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339 children aged 6 and 7 at Oxford primary schools took part in a study of arithmetic. 204 of the children had been selected by their teachers as having mathematical difficulties and the other 135 children were unselected. They were assigned to an Addition Performance Level on the basis of a calculation pretest, and then given Dowker's (1998) test of derived fact strategies in addition, involving strategies based on the Identity, Commutativity, Addend + 1. Addend - 1, and addition/subtraction Inverse principles. The exact arithmetic problems given varied according to the child's previously assessed calculation level and were selected to be just a little too difficult for the child to solve unaided. The technique was used of giving children the answer to a problem and then asking them to solve another problem that could be solved quickly by using this answer, together with the principle under consideration. The children were also given the WISC Arithmetic subtest and the British Abilities Scales Basic Number Skills Subtest. Performance on the standardized arithmetic tests was independently affected by both Addition Performance Level and group membership (unselected children versus those with mathematical difficulties). Derived fact strategy use was affected by Addition Performance Level, but there was no independent effect of group membership. (


Journal article


Cognitive Development


Elsevier Inc

Publication Date





401 - 410


Mathematical development, Derived fact strategies, Mathematical difficulties, Arithmetic teaching, Addition, Young children, Procedures and principles