A project led by Clare Lee, of Chipping Norton School, found that children following individual maths programmes spent little time discussing their work and struggled to remember the exercises they had done. When they were encouraged to speak about their work in class, however, their recall improved.

The research identified five components of mathematical conversation that enhanced understanding: * stating and restating the problem or task; * talking about numerical patterns in the problems to be solved; * working out arithmetical calculations aloud; * challenging others’ observations and providing answers when challenged; * speaking about their uncertainties.

Clare Lee says: “Sometimes it is necessary to become almost a foreign language teacher to teach the students new words or phrases and (to allow them) to use the words themselves in context. This shows pupils they can have access to the mathematics world.”

* Rather than look for new methods of teaching maths, infant teachers might find it more profitable to use the visual images that Catherine Stern devised to convey arithmetical concepts in the 1940s.

Teachers at two East Sussex schools discovered that when children were introduced to Stern’s structured images (see figure, right ), they made surprisingly rapid progress in arithmetic.

They began to count more quickly than pupils who were taught in a more conventional way and had a more developed understanding of pattern.The researchers from Peacehaven and Balfour infant schools started the study after finding that children consistently foundered at the same points in arithmetic.

“We realised that we had been teaching children procedural techniques which only the abler children could apply with understanding,” they said.

“The findings of this pilot study justify much larger-scale development work.”