Teaching Mathematics and Science to future teachers

I shall try not to waste too much time responding directly to Mr Philip Borg (The Sunday Times, October 24). It is quite pointless to argue constructively with a mathematics teacher who first announces to all and sundry that he has forgotten half of his university maths courses; reinforces this by stating that actually "most" of the mathematics he learnt after A-levels is irrelevant to his teaching and hence forgettable; and, in spite of this, he is enough of an expert to judge "far-fetched and pathetic" an example of a theorem which I pointed out as being relevant to teachers of mathematics.

At least, despite his disdain of knowledge of university-level mathematics, he realises that the greatest satisfaction a teacher can receive is the knowledge that he has instilled some love of the subject in his students. Good luck to him!

I shall try instead to address this question of subject content which teachers should have.

I must first emphasise that I do not intend to go into the current dispute of PGCE versus B.Ed., for a number of reasons. First of all, the tone in which this issue is being discussed is a throwback to days when the faculties of Arts and Science had been made extinct. This tone even includes slogans from that time, such as the one that final parts of the B.Sc. are devoted to specialisation or scientific research (and therefore irrelevant to teachers).

Secondly, I do not see the issue in the terms of one qualification against another. Certainly, neither I nor, if I am not mistaken, any of my colleagues have ever attacked the type or amount of pedagogical education given to teachers. Rather, it has been the amount of mathematics or science given to B.Ed. students which, almost periodically, comes under attack by persons like Mr Borg.

Ironically, it is the Faculty of Education which determines this amount and with which we collaborate so that we can teach it to future teachers. It is not forced on anyone and if they decide to reduce the subject content which we teach to B.Ed. students (which I am not aware they want to do, in spite of letters and articles such as those written by Mr Borg), then I suppose they are free to do so.

However, as persons interested in the well-being of our educational system (yes, we too are part of it!) we would voice our serious concern and warn of the sad consequences of such moves.

Thirdly, I want to restrict myself to the question of content matter because I want to write only on what I know a little about. Certainly, as a mere mathematician who, from Mr Borg's vantage point of self-confessed mathematical ignorance, would probably not even pass his own exams, I would not dare express opinions on topics outside my field. There are enough who would willingly follow such paths which others fear to tread.

So I shall address one simple question, maybe with variations: how much undergraduate mathematics should a future mathematics teacher know? I shall limit myself to mathematics and science in general not because I think that this issue should not be of prime concern also to other disciplines, but because, as I said, I only want to talk about the little I know.

First of all, some comments about the posing of the question itself are in order. I do not think that this question is generally asked by mathematics lecturers; rather, in my experience at least, it is often posed by those who teach pedagogy to future teachers.

Secondly, I find this question somewhat demeaning towards the teaching profession. We never really ask how much mathematics a physicist or an engineer, say, needs to know.

The emphasis of topics and the techniques learnt might vary from one profession to another, and constraints of time, for example, do exist (as they do for mathematicians themselves who would like to learn more mathematics), but deep down we accept that there is no natural mathematical boundary beyond which scientists should not venture. Yet this question, for some reason, is often posed for teachers of mathematics.

Finally, this question and similar considerations in other disciplines, is not an issue of survival of faculties or disputes between university academics, but should be of concern to everyone, not least because almost everybody has a son, daughter or other close relative at school.

So, in an attempt to put this somewhat ill-posed question in a better perspective I shall widen its scope by substituting science for mathematics and asking the question in this form. Who needs a stronger undergraduate scientific preparation: a science teacher, say, or an engineer, or a future scientist even? Asking this question might seem odd, since the obvious answer seems to be the scientist or the engineer. But let us look at the facts more closely.

A mathematics or a science teacher starting his or her career at, say, the age of 25, will be entrusted, for the next 35 years or so, to presenting science to future generations of pupils in a manner which captures their interest and also in synchronisation with concurrent developments in the field.

Just looking back merely at the technological advances in the past ten years should convince anyone that it would be rash to try to predict what new scientific ideas will emerge in the next 30 and, consequently, the changes that will be required in school curricula. So teachers do face an onerous task.

Now, scientists or engineers, by the very nature of their profession, generally find themselves in a working environment which, in itself, involves the person keeping up to date with developments in the field. However, science teachers, precisely because they are not scientists, do not have this advantage (this was quite well put by Mr Borg himself).

Teachers can and many do, of course, keep up to date by various means, such as reading relevant literature and attending refresher courses in subject content as well as teaching methods.

But where are the understanding of and the passion for the subject, which are required to sustain these efforts for so long, to spring from? In my opinion, this initial springboard should mainly be given by the scientific undergraduate preparation which the future teacher receives, and which generally coincides with the last time during which the future teacher is working in a scientific environment.

So I believe that future teachers of science or mathematics need to have a solid undergraduate scientific preparation no less than future scientists or engineers. This preparation includes not just the imparting of knowledge and love for the subject, but also the insight into how the bits and pieces of what initially looks like a jigsaw puzzle start to fit together.

I really believe that managing to avoid large parts of this undergraduate course can deprive a student from acquiring this insight, and force him or her to rely on memorisation rather than on understanding the subject.

At least, many ex-students like Ms Phaedra Agius, who also wrote last week, did gain this understanding and are grateful for it; so work which we did together with the Faculty of Education was not completely in vain. As she said, she happens to have been in the same course as Mr Borg. But it seems to me that they were living on different planets.

Professor Lauri is a member of the Department of Mathematics of the Faculty of Science of the University of Malta.