Charting the Development of
Children's Mathematical Graphics
There has been a great deal of research
into young children's developing mathematical understanding (e.g.
Gelman and Galistel, 1978; Ginsberg,1989; Sophian, 1996 and Nunes
and Bryant, 1996). However, until 2003 there had been no published
research on the development of children's own 'written' mathematics.
Our research led us to in-depth analysis of over 700 examples of
children's mathematical graphics that we had collected from children
at home, in nursery schools and in Reception classes and Key stage 1
- from settings and schools in which we had taught and in others in
which we have conducted research.
The taxonomy is
not strictly hierarchical but provides an overview of
children's development over time. We are sometimes asked if there is
a point at which children stop using their own mathematical graphics
and start to use the standard written symbols, layouts and methods.
Our research has shown that this a a continuous process: children
want to be a part of the culture in which they live and grow and
effective classroom cultures in school will support this. Children
integrate standard symbols and written methods as they develop their
understanding: when teachers and practitioners collect children's
mathematical graphics and use the taxonomy to chart their
development, this progress will become evident. Such evidence is
invaluable for sharing understanding with your team and with
The taxonomy charts their development that begins with their
earliest marks explored in play. Between the ages of three and four
years of age, children begin to identify separate meanings for their
marks, naming some as written messages or drawings: to others they
attribute mathematical meanings. These marks develop for different
purposes and children use them in many contexts where they are
thinking about numerals and quantities. These graphics are the
foundations of all the standard written mathematics that children
will meet as they move through school. The range of representations
and strategies that children use is huge. They move between the
different dimensions, exploring aspects of mathematics that are of
interest to them and meaningful in their play. Once children are
representing quantities that are counted, they begin to explore
calculations and our further analysis revealed how their own written
methods develop, and the complex strategies children use to support
their mathematical thinking. This is the first time that this
development has been identified and this research has provided new
insights into young children's understanding of mathematics.
Transition and continuity
Importantly, this taxonomy and the related research also supports
transitions into Key Stage 1 and continuity issues - showing how
children develop towards the standard abstract written mathemaitcs
in school over time.
Important: the dimensions identified in the
taxonomy are not aspects to be taught.