Is it mathematics or is it school mathematics?

Abstract

In my professional life, I have repeatedly had cause to return to the question of‘What relationship does the “mathematics” experienced in classrooms have to the mathematics studied in universities, or used outside academia? What relationship should it, and could it, have, and how do we get there?’It's time I began to frame some responses! In doing so, I am very aware that membership of The Mathematical Association is broad church, ranging from those with an amateur interest in mathematics (and mathematics education), through non-specialist teachers, to professional mathematicians. As such it is a rich community, but one in which it is challenging to address such questions in a way which is meaningful to all. However, I shall attempt to do so and I hope that the balance will in a small way also prove illuminating to the reader. In particular, I have a hope that it will point to the breadth and depth of what we expect from our teachers of mathematics, at all levels, and to a valuing of that.