Children\'s Mathematics

traced their development, a visible pattern began to emerge that was quite unex-

pected. When represented on paper the pattern looked like the highs and lows of a

patient’s temperature chart or the stock exchange (see Figure 3.7).

Tracing Aaron’s schema development

(See also, p. 53 ‘Observations of Aaron’s dominant schemas’.)

Beginning with the first observation of Aaron, I noted his interest inrotationat the

top of the chart (see Figure 3.7). I wrote Aaron’s subsequent schemas and I observed

across the top of the chart the order in which they were observed. I gave each written

observation a number (starting with 1 for the first observation) and mapped these

onto the chart. Where a number is repeated, this shows that I observed more than

one schema on one day: Figure 3.7 shows that two observations were made on the

first day (1,1).

Mapping the children’s explorations of different schemas provided us with a great

deal of information and all the children’s ‘maps’ shared certain features. The most

significant of these are that:

• when represented, each child’s ‘journey’ traces a similar zigzagging pathway that
  moves gradually forwards


• all children revisited some earlier schema interests, allowing them to add new
  understandings.

Figure 3.8 Key to the pattern of Aaron’s schema journey

Rotationand rolling up/unrolling

Lengthand height; comparing, measuring and estimating length

Direction

Vertical, up, down and through

Spirals

Enclosure

Connection

Horizontal, along and through

Zigzags

Grids

On top

Trajectories

Right angles

At the same time Aaron also explored:

Rectangles

Counting one-to-one

Writing letters and numerals

52 Children’s Mathematics

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