Abstract
Forty-four children between 6;0 and 7;11 took part in a study of derived fact strategy use. They were assigned to addition and subtraction levels on the basis of calculation pretests. They were 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; and test of derived fact strategies in subtraction, involving strategies based on the Identity, Minuend +1, Minuend −1, Subtrahend +1, Subtrahend −1, Complement 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. Children were given the answer to a problem and then asked to solve another problem that could be solved quickly by using this answer, together with the principle being assessed. The children also took the WISC Arithmetic subtest. Strategies differed greatly in difficulty, with Identity being the easiest, and the Inverse and Complement principles being most difficult. The Subtrahend +1 and Subtrahend −1 problems often elicited incorrect strategies based on an overextension of the principles of addition to subtraction. It was concluded that children may have difficulty with understanding and applying the relationships between addition and subtraction. Derived fact strategy use was significantly related to both calculation level and to WISC Arithmetic scaled score.
Highlights
The use of derived fact strategies might seem even more important with regard to subtraction than addition, since children are generally less able to retrieve subtraction facts than addition facts (Barouillet et al, 2008), so could benefit more from alternative strategies. It may be more difficult for children to use derived fact strategies for subtraction than addition, both because their relative lack of known facts gives them less of a base from which to use them, and because some derived fact strategies for subtraction, such as the “subtraction by addition” strategy (DeSmedt et al, 2010; Peters et al, 2013) depend on some understanding of the inverse relationship between addition and subtraction, which some studies suggest is difficult for children
Young children’s derived fact strategies total number of such strategies used in a task), whereas this study focuses more on the use of particular strategies
FOR ADDITION Table 1 gives the percentage of responses at each level using each principle in derived fact strategies for addition
Summary
There have been a number of studies of children’s use of derived fact strategies in addition and subtraction (Baroody et al, 1983; Russell and Ginsburg, 1984; Beishuizen et al, 1997; Carpenter et al, 1997; Dowker, 1998, 2009; Blote et al, 2000; Star and RittleJohnson, 2008; Jordan et al, 2009; Torbeyns et al, 2009; Cowan et al, 2011). The present study investigated 6- and 7–year-olds’ ability to use derived fact strategies, based on a range of principles, for both addition and subtraction. Its inclusion in the study is intended to investigate whether children tend to use the result of one operation to predict the result of another at all, over and above the particular principles that they are able to use in such predictions This principle has received relatively little attention, but would appear to be a cornerstone of the ability to use derived fact strategies. Most studies (Bisanz and LeFevre, 1990; Demby, 1993) suggest that strategies based on the addition/subtraction Inverse principle (a + b − b = a; if a + b = c, c − b = a) are among the later-developing derived-fact strategies, and are not typically used until the age of about 10. It was predicted that neither the addition/subtraction Inverse principle nor the complement principle would be used by a majority of children
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