It is well known that England does not perform well in mathematics in primary schools compared with many other countries. For that reason alone, the setting up of the review of its teaching in early years and primaries, under the chairmanship of Sir Peter Williams, was long overdue. It gave many of us hope that at last there would be an initiative that focused on actually improving maths in our primaries, rather than on improving test scores in national examinations.

We shall have to wait and see what the final report, due next week, will recommend. Yet it is clear from the interim report, published in March, that there is little agreement on how this situation can be improved and sustained in the longer term.

The interim report said little to help primaries reach a position in which they could be trusted to establish a solid mathematical foundation - rather than focusing merely on numeracy; one from which pupils could progress and extend into secondaries and later life.

Key recommendations in the interim report included: more intervention programmes for low attainers; more continuing professional development (CPD) for teachers; and more consultants to be appointed to oversee the initiatives. Yet it seems to lack clarity about an effective pedagogy for primary maths and does not offer any long-term solution that would not require intervention programmes, more CPD and yet more consultants.

Unless the final report is very different, this will be another short-term initiative that gives ministers good headlines and some short-term gains but will do nothing to bring sustainable improvement to children’s mathematical knowledge. Inevitably, there will be another committee in 10 years’ time to discuss what can be done to boost maths teaching.

Let’s look at some of the facts. First, what have we learnt from a decade of the national numeracy strategy? Initially, gains were made, but this was no surprise as schools were required to provide a numeracy lesson every day. Mental maths work has improved, but standards of written work have remained poor. Most people now agree that cascade methods of teacher development don’t work effectively. The interim report states that these strategies have worked well. If that really is the case, why is England still lagging behind in international tests, with an exceedingly long tail of underachievement?

Second, what can we learn from countries such as Finland, Russia, Hungary, Singapore and China? These countries, and others, are successful in providing pupils, and consequently workforces, with a successful mathematical education.

There are some obvious differences. In most of these countries, trainee primary teachers all study maths up to the age of 18, so they have the equivalent of A-level rather than GCSE grade C, as is often the case here.

Formal primary school starts at six, or even seven, with a foundation in maths from the outset, emphasising rigour and logic, rather than just numeracy. There is an integrated spiral curriculum that widens and deepens knowledge, challenging but revising and always progressing, using correct mathematical notation, language and layout from the start, rather than separating maths into discrete topics.

Whole-class interactive teaching predominates in these countries, with little group work. Instead, pupils demonstrate and articulate in front of the class. To minimise time off-task, lessons last about 45 minutes, with a 15-minute break between them. Each lesson normally consists of about seven or eight related activities, each having three phases: introduction, focused work and review, with differentiation through outcomes, not activities.

Pupils sit in pairs at tables, facing the front so they can focus on the teacher or board, and so that the teacher can have eye contact with all pupils. Children can easily get to the front to demonstrate solutions, and the teacher can quickly reach all pupils to see work or respond to queries.

Less able pupils are paired with more able ones, rather than grouping those of similar abilities together; there is continual monitoring of all pupils’ progress. Regular diagnostic testing informs teachers, pupils and parents, instead of national testing and levels of attainment. Classroom assistants or extra teachers provide struggling pupils with help outside normal classroom time to enable them to catch up with the class.

Collaborative practice CPD is used to enhance mathematics teaching and learning. This is led by expert teachers of maths, but with all staff teaching the subject involved and time made available for group planning, lesson observation and review, and action points agreed, rather than individual teachers attending courses led by numeracy consultants.

I would be relieved and encouraged if the Williams Committee adopted at least some of these strategies, but I fear it has opted for simplistic, non-challenging recommendations that will not enhance the teaching and learning of mathematics in our primary schools.

To illustrate what is really needed, I have compiled some questions for The TES that most pupils, at the age specified, should be able to answer correctly (see page 10). They are taken from the countries mentioned above.

These show that the development of a rigorous and logical foundation in maths is needed for students to become mathematical thinkers, rather than having the short-term emphasis now placed on reaching arbitrary and irrelevant levels of attainment at such young ages. I do hope I am wrong in my fears - or perhaps that the committee is right and I am misguided.

Professor Burghes was a member of the numeracy task force set up by the Government in 1997 that led to the introduction of the numeracy strategy

David Burghes, Director of the Centre for Innovation in Mathematics Teaching, Plymouth University.