Many children read mathematics word problems and directly translate them to arithmetic operations. More sophisticated problem solvers transform word problems into object-based or mental models. Subsequent solutions are often qualitatively different because these models differentially support cognitive processing. Based on a conception of problem solving that integrates mathematical problem-solving and reading comprehension theories and using constant comparative methodology (Strauss & Corbin, 1994), 98 sixth- and seventh-grade students' problem-solving behaviors were described and classified into five categories. Nearly 90% of problem solvers used one behavior on a majority of problems. Use of context such as units and relationships, recording information given in the problem, and provision of explanations and justifications were associated with higher reading and mathematics achievement tests, greater success rates, fewer errors, and the ability to preserve the structure of problems during recall. These results were supported by item-level analyses.
Stephen J. Pape, The Ohio State University, School of Teaching and Learning, 333 Arps Hall, 1945 North High Street, Columbus, OH 43210; firstname.lastname@example.org