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The sum of a good maths teacher

How numerate should numeracy teachers be? Tim Rowland, Margaret Brown and Mike Askew reopen the debate

THE suspicion that "mathematicians can't teach maths" is not easy to dispel. Perhaps too many people recall the misery of lessons at school with a "brilliant mathematician" who "couldn't explain anything".

It is as if actually knowing some maths is a distinct disadvantage when it comes to teaching the subject, even though this would seem a bizarre suggestion if it were applied to the teaching of French.

So what is the evidence to support the anecdotes, and could the common perception be true for maths at primary level as well as at secondary?

As Karen Gold reported (TES, November 24, 2000) the King's College research based on a sample of 90 primary teachers found that those with a degree or A-level in maths were on the whole less effective than their colleagues with just an O-level or GCSE pass. What has not been so widely reported is the outcome of a "concept mapping" interview in the King's study, which explored the links which these teachers were able to make between different number topics, such as fractions and decimals.

Arguably, this interview gave a better measure than qualifications of the teachers' current subject knowledge. It turned out that an ability to explain topic links in conceptual terms rather than by "rote" procedures was associated, albeit moderately, with higher pupil gains in tests over a six-month period.

This finding resonates with that of our own research between 1997 and 1999 with primary postgraduate trainees at the Institute of Education (TES, March 12, 1999). For professional development purposes, each student's maths subject knowledge was audited one term into the course. Later, on school placements, assessments of the students' teaching of maths were made on a three-point scale.

With two cohorts of more than 160 students, we found an association between subject knowledge and teaching competence. Here, a disproportionately high number of the "mathematicians" - as assessed by the audit - performed strongly in the classroom, whereas those with weak subject knowledge typically struggled to teach maths. Incidentally, there was no simple relationship between level of qualification in maths and the audited level of maths subject knowledge. Those with an A-level pass were distributed throughout the top two-thirds of the audit scores.

There are considerable differences between these two studies in terms of methodology and scale, and in the classroom experience of the teachers under scrutiny, but can we make some sense of the apparent agreements and disagreements? It would surely be dangerous to conclude from the King's research that subject knowledge does not matter, yet having an advanced qualification in mathematics is no guarantee of knowing how such advanced knowledge relates to the school curriculum.

There is another crucial dimension to this debate: how teachers' attitudes to maths are shaped by their own experiences as learners. A recent survey of secondary maths postgraduate certificate in education trainees in several universities found that few of them had really enjoyed their undergraduate study.

Given the kudos and apparent utility of advanced mathematics qualifications, it may be that most people study the subject until they cease to enjoy it. So here's a radical thought: maybe the teachers we need are those who gave up studying maths - at whatever level - before they learned to dislike it.

Tim Rowland teaches mathematics education at Homerton College, University of Cambridge.

February's TES Primary magazine includes a project on mathematical language. From newsagents, Price pound;2.

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