6Addition and Subtraction: Basic Facts/Number Combinations

One of our key beliefs is that interventions must have mathematical structure and credibility.


If you ask dyslexic or dyscalculic children, or indeed any child, to add 8 and 7 and explain how they reached their answer you will get a selection of methods, depending on each child’s experiences and own idiosyncratic ideas. Ackerman et al. (1986) call them ‘inconsistent’, for example:

  • Counting all: the child counts to 8 and then counts on the 7 (probably counting on fingers or on objects in the room).
  • Counting on: the child holds 8 in his head and counts on 7 counting through 9 to 15 (again, probably counting on fingers or on objects in the room). This strategy is prone to the common error where the child starts counting at 8.
  • Using 10: the child breaks 7 into 2 + 5, uses the 2 with the 8 to make 10, then adds 5, or works via 7 + 3.
  • Using doubles: the child uses (2 × 8) − 1 or (2 × 7) + 1.
  • Straight recall: the child ‘just knows’.

Carpenter and Moser, quoted in Thompson (1999) identify five levels of sophistication of addition strategies used by young children when solving simple word problems:

  • Count all.
  • Count on from the first number.
  • Count on from the larger number.
  • Recall/retrieval of a known fact.
  • Deriving the fact from a known fact (as in using 5 + 5 to access 5 + 6).

In their research on basic addition, Gray and Tall (1994) observed that children rated as above average in maths by their teachers either ...

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