My first head of department was a great believer in the power of competition, and was frankly only interested in winners - hence his decision that the job of drawing up a scheme of work for "the remedials" could easily be done by a beginner at teaching (me). "Bottom sets", in his view, could make do with a minimum of expenditure on resources, and whichever teachers and rooms were left once those for higher sets had been allocated.
Yet teaching low attainers, whether in sets or not, demands a great deal of the teacher if those pupils are to make progress. A bottom set is likely to include a wider range of ability than any other group; one group of Year l0 pupils I worked with included a boy who could not count five objects reliably, and another who could tell you the change if you spent Pounds 2.47 and you handed over a Pounds 5 note.
Many pupils will have problems with reading. This may even be the reason they have difficulties with maths because reading is essential to follow a particular scheme. Some will find it hard to concentrate, easy to forget things, and difficult to deal with abstract ideas.
Sometimes pupils' problems have been caused by poor teaching in the past, and are then made worse. The problem is not always the lack of a specialist maths teacher - for example, I have seen excellent remedial maths taught by a French teacher who realised that "Quelle heure est-il?" needed some earlier work on "What's the time?".
However, being taught by someone who lacks confidence in maths, or who resents being timetabled to teach it, often results in a vicious circle. For lack of any alternative, the unhappy teacher often uses the methods of teaching which were used with them when they were at school - despite the fact that these failed to produce someone who was confident with and enthusiastic about maths.
I once taught bottom-set French for a term. It was a salutary lesson on the importance of a good scheme of work, and of the value of good teaching materials. I relied on the textbook to give me a framework for each lesson, and I knew I was becoming more confident when I started to pick and choose which parts of the pupils' book I would use. But without any textbooks to start me off, I think it would have taken me much longer to reach the point where I felt I was doing some good.
What are the important features of good textbooks for low attainers in maths? First, I think they must be attractive and motivating, using contexts which are relevant to the age of the pupils, and problems which they will want to solve. It is much easier to concentrate if you are interested in what you are doing, and if you can see the point in it.
As a writer of publications for low attainers, I know it isn't always easy to predict which contexts will remain interesting for long enough to make them worth putting in print. For example, if you teach key stage 2, would you include "pogs" or "tazos" as a context for counting, or will they be out of favour too soon? At key stage 3 and 4, will cassette tapes still be used in a few years, or will CDs have superseded them? And there is the perennial problem with money, trying to make sensible guesses about the likely rate of inflation when including the prices of anything. I can understand why some writers of maths materials stick to pages of sums, out of context, but I am sure it is not as useful to our pupils, who need to be able to apply their skills in real life.
The reading level of maths materials is a prime concern of many teachers. I do not think any maths scheme can provide interesting materials which pupils with reading difficulties can use on their own.
To achieve a very low reading level, you would have to sacrifice many valuable contexts, and the maths would become less purposeful. In any case, for many topics it is unlikely that individual work is the best way of learning, particularly for students who need to be sure they understand something well because otherwise they will not remember it. Discussion and asking and answering questions help firmly establish knowledge.
Reading can be supported in many ways. Textbook pages with a clear layout, good illustrations, and straightforward language, become even more accessible after an introduction by the teacher.
A suitable maths textbook can improve pupils' reading skills: non fiction can provide more opportunities for repeating vocabulary and common phrases than fiction, particularly when giving instructions or asking questions. Liaison between a pupil's maths and reading teachers is also helpful.
One obstacle to pupils making progress in the past was the misguided view that if you are poor at maths, you should concentrate all your efforts on the four rules of arithmetic. The advent of the national curriculum seems to have improved the range of maths offered to all pupils, but it also highlights two difficulties for teachers of low attainers.
First, it can seem that a pupil is making no progress, when they are assessed as being at the same level from the beginning of one key stage to the next. Second, many mathematical topics receive only a brief or no mention in the relevant study programmes, and yet they are ones that many teachers of low attainers would like far greater guidance.
A well-organised published scheme can provide a structure which demonstrates to pupils, their families and teachers that they are progressing, and can give advice and suggestions about successfully tackling mathematical ideas.
It can be difficult to judge what balance to strike between helping pupils and expecting them to do things on their own. One side effect of a pupil being given a lot of help, and of their teacher "breaking things down into steps", can be that they learn dependence, instead of working independently.
It is important to promote an atmosphere in which pupils are not afraid to try something without the teacher's help, and where they are encouraged to discuss their ideas and reasons for doing things with each other and you. We should make sure pupils know that mistakes are useful; we can all learn more by making a mistake than by accidentally getting the right answer.
Any improvement in working methods that benefits low attainers is likely to benefit pupils across the ability range. We need an approach that encourages pupils to make decisions about how they are going to do something, and which uses discussion, questioning, direct teaching, practical activity, games, role play and other ways to provide for the varied needs of our learners.
Rose Griffiths is a lecturer in education at the University of Leicester, and is seconded to the School Mathematics Project's "Amber" project, writing materials for low attainers in Years 9 to 11