choose to write these contextual numbers, they have converted what they have read
and understood into a standard symbolic language. For example, Matthew, 3:9, drew
one of his favourite storybook engines, ‘James the Red Engine’ and ‘5’ which was the
number of the engine (Figure 6.5). Matthew was very interested in numbers, not only
on trains but also on buses and as regards their destination.Figure 6.5 Matthew – ‘James the Red Engine’Representation of quantities and counting
Representing quantities that are not counted
Celebrating what he refers to as young children’s ‘unschooled minds’ Gardner com-
ments: ‘the five-year-old is in many ways an energetic, imaginative and integrating
kind of learner; education should exploit the cognitive and affective powers of the
five-year-old mind and attempt to keep it alive in all of us’ (Gardner, 1993, p. 250).
The marks an un-schooled child makes can be unique, dynamic, energetic and
exciting because they have many unrestricting influences. It is this dynamic form
that teachers may see in children’s mathematical marks when they enter school, for
example Charlotte’s ‘hundreds and pounds’ (Figure 2.2) or Joe’s spider (Figure 2.3)
where he represented something of his sense of its many legs. We also categorise
Figure 10.3 as dynamic: as she played her dice game, Amelie’s graphics show some-
thing of her excitement, enthusiasm and her mental energy. We are in agreement
with Gardner who emphasises that keeping the spirit alive and thinking is crucial
‘to educate students for understanding’, in this case for mathematics (Gardner,
1993, p. 250).100 Children’s Mathematics8657part 1b.qxd 04/07/2006 18:18 Page 100