Children\'s Mathematics

withhold standard letters, printed texts and punctuation. What is important is that

we provide children with the whole picture – and for addition and subtraction this

will include the standard symbols (see Chapter 10 on ‘modelling’ mathematics). It is

clear that teaching early writing and early mathematics can pose difficulties for

teachers, and that misconceptions are often perpetuated (see Chapter 4 on early

writing and Chapter 5 on the difficulties teachers face).

Hughes’s final comment on the findings of his studies shows that they differ from

ours. He observes that they showed ‘a striking reluctance on the part of school-age

children to use the conventional operator signs of arithmetic’ (Hughes, 1986, p. 78).

We do have examples of some children from 5 years of age choosing to use standard

symbols, although we do not suggest that doing so should be a goal for all young

children. The examples in this chapter show that whilst children often use other

marks, words or strategies in place of symbols, some may also use implicit symbols

and others may use the standard symbols by choice. As we argue throughout this

book, children should be able to choose the graphical form and written method and

be supported in their developing understanding.

Standard symbol use when adding small numbers:

Addition Subtraction

• The use of standard numerals and • The use of standard numerals and
  symbols in a horizontal layout symbols in a horizontal layout
  (see, for example, Anna, Figure 7.10
  
  
  • and for the features below)
  
  
  
  


• The operation is shown in three steps • The operation is shown in three steps


• Often calculations are separated from
  each other by a line, circle or box

Anna, 6:3, chose to represent her calculations in a standard symbolic form (see

Figure 7:10).The context of this was of the ‘dice game’ that Amelie (Figure 10.3)

also played.These children were in a class of 4- to 6-year olds and Anna was a

little over a year older than Amelie. As we showed in Figure 7.5, there can be a

wide variety of graphical responses from children in one class.Whilst Amelie

represented the dots on individual dice in a dynamic and highly personal way,

Anna used the opportunity to add the amounts on the two dice thrown each

time, shown in Figure 7.10, and represented what she had done in a standard

form. She also chose to draw a ‘box’ or circle around each calculation, a feature

that she had copied from her peers though this had not been teacher-modelled

or taught.This separation shows her clear understanding that each calculation

was a separate entity.

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