It is time that the Government's new numeracy task force started listening to primary school teachers in its search for better teaching strategies.
Everyone agrees something should be done. Even the most optimistic of us cannot ignore the plethora of highly publicised studies that give serious cause for concern about the state of maths teaching.
One option is to imitate the countries which appear to be doing better than us. However, it is by no means clear which particular practices contribute most to success. Many countries make children repeat the year if they have not reached a certain standard; most teach the whole class for much of the time; some have national schemes of work; and many either stream children or teach them in ability groups.
And then there are wider, socio-cultural factors. In some countries, teachers have a higher status than they do here. In many, schooling is regarded as crucial by parents. And class differences are less marked in some countries than in others. For all these reasons, therefore, it is very hard to talk convincingly of cause and effect.
I teach once a week in a primary school, so I am fortunate to have access to a lively, friendly staffroom full of colleagues who are continually talking and thinking about the best ways of helping children to become numerically fluent. I also travel around the country doing in-service training, meeting large groups of teachers. I have become aware of a remarkable consensus, and it is the more noticeable for being largely missed by those formulating policy. So, drawing on conversations with teachers in schools as far apart as Devon and Yorkshire, I have compiled ten points for consideration by the numeracy task force.
1 INTERACTIVE TEACHING IS NOT A RETURN TO CHALK-AND-TALK; TEACHING IS NOT TELLING
We can tell children all manner of things that will flow over them as the proverbial water off the duck. The demand for more "up-front" teaching is certainly justified, but it cannot mean a return to chalk-and-talk. Didacticism will simply increase discipline problems and playground and out-of-school violence.
There needs to be an extension of "maths-on-the-rug" or whole-class, up-front teaching. However, we need to be clear about what this looks like in primary classrooms. Teaching, as construed by the National Numeracy Project and others, is an interactive and energetic process. Teachers are conversationalists, they are performers, they are instructors, they are explainers, they are story-tellers, and they are even entertainers. If any learning is to take place, then what happens between teachers and pupils must be a dialogue, not a monologue. It should also be enjoyable - on both sides! Teaching is an art, not a science.
If we are to increase and improve whole-class interactive teaching, we need to support teachers with high-quality in-service training, rather than berate them. Teachers are keen to acquire new strategies for teach-ing numeracy. Good INSET means modelling good lessons, demonstrating effective and versatile teaching strategies, dealing with issues of classroom management and control, and, above all, inspiring teachers. This can be done only by those immersed on a daily basis in primary education.
If we are agreed that the process of teaching numeracy begins and ends with teacher-focused explication, what activities should accompany it? Many experienced primary teachers believe that providing the same activity for all, regardless of ability, is worse for the children, unlikely to raise standards, and largely unworkable. The discipline necessary to keep the whole class quiet when one third is bored and one third is struggling is a feature of many secondary classrooms which we would not wish to emulate.
We agree that teachers should provide follow-up activities for - at most - three groups of children. To put it bluntly, we need one activity for the bulk of the class, one for the high-fliers, and one for the strugglers.
4 NUMERACY LESSONS
Many would argue that over the last couple of decades we have lost the focus on numeracy in the early years which helps make other countries' maths teaching a success. The National Numeracy Project calls for a minimum of four focused lessons a week, with a substantial element of up-front teaching. "Numeracy" is defined as including the application of number in measures, geometry and data-handling. This model, which includes some on-the-rug teaching, followed by differentiated tasks or activities, is in line with OFSTED's model of good practice.
5 DAILY MENTAL MATHS
Most primary teachers agree about the importance of developing children's mental numerical strategies. One technique is to do 10 minutes a day quick-fire mental maths practice. This consists of short teacher-focused activities and games which address an aspect of mental agility. The key to success is "little-and-often" rather than lots occasionally.
6 FOCUS - BLACKBOARD OR FLIP CHART
Classrooms need a blackboard or flip chart for on-the-rug sessions. These often need a focal point, upon which the teacher or the children can write, and to which their attention is drawn.
7 SCHEME OF WORK
Both the National Numeracy Project and the Hamilton Maths Project in Oxford support teachers by providing a scheme of work. Listening to teachers from Land's End to Newcastle, I hear the same refrain: "If you tell me what I need to cover, and the order in which it is best done, I can get on and teach it in my own style and with my own enthusiasm." Far from considering an ordered programme of content to be an unwarranted interference, most teachers welcome this as a tool to help them get on with the job.
It's tempting to look at countries doing well and to say, "What books are they using - we'll import those and everything will be fine." However, as any teacher is aware, a change of textbook is a bit like a change of T-shirt - it is an improvement only if what is wearing it has changed too.
This is not to say that textbooks are irrelevant nor that their quality does not matter. It is crucial to provide teachers with good, graded practice materials in numeracy. We can introduce children to good mental strategies; we can model these strategies and then practise them in our 10-minute mental maths sessions. But we cannot be sure that children will retain these strategies unless we "load the dice" in our practice.
So I can suggest that young children add up by "counting on". I can show them that they do not need to count the first number in adding 7 and 4. But if I really want them to adopt this strategy then I need to grade their practice. First I give them a page of 8+1, 11+2, 17+1, and so on. This loads the dice in terms of how they do these sums. They are more likely to count on. Then I give them a page of 16+3, 19+4, 18+3, and so on. This contrasts sharply with the current provision of "easy sums" practice with no idea of strategy - starting with 4+3, 2+5...and moving to 6+7, 5+9, and so on.
If in-service training is to change practice, it must be linked to high-quality resources. As we discuss, explain and model up-front interactive teaching, we explore specific sets of strategies. These teaching techniques draw upon equally specific resources, such as the number line, the number grid (complete with spider!), cloth bags and dice. In general, if we are interested in changing teacher practices, the provision of these things, plus a good flip-chart, is an efficient way of spending money. Good quality inset, where every teacher gets the resources needed for the strategies provided, in conjunction with a clear scheme of work or framework would go a long way towards bringing about the type of teaching we would all hope to see in primary schools.
10 CLASS SIZE
It always makes me cross when researchers or politicians equivocate over class size. Parents know very well that teaching 25 children is less effective than teaching 35 children. The problem of large classes is compounded by the emotional, social and economic difficulties faced by many children living in our cities in the 1990s. It is certainly relevant that nearly one in three children in Britain are living in poverty, as defined by the Child Poverty Action Group (The TES, August 22, 1997).
Primary teachers agree with the call for more active teaching of numeracy. The questions to be answered are: what does this active teaching look like, and how do we support teachers to do it well? Good primary teaching is not secondary teaching taken down a few years and writ slightly larger. It is a specialised skill, and if we want to do it well and extend its applications we can do no better than consult the good primary teachers we already have.
Ruth Merttens is co-director of the Hamilton Maths Project in Oxford. Comments to the national numeracy task force can be sent to its chair, David Reynolds, at the University of Newcastle, St Thomas Street, Newcastle NE1 7RU