CALCULATORS AND COMPUTERS - TRAPS FOR THE UNWARY

Abstract

The advent of powerful calculators and computer algebra systems brought with it the promise of enormous change in the mathematics curriculum at the secondary and lower tertiary levels. There was the idea that, now that the hard, time-consuming graphing and calculation can be done by the calculator/computer, teachers could fit in so much more 'real mathematics'. In fact, the range of topics covered has not changed significantly. One reason for this is the need to spend time teaching students the judicious use of this powerful new technology. This is needed to combat the very real danger that students will happily accept whatever answers the technology gives them, which in many cases could be totally incorrect. The reasons for these wrong answers are many and varied. The easiest to cope with is when the message ERROR (or its equivalent) appears as a prompt. But what should the student do when a seemingly correct answer is produced? Our experience is that students will just accept the given answer. In this paper we consider some of the common pitfalls that arise in both teaching and assessment and discuss measures to avoid and/or redress these. Obvious ones are simple data entry and round-off errors, although the latter can be quite subtle. Less easy to detect are the errors that arise from the internal implementation of the particular algebra system used by the calculator or computer itself. We shall give illustrations here with examples from Scientific Notebook (which uses a MAPLE engine) but there will be corresponding examples for any of the many available calculating and graphing devices.