The fundamental theorem of calculus: An investigation into students' constructions
Abstract
This study was designed to investigate the question, "How can the Fundamental Theorem of Calculus be learned, and how do computer activities and the pedagogy of a particular kind of non-traditional calculus course affect this learning?" The subjects for the study were students in an intact section of a non-traditional calculus course which utilized computer activities and cooperative learning and which was designed on the basis of a constructivist epistemology. Students were videotaped in class and in the computer laboratory, samples of their work on computer laboratory activities and on an exam problem were collected, and six students, including all three members of one intact group, were interviewed. Prior to the study, a preliminary genetic decomposition (briefly, a description of the constructions a student might make in learning a topic) was hypothesized. On the basis of the data collected, it was found that the learning of this topic was far less linear than reflected by the preliminary genetic decomposition. A revised genetic decomposition was constructed to better reflect the constructions apparently made by the participants in the study. Students' interactions with the computer were found to fall into six categories: interactive/exploratory, mechanical, organizational, word processing, demonstrating, and gaming/Internet. It was found that the computer activities which were assigned each addressed one or more steps in the genetic decomposition. Additionally, it was discovered that the participants' function schemas contained a misconception. The students believed that the name of the independent variable was a significant characteristic of a function, and that it was a characteristic which was subject to being changed when a process such as differentiation was applied to the function.
Degree
Ph.D.
Advisors
Dubinsky, Purdue University.
Subject Area
Mathematics education|Curricula|Teaching
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