Several lines of thought led up to the present experiment in cooperation which has just started in Abingdon. I would like to start by trying to summarize them.

We are apt, in the grammar schools, to criticise the universities. We may say that their influence on our syllabus is bad. We may think that the teaching they give to our prize pupils is poor, the supervision unsuitable, the courses wrongly devised. These things we say and think and I am not concerned here with the rights and wrongs; but do we realize that these are precisely the things that primary teachers are saying and thinking about us?

In the concluding chapter of “On Teaching Mathematics” (1), we said (a) Mathematics is a subject which must be taught well at an early stage of a child’s schooling, and (b) the youngest children should not be taught by those insensitive to the subject. How much do we in the grammar schools know of the primary teacher and of what is being taught today in the primary schools?