Booklets that bind

The Schools Maths Project was a response to the growth in popularity of mixed-ability maths classes for the first two years of secondary education.The SMP 11-16 booklets, of eight or 16 pages, enabled pupils in the same classroom to work at their own pace on any number of different topics. They remain useful despite the many changes since their introduction, such as the various versions of the national curriculum and the change from O-level to GCSE.

For many school managers the booklet scheme was a godsend, because it enabled pupils to make apparent progress despite a shortage of suitably qualified mathematics teachers. It enabled a well-organised non-mathematician to provide structured opportunities for pupils to learn. But good maths teachers sometimes found it more difficult to use their skills, and poorly organised teachers had real difficulties.

I have used SMP 11-16 materials in two successful Suffolk schools. My colleagues and I have learned what works well, what to adapt and what to ignore in the booklets. Like many others, we have organised the booklets into modules of work with a common focus, intended to last three or four weeks and including some whole-class teaching. Even so, the need to differentiate within each topic means that the whole-class teaching element has been restricted; teachers have usually been "facilitators".

Crucially, the system still relies on most pupils having unchallenging work so they can keep going with only a few minutes of teaching assistance.

The reality is that pupils working at their own pace do not necessarily learn much. Many good teachers find mixed-ability teaching frustrating and secretly or openly revert to whole-class teaching. They do this to avoid being relegated to the role of facilitator, whose main task is to tell the pupils which book to tackle next. Most try to maintain the differentiation by splitting the class into two or three groups, with each group following a different SMP booklet.

The problem with this is that teachers have to rely on self-marking when pupils are working from many booklets. This can be unreliable for several reasons. For example, pupils may:

* tick all answers whether they are right or wrong;

* mark a string of answers wrong because they did not precisely match the ones in the answer book (particularly prevalent when approximate answers are expected);

* copy answers from the answer book or from a friend;

* write only the answers, without any evidence of the thought processes involved;

* use a calculator to answer any question involving a calculation, even in booklets designed to develop mental methods;

* race to finish the book, ignoring any section which requires reading or an activity which is not a numbered question;

* leave out any question they do not understand;

* choose the easier booklet if given a choice by the teacher;

* work slowly and "forget" to check any answers.

Some of my own pupils have used these methods. Even though I was aware of the tricks, I found it difficult to deal with them early enough. The real problem was that some teachers, including me, began to condone some of these practices, albeit guiltily and not all the time. Others gave up the battle completely and allowed lists of answers, shorn of any working or explanation, to become the norm.

Of course, we can all tick off national curriculum statements by checking which booklets have been completed, but we mustn't kid ourselves that this indicates effective teaching. We devise time-consuming assessment systems to check what pupils have learned from the booklets, but the problem they reveal, of pupils failing to progress in Years 7 and 8, is difficult to address within mixed-ability classes.

I am not opposed to mixed-ability teaching in principle, and I know some teachers who can make it work. In choosing to support setting for maths from Year 7, I recognise that my colleagues and I are less effective in the mixed-ability environment.

I believe that SMP 11-16 has harmed children's education. It has:

* masked the shortage of properly qualified mathematics teachers by providing a course that can be administered rather than taught;

* encouraged schools to let pupils work at their own pace, even if this is too slow (or too fast);

* encouraged the retention of mixed-ability grouping in schools with teachers who are more effective teaching whole classes;

* de-skilled good teachers by reducing their opportunities to use their knowledge and understanding;

* discouraged variety by making it possible for every lesson to be "working through booklets";

* encouraged pupils to adopt self-defeating "learning" strategies such as those listed earlier;

* encouraged uncritical pattern-spotting in preference to more rigorous thinking;

* fostered an "answer only" culture which persists well beyond Year 8.

The problem goes deeper than any one scheme or method of teaching. Too many of our teachers present something which has only the outward appearance of mathematics: they tell pupils how to answer questions without revealing any of the underlying principles.

There are few occasions in school mathematics where a new topic involves a fundamentally new idea; in most cases, pupils need to exploit their existing knowledge. Our best teachers develop mathematical thinking by presenting problems that invite pupils to construct solutions from what they already know. They present mathematics as a richly interconnected web of ideas.

Many SMP 11-16 booklets are undoubtedly excellent resources that can be used alongside other approaches and materials as a basis for good whole-class teaching. The original SMP team included many excellent teachers who did their best to encourage mathematical thinking. It is not the booklets that have caused the problems but the way they are often used in the classroom.

Most 11 and 12-year-old pupils are not good at independent study and need a teacher's help to form a network of mathematical concepts. Yet mixed-ability systems reduce the amount of teaching guidance available for individual students and increase the conscientious teacher's burden. A good individualised scheme like SMP 11-16 may promote more learning than poor whole-class teaching, but if your school has decent mathematics teachers, free them up to do their job: ditch the mixed-ability arrangement.

Steve Abbott is deputy head of Claydon High School, Ipswich, and editor of 'The Mathematical Gazette'.

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