Primary schools taking part in the Government’s National Numeracy Project will be able to compare their progress and achievements against national and local averages.

Tests of pupils’ skills in calculation and problem-solving will set a baseline for measuring each school’s achievement in raising standards. The participating schools - around 200 so far - will each get a detailed analysis of their results.

They will find out what types of problems their pupils can and cannot do. The project will even look at such issues as whether children with English as a second language have more difficulty with word problems. Schools will receive standardised scores for each child and a mean score for the school, and will learn how they compare with others in the project nationally and locally, says Anita Straker, director of the project, which is based in Reading.

The National Literacy Project is running similar testing with its 200 schools. Both projects were set up earlier this year by Education and Employment Secretary Gillian Shephard, who decided to establish 25 literacy or numeracy centres in 25 local authorities in a bid to raise standards.

Schools taking part in the numeracy project, which are starting to implement its comprehensive requirements this term, are testing their pupils in Years 2, 3 and 5. The pupils will be re-tested a year later, and again when the school leaves the project in two years’ time. Over five years some 1,000 schools in 12 local authorities will take part on a roll-on, roll-off basis. By the end of two years, schools will be expected to have incorporated the project’s aims and methods into their way of working.

The numeracy project syllabus is based on the national curriculum, but sets out its objectives in minute detail. At its heart is the “numeracy hour” - actually 45 to 50 minutes four times a week - when each class focuses only on mathematics in a highly structured way. The session must have a clear emphasis on instruction by the teacher and on mental calculation.

“During the lesson, you should aim to spend close to 100 per cent of your time in direct teaching of either the whole class or a group of pupils,” says the handbook for the project, which has gone to participating schools this month. “Each pupil should have approximately 60 per cent of his or time in a direct teaching relationship with you.” There should be four or five groups per class, usually formed by ability.

The typical lesson will begin with 10 minutes of oral work and mental calculation with the whole class, re-inforcing what has previously been learned, developing mathematical vocabulary, and learning new strategies. This is followed by the main teaching activity, with children working in groups. Teachers should “make clear to children what they are going to learn and what they need to prepare for the plenary session”. The plenary session at the end provides a deadline for completing work, time for children to present and explain their work, and a chance to set targets for what has to be learned next. The session should run at a brisk pace, says Mrs Straker. “There’s such a lot of time wasted in maths lessons,” she laments. “Go and get a pencil, and so on.”

Mrs Straker says there have been few complaints from teachers about this degree of prescription. A “handful at most” of infant teachers committed to the integrated day have not been happy, she said. But ensuring progression within an integrated day is difficult, she says.

Numeracy is more than arithmetic, she stresses. “It has to do with explaining your maths.” Children should be able to tell how they have done something, and make decisions about how to tackle a problem, asking themselves questions such as: Is it multiplication? Can I do it mentally? Do I need a combination of mental arithmetic and paper calculation?

The numeracy framework sets out a ladder of progression for a large number of skills and processes - place value; estimating; fractions; measuring - even including how to use a calculator. “I know it sounds very silly but five-year-olds need to know how to switch it on and off”. Older children need to know, for instance, how to key in Pounds 6.50.

The framework’s definition of numerate pupils includes: * knowing basic number facts and recalling them quickly;

* calculating accurately, both mentally and with paper and pencil, drawing on a range of strategies;

* using a calculator sensibly;

* recognising which operation or operations are needed to solve a problem;

* know for themselves that their answers are reasonable;

* explaining their methods and reasoning and using correct terminology;

* explaining and making sensible predictions.