History lessons in maths

Top students in Hong Kong have no trouble solving a lot of maths questions in a short time. But most become mute when asked why it is true that -(a+b) = -a-b and axb = bxa. Often even their teachers have no idea.

'Everything in maths can be explained,' said Dr Chiang Yik-man, assistant professor of mathematics at Hong Kong University of Science and Technology (HKUST) and a key member of the university's Education Development Programme. But he said students were often only trained to calculate mechanically by memorising formulae. They learned the sophisticated concepts that great mathematicians spent millennia theorising, but the intricate ideas and steps involved in the process of discovery were usually overlooked.

The fact that Hong Kong students were ranked high in maths in the Third International Mathematics and Science Study said little about their genuine ability in the subject, said Dr Chiang.

'Calculation is only a technique, which has no mathematical value. Maths is about conceptual thinking,' he said.

The root of the problem was that many teachers were educated using the traditional approach where maths was equated merely with calculation.

To raise the level of maths learning, HKUST's Education Development Programme has, since 1997, held workshops and seminars for primary and secondary school teachers. One of the themes explored is the role of maths history in maths education. History is not totally excluded from local maths textbooks, but it is often placed where teachers and students are encouraged to pass over it rapidly. For instance, in one of the most popular maths textbooks used in Hong Kong secondary schools the chapter on Pythagoras' Theorem begins with a full-page picture of Pythagoras. Underneath is a statement that 'the square of the length of the hypoteneuse of the triangle equals the sum of the squares of the other two sides' for any right-angled triangle. How the statue pictured and the statement are related is not stated.