In a posting on *http://conservativehome.blogs.com/localgovernment/2012/02/teach-tables-and-long-division.html* John Bald complains that in my best-selling book *Mathematics Explained for Primary Teachers *I do not describe or subscribe to long division, and that I do not explain how to teach multiplication tables.

His criticism is based on a quotation from an old edition of *Mathematics Explained for Primary Teachers*. In the current (4th) edition, published 2010, I do actually outline the steps involved in long division – although I continue to encourage the use of other methods that can be taught with understanding rather than learnt by rote. The fact that John Bald has managed to drill a dyslexic 12-year-old into reproducing the long division algorithm does not undermine my position. When I said that I had been unsuccessful in teaching the method, I was using the word 'teach' in a sense that does not just mean 'instruct' and that is in relation to classes of children in schools, not individual drill-and-practice tuition.

The first obvious question is whether Mr Bald's pupil will still be able to carry out this procedure in a year's time, without spending more valuable learning time continuing to rehearse it with further practice examples at frequent intervals.

The second question is whether the experience will have helped this young man to learn how to learn mathematics in a meaningful way? It is more likely that it will have reinforced a rote-learning mind set in the learner.

The third question is whether it was worth all the effort! I would be pleased about the teacher's success here if he had given the young man something that would be really useful for him. But in fact I feel sorry that this young man has had to spend so much of his time mastering something that is of such little value. Perhaps he can now move on to learning how to extract the square root of a number? Then on to how to calculate the cost in pounds, shillings and pence of quantities measured in hundredweights and stones?And then how to hunt sabre-tooth tigers?

What is it about long division that gets some people, particularly non-mathematicians like Bald, so heated? Do they not want children to have every opportunity to learn with understanding? Do they really think that learning to reproduce this one particular algorithm is the pinnacle of achievement in primary school mathematics? Do they really want children to spend so much of their time in primary schools mastering a technique that is not required in any of the questions in the end-of-Key-Stage 2 National Tests (SATs) for mathematics? Is there not enough mathematical material much more interesting and helpful and meaningful to teach anyway? There are 183 pages in *Mathematics Explained for Primary Teachers* on understanding number and calculations!

John Bald does concede that I advocate children being taught to memorise the multiplication tables, although again I stress that they do this with an emphasis on understanding the relationships involve – and I give examples of how this can be done. But *Mathematics Explained for Primary Teachers *is not a book that sets out principally to tell people how to teach. Although it contains numerous teaching and learning points, the main focus is on helping primary teachers themselves to understand the mathematical concepts and principles that underpin what they teach. The huge sales of the book and the continued positive feedback from teacher-trainees suggest that they find this approach really helps them to feel more confident in their teaching of a subject about which many of them had previously felt insecure. They tell me that to their surprise they discover that mathematics is a subject that can be understood, and that it is is not just about memorising meaningless rules and recipes for doing various kinds of questions.

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