Gimme sum loving
Since the publication of the Government's "desirable outcomes" for children starting school, far more attention has been paid to the development of basic skills in the nursery, including maths. But can nursery teaching ensure that children begin school with adequate maths skills?
There is considerable debate over whether young babies' ability to distinguish small quantities is innate or learned over the first few months of life. What is certain is that very small children have intuitive knowledge of quantity long before they learn the names of numbers or terms such as "more", "many" and "a little". Babies develop primitive concepts and then gradually map the language on to them. As children's social and linguistic abilities grow, they meet a variety of mathematical concepts that are embedded in everyday life. Domestic activities such as shopping, meal times, wash days, gardening or sewing are rich in mathematical challenges, as are many play activities.
It is a truism that maths is all around us, yet the language and interaction used to draw young children in to these activities will determine whether they grow to recognise the maths involved in them. It takes time for children to understand that there are mathematical - as opposed to, for instance, social - elements in such activities. Young children are naturally attuned to social aspects of the world around them.
This means that when they're helping to sort the washing they're more concerned about the ownership of each garment than its relative size. When they help in the garden they're more interested in adults' intentions than in the number of seeds that go in each hole. When they're helping with the baking they're more interested in the end product than in the measuring and weighing.
Small children must satisfy their social curiosity before moving on to a discussion of the maths. We can use children's natural concern with social meaning to draw them in to a dialogue about the more abstract qualities of number and logic.
There are important differences between home and school learning. Home learning is leisurely, gives plenty of opportunity for incidental learning, is responsive to the child's needs and is rich in the adult-child interaction that nurtures language development. Children who have plenty of experience of everyday maths will begin to use the language of maths before they go to school. They will also begin to reach the level of understanding at which they can reflect on and talk about mathematical aspects of familiar situations. Important concepts will build up gradually.
Home maths, however, has such a different agenda from school maths that children can find it difficult to link the two. This often leaves primary teachers believing that children know nothing about number, and that they must be taught simple concepts such as one and two.
Nursery maths can form a bridge. In the nursery, we usually offer "self-service" maths, where the children are expected to help themselves to key experiences. This contrasts with children's home learning, and that can cause difficulties. Research shows a minimal maths content in children's nursery activities - much smaller than children would be receiving in a stimulating home environment. This varies, of course, with the nature of the nursery provision and the experience of the teacher.
Studies of nursery schools also show that when staff judge children to be "learning maths" for 80 per cent of the day, they are in fact using numerical skills for only 2 per cent of their day. This suggests there is something deeply problematic about delivering maths in the nursery. Compared with literacy activities (which can take up almost half a child's playing time), maths activities seem to occupy a fleeting and incidental position in children's daily lives. Why should this be so? Every nursery includes maths in the curriculum, but children starting school usually know far less about maths than they do about reading. There are three interrelated problems that make maths especially difficult to offer at nursery level.
* There is no concrete focus for maths activity, as there is for literacy in stories
There is no focus for maths to compare with print as a focus for learning about reading. It is a purely mental activity, and it's easy for children to miss the point of what they are supposed to be doing. For example, investigating the capacity of pots and pans in the water tray is a popular maths activity. However, there is no guarantee that children will pay any attention to the issue of which pot holds the most.
* Adults are often not confident about the maths curriculum for nursery children
While the maths specialist might be able to identify learning opportunities and develop activities, most nursery practitioners find this difficult. For example, pre-school children don't immediately connect counting with quantity. It's quite common for young children to count a series of objects, and then on being asked "How many are there?" to respond by counting again from the beginning. This can be quite unnerving for the practitioner who expects a simple prompt to be helpful.
* Nursery children's levels of understanding can vary enormously. we cannot generalise about the maths experiences they need
Adults need to understand what level a child is at before they can be confident they are offering useful experiences. For example, you may play a dice game with a three-year-old and a four-year-old. The four-year-old pays attention to the number on the dice and the number of moves. The three-year-old is quite happy to shake the dice and hop a counter round the board. A happy compromise can be reached only if the adult knows that both the children are operating at their optimal maths level.
The following principles will help nursery teachers make maths explicit without talking over children's heads.
* Ground activities in familiar nursery contexts
Maximise the daily maths opportunities that are already a part of children's lives. Avoid the seriousness and formality that seem to accompany so many maths materials
Use familiar contexts to encourage children to focus on the properties of small numbers.
* Use language that is at the children's level
Young children need conversation that is at their level. It's not enough for adults just to model the correct mathematical terms; they need to engage in conversations that are meaningful to the children. For example, children need to be encouraged to describe shapes made in creative play in their own words. They need to call things "wiggly" and "pointy" as well as to learn to use terms such as "curved" and "straight".
* Make sure that activities are open-ended
Just as children can join in a story time without always following the plot, so they can join in activities without understanding the maths. The experience itself, and the opportunity to join in, is what's important, not whether they grasp the maths principles. Young children can be drawn into mathematical activity without really being aware of the goals. Once they've mastered the practice, it's the teacher's role to make sure they begin to understand and talk about the implicit goals. For instance, most children can count before they go to school. What they really need to know is why people count things - something that many high achievers understand long before they start school.
* Use Interactive games to introduce children to the language of maths
One way of involving children in a mathematical language is to set up repetitive activities that require a stereotyped "response" from the child. Just as babies learn the rules of conversation by starting with turn-taking games, so older children can learn the rules of mathematical discourse by starting with repetitive interactive games.
It has long been documented both that children learn much of their early maths in the home, and that they often struggle to link their home-learned knowledge with the formal school curriculum. The nursery is a place where, with the right curriculum, children can be helped both to expand what they've learned at home and to prepare for the formal curriculum that lies ahead.
LEVELS OF DEVELOPMENT IN PRE-SCHOOL MATHS
(derived from the American researcher, Herbert Ginsburg)
The beginner deals intuitively with quantities, shapes and directions. At this level, children don't count, for instance; they deal with quantity in a purely visual way. They can see the difference between "a lot" and "a little" and they can name or match small quantities (up to three or four) without counting. They will join in with counting, but they can't always recite the number words on their own. This represents the earliest level seen in nursery, yet even at this level children will benefit from joining in with older children and imitating goals that they don't yet grasp.
The apprentice mathematician uses language to engage with mathematical experiences, but doesn't grasp much of the logic or rules. At this level, children's understanding is social rather than mathematical. For instance, they may know how to use a thermometer but will be more concerned about the social meaning of a high temperature (the consequences and the appropriate role) than its mathematical meaning. This is a vital stage in children's understanding and represents the level most commonly seen in nursery schools. This social curiosity leads children to play with and repeat mathematical goals.
The independent mathematician is beginning to use mathematical rules. At this level, children can reflect on their mathematical experiences; for instance, they can use number logic to interpret and order the world. This reflective activity represents the highest level seen in nursery school and allows children to discuss specifically mathematical goals.
Penny Munn is senior lecturer in developmental psychology at the University of Central Lancaster; Sue Gifford is senior lecturer in primary mathematics education at Roehampton Institute; and Patti Barber is lecturer in primary education at the University of London. They are authors of Nursery Mathematics (Heinemann)