Less chalk and more talk is the latest advice for maths teachers - but it's the pupils who should be doing the talking. Research with secondary maths teachers found that using speaking and listening during lessons with lower sets helped pupils' understanding, encouraged them to participate, and also gave greater insight into their mathematical knowledge.
The report and DVD of the project, "Many Right Answers", carried out by the Basic Skills Agency, with support from national maths advisers, is being actively promoted through the National Centre for Excellence in the Teaching of Mathematics.
Local authority maths consultants are being encouraged to disseminate its ideas. The report asks teachers to question ideas about maths learning - it says some lower attaining pupils might benefit from skipping a level and returning later, and over-simplifying the subject should be avoided.
Some of the teachers found it a challenge. John Moran, head of maths at St Joseph's Catholic High School in Slough, says: "It was a bit difficult for me. In traditional maths lessons you teach pupils how to do something, do five examples and get them to do the next 20.
"Obviously things have changed for me. I am still very wary of group work but I think it is a matter of control. You don't want the headteacher to stick his head around the door and see children all chatting to each other - there is the idea that they are not working if they are talking to each other and the teacher isn't in control. I suppose you have subconscious fears about that."
The project brought together six teachers with an academic. They spent a day discussing how speaking and listening techniques might help pupils'
learning, with expert input from Dr Els De Geest, researcher in mathematics education at the University of Oxford, on how their suggestions were supported by existing educational theories and research.
One suggestion they explored was that lower-attaining pupils often end up repeating the same basic maths techniques, but they might be able to cope with harder, more interesting, mathematical concepts.
They then taught their experimental lesson to their lower set pupils, and gathered again to discuss how the lessons had gone and how they might work better in future.
John Moran's Year 9 lesson involved getting pupils to describe 3D shapes to each other. It did not go quite as he wanted, but John has since refined the lesson and says more pupil interaction is to be welcomed. Most adult learning - such as driving - is done this way, he points out.
"The lesson I taught was something I'd done a number of times, but I gave them more leeway. It didn't work from the point of view of using vocabulary I wanted them to use, but getting pupils to think and express themselves was good. Even if they were not learning any maths they were learning to listen to each other. That was my take on it.
"Pupils learn more from each other than they do from the teacher. As long as one is a little bit ahead, there is a lot of pulling up by the bootstraps effect. What I liked was Els had a lot of research which supported the ideas."
Researcher Els De Geest was delighted. "All the teachers were very enthusiastic. When you use speaking and listening you can find out what pupils are thinking and what they understand and don't understand. When you're explaining things, you are explaining them as they make sense to you as a teacher - they can explain to each other how they understand things as pupils."
Els says the techniques would work equally well with any ability, but was interested in the debate about whether the national curriculum might be hindering the progress of lower achieving pupils in maths.
"I am working with three teachers in a school that is radically changing the way it teaches lower attaining pupils. Their maths thinking is so much higher than the kind of level they get on tests. That's because lower level questions on tests are about numeracy - they've been doing that for seven years, can't do the numeracy but can do many other things.
"What they can do is think in a mathematical way about defining concepts, for example shape and space. They can work on imagery and patterns, and once they can see the patterns they can develop the language to move to algebra. They can generalise and see structures and define things and see when something's applicable."
Back in Slough, John Moran is still experimenting with speaking and listening. "I have done similar lessons since then, but I structure them a bit more. I've done it with a bottom set and it was really good for them, with a bit more scaffolding."
Many Right Answers: learning in mathematics through speaking and listening is available at pound;20 from the Basic Skills Agency. More information for continuing professional development and resources: www.basic-skills.co.uk
JOHN MORAN'S LESSON
* Draw 3D shapes on paper
* Write useful mathematical vocabulary on board
* Divide class into pairs
* Get one member of each pair to view shape. They must then describe it to their partner, using mathematical language
* The partner can ask questions and draws the shape.
This addresses curriculum requirements for 3D shapes, vocabulary of 3D shapes and symmetry.