The Evolution of Proportional Structures in Children with and without Learning Differences

Abstract

Children in grades 2 and 4 through 7 of average intelligence with (a) learning disabilities (LD, n=29) and (b) not identified as having learning disabilities (NLD, n=30) were individually tested in a task that investigated the development of proportional structures of thought. Four of the children in the LD group were not classified but were receiving basic skills instruction due to their poor performance in mathematics both on standardized testing and in the classroom. Mathematical knowledge was additionally assessed on the Woodcock-Johnson Tests of Achievement-Revised (WJTA-R). In this cross-sectional design, students in both groups coordinated increasingly more complex relationships among the elements of the problem as a function of grade. However, significantly fewer children with LD had constructed second-order logical structures necessary to act on problems using multiplicative and preproportional reasoning. No children in either group demonstrated formal proportional reasoning although a small minority evidenced qualitative proportional reasoning. On the applied problems test of the WJTA-R, the students with LD generally performed below same-aged peers, although they achieved approximately at grade level on this task. For both groups, the explicitly taught procedures to solve computation and word problems as measured on the WJTA-R failed to accurately represent the degree of operational logic in children's biologically based structures of logical-mathematical activity. Diagnostic and remedial implications are discussed.