Guest Editorial: Computers in Mathematics

Transcribed from the printed issue; not yet reviewed. Read it in the PDF of the issue, page 3

APL is quite simply the best programming language for teaching mathematics. This is the claim which we made last July to promote the teachers' course, and which I-APL will make again to support its campaign for APL to become an everyday language in schools and colleges.

While few readers of this magazine will wish to contest the generalities of this claim, the onus of proof is on APL supporters to explain to the as yet unpersuaded mathematical world not just the fact of the claim, but its practice: that is how in the classroom and the maths lab APL can be applied to make mathematical education more effective and what are its special qualities that put it way ahead of other programming languages for this purpose.

A symposium held at Strasbourg in 1985 by the International Council for Mathematical Instruction was devoted to the influence of computers in Mathematics and its teaching. At this conference no whisper of APL was heard, a situation which strenuous efforts will be made to rectify at the next ICMI conference in Budapest this coming July.

A selection of papers from the Strasbourg conference has been published by Cambridge University Press with Professors A.G. Howson and J.P. Kahane as editors. It costs £6.50, and is recommended to anyone for whom the combination of computers and mathematics teaching is a concern. Some fascinating issues are considered, e.g. would a present day Newton or Gauss be beguiled by computers to the detriment of mankind. A real danger is that the mindless execution of computers becomes a substitute for hard thinking, and the challenge is that of providing a powerful tool, which does not become, in Professor Burkhardt's words, "a net absorber of effort and attention". Surely this is where APL has an answer in providing a resource which is as natural to mathematicians as pencil and paper.

We must not of course behave as if computers addressed all parts of the mathematical curriculum equally. On reading the above book one is struck by the emphasis on symbolic mathematics as exemplified by the packages MACSYMA and MUMATH, the latter of which is well within school budgets. Of course what APL offers is much more, but at least APL people should be sensitive to what is seen as the perceived need by the mathematical educators themselves.

Investigation and exploration are other areas in which the application of APL is to the APL enthusiast "obvious", but the practical realities of accommodating teaching style to embrace the possibilities is quite another matter - how to effect the change in "classroom dynamics" that the micro as "teaching assistant" demands.

A forthcoming Open University course (M371 - Computational Mathematics) addresses this problem for the distance learning student. The accompanying software has two components; the first uses the Amstrad micro as a tutor, and the second is a mathematics package in the accepted sense. This may well be the first attempt at such a software combination on this scale, and it certainly merits scrutiny beyond that of the immediate course population.

Ultimately computers in mathematics will only be valuable to the extent that they provide a bridge to the abstract thinking which is the true substance of mathematics. While the availability of APL in schools is to be welcomed, the real educational challenges are only now about to begin.