Problem Representation and Mathematical Problem Solving of Students of Varying Math Ability

The purpose of this study was to examine differences in math problem solving among students with learning disabilities (LD), low-achieving (LA) students, and average-achieving (AA) students. The primary interest was to analyze the problem representation processes students use to translate and integrate problem information as they solve math word problems. Problem representation processes were operationalized as (a) paraphrasing the problem and (b) visually representing the problem. Paraphrasing accuracy (i.e., paraphrasing relevant information, paraphrasing irrelevant linguistic information, and paraphrasing irrelevant numerical information), visual representation accuracy (i.e., visual representation of relevant information, visual representation of irrelevant linguistic information, and visual representation of irrelevant numerical information), and problem-solving accuracy were measured in eighth-grade students with LD (n = 25), LA students (n = 30), and AA students (n = 29) using a researcher-modified version of the Mathematical Processing Instrument (MPI). Results indicated that problem-solving accuracy was significantly and positively correlated to relevant information in both the paraphrasing and the visual representation phases and significantly negatively correlated to linguistic and numerical irrelevant information for the two constructs. When separated by ability, students with LD showed a different profile as compared to the LA and AA students with respect to the relationships among the problem-solving variables. Mean differences showed that students with LD differed significantly from LA students in that they paraphrased less relevant information and also visually represented less irrelevant numerical information. Paraphrasing accuracy and visual representation accuracy were each shown to account for a statistically significant amount of variance in problem-solving accuracy when entered in a hierarchical model. Finally, the relationship between visual representation of relevant information and problem-solving accuracy was shown to be dependent on ability after controlling for the problem-solving variables and ability. Implications for classroom instruction for students with and without LD are discussed