We have a choice. We may become a high-skill high-wage country, or a low-skill low-wage one. Our current position as a low-skill high-wage economy is unsustainable.” This is a commonplace of political comment around the developed world. It is recognised that the power to tackle practical problems mathematically, including the use of information technology, is a key element in the high-level skills needed.

This thought-provoking collection of papers asks whether we are teaching the right kind of maths, and enough of it, to enough of our children for long enough. It looks at the teaching and learning of maths, comparing England and Wales with other countries. It should be compulsory reading for all who are concerned with education policy.

Is the current numeracy hour a high-skills programme? Do the key stage tests assess such skills? Does our structure, where most students finish their maths with intermediate or lower-tier GCSE, cover enough ground, or the right ground?

The studies reported or referred to here provide compelling evidence for concern. They bring out key changes over the past decade, such as the further fragmentation of maths as learned and tested in schools.

The early chapters describe and comment on the education system, and the effects on life-prospects of different levels of mathematical attainment, as measured by qualifications. There are contributions from economists as well as educationists.

Algebra is the key to high levels of mathematical power. Rosamund Sutherland grasps the nettle of how best to teach it to most students. While she gives an interesting analysis and puts forward constructive ideas, she also recognises that this is a complex, largely unsolved problem.

The final chapter on What Mathematics Should Our Children Learn, by Celia Hoyles and Richard Noss, sets out a range of sensible ideas, emphasising the central role that ICT plays in doing maths at all levels - except currently in schools.

Like many collections of papers, this is rather a scattershot book. It sends mixed messages on linking maths and the real world. There is some tendency to blame past experts, often by selectve quotation, and imply they should have known better - the distorted picture of the Cockcroft Report is a breathtaking example. The difficulties of realising planned profound changes on a system-wide basis, true in most systems worldwide, are not sufficiently recognised as a challenging and unsolved problem.

The book is stronger on diagnosis than on treatment; I believe this is a strength not a weakness. Research can provide insights and suggest possibilities. To provide solutions that work well, high quality development is needed. Support for such development, building on research and combining flair in design and care in systematic refinement, is still rare.

The Government has begun to support it on a small scale but the tendency to regard development as a straightforward job, rather than a challenging and complex problem, still dominates.

As in any highly-skilled occupation, the range of performance among maths teachers, and improved system performance depends on everyone getting more skilled, but particularly the majority in the middle of the range. Yet there is just one development project for the National Numeracy Strategy, largely inspired to help “failing teachers”.

In contrast, when the US established a set of standards for school maths, its National Science Foundation funded several parallel projects for each stage of education, 12 in all. The choice this provides has been widely welcomed.

But what about the cost of such development?

The education system in Britain costs more than pound;30 billion a year; that is the bottom line. What proportion of turnover would a well-managed organisation, facing recognised challenges, devote to systematic research and development aimed at improving the overall performance of the system?

In industry, 5 per cent to 15 per cent is typical. In education, substantial and steady progress could probably be achieved for 1 per cent (a few extra students per school). But at the current level of about 0.1 per cent (pound;30 million a year), we will remain in the domain of speculative fixes that half work. This book details some of the problems that follow.

Professor Hugh Burkhardt is at Michigan State and Nottingham universities. He is a director of the Mathematics Assessment Resource Service and the Shell Centre Team