Elwin Savelsbergh
University of Twente, Enschede, The Netherlands
and Eindhoven University of Technology, Eindhoven, The Netherlands.
Email: E.R.Savelsbergh@tm.tue.nl
Introducing a computer algebra system (CAS) in a -physics- tutorial is not a straightforward issue. To start with, a primary concern should be to determine what the educational goals are, and how a CAS could help in attaining these goals. Among the goals that could be possibly achieved by employing a computer algebra system are: envisioning problems, stressing the precise specification of problems, and stressing the choice of a solution approach instead of spending too much effort on working out the small steps involved in working out a problem. Secondly, a CAS as such will not provide much guidance to the learner, thus there is a need for exercises, assignments, examples etc. and these are different from the ones used in a traditional tutorial. Since we do not wish the learners to spend all their attention on finding out how to type in the next command to the CAS, it is necessary to present all required commands and syntax in examples, without, of course, giving away the -physical- clue of the following exercises.
We have implemented some modules of a course on electrostatics in Mathematica 3.0. We tested these modules with a sample of first-year physics students who had already taken a short course in Mathematica. One group of students spent about 7 hours working with the computerised modules. A second group of students spent the same amount of time working on the same topics using paper and pencil only. Both groups worked under the guidance of a tutor. We compared the learning outcomes between both groups for quantitative computation tasks and for more intuitive tasks. Results indicate that for the weaker students in particular working with Mathematica places an extra burden on the learning process. In addition to measuring learning outcomes, we collected students' opinions about the course they had taken. The students indicated they liked the course. They tended to think that they had gained more insight into working with Mathematica than they had into electrostatics. They indicated, however, that during the course attention had shifted from Mathematica problems to physics problems. A major problem in using Mathematica as a problem solving tool appeared to lie in the way students deal with computer generated output: a much signalled pitfall was that the relative ease of generating a formula, combined with the ease of visualising the formula, is detrimental to the effort spent on understanding what the formula means. Likewise, with a Mathematica generated graph there is little urge to pay any attention to the order of magnitude of the quantities plotted along the axes.
In the present workshop we will discuss the possibilities and the limitations of the use of computer algebra systems in education, guided by the case study of our physics course.
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