The crisis in applicable maths for schools

In the first paper in this series I remarked that there have been three successive paradigms which have dominated school mathematics since 1960: three “eras” of predominant pedagogy –“traditional” maths, “new” maths and “applicable” maths. The main theme of the first paper was, however, that the new degree of involvement of school mathematics with applications – which came about as a result of the third paradigm – can hardly be unlearned. It will be very difficult, if not impossible, to disengage from paradigm 3. Society is most unlikely ever to let school mathematics revert to a condition of explicit, high-academic, mandarinstyle leadership, whether of the traditional pure mathematics or the modem pure maths allegiance. Yes, the third paradigm looks as if it may be beginning to falter, but the reason, I suggest, is that we are not getting the full pedagogic benefit from the particular genre of applications we are using, and from the particular style of application-mindedness we are building into our teaching.