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Children's Mathematical Graphics

    © Copyright M. Worthington & E. Carruthers 2012

Representation – or recording? Process – or product?
 
The emphasis in children’s mathematical graphics is on children’s own mathematical thinking, meanings and understanding about all aspects of written mathematics and symbols. The value of using paper to explore their thinking is that their own representations support understanding by allowing children to see some of their emerging understanding of ‘written’ mathematics. In a sense children’s mathematical graphics are their mental methods – on paper. Using their own mathematical graphics helps young children to 'translate' between their early informal marks and the standard symbols and written language of mathematics. Children need to be free to choose how they will represent their mathematical thinking that best fits their purpose, the particular mathematical context or calculation they are exploring, or the problem they wish to solve.

In children’s own mathematical graphics the emphasis is on processes of mathematical thinking  (creative thinking, reasoning, meanings, understanding, problem solving, negotiation and co-construction of understanding) rather than products (recording something done practically). Real contexts for their mathematics will allow children to make greater sense of their mathematics when they explore their thinking through their own representations.

Recording what they did following a practical activity has limited value and involves lower levels of thinking. Children do not need to record mathematics if they can do it mentally; neither do they need to record something they have worked out in a practical context. Recording places the emphasis on marks and drawings as a product and is a lower level of cognitive demand (thinking) in mathematics. The difference between representing mathematical thinking and recording is one of quality and depth of thinking.

Understanding, supporting and assessing
Children’s mathematical graphics also have tremendous value for teachers since they reveal each child’s thinking about all aspects of written mathematics. Annotated pieces also offer an invaluable tool for assessment in mathematics when used with the taxonomy.

 

Origin

Practical mathematics

Challenges for children

Mark making

Williams Maths Review: Early Years (DCSF, 2008)

The Williams Maths Review: Mathematical Mark-Making (DSCF 2008)

'Mark Making Matters' (DCSF, 2008)

Publications

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