Children\'s Mathematics

experience in providing the content of representation’. She argues that these first-

hand experiences could be called the ‘stuff’ or ‘content’ of mind (Athey, 1990, p. 58).

For the spiral explorers we walked across a pedestrian bridge that crossed a major

road near the school. At either end the bridge descended in a curve which the local

children referred to as the ‘curly-whirly bridge’. Many children had been exploring

rotation,linear movement,trajectories,maps,zigzags,spiralsand arrows, and linked

these to spirals. Because schemas are rarely explored in isolation, there were links

between different schemas as Figure 3.7 shows.

Figure 3.7The pattern of Aaron’s schema interests (part)

Mapping patterns of schema exploration

We had been looking for the ‘pattern’ of repeatable behaviour to which Athey refers

(1990). When we looked at several weeks worth of observations of each child and

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