Middle School Students' Mathematical Problem Solving: An Analysis of Think-Aloud Protocols

Using a cognitive-metacognitive theoretical framework, this study examined the verbalizations of middle school students as they thought aloud while solving three mathematical word problems. Middle school subjects who had been identified as learning disabled, average achieving, and gifted were given demonstrations and practice in thinking aloud and were then instructed to solve one-step, two-step, and three-step word problems while thinking aloud. A priori categories were developed based on information-processing theory and a cognitive-metacognitive perspective of mathematical problem solving. Verbalizations were coded, and between-group and grade comparisons of the number of verbalizations within categories were conducted. The relationship between type of verbalization and overall performance was also analyzed. The findings support Ericcson and Simon's (1980) view of concurrent verbalization as a technique for assessing cognitive processes and Swanson's (1988) notion that students with learning disabilities may use a qualitatively different approach to problem solving than their nondisabled peers.