Associativity and Understanding of the Operation of Addition in Children with Learning Differences

Abstract

This study sample consisted of children from two learning categories, learning disabled (LD, n = 27, x̄ = 9.08) and not identified as learning disabled (NLD, n = 42, x̄ = 7.46), who were individually tested on three different mathematics tasks. The modified nonverbal task and the associativity of length task investigated the quality of students' structures of organizing activity by noting the complexity of grouping relationships abstracted among and between object sets (i.e., composite unit structures). Additionally measured in these two tasks was response accuracy. The flashcard task measured accuracy in response to the same number problems as in the modified nonverbal task as well as strategy type used. However, the strategies scored on the flashcard task were indicative of explicitly taught procedures regardless of children's structures of organizing activity. Significantly more NLD children abstracted composite unit structures suggestive of operational logic on the modified nonverbal and associativity of length tasks, although there were no significant differences in the rate of success on the modified nonverbal task. On the flashcard task, there were no significant differences between the two groups on strategy type used, although the LD children achieved greater success. These results suggest that although children state correct answers on the flashcard and modified nonverbal tasks, they may be reflecting on the tasks using thought structures that are not yet operational.