Backwards and Forwards: Reflections on Different Approaches to Algebra

Abstract

The meaning I give to the claim of "algebra for all" is that everyone should have a real chance to be introduced to the algebra culture and allowed to enter it if they want to. We don't yet know how to achieve this level of opportunity and we will have to work extraordinarily hard to find out, but it is unnecessary and unwise to invest in the hope that everyone will immediately run to take advantage of the offer.