Throughout time and now throughout a greater part of the world, print – and other
marks that humans make in order to reflect on and communicate their ideas – have
been a significant and powerful feature of our development. In many countries still,
literacy has the capacity to lift people out of poverty. The potency of the written
word which is, in essence, the power of peoples’ thoughts, has at different times in
our history been seen both as a threat and as a strength. Written words and other
graphical languages hold significance in the lives of millions of people today more
than at any time in our history.
Perhaps it is now right to recognise the huge potential of children’s early mathe-
matical marks in helping them understand the abstract symbolism of mathematics.
As we have argued throughout this book, children need to become bi-numerate to
understand the abstract symbolism of mathematics. Leone Burton stresses that the
individual strengths, interests and cultures of the children provide them with a
familiar basis from which the mathematics can emerge; this ‘encourages curiosity
and excitement because the learner begins with a feeling of comfort’ (Burton, 1992,
p. 19).
We have based this book on our mathematical research in the home and class-
room. Combining the two has been essential to find the translation pathways that
loop between informal and abstract mathematics. As a parent, Heidi Mills (1995)
reflects that the process that has remained a consistent feature and driving force in
her children’s growth is the constant search for connections between higher experi-
ences and their current ones.
Teachers have a vital role in the process of bi-numeracy since it is they who can
help children make connections. The flame of mathematical intuition is within chil-
dren but teachers need to be aware of the interactive networks within children’s
brains, to keep the flame burning. Wilkinson emphasises the importance of teach-
ers’ views of the nature of mathematics and of knowledge, society and the future.
She argues that ‘officially and effectively, teachers are the formers of the nation’s
mind’ and ‘if teachers are too narrow, too limited in their view of themselves as edu-236Reflections
8657part 2.qxd 04/07/2006 17:41 Page 236