Rotationand spiralschemas also complemented each other. The observations above
show the way in which Aaron added to his understanding over an extended period
of time and it is important to remember that all these observations were of child-ini-
tiated and often spontaneous play, and not direct teaching. This underlines the sig-
nificance of opportunities for children to play in ways that support their deep
cognitive concerns. Aaron could not have explored these schemas in a setting in
which child-initiated play was not valued or where staff gave no time and opportu-
nities for this.
During the nine months in which these observations were made, Aaron also
explored various schemas when choosing to write letters and numerals: these were
clearly linked with vertical,horizontaland connectionschemas, and this is explored
further in Chapter 4.
Looking at Figure 3.7, Aaron’s ‘journey’ of schema explorations can be seen to
move forwards, as he visited new and often related schemas, then revisited previous
schemas. Although Aaron appears to be constantly changing his focus, it is clear that
there were relationships between his behaviours. Athey proposes that rather than
describe children’s changing interests and play behaviours as ‘flitting’, through
knowledge of schemas we can often see that the child is ‘fitting different but appro-
priate content’ into their latest ‘form’ (Athey: 1990, p. 107).Making meaning through mark-making
As the children’s schemas developed from action to thought they recorded and rep-
resented their schemas with resources and materials to hand. As we have shown, the
children represented their cognitive constants using objects such as their actions
with their bodies, toys, cut-outs from paper, sand, grass, clay, block play, objects
made with different materials (technology), constructional apparatus, pencil sharp-
eners, yoghurt and cakes. They also recorded and represented their schemas through
making marks on paper with pens, crayons, paint and pencils.
In his significant study of young children’s art, Matthews highlights the view of
Thelen and Smith, (1994), ‘who have thought of these actions as “attractors” ...
emerging in specific contexts’ (Matthews, 2003, p. 23). This perspective points to
such patterns of behaviour as dynamic processes ‘in which the child takes advantage
of the avenues of action which present themselves’ (Matthews, 2003, p. 29). Describ-
ing aspects of the infant’s and young child’s worlds to which they are drawn,
Matthews argues that their ‘attractor systems operate like searchlights, which illu-
minate for the child aspects of the world in a systematic way’ (Matthews, 1999, p.
80). Reading the observation notes of Aaron on p. 53 the extent to which certain
forms and actions acted as attractor systems for him is clear.Schemas highlight the mathematics in the world
When we observe children exploring a schema it enriches our experience of how they
think and learn. Mathematics can be seen in the broadest sense through children’s54 Children’s Mathematics8657part 1b.qxd 04/07/2006 18:08 Page 54