Children\'s Mathematics

Separating sets

Addition Subtraction

Features may include: Features may include:

not know if children are counting or adding when they do this, but if they write ‘1

+ 1 + 1 + 1’, then we suggest that they are beginning to use the addition sign to good

effect. Repeated addition is a strategy that they will later be able to use in the early

stages to work out multiplication problems. Furthermore, it appears that as children

move through increasingly efficient and economical strategies, they revisit their

already familiar strategies in which they already feel secure.

Exploring symbols

As we have shown in some of the examples above, children explore both the role

and the appearance of symbols. Some children who have begun to make explicit use

of symbols may move on to increasingly choose to use standard symbols.

• The calculation written as a narrative,
  in words (for example see John, Figure
  7.8b)
  
  
  • The calculation written as a narrative,
    in words
  
  
  
  


• Some use of invented signs, for
  example a single line for ‘=’: (see for
  example Jack, Figure 7.7c)
  
  
  • Some use of invented signs, for
    example arrows in place of ‘–’ (as in
    Figure 7.5)
  
  
  
  


• Use of a hand to show how many
  have been added to the first set: we
  come across examples of this less
  often in addition than in subtraction
  (for example see Fred, Figure 7.8a)
  
  
  • Use of a hand to show how many
    have been taken away from the first
    set. The hand is now drawn in the
    centre of the calculation, so that it
    can be ‘read’ in a standard way (for
    example see Figure 7.5)
  
  
  
  


• Use of words to represent the total, for
  example ‘6 all together’ or ‘there are 7
  now’ (see for example Figure 7.7a and b)
  
  
  • Use of words to represent the total
  
  
  
  


• Use of word ‘and’ to represent ‘+’ (for
  example see Louisa and Scarlett, Figure
  7.7a and b)
  
  
  • Use of words ‘take away’ to stand for
    ‘–’. We have seldom found this: at
    this point children seem more likely
    to use some of the strategies shown
    in Figures 7.4 and 7.5
  
  
  
  


• Children represent items to be added,
  in separate sets
  
  
  • Children show two separate sets or
    numbers and a third set or number
    for the answer
  
  
  
  

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