LET’S start with a few facts. The research project Effective Teachers of Numeracy, funded by the Teacher Training Agency, concerned 73 teachers of Years 2 to 6 in 11 schools. The classes of the 10 teachers with A-levels in mathematics (of whom two had maths degrees) had slightly lower gains in numeracy scores over the year on average than teachers without an A-level pass, although the difference was not significant.

Since then, as part of the Leverhulme Numeracy Research Programme, we have found the same result (lower but not significantly lower gains) for the nine Year 4 teachers who had A-level maths out of 74 teachers in 38 schools in 1997-8, and among six Year 5 teachers with A-level maths out of 69 teachers in 37 schools in 1998-99. The A-level grade was not significant. Perhaps more important, the same result was also found with teachers in more than 200 schools involved in the National Numeracy Project.

However, this certainly does not mean that research shows that subject knowledge is irrelevant to teaching performance. Nor does it contradict Tim Rowland’s findings that the teachers with the best understanding of primary maths are the best teachers.

In the TTA project we assessed, in lengthy interviews, the mathematical understanding of 16 teachers, six whose classes averaged low numeracy gains, four showed average improvemet and six which had high gains. Those teachers who were, at best, only able to talk about the links between different mathematical ideas in terms of procedures for calculation all had low gains, and this included two of the teachers with A-levels.

Five of the six teachers with high gains, on the other hand, all explained relationships conceptually and were able to talk fluently about different approaches they used in class to explain these relationships.

One of these teachers had A-level maths, but all had taken part in protracted discussion about maths teaching, either on a 20-day course, by planning over several years with a knowledgeable teacher, or by informal conversations at home.

As part of the Leverhulme project we are working with a group of teachers to explore the relationships between subject knowledge and quality of teaching in greater depth, and will be able to report within the next two years.

We already know from our earlier data that one of the key problems is that most teachers with maths A-levels and degrees are very negative about this further study. Many gained the qualifications with very little understanding of the fundamental ideas in maths, which are so important to a teacher. This suggests that the narrow and procedural A-level and university courses need urgent reform.

Margaret Brown is professor of maths education at King’s College London. Mike Askew is lecturer in maths education at King’s