I Do and I Understand

This guide explains the intentions of the Nuffield Mathematics Project, gives detailed descriptions of the ways in which a changeover from conventional teaching can be made and faces many of the problems that will be met.

The contribution of the psychologist Piaget to the development of mathematics is described, as is the significance of language and discussion, both of which had been given little credence in previous mathematics schemes.

The emphasis here is on how to learn, not on what to teach. The principle behind this approach is that children must be set free to make their own discoveries and think for themselves, and so achieve understanding.

There are direct teaching suggestions, examples of apparently un-mathematical subjects and situations which can be used to develop a mathematical sense, examples of children's work, and suggestions for class discussions and out-of-school activities.

The children's work that has been reproduced in these books is not supposed to be taken as a model of perfection. Some of it indeed contains errors. It should be looked upon as an example of work that children might produce rather than a model of work that they should produce.

A child's attitude towards a subject is formed in a variety of ways and this project states that to ensure a good attitude towards mathematics, at all times and at all levels, children should have a real understanding both of the problem involved and the possible ways in which it might be approached. Also, that means should be found to enable children to gain some insight into the nature of the subject - that it is forged for man's purpose and therefore variable and that it is an imaginative and creative subject and therefore fascinating.

Teachers have discovered that knowledge can be acquired and facts gradually stored through 'active learning', and that when children are actively involved in real situations the process can be most exciting for teachers as well as children. The work of Piaget would seem to indicate that the majority of the children in primary schools are passing through what he terms the stage of concrete operations, that they are able to deal confidently with real problems arising from the use of concrete materials.