Professor Merttens, a mother of six, is the founder of IMPACT, a homework project to involve parents in their children’s maths. She began developing her scheme for Ginn five years ago, when ideas which placed teaching at the heart of classroom maths seemed way-out and even reactionary. Now the pendulum is swinging back, with concern over standards in maths reverberating across the curriculum.

Abacus consists of a file of teachers’ cards, which list teaching strategies for each unit (typically, for infants, a number unit and a non-number unit each week); a resource pack giving handy tools such as number grids; workbooks, with home and do-in-class sections; and a book of “simmerings”. Simmerings are do-on-the-rug activities mental arithmetic for the “10 minutes between coming back from PE and going out to break”.

The philosophy at the heart of Abacus has three strands. Ruth Merttens describes it thus: “Teach, make sense, practise.” At its core is the notion of active teaching, including interrogating, explaining, informing, instructing, narrating and demonstrating. Once a concept, say adding tens, has been thoroughly taught in this way the class moves on to making sense of it. To this end, practical activities, puzzles, investigations and stories are pressed into service. Practice involves consolidation on the part of the pupil in his or her workbook and also assessment on the part of the teacher who can see how far an individual has succeeded in making sense of each concept.

How might this work in the classroom? The adding tens task, for example, is accepted on the continent as a skill suitable for 7-8 year-olds, but not widely achieved here.

First of all the teacher might use fingers “I always tell the children God gave you fingers for a purpose: count with them,” says Professor Merttens. He or she might go on to use a numberline and tell a story about a goose which laid eggs. Children would develop this theme, often by using money: “It’s decimal, children are familiar with it.”

Crucially, says Ruth Merttens, each topic is started with all the children together. She deplores the “fanning” effect of individualised learning schemes, which end up with some children so far behind that they never even get on to a topic. Differentiation is built into the scheme, with follow-up materials and practice elements allowing for a wide degree of difficulty to be explored. At the beginning of each topic the whole class assembles together to be taught a new step. “We depend on the initial dialogue between child and teacher, ” explains Professor Merttens.

In recent years, there has been so much stress on active learning that the imparting of knowledge has been seen as a handmaid to its acquisition. With such tactics as centralising teaching, using fingers, chanting, mental arithmetic and practice, Ruth Merttens is conscious that she may be accused of turning back the clock. But she insists that every strategy has been tried and tested in Blake primary school in Witney, Oxfordshire, where she teaches part-time.

Abacus aims to get every child leaving infant school adept at number bonds up to 10, counting on, adding tens and proficient at money calculations. With four more stages covering the rest of the primary curriculum to come in the next couple of years, it remains to be seen if active teaching will rescue key stage 2 maths from the slump in which it is perceived to have fallen.