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Salient. Newspaper of Victoria University of Wellington Students Association. Vol 41 No. 3. March 13 1978

The Particular Problems

The Particular Problems

The teaching of mathematics presents a range of problems different from those encountered in most science subjects. Trapped to some extent by its importance as a service subject for other fields of science, the teaching of mathematics seems to have resolved itself into the teaching of a problem-solving skill. This is not a bad thing in itself, indeed it adds a challenging new dimension to mathematics which the other sciences lack.

Sadly it has only recently been realised that sitting in a lecture theatre observing the dexterity with which lecturers solve problems is neither an efficient nor effective method by which students can aquire those same skills. The problem being that to identify the problem and then find the "dodge" which will resolve the matter can only be grasped through personal experience (will watching pot-black teach you to play snooker?).

Nor are the assessment procedures likely to give a true indication of ability and understanding. While the argument that, if one is truly conversant with a theory, one should be able to expound it in most circumstances(although whether these circumstances include the unnatural stint at an examination desk is unclear), will apply to most other sciences, in a mathematics examination it is the rapidity of one's aquired problem-solving skills which is examined. The kernel of any mathematics problem is that "flash of inspiration" (too pretentious perhaps!) which enables one to see how to attack the problem, after which it becomes a mere exercise in algebraic manipulation.

Many students will have had the experience of puzzling over a problem and rapidly getting nowhere, finally giving up, taking a break and returning to find the answer just sitting there. For some reason this is assumed not to happen in an examination. It would seem that in addition to the general flaws in examinations, those in mathematics have an additional factor (one could almost call it luck) which makes their results a very dubious guide indeed.