Children\'s Mathematics

in a second language. These research findings support what we have found when

children learn their second (abstract) mathematical language. For the speaker, a

condition of code switching is that both speakers know the two languages used

(Cook, 2001). In children’s developing understanding of abstract mathematical

symbols, we repeatedly see examples of code switching as children switch between

different forms of mathematical graphics. The most significant switches occur when

they use either:

• implicit symbols


• their own symbols
  or when they begin to experiment with


• standard symbols within their own mathematical graphics.

Exploring the role and appearance of symbols

Addition Subtraction

• A ‘box’ or circle drawn around the
  calculation: children who do this
  appear to understand that each calcu-
  lation is separate and complete in
  itself (see for example William, Figure
  7.9c)
  
  
  • Children may draw a box or circle
    around their calculation
  
  
  
  


• Some children have begun to show
  the operation in three steps (the two
  amounts to be added and the total
  (see, for example, Peter, Figure 7.9b)
  
  
  • Most children show the operation in
    three steps
  
  
  
  


• The use of implicit symbols (see for
  example Mary, Figure 7.9d)
  
  
  • The use of implicit symbols
  
  
  
  


• Interestingly, whilst children at this
  stage often use icons to represent the
  amounts to be added, they generally
  use a numeral for their total (see for
  example Jack, Figure 7.7c)
  
  
  • Again, whilst children often use icons
    to represent the first two sets in the
    calculation, they use a numeral for the
    total (see for example Francesca and
    Jennifer, Figure 7.5)
  
  
  
  


• The use of personal symbols, to
  represent ‘+’ or ‘=’ (see for example
  Jack, Figure 7.7c)
  
  
  • The use of personal symbols to
    represent ‘–’
  
  
  
  


• Children choose a combination of
  icons and numerals (see for example
  Fred, Figure 7.8a)
  
  
  • Children choose a combination of
    icons and numerals
  
  
  
  

Features of this stage may include:

• The use of ‘+’ but ‘=’ is implied rather
  than written. Children who do this
  appear to introduce the standard ‘=’
  symbol at a later stage

Features at this stage may include:

• The use of either ‘-’ or ‘=’ are implied
  rather than written as the abstract
  symbol (see for example some children’s
  methods in Figure 7.5)

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