Modern Elementary CALCULUS: Assessment with Technology

Abstract

The easy availability of high-powered calculators and computer algebra systems has brought with it a number of implications for teaching and assessment of a modern elementary calculus unit. There has been little change in the list of topics to be covered in a one-semester unit but there needs to be a great deal of change in how these topics are approached and in how a student's understanding of the material is to be gauged. The approach taken by the so-called Reform Calculus is that, if at all possible, topics should be presented geometrically, numerically, analytically and verbally. However, it is very difficult to cover all of these aspects for each topic in the limited time usually available, particularly when the students involved have neither the requisite calculator/computer skills nor a sound grasp of precalculus concepts such as algebra and trigonometry.

We provide here a partial case study, using a first year tertiary elementary calculus unit we have recently taught. The students involved comprised a mixture of mature-age students and school leavers with a wide variety of mathematical backgrounds. They were also studying calculus as service unit for a number of different major programs. We used a Reform Calculus textbook and the students were expected to own and use a suitable highlight the difficulties involved both in teaching and in assessment and offer some solutions to these.