Mathematics in a child-centred curriculum

Constructivism - part 1

Constructivist approaches are central to this mathematics curriculum. To learn mathematics children must construct their own internal structures. As in reading and writing, children invent their own procedures. We accept that children must go through the invented spelling stage before they begin to develop a concept of the structures of spelling. The same is true of mathematics.

Young children attempt to count or order things in the environment and they develop rules for themselves to do so. They should be encouraged to try out these personal strategies, to refine them by discussion and to engage in a wide variety of tasks. It is in the interpersonal domain that children can test the ideas they have constructed and modify them as a result of this interaction.

When working in a constructivist way, children usually operate in pairs or small groups to solve problems co-operatively. Tasks that are written on one sheet can be given to groups of two or more children. This makes consultation, discussion and cooperation essential. Children work at their own pace but are encouraged to complete the task as fully as possible within the set time. They are expected to respect one another’s solutions, not to discredit partners’ reasoning, and to discuss the train of thought used in the process. This sociocultural theory sees cognitive development as a product of social interaction between partners who solve problems together. It acknowledges the importance of the home and family in the child’s learning and focuses on group interaction. It is a process approach rather than a step-like, incremental one.

One form of instruction used is scaffolding. Here the teacher modifies the amount of support according to the needs of the child by modelling the behaviour, for example possible methods of approaching a problem. The teacher breaks down the task and makes the task manageable for the individual child, thus supporting the development of the child’s own problem-solving skills.