ABSTRACT
Many of us in mathematics, when faced by the question why so many people fail at the subject or dislike it, reply that it is badly taught or that the learners can’t learn it. We pathologize the teachers and the students. ‘The students are often incapable, do not have the right background or were taught badly.’ Teachers of mathematics, we claim, are unimaginative and uncreative. They enjoyed learning the subject and follow the same paths they themselves met. We would like them to become more creative, to be more lively and to try new and original approaches. I like to call this pedagogical polishing. Polishing has an important effect on the look of furniture but it is marginal in that it cannot make a poor piece of furniture into a good one. If we need a different piece of furniture then we have to change the whole piece, from the start. In terms of mathematical education we need to look at not only pedagogy but at the curriculum as well. We have to look at the purpose of the whole enterprise. We need to question the social setting in which teaching and learning mathematics occurs. Instead of pathologizing the students and the teachers we need to problematize the institutions in which they work whether these are local (schools and colleges) or national structures like ABET, The Basic Skills Unit in the UK, or policies that specify national standards and curricula or even the edifice of mathematics itself.
