The children sit over their Think Boards large, laminated placemats and think about farmer Tom and his sheep. Farmer Tom had three sheep in his field. He went to the market and bought four more. How many does he have now?
To help them solve the problem, the pupils can fill in any of the four sections on their board: drawings, materials, important bits and number sentence. They might begin by using actual models of sheep or cubes to represent the sheep in the materials section.
Then they might draw the sheep in the field and the market in the drawings section. Next, guided by questions from their teacher (such as: "Do we need to know they're sheep?") they might represent the vital parts of the sum three dots and four dots, say in the important bits section. Finally, when they're ready, they can write the number sentence: 3 + 4 = 7.
The children are learning to add by moving from touch, to visual representation, to symbols, to numbers, to mental working. This progression is central to the First Steps in Mathematics approach, devised by academics in Western Australia and used in primaries in a number of English and Welsh authorities, such as Torfaen in south Wales. It aims to tackle children's understanding of basic mathematical ideas.
Nicola Thain, maths co-ordinator at Hollybush Primary in Torfaen, has been introducing the scheme and training staff to use it for the past two years. She is excited by the growing confidence of children who are learning to solve problems for themselves. "We can diagnose pupils' misconceptions and then teach them to overcome them," she says. "Last year, we had a really bright little boy in Year 56 who couldn't solve a problem such as adding two lots of jelly beans without drawing them.
"He'd gone through all of primary school without that missing link. I took him aside and showed him how to represent the beans in another way with tallies and then numbers. Then he progressed to working mentally, and now he's flying."
For information about First Steps in Mathematics, contact Sue Dean, national manager of Steps Professional Development, a not-for-profit company owned by the University of Western Australia, at firstname.lastname@example.org. For details of courses for teachers or facilitators and training materials, visit www.stepspd.com.
Using and applying mathematics: solve problems involving counting, adding, subtracting; describe a puzzle or problem using numbers, practical materials and diagrams.
Using and applying mathematics: present solutions to puzzles and problems in an organised way; explain decisions, methods and results in a pictorial, spoken or written form, using mathematical language and number sentences.