The Influence of a Computer Algebra Environment on Teachers’ Practice

Using a computer algebra system (CAS) in the classroom provides many opportunities for improving student learning. However, to take advantage of such a powerful instrument as CAS requires changes to many aspects of the classroom. The different ways in which three pioneering Australian teachers adapted their teaching to use CAS are described (see also Appendix 4-1, for a comparison with similar experiences in other countries). Two of the teachers taught an eight-week course in each of two consecutive years (the CAS-Calculus project) at secondary school level, using a symbolic calculator. They gave CAS different roles in the instruction and in defining their curriculum goals. One teacher used CAS in a restricted way with the primary goal of increasing understanding while the second teacher adopted CAS as another technique freely available for solving standard problems and emphasized efficient routines. Over several years (in a separate project, at university level, using the computer program DERIVE), the third teacher has evolved a method of teaching with CAS, moving from an early emphasis on teaching about CAS as a tool and using it for difficult problems to incorporating its use for primarily pedagogical aims. In reporting on these case studies we comment on different ways of organising the classroom; the variety in approaches to teaching the use of CAS; the increased range of methods for solving problems and for teaching; the contrast between using graphics and symbolic calculators; the place of paper-and-pencil skills; devoting time to mathematics or technology; and finally the curriculum and assessment changes required in schools.