This study is a comparative case study of what three college calculus teachers did in their classrooms and what their students understood about the concept of derivatives. The teachers were solicited on the basis of peer, supervisor and student recommendations as being good teachers; several volunteer student subjects were selected from each class. Using a naturalistic participant-observer paradigm, the data were collected primarily via extensive classroom observations and in-depth interviews with the teachers and students. Examination of written work, such as student exams, was employed for additional confirmation of hypotheses generated in the field. This study contributes to the bodies of knowledge on pedagogy, effective teaching, classroom dynamics, student understanding and teacher beliefs. The results should be of interest to teachers, teacher educators, mathematics text authors and people interested in how students learn and think about mathematics at the collegiate level. The study of these three classrooms reveals that there is a variety of effective teaching models for undergraduate calculus classrooms. There were, however, important commonalties among these models, the examination of which leads to some characterization of effective teaching practices. These teachers kept the focus on what their students were learning, rather than on covering material. In three different ways, these teachers each gave their students the opportunity to interact with the mathematics before the lesson ended. All three teachers displayed a willingness to grow and learn as teachers. Calculus students do not always learn what their teachers think they have taught. The students in this study displayed a variety of mistaken ideas about the concept of derivative and about other mathematical topics. For example, many students had trouble distinguishing between properties of the function and properties of the derivative. Some students believed that the derivative at a point was a line, rather than the numerical value associated with the slope of a line. Students and teachers disagreed about the correct definition of the derivative, with students attributing little importance to the idea of limits.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/288725 |
| Date | January 1997 |
| Creators | Rabb-Liu, Amy Felice, 1968- |
| Contributors | Willoughby, Stephen S. |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | en_US |
| Detected Language | English |
| Type | text, Dissertation-Reproduction (electronic) |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
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