In classrooms where children are not given the opportunity to put their thoughts
on paper, it never happens anyway. In such classes children’s mathematical graphics
do not fit the norm, and for many pressurised teachers it is too much to cope with:
it disturbs the equilibrium. And teachers are often too busy to reflect on what the
marks might mean. Yet a decision to explore further the meanings of their marks
could render different perceptions. As Litherand contends:
for the teacher who views learning as a process of development and construction
rather than a process of association, knowledge could be seen as of personal and
social construction rather than fixed and immutable, as dynamic rather than static.
The impact of such differences upon the criteria by which teachers judge achieve-
ment is significant. (Litherand, 1997, p. 11)Conclusion
Although the idea of bi-numeracy – the translation of informal (home) mathematics
to abstract (school) mathematics – is relatively clear, the difficulty lies in the solution.
‘Bi-directional translation’ was a key feature in Maclellan’s study, where teachers in an
experimental group were constantly making connections in their teaching from infor-
mal mathematics to formal (Maclellan, 2001). This was a small study but it does add
weight to the fact that the key feature indicated success in helping to translate. She
emphasises: ‘informal knowledge serves as a powerful base on which to build more
formal knowledge; and secondly, that by linking informal and formal knowledge the
learner develops greater “power” to apply the formal knowledge’ (Maclellan, 2001, p.
76). And for teachers one of the strengths of encouraging children to use their own
mathematical graphics – their thinking – in their own ways, is that it gives adults a
‘window on to their thinking’ that may otherwise be inaccessible.
In Chapter 6 we show how young children use their own marks to develop their
understanding of mathematics. We introduce categories of forms of mathematical
graphics and explore some early beginnings of number that children represent on
paper, from numerals to representing quantities and counting.Further Reading
The mathematics- Brizuela, B. (2004)Mathematical Development in Young Children: Exploring Notations,
Columbia University: Teachers College Press. - Hughes, M. (1986) Children and Number: Difficulties in Learning Mathematics.
Oxford: Blackwell. - Nunes, T. and Bryant, P. (1996) Children Doing Mathematics. Oxford: Blackwell.
Bi-literacy
Kenner, C. (2004a) Becoming Biliterate. Stoke-on-Trent: Trentham Books.
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