The current scene - Maths Education

One potential advantage of a National Curriculum is that, with the content at least partly specified and ordered, we can move our energies from consideration of the what to consideration of the how. It is a challenge for teachers to work together on effective ways of approaching chosen topics. How this is done is likely to have a more lasting effect on pupils' learning and their attitudes to the subject than the particular content selected. Perhaps, since of its very nature a national curriculum cannot be idiosyncratic and must compromise, it will seem rather conventional to forward-looking teachers. This does not make me pessimistic. With some teachers at least, I sense an emerging re-orientation in which a chosen published scheme, rather than defining the course to be followed, is being used more selectively to meet national curriculum requirements. This opens the possibility of teachers taking greater control over what they offer their students, potentially to the great gain of the latter.

In a previous article I suggested three major issues on which we in ATM ought to be working during this decade: 

(i) resolving the content/process dichotomy;

(ii) developing ways in which pupils can be helped to reflect on their learning;

(iii) removing the unfortunate polarization of the teacher's role into that of either instructor or facilitator.

These issues are germane to the whole educational debate and are not confined to mathematics. Hence the need to discuss them with fellow professionals and others with a public  interest. More particularly, and despite changes over the years, I believe that we are far from achieving a consensus about approaches to teaching within the mathematics education community itself. Why, for example, do many authors of texts take on the impossible task of trying to create the whole context for the learner on the written page when, as I believe, mathematics must necessarily be created 'in the air' of the classroom? I long to see more  straightforward treatments of mathematical topics, enriched by descriptions of the historical and cultural context of the subject and with appropriate challenges for the reader. Lets have more dictionaries and reference books! Even the old fashioned mixed bag of exercises is a good resource, particularly when pupils have to classify examples by type, sort out which they can solve and what methods are appropriate!

If we are to get our own house into better order, it is as important to tease out significant differences of interpretation as it is to emphasize similarities. In this article I shall first explore a model of teaching and learning which still seems to me to be too prevalent in mathematics classrooms. I shall consider some of the reasons why this model remains socially acceptable. I shall then describe an alternative model and indicate some of the ways in which it might be developed in the classroom.