The evolution of proportional structures in children with and without learning differences

Children in grades 2 and 4 through 7 of average intelligence with (a) learn ing disabilities (LD, n = 29) and (b) not identified as having learning dis abilities (NLD, n = 30) were individually tested In a task that investigate d the development of proportional structures of thought. Four of the childr en in the LD group were not classified hut were receiving basic skills inst ruction due to their poor performance in mathematics both on standardized t esting and in the classroom. Mathematical knowledge was additionally assess ed on the Woodcock-Johnson Tests of Achievement-Revised (WJTA-R). In this c ross-sectional design, students in both groups coordinated increasingly mor e 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 fo rmal proportional reasoning although a small minority evidenced qualitative proportional reasoning. On the applied problems test of the WJTA-R, the st udents with LD generally performed below same-aged peers, although they ach ieved approximately at grade level on this task. For both groups, the expli citly taught procedures to solve computation and word problems as measured on the WJTA-R failed to accurately represent the degree of operational logi c in children's biologically based structures of logical-mathematical activ ity. Diagnostic and remedial implications are discussed.