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2. That pupils will listen and think and reflect about the mathematics, even if they are not answering questions or writing on the board or discussing ideas or asking questions.

The Teachers
1. Teachers require good questioning techniques and a real understanding of the mathematics. The method probes their understanding as well as that of the pupils; a good grasp of mathematics is a pre-requisite for being able to ask probing questions in the correct order!

Note: Perhaps developing "WCIT" skills would simultaneously give non-specialist Mathematics teachers good questioning skills and the mathematical knowledge required?

2. In good (old-fashioned?) whole class teaching (WCT as distinct from WCIT) - with the stress on the word 'good' - teachers did ask questions. The questions were/are usually closed and always asked by the teacher who expected answers from the pupils. It was not the norm for pupils to ask the questions (except of the type "would you help me with this exercise?").

To a certain extent, this may be said to be interactive but WCIT is much more interactive (in-depth, deeper) than that: the special feature of WCIT is that the teacher expects real discussion of the problem and round the problem, often prompted by pupil errors which are a most useful 'tool'. Both the teacher and pupils join in asking questions and answering questions, both open and closed, depending upon the nature of the mathematics under discussion. Both teacher and pupils tell the rest of the class how to do something, sometimes using the blackboard (OHP), and explain ideas and explain why something is true/right. Under the teacher's skilled guidance, the pupils gain a good understanding of the concept/method etc. by this cooperative "give-and-take" process.

This interactive part of the lesson may last as long as 30 minutes, or exceptionally even longer; and there is as yet no written work done except at the board (OHP). The pupils are now ready to do a few examples themselves in their books, and one or two for homework.

It is important that no pupil questions or comments are regarded as silly or stupid by the teacher or by any other member of the class. Every comment from a pupil Is a reflection of his/her state of knowledge or understanding. The discussion that follows, even including a mistaken idea, (especially including a mistaken idea) will help every member of the class to gain a better understanding. This is good cooperative learning where every pupil, including those who make mistakes, can feel that they are contributing to the lesson. A good classroom atmosphere in this respect will allow every pupil, including the weakest, to contribute without feeling that they may get a response which de-values them.

3. The average teacher must be able to develop these skills, for obvious reasons. How do they do it on the Continent? Are their 'average' teachers better qualified than ours? Is mathematics teaching on the Continent WCIT all the time, and by all mathematics teachers?

The description of WCIT above corresponds to the old-fashioned WCT part of the lesson. After that part in old-fashioned WCT, exercises are set etc. with pupils all doing the same exercise but working in pairs or groups and at their own pace; the teacher goes round helping and discussing and marking. What happens with WCIT? There is a need for a follow-up of pupils working through exercises/problems backed up by more WCIT when teachers need to go over problems, or when teachers need to intervene again for any reason. And perhaps some lessons will be wholly given over to exercises and

4. WCIT is hard mental activity, even in an ideal situation of the pupils being on task all the time. Can we expect teachers to be able to cope with so few non-contact lessons per week?

The pupils In many classrooms, children are accustomed to working at their own pace, sometimes with no teaching from the teacher. This has resulted in many undisciplined pupils, even with teachers who have no 'discipline' problems; working at a pupils own pace means doing no work at all and most of the time they are chatting quietly with friends in the class. Thus the thought of having a class sitting and listening and thinking and discussing mathematics for as long as 30 minutes (or even 5 minutes!!), will cause even experienced teachers to say that ''WCIT is not possible in today's classrooms"

For WCIT to be effective, we must have pupils on task all the time in an environment where they may not be writing. And for this to happen, the pupils need to become accustomed to the WCIT mode of working. It would be difficult enough for some pupils to sit through 15 minutes of good 'WCT' exposition let alone 30 minutes of WCIT in which real mental activity is expected. Thus if WCIT is the way forward, then not only do the teachers have to develop the appropriate skills, but the pupils have to learn how to operate in this way.

Most MEP teachers seem to think that a start in year 7 is the latest that this training must start. Many believe it must begin in the primary schools. If this coincides with raising standards in primary schools, and there are already some trials going on, then this is the obvious way forward. For those primary teachers who feel that WCT is inappropriate in primary classrooms, perhaps they could be persuaded to try it for 30 minutes per day every day for mental arithmetic and other topics and see how it works. Of course, they must give their pupils time to adjust before making a judgement on its failure/success. In any case, even trying it out for 30 minutes per day every day from year I to year 6 must have a beneficial effect on children's attention span, and those teachers who have tried it say that children love it.

Note: we are naturally gregarious and so WCIT Is bound to be better laced than Individualised learning. Each child will get sore attention from the teacher each day than In Individualised learning - and this must be beneficial.

The Management
1. Organisation of the room is crucial. The pupils must be able to get to the blackboard or OHP easily; so the room must be large enough for reasonable sized aisles between the desks (and no huge bags on the floor).

2. Size of class less than or equal to 25 pupils.
3. Lengths of lessons: 45 minutes. (anything longer than 50 minutes is too long and a part of the lesson is wasted)
4. Frequency of lessons: one lesson per day every day.
5. Classes must be set for ability.
6. Teachers need a certain minimum of 'free' lessons.

Educationally and theoretically, this mode of teaching and learning must be good. It will have other educational benefits such as enabling all children to become more confident and articulate. And mistakes will be a positive part of the learning process, rather than something to be ashamed of.

This must be thought through in advance. We have already had two disastrous experiments on school children in mathematics in the last 30 years which has resulted in the present state of affairs. So how can WCIT be implemented successfully?

WCIT backed up by WCT may be the best way forward. Then as WCIT feeds through from the primary to the secondary school, secondary schools will be ready to change over; the children would be ready to benefit from the developing skills of the teacher.

Note: Those teachers nationally who are not class teaching at all have quite major step to sake to become effective Classroom teachers. They require practice in the ordinary question and answer sessions and from this develop the more intensive WCIT type of mathematics discussion, perhaps with INSET to help then Those teachers who already do ordinary class teaching have an advantage.

Fowey Mathematics Faculty