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    Copyright M. Worthington & E. Carruthers 2012

Development of children's mathematical graphics:
Development of early 'written' calculation
It is important that children build on their early personal (intuitive) mathematical marks and explore early calculations in their own ways. This helps them develop their mathematical thinking and represent what they understand. It allows them to gradually integrate standard numerals and mathematical symbols with understanding.
Range of Marks (Forms)
   
Development of Written Number and quantities
   
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Counting continuously
Alison: ‘Seven toys and seven children’ - 5 yrs 1 month
Separating sets
Fred: adding grapes
5 yrs 8 months
Exploring symbols
Barney: subtracting beans
5 yrs 7 months
   

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Standard symbolic calculations with small numbers - Anna's dice game:
5 yrs 3 months

Calculations with larger numbers supported by jottings – Alison: multiplying by 99
7 yrs 3 months

Development of early 'written' calculation:
Counting continuously
- children begin to understand the separation of two quantities and are developing a sense of addition (or subtraction)
Separating sets - children use a range of strategies to show that the two amounts are separate. They may put a space between the two sets they represent; separate the set with words; put a vertical line between the sets or use an arrow or other personal symbol between them
Exploring symbols - children explore the role and appearance of symbols, by either using invented symbols or approximations, or by the use of implicit symbols
Standard symbolic calculations with small numbers - this stage arises out of the previous ones. Children now choose to use standard numerals and symbols in a horizontal layout
Calculations with larger numbers supported by jottings - children draw on a range of strategies including earlier personal methods, taught 'jottings' (in England) and often use novel strategies to solve problems.

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