This is the summary of a presentation given at the Joint Mathematics Meetings, January 10-13, 1996, Orlando, Florida.
Using Problem Solving to Encourage Active Learning
Constructivist theory that is prevalent in education today emphasizes that learners are "active meaning makers." In applying this theory, teachers do not teach "thinking skills" in isolation, but instead, they include active thinking, problem solving, and meaning making into all instruction. Compared to the skills approach and the conceptual approach, the problem solving approach fosters development of mathematical thinking and focuses on the processes of mathematical inquiry (e.g., problem solving, reasoning, and communicating). The purpose of this paper is to describe three courses which involve preservice teachers in active learning utilizing a problem-solving/inquiry approach. Our intent is that through modeling this approach and requiring students to solve problems and design problem solving lessons we will encourage future teachers to implement this approach in their own classrooms. In the three courses in which we have implemented this approach, the instructors begin with an instructional problem that will provide the focus for the lesson. The students are required to find solutions to the problems presented through use of cooperative group work, library research, whole group discussions, discovery learning, the use of manipulative materials, and computer technology. After the instructors have modeled this problem-solving approach, students are required to create lessons that use this approach to help elementary school students construct understanding of concepts and develop skills and attitudes.
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