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This paper was presented at the XVIII International GIREP Conference, held at the Universitat Autonoma de Barcelona, during the week of August 28th-1st September 2000. The author describes the design and initial data analysis of an ongoing study to determine the important elements, as perceived by faculty, of the learning and teaching of problem solving in the context of an introductory calculus-based physics course. This paper discusses the preliminary results of a comparison of two instructors who are known to differ primarily in their approaches to the teaching of problem solving. To elicit instructors' beliefs that inform their instructional choices, an interview around three concrete situations was designed: instructors' solutions, students' solutions, and actual practice. There is evidence to suggest that the primary difference between the two instructors is not in their vision of the expert problem solving process, but in the presence and treatment of competing models of learning and instruction. This article, along with others, have been compiled in a book.
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