Content knowledge for mathematics teachers

Mr Philip Borg (The Sunday Times, October 10) sounds almost pleased that he has forgotten half of the mathematics he has learnt at University. This is no mean feat, especially for a mathematics teacher who has also taught up to A-level, and quite successfully, by his own reckoning. It is no wonder that he also managed to forget in which Faculty the "Department of Mathematics" resides.

But if Mr Borg's attitude towards knowledge of mathematics by mathematics teachers is anything to go by, then it does not seem like good news for those who might be concerned about the level of mathematics teaching in our schools. His argument seems to be that a teacher does not need to know much more than what is actually taught in schools.

By the same token, his A-level students need to learn only a little more mathematics in order to become good sixth form teachers. Taking this argument to its absurd limit, a primary school teacher only requires to be a little above the level of the most basic numeracy in order to teach maths at that level.

I believe the opposite to be quite the case. For example, among the theorems which Mr Borg might have forgotten, there is one which describes in a rigorous mathematical way how fractions are constructed from the integers and embedded in the field of real numbers.

Now this construction is surely not to be taught at primary (even secondary) level, but the knowledge that the construction of fractions is an inherently difficult mathematical notion, and why it is so, must help any teacher understand why children find fractions difficult, and should enable the teacher to judge with some authority new ways of teaching fractions without having to accept new methods with the same fervour as one accepts religious dogmas or fashion trends.

One can further this argument in several ways. Are we to say that teachers are a particular breed who should not learn more than some specified limit about the subject they are teaching? Would not "extra" knowledge help any teacher make the curriculum more exciting and palatable for students of all abilities?

And would this background preparation not put the teacher in a better position to enable the students to see any subject in a wider context, as a part of our culture and civilisation, and not unrelated to other, seemingly different, disciplines?

Which really brings me to my final point: Mr Borg's attitude towards knowledge of mathematics required by mathematics teachers goes against the very principles he recommends for good teaching. By his reasoning, a teacher, seen from the subject content point of view, is a depository of knowledge, topped up with a little more than what is actually required.

This makes the teacher a passive conveyor belt transmitting recorded information, and not an active processor of knowledge which is then shared with students. If we start by preparing teachers in that way, how can we expect that, along the line, teachers can achieve the high goals set by Mr Borg himself?