Quadrilateral thinking

1st December 1995 at 00:00
Children can thrive on complex mathematical concepts and algebra is the key , say Susan Jennings and Richard Dunne

Maths teaching needs to change - urgently. Forget a committee of inquiry; forget rewriting the national curriculum or doing more research.

All that is needed is for teachers to use what is already known from existing research. This can inform planning so that methods are used that give pupils access to worthwhile mathematics.

Some pupils need maths to be made more accessible, but the subject should not be reduced in order to make it amenable to everyone. The special contribution that can be made by whole-class teaching must be recognised and the skills needed for this refined. Publishers must be prepared to accept books that provide detail for teachers rather than colourful near-comics for pupils. Teaching must be recognised as a legitimate and complex activity rather than the management of individualised tasks. And the assertion that mathematics is only worthwhile and accessible to the extent that it is relevant to pupils' lives must be rejected.

The sheer fascination of maths for its own sake can be conveyed to all pupils sufficiently to "rouse their minds to life" (as Tharp and Gallimore's important book Rousing their Minds to Life suggests).

Our research into mathematics teaching in France reveals just how much exploration is made possible when algebra is taught as a generalisation and applied to specific situations. It supports other research which insists that letters should be introduced as generalised numbers from the beginning, otherwise children may interpret them as objects. What is especially interesting is that algebra makes maths accessible to a wider range of pupils.

Of course, it is not easy to make complex maths accessible to all pupils, but achieving this has got less to do with giving pupils individual attention and more to do with course design so that they all can be taught beyond the demands of the curriculum but assessed within it. This is different from providing some pupils with additional work to "stretch" them. It is algebra, carefully taught, that provides access.

Alan Wigley (TES Maths Extra, October 6) correctly says that algebra is "an essential foundation for higher maths and its application", but the activity he describes with Cuisenaire rods is not in fact algebraic. What we see is how a superficially attractive method, selected because "pupils have no difficulty with the notation", diverts them from the essential nature of algebra. It is this that is endemic in the English system: making maths attractive by reducing the complexity of the task, rather than analysing the essential nature of the task and assisting pupils to understand it.

We can understand why Wigley has been misled into advocating an unsuitable task. His concerns typify those that guide most curricula, especially when he assumes that "learning for themselves the rules for transforming equations" is a guiding principle. What we see here is an example of the tendency to assume that learning for oneself is of greater importance than what is learnt, so that we are invited to "pause to think how students might feel when invited to engage in this kind of exploration". We would rather stop to think what they might learn from principled teaching of algebra which he too readily dismisses as "traditional teaching" on the assumption that it prevents exploration.

Sue Jennings and Richard Dunne are mathematics lecturers at Exeter University's school of education.

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