The "Maths Labs"
The use of Mathematica in the chemistry department at Imperial College began in 1994. Then, as now, chemistry and mathematics staff cooperated in the design of the computer-based course materials and in the way they were implemented. In those days, however, we in the mathematics department had very much the dominant role in the authoring process. No doubt partly for that reason--partly, too, because of our brief as what was then a government-funded project--there is very little chemistry in those five-year-old materials. "Learn the mathematics here, then apply it in your other courses" was the--perhaps unspoken--model.
But we gradually became aware of a problem with this approach. Based on observations of the materials in use, and our reading in the educational research literature, we began to have doubts about whether an approach based exclusively on "learn, then apply" was the best we could do. Students find transferring knowledge from one area to another notoriously difficult, and although "learn, then apply" is valuable in higher education, indeed probably indispensable, we felt it was legitimate to wonder whether it was enough on its own. We began to look for ways of building in explicit links between mathematics and chemistry right from the start of the course, and we became convinced that Mathematica offered us a way of doing that--a way that compromised the integrity of neither discipline.
Briefly put, our idea was this. Explicitly linking mathematics and chemistry as you go along is difficult in general, because first-year students at the start of their courses rarely know enough mathematics for the exercise to be meaningful, and if they are restricted to trivial and contrived chemistry problems, the point is lost. However, if the students have at their disposal powerful mathematical software, then it is possible to give them access to problems of more intrinsic interest to the would-be chemist. In this paper, I report on our experience with the Mathematics Laboratories we have been running with this aim in mind.
The term Mathematics Laboratory was one we coined early on, but with hindsight one can see that it was something of a misnomer five years ago. Then, it was simply meant to suggest an approach to teaching that encouraged students to pose and to test conjectures. The usage has grown more apt with time, though, as we have introduced a measure of explicit scientific content into the first-year mathematics course in chemistry. For an important part of their time on the course, students work on problems that genuinely belong to the field of physical chemistry, but they bring mathematical and computational tools to bear on them.
Actually, various kinds of activity go on in the Maths Labs: learning how to use Mathematica, for instance, or performing statistical analyses of experimental data, to cite two examples I shall not be discussing at all in this paper. What I want to focus on here is what I have described in broad terms above: the study of chemical problems, with the help of Mathematica, to motivate and aid the learning of mathematical topics.
Converted by Mathematica September 30, 1999 [Next Page]