Figure 9.15 Nectarines for a picnic: AnnConclusion
In their play the availability of resources for making marks and sensitive support,
resulted in some rich and very relevant mathematical graphics. The teacher-led
models were planned to be sufficiently open to allow children to decide how they
would respond and, if they chose to use graphics, which written method would be
the most appropriate (see ‘modelling mathematics’ pp. 205–12).
These case studies show the range of marks – both informal and some more stan-
dard symbols – that they chose to use. They also show that these children were never
afraid to use their ideas and to change direction if what they had started was not
useful to them. Because each child had chosen their own graphics and ways of
working they understood what they had done. The important point is that in sup-
porting children’s own marks, they will develop independent techniques to not only
use standard methods of calculation but to understand the methods. As the range
(children from 3 to 8 years) in this chapter also demonstrates, their early informal
marks do develop over time in to standard ‘school’ mathematics.
In Chapter 10 we look at ways in which teachers may support children’s under-
standing through effective assessment and modelling of written forms including the
use of abstract symbols.
In this chapter we have focused largely on creating environments in which chil-
dren can freely explore their mathematical thinking on paper: however, it is impor-
tant to emphasise the need to make provision for children to make and explore
personal meanings in many contexts and in multi-modalways (see pp. 91–2, 135).190 Children’s Mathematics8657part 2.qxd 04/07/2006 17:35 Page 190