Relational Processing in Children’s Arithmetic Word Problem Solving

Abstract

Solution of arithmetic word problem requires a mental model of task structure that represents variables and relations between them. In arithmetic addition, three variables (augend, addend, sum) are related by the addition operation (English & Halford, 1995). Flexible access to the components of the relation is required especially in non-canonical word problems, in which the augend or addend is missing. Relational processing allows all components of a relation to be accessed, but it is effortful, and is slow to develop during childhood. Therefore, the difference in accuracy between noncanonical problems (augend or addend missing) and canonical problem (sum missing) should be greater in younger than older children. Furthermore, relational processing capacity should predict accuracy on non-canonical problems. In the current research, 132 children aged 6-, 7- and 8- years completed arithmetic word problems in which either the augend, addend or sum was missing and two measures of relational processing ability. Mixed ANOVAs showed significant position effects. Accuracy was lower for problems where the missing sets were in augend and addend positions than in sum position. Hierarchical regression analyses showed that after controlling for accuracy on sum problems, relational processing capacity accounted for more than half of the agerelated variance in accuracy on augend/addend problems and also for significant unique age-independent variance. Findings demonstrate the importance of relational processing in development of children's arithmetic addition, and have implications for designing word problem teaching strategies.