From here to infinity
At Stoke Hill first school in Exeter six and seven-year-old pupils sat down with their parents and contemplated the question of the day written on the blackboard. What did they know about money?
With the help of mothers and fathers they were to write down everything they knew before joining the morning circle, sitting on the floor with the rest of the class to discuss their findings.
They had been busy. Max said that French money was very different to English money and that in America they called it the dollar. Gemma was most concerned that you needed lots of money to buy clothes and food. Claire liked notes better than coins "because they were bigger". Another child announced she was taking a trip to the bank with her mother: "Because of all the work she's done she's going to get Pounds 100."
Elizabeth Carruthers, their class teacher, was sitting in the circle and listening carefully. This was a maths lesson and her main concern was to find out how much the children already knew about their subject.
Splitting them into groups subsequently she worked with one on the concept of sharing money; another could choose from the "choice wheel", offering 10 activities based on the art, science, technology and maths areas of the classroom.
One section of the room has been made into a post office, based on the theme of The Jolly Postman, the Ahlberg classic that the class had been reading together. Here Claire had decided to make coins from cardboard and was supervising the weighing of parcels, charging and exchanging currency with friends. The value and uses of money were obviously uppermost in her mind.
Elizabeth Carruthers is one of a group of Exeter primary teachers which believes that all young children come to school with innate mathematical ability which needs to be encouraged and developed.
They study the way early learners express themselves mathematically and with one eye on the national curriculum, create their own maths schemes to take account of this.
Calling themselves the Emergent Mathematics Working Group, they have taken their cue from the influential emergent writing and literacy movement which believes that children are natural readers and writers, and that the teacher's role is to extend the natural symbols and marks that young children make.
Elizabeth Carruthers, who has long been interested in emergent writing, realised there was a huge disparity between the way she taught English and the way she taught maths. She said: "For a long time, I didn't think that really mattered. I thought that maths was a subject some people were good at and others, including me, were not, and that was life."
Now she believes all children are innately interested in mathematical concepts and in her teaching tries to take each child as far as he or she can go. Her children are currrently working on multiplication. Two girls had come up with the idea for a multiplication game. They made strips from paper, each with a number on, and taped them together. This was called a multiplication roll. Their strips were marked with the number one, so other children had to count the strips and multiply them by one to obtain the answer.
Elizabeth then invited other children to choose another number to mark the strips and make up other rolls. The box of multiplication rolls has now become a playtime game where children test each other.
She said: "Once they realised that multiplication was repeated addition, they became really excited. Some even wanted to start doing times tables because this is what older brothers and sisters were doing at school."
As maths coordinator for her school Elizabeth Carruthers has formulated a policy based on meetings with parents, governors and teachers. This policy says that maths can be achieved by all, that it is a developmental process and that teachers must concentrate on the way children learn as much as on the subject itself.
Heather Tozer, the school's headteacher, said Elizabeth had made her realise that the national curriculum maths scheme the school used previously was much too narrow. She said: "We now realise how important it is to look at how children are involved in using maths."
Louise Bunce, a parent governor, said the policy meetings had encouraged parents to realise that they could help their children with maths. She said: "Many parents think they are no good at maths and they eventually pass that sense of failure on to their children. They like formal maths schemes because it is comforting to see pages of sums marked. But to understand that there is no single way of 'doing' maths, that we can all contribute, is very helpful. " Elizabeth Carruthers deliberately involves parents in her maths classes as a way of building up their own confidence in the subject.
Maulfry Hayton, a member of the group and reception teacher at Ide first School, Exeter who has also lectured in early years maths, believes maths projects should be made as purposeful and meaningful as possible. She said: "If, say, we have a school trip then we get the children to work out how the refreshment has to be divided up or how much bus fare is needed.
"Or I might make some jam tarts and ask the children to bring in their teddies. I might then create a situation where you have five jam tarts to be shared between three teddies. That takes us into concepts of division, fractions and moral aspects of sharing such as fairness. The possibilities are open-ended."
The Exeter group believes it is as important to look at how children have arrived at their answers as to look at the actual answer. The group has been meeting for three years and holds annual conferences, inviting teachers, parents and academics to watch them put their theories into practice on groups of children.
Chris Athay, a speaker at one of these conferences, is author of the book Extending thought in young children, the result of years of research at the Froebel Institute in Roehampton.
In this she set out the importance of looking at the processes of a child's learning as well as the product. She said: "If you merely put a tick or a cross next to a product of maths then it doesn't mean anything to anybody. If you look at how the child has arrived at that answer then you really begin to understand something about their cognitive ability.
"Certain methods are thought to be more efficient in maths, but only in theory. Part of the problem with maths is that children get the idea that they have to accept the school method in arriving at solutions, in order to behave properly, when they might not understand that method."
Interest in developmental maths is growing, and the Exeter group's coordinated approach has led to an invitation to hold workshops with Birmingham teachers in May.
The group came together under the auspices of Mary Wilkinson, an Office for Standards in Education primary inspector who became interested in developmental mathematics during her long headship of a primary school.
Mary, who was also a former primary maths adviser for Devon, rejects the use of formal maths schemes which she believes are constricting. Colouring in and ticking boxes hindered children from working out meanings for themselves. Children, she said, needed to be encouraged to behave like mathematicians: "There is nothing in the national curriculum which says you shouldn't love maths."