New schemes launched or partially launched include the New Cambridge Mathematics, Abacus by Ginn, Longman Primary Maths and Maths 2000 by Nelson. Local authorities (like Barking and Dagenham’s maths team) and publishers like the Islington-based BEAM (Be A Mathematician) project are also producing material.

The principal reason for this activity is that schemes in many primary schools are obsolete. Changes in the national curriculum have combined with concerns over calculator use, the on-going standards debate and other anxieties to create dissatisfaction with such previous monarchs of the maths cupboard as SPMG.

But apart from it being “time for a change”, as Paul Harrison, one of the authors of Nelson’s Maths 2000, says, what do the new schemes have to offer?

All of them try to conform to Dearing’s curriculum. Some, like Maths 2000, separate number from other topics. Others, like Cambridge, the most universally acclaimed, integrate number into shape and data-handling, but still preserve the need to get the group working mentally on number before trying sums. Abacus specifies mental arithmetic and offers mental exercises across the age-range.

The Cambridge teachers’ guide encourages teachers to help children develop ways of working, basing its stance on the thinking behind the national curriculum. Shirley Clarke at London’s Institute of Education calls it the “best Pounds 10 you could spend”. Marion Devine at the Scottish Education Research Council enthuses over its emphasis on developing language among children as they work together. But Anne Woodman, an author of Collins’s Steps and an independent consultant, adds a cautionary note. “Teachers need to teach use of the spoken language. Too often it is only when they are stuck that children speak to the teacher. Group work does not mean working without the teacher.”

Like every other authority consulted by The TES, Ms Woodman was unhappy at the thought of schools buying maths schemes without also buying in-service training. “Mathematics won’t happen if you are just working through texts, ” she says. “Teachers need to teach.” Over-reliance on schemes can be a danger. HMI’s recent report on primary maths pointed to lessons in which there was “very little teaching going on”.

Individualised schemes can lead to a false sense of security in teachers and pupils. Primary teachers, who are, of course, generalists, may not know as much maths as they think they do, says Anne Woodman, citing even such basics as place value. “Teachers should never assume their own knowledge.” Purchase of a scheme needs to be informed. “Schools shouldn’t just buy a scheme. You need to evaluate your own school’s aims, achievements, schemes of work, policies. ”

Ms Woodman urges that before investing in a scheme, teachers should read the programmes of study in the revised curriculum, which insist that maths, especially data handling and problem-solving, is generated by real-life situations. No scheme can deliver that. “Never use a scheme from page one on. Use the scheme, don’t let it run you,” she says.

Indeed, problem-solving in groups is one of those skills that is easy to prescribe but hard to facilitate. Another bone of contention, calculators, are either useful or the sorcerer’s apprentice of maths, breeding confidence with numbers or spreading inexactitude and inadequate number bonds, depending on your point of view.

On these matters schemes have different biases. For example, says Shirley Clarke, the Cambridge scheme is strong on applications and problem-solving, Nelson on investigating methods and algorithms. Nelson was first to produce (in an earlier scheme, in 1990-91) the box of games, now standard fare in maths schemes.

But teachers, notoriously lacking confidence, may not feel so playful when they consider the cost of buying a scheme. It can be, says Marion Devine, “horrendous”. Variously estimated from Pounds 300 a class up to Pounds 5,000 per large school, the cost of a maths scheme will not be for most schools a purchase “every five to seven years”, as Paul Harrison suggests.

In the meantime, the School Curriculum and Assessment Authority is running a research project looking at the use of calculators in schools and an evaluation of research on the effective teaching and assessment of number (about to report). SCAA is also starting research looking at resources used in maths teaching. The Teacher Training Agency is launching its own project next year to assess the effectiveness of the teaching of number, and plans to publish guidelines in 1997. For those who cannot wait, the Department for Education and Employment begins its five-year project in September with numeracy centres opening in 12 LEAs.

It will be surprising if the TTA project does not conclude that more INSET is needed to help teachers make their knowledge of the subject more coherent before they buy expensive packages to help their pupils.