The idea that maths is in crisis in Britain has long been reported. A study by the think tank Reform said the subject was widely perceived in the UK as “dull, difficult and geeky”.

“It has become acceptable to say, ‘I’m no good at mathematics’,” it said. “But people would be ashamed to admit that they could not read.”

The concerns have been exacerbated by the fact that maths teachers in England’s secondary schools lag behind those in competitor nations, and the UK’s 15-year-olds dropped to 18th place out of 30 in an international league table for the subject last year.

But the picture in England’s primary schools is significantly different from that in its secondaries. When 10-year-olds in England took the same test as children in 24 other countries in 2004, they ranked in 10th place. The improvement in their results since the international test nine years before was more marked than any other nation. Indeed, their results in the Trends in International Mathematics and Science Study (Timss) had risen by 10 per cent, allowing England to overtake Australia and the United States.

Whether England will perform as well in the latest round of the tests, to be published in December, remains to be seen. However, reports by Ofsted do give some cause for hope. When inspectors examined each of the main subjects in primary schools in 2005, they found that achievement was stronger in maths than all others.

But they also found that achievement had risen fastest for the high and middle ranking pupils, rather than for those struggling - which is one of the reasons why the Williams Review of primary and early years maths teaching has focused on those falling behind.

Part of the reason for overall improvements may well have been the national numeracy strategy, introduced to primary schools in 1998. Over the past 10 years, the proportion of 11-year-olds meeting the expected level in national maths tests has risen from 59 to 77 per cent, although the speed of improvements has slowed recently.

The decline in performance once pupils reach secondary school could be connected to the fact that it is easier to engage young children in the subject. As Sir Peter Williams wrote in his interim review report in March: “There is an inherent beauty in mathematics, which finds expression in the natural and physical world and is readily appreciated by young children.”

FOUR CATCH-UP SCHEMES AND HOW THEY HELP PUPILS STRUGGLING WITH MATHS

MATHEMATICS RECOVERY

- What type of scheme is it?

One-to-one intervention from a specialist teacher.

- Who started it?

Developed in Southern Cross University in New South Wales, Australia, in 1995. Based on earlier American research.

- Where is it now?

Used in the UK, mainly in the North West. Also in Australia, USA, New Zealand, Canada and Ireland.

- How long does it last?

Daily 30-minute sessions for one term for pupils in Year 2.

- Does it work?

During 1992-1997, more than 75 per cent of the pupils who had undergone the intervention reached age-appropriate or higher levels in the topics tested, despite the fact that all had been performing below age level in at least some of the topics at the start of the intervention.

- How can I find out more?

www.mathsrecovery.org.uk or email membership.mrc@gmail.com

NUMERACY RECOVERY

- What type of scheme is it?

One-to-one intervention from a specialist teacher.

- Who started it?

Developed in Hackney, east London, in 2002. Modelled on Reading Recovery.

- Where is it now?

Used in nine schools in Hackney.

- How long does it last?

Daily 30-minute sessions for one term in Year 2. They are held in a dedicated resources room.

- Does it work?

Over the past three years, 412 children who were not predicted to attain level 2 by the end of key stage 1 have been on the programme. After intervention, 83 per cent of reached level 2.

- How can I find out more?

The programme is not yet widely available outside Hackney.

CATCH UP NUMERACY

- What type of scheme is it?

Alternate sessions of one-to-one and small group intervention from teachers and teaching assistants.

- Who started it?

Under development by Catch Up, a charity, based on the research of Dr Ann Dowker, of Oxford University. It started off with the name Numeracy Recovery, which is now used by a separate programme.

- Where is it now?

Being trialled in 89 schools in 17 authorities.

- How long does it last?

Two 15-minute sessions per week for two terms.

- Does it work?

An independent evaluation by a researcher from Cardiff University found that the number age - equivalent to reading age - of children on the course progressed by more than 11 months in just five months.

- How can I find out more?

Bookings are now being taken for training to be delivered from September onwards. Email training@catchup.org.uk, visit www.catchup.org.uk or call 01842 752297.

NUMICON

- What type of scheme is it?

A number of schemes that use tiles developed to represent numbers.

- Who started it?

It is based on a classroom-based research project funded by the Teacher Training Agency, carried out by Dr Tony Wing, of Brighton University, and Ruth Atkinson and Romey Tacon, of Peacehaven Infant School in East Sussex.

- Where is it now?

Trials have been conducted in Leeds, Cambridge, Devon and Brighton and Hove.

- How long does it last?

The resource can be used throughout primary. It is for general teaching as well as individualised interventions.

- Does it work?

A small study in Leeds found that for basic maths the average progress before using Numicon was 2.1 points on the performance indicators for value added target setting (Pivats) scale, which describes the pre-national curriculum levels and the national curriculum levels in smaller steps. After one term using a multi-sensory maths programme, average progress was 7.1 Pivats points.

- How can I find out more?

Visit www.numicon.com

The Williams Review also recommended these schemes: Making Maths Make Sense, Talking maths, RM Maths and Maths Extra.