Shifting attentions in mathematics: developing problem solving abilities through problem-solving groups

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McIntosh, Blaine
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The purpose of this study was to improve problem solving attitudes and abilities in students of mathematics through the exploration of John Mason’s general problem solving strategy and the use of problem solving groups, and to document and understand this improvement process. The types of problems and tasks assigned to students as well as assessment practices were also examined. A Design-Experiment Research approach was used with thirty grade 9 students participating throughout the year-long study. A teacher-researcher journal, student problem-solving journals, and surveys were used. The study showed that using a general problem solving strategy with groups of students working together to solve problems can improve problem solving attitudes and abilities. Students made significant improvements during initial engagement of problems, in specializing and generalizing, and in communication. Almost all students expressed a more positive attitude toward problem solving and their problem solving abilities. The study demonstrates how focusing on initial stages of the problem solving process like the understanding of the problem in a group context can reach multiple learning objectives and positively impact later stages of problem solving. In addition, recommendations for classroom teachers are provided concerning the roles within the groups, the nature of beneficial problem types and student tasks, and concerning the role of the teacher as researcher of his or her own teaching practice.
problem-solving, groups, teaching, strategies, Mason, Polya, metacognition, communication, attitudes, abilities