Setting up the National Numeracy Project (NNP) in more than 400 schools across 15 local education authorities has been a fascinating challenge. I have had a stream of suggestions and questions on what numeracy means and how standards should be improved - from LEA advisers inside and outside the project, university mathematicians, researchers, teacher trainers, professional associations, publishers, broadcasters and, thank goodness, primary headteachers and teachers themselves.
Given the strength of the views expressed from such different perspectives, the number of broad areas of agreement reflected in the NNP's work is remarkable. These are: * There is a real need to raise standards of numeracy in primary schools and to do so as quickly as possible. Not everyone accepts that standards have fallen over the past 10 to 20 years - although I find the evidence sufficiently convincing - but all agree that there is never a case for complacency in education and every school should strive to do better.
* The foundations of numeracy must be laid in primary schools and teaching time allocated to ensure that this happens. NNP schools commit themselves to daily mathematics lessons of 45 minutes in key stage 1 and 50 minutes in KS2.
* The ability to calculate mentally is of prime importance. This should include learning "number bonds" and times-tables by heart and be firmly-established before standard written calculations are introduced. Our in-service training programme devotes significant time to the teaching of mental calculation, with audio tape and videos to illustrate the mental strategies children can learn. We are using standardised tests of mental arithmetic to monitor pupils' progress.
* Primary schools benefit from clear guidelines on what to teach each year group to secure good progression. Far from rejecting the project's Framework for Numeracy as too prescriptive, teachers say it allows them to concentrate on how to teach rather than worrying about what to teach.
* A key feature of the best mathematics lessons is high-quality interaction between the teacher and the children. Teachers in NNP schools are developing perceptive questioning and using clear explanations and demonstrations. They give good attention to correct mathematical terminology, expect children to explain and demonstrate their methods of calculation and discuss which method - whether it be mental, paper and pencil, or supported by apparatus or a calculator - is best for the numbers involved. Teachers are also enthusing and motivating children through a growing repertoire of interesting activities and greater confidence in teaching at a brisk pace.
* Individualised work minimises rather than maximises opportunity for interaction and direct teaching. Our lesson model includes sustained periods of oral work with the whole class, especially at the beginning and end of lessons, giving every child the chance to take part in question and answer sessions.
* Teachers need time to understand and reflect on new ways of working. The project's consultations provide extended out-of-school courses plus in-school coaching to help put new ideas into practice. Training in numeracy support is also available for classroom assistants.
* Family support for numeracy makes a big difference to a child's progress. In the autumn, we are planning a drive to involve parents through discussions at school and in work with children at home.
However, there remain two main areas of contention among the interested groups, both of which require careful evaluation. The first is whether any differentiated work is desirable or possible in whole-class teaching.
The greater the gap between the highest and lowest attainers in a class, the more difficult it becomes to teach the class as a whole. In the countries that do best in primary mathematics (judged by international tests and observations of lessons), a relatively narrow range of attainment in each class may be achieved because of the school system. Pupils sometimes repeat a year, or entry to school may be delayed; special needs pupils may be withdrawn from mainstream classes rather then integrated. As a result, in some countries where mathematics achievement is strong, 25 per cent of pupils aged 11 may be working in classes with younger pupils, a figure that can rise to more than 40 per cent in areas of social disadvantage.
The school system is different here. For the foreseeable future we are likely to have a wider range of attainment, particularly in older classes, and in the mixed-age classes that are unavoidable in many of our primary schools because of their size.
The numeracy project's approach is a pragmatic one. Schools must do justice to the pupils in their classes now. Teachers begin and end their lessons with the whole class, having considered carefully what they will do and the questions particular children will be asked. For the middle of the lesson, they plan manageable, structured tasks: work for the main group of middle attainers, with extra challenges for the more able and simplifications for others. For this work, the class is usually organised in four groups of from six to eight pupils. The teacher sits with the groups in turn and continues the all-important direct teaching.
The second issue on which opinion diverges is the extent to which calculators should be used in primary schools.
Our approach is again pragmatic. The framework is designed to help schools teach the national curriculum. This requires pupils in key stages 1 and 2 to use calculators from time to time to help them understand the number system and calculate with big numbers.
The NNP promotes a carefully structured and controlled development of calculator skills. It places great emphasis on mastery of mental and written calculations so that children are not excessively dependent on calculators and recognise when calculator use is inappropriate.
Numeracy project schools have got off to a very positive start. Early suspicion about what might be involved has mostly been replaced by considerable enthusiasm and ready willingness to make it work. There is also recognition that these are early days. We need to make sure that the good start is sustained and find out what adjustments to the framework, teaching approaches, training materials and support for teachers may be needed to make them even more effective.
Anita Straker is the director of the National Numeracy Project
Letters, page 22, and Primary Literacy and Numeracy projects, TES2, pages 11-13