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CM Network 2007 |
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. |
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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:
6 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. |
