An Investigation of the Effects on Students' Attitudes, Beliefs, and Abilities in Problem Solving and Mathematics after One Year of a Systematic Approach to the Learning of Problem Solving

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This study investigated the effects of Oregon's Lane County "Problem Solving in Mathematics" (PSM) materials on middle-school students' attitudes, beliefs, and abilities in problem solving and mathematics. The instructional approach advocated in PSM includes: the direct teaching of five problem-solving skills, weekly challenge problems, and guided discovery lessons. Two 6th-grade teachers and four 7th-grade teachers, and their students, participated in the study. Half of the teachers at each grade level received training in PSM and used the heuristic materials with their students over a 1-year period. The others did not. The study contained both qualitative and quantitative components. Quantitative results indicated that the heuristic students placed less emphasis on the role of memorization and expected their teachers to ask thoughtful questions and not answer questions when the students did not know the answers; believed real mathematics problems could be solved by common sense; and were less dependent on the teacher and the textbook for identifying incorrect answers to mathematical problems. Qualitative results indicated that heuristic students preferred problems that made them think and believed that mathematics was useful, regardless of ability. The study concludes that the process of engaging in mathematical problem solving may positively affect students' attitudes and beliefs. Contains 35 references and the student interview guide.

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