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Children's Mathematics Network

    Copyright M. Worthington & E. Carruthers 2012

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.
With the publication of our research in Children's Mathematics: Making Marks, Making Meaning (first published in 2003) and a research paper: 'Making sense of mathematical graphics: the development of understanding abstract symbolism (published in 2005) our taxonomy has been available to teachers and practitioners throughout the Foundations Stage and Key Stage 1 (birth to 8 years). The taxonomy is often cited by teachers and practitioners as a valuable tool that supports their understanding of young children's development of early 'written' mathematics (children's mathematical graphics) and significantly, has a key role in assessment for learning.
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 parents.
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.


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