Given recent concerns about standards of numeracy, it may seem odd that the Royal Society and Joint Mathematical Council were sufficiently worried about the future of geometry to set up a joint working group, which reported last July. But there are many reasons why geometry, the study of shape and space, should not be squeezed out of the curriculum.

First, the availability of powerful computers has led to the need for everyone to become more visually literate, and able to use graphics and computer-aided design packages.

To communicate with other professionals and with the public, people such as scientists, engineers, manufacturers, surgeons, architects and designers (whether of airport terminals, brain scanners or web pages) need precise ways of describing shape, location and movement. They also need familiarity with the effects of manipulating shapes, in particular converting between 3-D space and 2-D images. Knowledge is needed about the building bricks of geometry and how these behave and relate, for example lines and planes, polygons and curves, similarity, rotations, enlargements and vectors.

Second, because of the immediacy of the ideas involved, geometry is a fruitful area in which to encourage logical reasoning, leading on to complete proofs. Deductive skills are needed by mathematicians, but they are also necessary for anyone who is arguing a case from given assumptions.

School geometry got a bad name in the 1950s because many students found learning proofs difficult and pointless; hence the renaming of geometry as “shape and space” in the 1989 national curriculum. The working group felt that it was time to restore the traditional and more mathematical name, but not the 1950s approach.

It recommended that students should meet theorems, but mainly those that they can explore and which are both interesting and surprising. Even primary pupils can find it intriguing to discover empirically that, whereas there are infinitely many regular polygons, there are only five regular solids. The reasoning in to the proof of this theorem should arise easily from playing with construction kits, with only a Year 6 knowledge about angles needed. Although mathematically advanced children find geometrical patterns and relations fascinating, many who find it difficult to remember multiplication tables are equally interested in them.

we certainly need every possible way of making maths more approachable yet challenging for everyone.

It helps that geometry is also an important part of our cultural history, from the introduction of perspective in medieval art, through the problems of mapping the world, to the discovery of the helical structure of DNA, and the almost ellipsoidal pods on the London Eye.

The working group concluded that the geometry in the national curriculum was broadly satisfactory (although the 16-19 syllabuses need review). However, the narrow examinations and many associated textbooks encourage boring teaching. Geometry is both fascinating and useful. But sometimes it seems as though our way of teaching it is calculated to hide this from pupils.

* To receive a copy of the report Teaching and Learning Geometry 11-19, send an A4 self-addressed envelope to: The Royal Society, 6 Carlton House Terrace, London SW1Y 5AG; tel: 020 7451 2572; e-mail: education@royalsoc.ac.uk; web: www.royalsoc.ac.uk Margaret Brown is professor of mathematics education at King’s College London