However many members of the Association of Teachers of Mathematics would agree with Dr Gardiner that there should be a challenge in "hard mathematics". There should be exciting lessons and good teaching, but for all pupils. Why should the encouragement of the mathematically gifted have to be at the expense of "the other 50 per cent"? Conditions to enable the most gifted should also enable their less gifted colleagues. Raising attainment for all does not need to be at the expense of the gifted few.
Contrary to his opinion, the national curriculum, misquoted in the article, cannot be held responsible for the lowering of standards he detects. First because it is too recent, and second, the improvements noticed in recent reports have been in schools where the national curriculum had been successfully introduced. For many children, particularly at key stage 2, the national curriculum has brought a richness and a breadth of mathematical experience which they did not have previously.
Members would also agree with Dr Gardiner that, when working mathematically, using the most efficient methods would seem like common sense. However, much research is available to indicate that memory alone is an unreliable tool for learning. Pupils continually surprise teachers with their achievements when encouraged to develop their own methods and ideas. Learning with understanding must always be better than learning by rote.
Teaching and learning are co-operative activities. The power to learn rests with the learner. The teacher has a duty to engage the power of the learner. This does not mean there should be any lack of rigour, nor that the teacher denies access to the necessary knowledge and the techniques. One of the aims of the ATM is to encourage and enable increased understanding of the learning process. Let us hope that the debate continues and will result in further research in this area and a more widespread understanding of the issues involved.
MARJORIE GORMAN Honorary Secretary The Association of Teachers of Mathematics 7 Shaftesbury Street Derby