Obey the rules - and no thinking
There are plenty of documents exhorting teachers to do better, and some which suggest how this might be achieved. It is time for a fresh approach. I intend to share the traditional craft knowledge and trade secrets of how to teach mathematics badly.
It is important to begin with a clear perception of the nature of mathematics. It is essentially a series of unrelated routines or "rigmaroles", as we call them in the trade, from which the Correct Answer appears. Make no mistake, listen to no trendy views: the Correct Answer is the only important part of the whole business. It is important for the exams, the teacher's morale and the pupil's sense of achievement. But how is it achieved?
Well, it's obvious really. You just tell them how to do it and give them plenty of practice. The secret of meaninglessness in maths is normally achieved with 1 per cent teacher exposition and 90 per cent pupil perspiration .
Obviously it's not quite as simple as that. It's not just what you do, it's the way that you do it. Let me give you an example, then you can practise.
The exposition must be directed solely towards the practice that is to form the bulk of the lesson. No links with other parts of maths should be made as these could lead to - well, who knows? Pupils should be clearly instructed in the rigmaroles and discouraged from using any preconceived ideas of their own. The teacher should use phrases like, "No, not like that, do it like this, "; "Look, it's dead simple"; "All you've got to do is . . ."; or "What on earth have you done it like that for? If I've told you once . . ."
For example, when teaching averages, one must tell pupils to find the mean using the rule "add up the numbers and divide by the number of numbers". The mode should be found in a different lesson using another rigmarole, and the median in a third lesson. Remember: one lesson, one rigmarole. At no time may pupils meet all three in the same lesson as this would lead to confusion -and thought-provoking questions such as, "Why are there three ways to find the average?" Obviously the exposition of mathematical methods must be made as simple and fool-proof as possible. All challenge, surprise, paradox and mystery should be surgically removed.
This is best achieved by the teacher breaking down the Method of the Day into a set of rules, such as two negatives make a positive. Whenever possible, the rules must appear to be arbitrary, and pupils should always be required to learn them. Wherever possible the rules learned in today's lesson should conflict with rules applicable in previous or subsequent lessons - a negative and another negative makes a negative, for example. Pupils must realise that failure in maths is due to failure to learn the rules; it's their fault, not the teachers.
Finally, in the staffroom try to use of phrases like "My class are all thick. I told them how to do it only last week and now none of them can remember. "
Jim Smith lectures at Sheffield Hallam University Mathematics Education Centre. He is writing here in a personal capacity