# Sum total: how important is subject knowledge?

2nd December 2005 at 00:00
The Clay Mathematics Institute in Massachusetts has offered \$1 million to anyone who can solve one of seven problems that have so far defeated the world's greatest mathematical minds.

But an eighth question could be added to that list: "What does it take to be an effective maths teacher?"

Humour, of course, helps. You can always try a snatch of Gilbert and Sullivan, and risk some blank looks from the bottom set:

"About binomial theorems I'm teeming with a lot of newsWith many cheerful facts about the square of the hypotenuse."

(The Pirates of Penzance) But how much of a maths "expert" do you need to be to teach the subject well? Can someone like Suzie Hardwick, who showed no aptitude for maths in school, be transformed into a competent teacher.

Research suggests it is quite possible, provided the teacher is well trained. Academics at King's College London who monitored the effectiveness of 73 primary teachers in the late 1990s found that children actually made less progress in numeracy in the 10 classes taught by teachers with the highest qualifications in maths. Other studies in England have since produced similar results. And only last month it was revealed that even in Hong Kong, a world-beater in maths, many primary teachers have only a GCSE equivalent in the subject.

But that does not mean that subject knowledge is irrelevant. Far from it.

Professor Mike Askew, who led the King's study, found that although the best numeracy teachers were not highly qualified, they had a sound understanding of maths. They also had a clear mental map of the underlying relationships between topics. They understood, for example, that decimals, fractions, ratios and percentages are all ways of comprehending numbers that are not wholes.

These teachers, dubbed "connectionists", also tried to challenge children, believing almost all could become numerate.

Although this research covered only primary teachers and therefore answers only part of the \$1 million question, leading maths educators acknowledge that the findings may well apply at all levels of teaching.

As Professor Askew has said, they indicate that something is wrong with A-level and degree courses. "Many people gained these qualifications with very little understanding of the fundamental ideas in maths, which are so important to the teacher. This suggests these courses need urgent reform."

To try the \$1 million questions go to www.claymath.orgmillennium

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