In the spirit of Antoine de Saint-Exupéry’s internationally known and deeply
moving fable, we have written this book to help ‘the grown-ups’ understand the• Categories of children’s mathematical graphics
Children’s mathematical graphics
This book is a study of young children’s own mathematical graphics and the way in
which they can use their own marks to make their own meanings. This allows chil-
dren to more readily translate between their informal ‘home mathematics’ and the
abstract symbolism of ‘school mathematics’: we argue that childrens’s own mathe-
matical graphics (‘thinking on paper’) enables children to become bi-numerate.Why write about children’s mathematical graphics?
For the past fifteen years we have developed our practice and explored the theories that
underpin this book. Because we were teaching for a greater part of this period we were
able to trial ideas, hypothesise and generate our philosophies and develop our pedagogy
in our own settings. As our excitement in the development of children’s own mathe-
matical marks and their meanings grew, we focused on a number of research projects
that have helped inform and guide us. Where they have relevance for the subject of this
book, we refer to our findings (see Appendix for a list of our research topics).
On numerous occasions we have been invited to share our practice, understand-
ing and some of the hundreds of children’s examples we have collected – with stu-
dents where we have lectured and with teachers on professional development
courses and at Early Years conferences. Students’ and teachers’ responses are almost
always of surprise and great interest – that it makes sense to encourage this, that
working in this way offers a real alternative to the use of worksheets and, above all,
that it offers tremendous insight into children’s understanding and development.
But the benefits are greatest for the children.
We had come to children’s early mathematical mark-making through our own
interest and following many years of experience in supporting emergent writing in
our classrooms. We had seen wonderful progress in children’s early writing and
began to make comparisons with children’s early recorded mathematics. A signifi-
cant element in our development as teachers was the period in which we were
members of the ‘Emergent Mathematics Teachers’ group’ (see this chapter).
As we developed our practice and theory we collected samples of children’s math-
ematical marks.. For a greater part of this period we taught mainly in nursery and
First Schools, and also through the primary age range to 11 years. Although we con-
centrate on the 3–8 age range in this book we feel the development of children’s own
mathematics through the school is important.
It took time to develop our practice in order to support children’s mathematical
graphics. Working with local groups of teachers encouraged us to question assumptions
and consider different perspectives on teaching mathematics in the Early Years. As we
slowly developed our practice we also traced the pattern of children’s early development2 Children’s Mathematics8657part 1b.qxd 04/07/2006 18:05 Page 2