Academic journal article Learning Disability Quarterly

Middle School Students' Perceptions, Persistence, and Performance in Mathematical Problem Solving

Academic journal article Learning Disability Quarterly

Middle School Students' Perceptions, Persistence, and Performance in Mathematical Problem Solving

Article excerpt

Abstract. The purpose of this study was to explore middle school students' (N= 54) perceptions of problem difficulty, persistence, and knowledge and use of problem-solving strategies in solving mathematical word problems. Students identified as learning disabled, average achieving, or gifted were tested individually as they solved six word problems classified as 1-, 2-, or 3-step problems. After the examiner read each problem, the student rated the problem's difficulty on a 1-to-6 scale (very easy to very hard) and then solved the problem. Results indicated that students with learning disabilities rated problems as significantly more difficult and had a significantly lower total word problem score than both average and gifted students. In comparison, average students rated problems as significantly more difficult than gifted students but did not differ significantly on total word problem score. There was no significant difference between students with learning disabilities and average achievers in the length of time they spent solving problems, but both groups took significantly longer than the gifted students. Students with learning disabilities used significantly fewer problem-solving strategies on

the two- and three-step problems than both the average and the gifted students, who did not differ. Findings suggest that although students with learning disabilities perceive problems as more difficult than do their more successful peers, they do not spend more time solving problems. Even with greater persistence, however, they would still be at a serious disadvantage compared with better problem solvers because they seem to lack important problem-solving strategies for effective and efficient mathematical problem solving.

This study explored middle school students' perceptions of problem difficulty, persistence, and knowledge and use of problem-solving strategies in solving mathematical word problems. Previous research indicates that despite a positive attitude toward mathematics, students with learning disabilities (LD) are significantly poorer mathematical problem solvers than nondisabled students (e.g., Montague & Applegate, 1993a). Research also suggests that students with LD have strategy deficiencies that may be related to poor academic performance (e.g., Swanson, 1990). For mathematical problem solving, the most salient deficiency seems to be in problem representation processes and strategies, which are critical to effective problem solving (Hutchinson, 1993; Mayer, 1985; Montague, Marquard, & LeBlanc, 1993; Zawaiza & Gerber, 1993).

Problem representation strategies are needed to process linguistic and numerical information, comprehend and integrate the information, form internal representations in memory, and develop solution plans (Silver, 1985). These strategies facilitate translating and transforming problem information into problem structures or descriptions that are verbal, graphic, symbolic, and/or quantitative in nature (Heller & Hungate, 1985; Janvier, 1987; Mayer, 1985). These verbal and visual representations in turn assist in organizing and integrating problem information as the problem solver develops a logical solution plan. Specific problem representation strategies include (a) paraphrasing or restating problems in one's own words; Co) visualizing problems by drawing pictures, constructing diagrams or charts, and making mental images; and (c) hypothesizing or establishing goals and setting up a plan to solve the problem.

Research has also suggested that academic performance may be influenced not only by cognitive factors such as ability to represent problems, but also by noncognitive factors, for example, self-perceptions of ability or academic competence and perceptions of task difficulty (Heath, 1996; Montague, 1997b). Meltzer, Roditi, Houser, and Perlman (1998) found that, although students with LD rated their academic performance and organization as average to above average in seven of nine academic domains, their ratings were still significantly lower than the ratings of average achievers in all nine domains. …

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