Using Computer Algebra Systems in Secondary School Mathematics: Issues of Curriculum, Assessment and Teaching.

Abstract

In 2002, a group of students in Victoria, Australia, studied a final year secondary mathematics course for university entrance that permitted use of a computer algebra system (CAS) for the first time. In this paper, I will summarise the changes to curriculum, assessment and teaching that occurred. The curriculum, which is set by the state, was designed to parallel a subject allowing only graphics calculators. Some additional material was added and other topics were extended by taking a more general approach. Although it is easy to over-estimate the time that will be freed when students have CAS to support learning routine skills, teachers were able to cover topics more quickly. The four teachers adopted quite different teaching styles with CAS, although they all stressed by-hand procedures as the basis of understanding. I will illustrate some of the new practices that emerged. Teachers spent time developing students' appreciation of judicious use of CAS and the algebraic insight that is needed to deal with the sometimes surprising answers provided by the machine. Students need to know a lot of algebra to use CAS beyond very routine tasks. The final examination assessment needed very careful design, especially to ensure that users of different CAS were treated equitably. Students omitted fewer questions than is normally the case. They used CAS very widely in the examinations, more than their teachers expected and for purposes which had not been expected. These findings will be illustrated by examples of students' work. In summary, the trial was a success and is expanding to more schools. Further details are available from the project website http://www.edfac.unimelb.edu.au/DSME/CAS-CAT.