Over the years the pages of this magazine have been used as a vehicle for criticising many of the departments of this university. Those in the science faculty however seem to have remained immune from these attacks, indicating that either the departments in this faculty have reached a level of perfection yet to be realised in the arts faculty, or, as seems more likely, that the critical faculties of science students have long since atrophied, allowing many departments to retain teaching and assessment procedures long outmoded.

Here the Mathematics department will be briefly examined. It is not the worst offender in the matter of poor teaching methods, for over recent years the department has not only been involved in course-evaluation, but the appearance of the Keller plan based courses indicates a more positive response to these evaluations than is usually found in this faculty. Therefore it is particularly important to stimulate some student discussion of the department's teaching programme as, with typical apathy, students have been far behind staff in both ideas and criticisms, and it is crucial that they raise themselves from their textbooks and become more actively involved with the changes around them.

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.

The Response

The department's response to these problems has been to introduce the "Keller plan" system, the two-year trial period in the Math 205 course now augmented to include Math 115. This is a little hard to fathom. Either the trial in Math 205 vindicated the scheme, in which case why does it not see much wider application, or it did not, in which case it should be scrapped. It seems hard to believe that after a two-year trial a definite decision has not been reached.

The Keller Plan appears to counter arguments about the imappropriability of lectures by eliminating them altogether, the material being presented in modules including a comprehensive range of exercises designed to increase familiarity with the material. By replacing one big exam with a series of little tests many of the arguments regarding one-off exams are also countered.

Unfortunately for all its strengths the system has some major failings. As it stands stands at present, maximum benefit from the system depends strongly upon a regular series of tutorials, where hopefully the bulk of the learning would take place in a group situation However last year in

Math 205 the tutorials were very poorly patronised, the majority of students preferring to work completely on their own or in groups of friends. Part of the reason for this failure may have been the tutors' inability to fulfil the role which the students page 7 asked of them.

Questions requiring a simple yes-no answer were met by involved and tortuous explanation while those which revealed a fundamental lack of understanding received the "put this here, that there — bingo!" type of response. Basically the tutorials failed because the department did not realise that this type of teaching approach requires more staff time combined with more aware and sympathetic tutoring of a kind not required in the mass-production lecture based courses. Hopefully this type of problem will gradually disappear as both staff and students become more aware of the strengths and weaknesses of the system.

Further Problems

The Keller Plan has however another class of problem altogether which must be resolved before its full benefit can be realised. The assessment procedure adopted at present involves a very cunning blending of quantity and quality of work which in theory should provide a very fair indication of progress. The trend which developed last year in Math 205 spoilt this idea somewhat, as the crafty students realised that a large amount of work done indifferently rated more highly than a lesser amount performed with greater care. Thus many students completed the course without having come fully to terms with some of its fundamental ideas.

I have not been able to find out whether the course content of the Linear Algebra component of the Math 205 course increased with the introduction of the Keller Plan, but it seems likely that some of the latter modules include additional material. This is not surprising as the course offers a heaven-sent opportunity for including material not normally offered in undergraduate courses.

In a less success-oriented environment no great harm would have resulted but perhaps those who designed the course forgot to allow for the "Average Student Philosophy" (for which the university must accept much of the blame as it seems an inevitable by-product of the type of tertiary institutions we are at present blessed with). In this one must seek the highest mark possible for the minimum amount of effort expended.

The most obvious solution to the problem would be to reduce the number of modules so that students who wished to do the lot would be able to without feeling the necessity of tearing hell - for - leather through them to get to the end and secure a good grade for the course.

Conclusion

Faults and all though, the Keller Plan must be welcomed as a tremendous improvement over the traditional teaching methods so widely practiced at this university. A wider field of application, at least throughout the Mathematics department if not through the whole science faculty, is to be hoped for.

The main method of assessing courses in this department has been through questionnaires prepared by the Teaching and Research Centre, which, while fulfiling a valuable role sometimes fail. Questionnaires can omit important questions and tend to concentrate on the mechanics of courses rather than on their basic strengths and weaknesses. Salient is an ideal vehicle for more student-oriented criticism. It remains to be seen whether students can be bothered to take advantage of it.

Peter Beach