, while students quickly come to appreciate the availability of CAS to check their answers, several key factors influence the development of their use of the facility of CAS to extend both access to mathematics and support learning of mathematical concepts. First the institutional value which the technology is afforded influences the degree to which students are willing to apply themselves to the task of learning technical skills necessary to work with CAS. Second, the use of multiple representations may both increase students’ conceptual understanding and provide them with alternative methods through which to progress solution of problems. Finally students need to be guided in judicious use of CAS. This will involve teaching students to be discriminating in their use of technology for functional purposes, that is to find solutions to difficult or time consuming problems, and strategic in their use of CAS to explore patterns and link representations in order to gain greater insight into mathematical processes and concepts.