Shopping around for answers
My attention was drawn to children's level of understanding when working in a nursery class. I noticed that they paid little attention to counting as they talked in a home corner and shop specifically designed to prompt opportunities to use number when serving and buying. Lists, pictures and stories they produced spontaneously in the course of these activities also showed a worrying absence of written numerals. However, in more formal maths activities, when asked to write "how many" on their drawings, most were confident about writing numerals. They were also able to identify numerals in picture books or wall displays without hesitation. The fact that they made little spontaneous use of number as they played suggested that it did not come naturally and that it had not become a part of everyday communication.
In the research project that followed, in-depth interviews were conducted with 48 children of nursery and reception age in two schools in contrasting social areas. Activities were designed to assess directly understanding of the meaning and uses of number. As part of a shopping activity, the children were asked to write a note for the milkman, and to label tins to show how many bricks were in each. In both activities there was little use of numerals, for example, the children chose instead to make marks or draw pictures to represent the number of bottles.
I decided to probe whether the lack of spontaneously written numerals was because number was not part of the children's everyday thinking.
Tasks were devised around ordering fast-food for a party. An order was agreed for each guest, recorded pictorially and, referring to the picture, the children were asked to telephone the order through. These results were perhaps the most revealing. Hardly any of these children of nursery and reception age made use of their counting skills - they did not use number in their speech. Instead they simply said "milk shakes" or "some burgers ...."
These findings contrasted greatly with research showing how much is learned about reading in the pre-school years.
What are the causes of this mismatch between understanding the purpose of numbers and the ability to write, read and recite them when asked to do so directly at other times?
The second part of this project probed what the children had learned about number. The results were equally surprising; in contrast to uncertainty about numbers for counting, these three and four-year-olds were highly aware of numbers as "labels", for instance on telephones and birthday cards, and competent at explaining why they were there. Several knew about route numbers on buses and a few about the "2" on a 2p coin. These children were also sophisticated in their knowledge about house and telephone numbers, were able to write parts of their address and phone number, as well as the time and date of a party on an invitation card. (The results can be seen in Early Child Development and Care Vol 125.)
This seemed to raise three issues.
* There is a need to assess number in greater detail. Asking a child to count or to label a picture does not indicate a grasp of how to use, apply or transfer school learning to solve or deal with everyday situations. This has fundamental implications for the design of baseline assessment.
* How can we address the imbalance in children's experience and learning about number during the pre-school and reception years?
* An issue that pervades all key stages: the difficulty in making cognitive links between "formal" maths and practical or oral activities. A fundamental weakness may exist in the foundations of children's understanding - and in their security and confidence with mathematics. Could this shed light on the lack of confidence and under-achievement which escalate as children move further along the school system?
I have since replicated the research with a further 48 children in two schools in Sweden and with 72 children in three schools in Japan. The results (as yet unpublished) in all three countries were remarkably similar. Perhaps this reflects the maths to which we expose our children in modern times. If Japanese children later achieve better results in some aspects than British children, we should be asking what is the nature of the primary curriculum in Japan that enables their children to eventually overtake our own? Children's ability to understand is not in question.
The national curriculum's requirements for teaching about using and applying maths was a welcome addition to the maths content covered in schools - yet inspection findings continue to stress weaknesses in this area. How much time and emphasis do teachers feel able to devote to it? If we are to address this issue right from the start, we will need to look at what is taught about number and how it is assessed in the nursery and infants, and to allow for greater integration of using and applying into "everyday" activities in the classroom. Any new proposals should be evaulated for detail, integration and overall balance.
Jennifer Rogers is currently lecturer in education at the Open University and co-ordinator of the Primary PGCE. In September she will become lecturer in primary education and mathematics at the University of Leicester.