Calls for reform in the way that calculus is taught stress the importance of instruction focused on graphic as well as analytic representations of functions and derivatives. The value of calculus lies in its potential to reduce complex problems to simple rules and procedures. However, students taught only rules and procedures often emerge from calculus classrooms without the ability to analyze graphs and lack an understanding of the conceptual foundations of the slope of a tangent line. Study based solely on analytic representations of functions and their derivatives often produces only procedural understanding. / In this study, two undergraduate calculus students were confronted with graphic representations for functions and their derivatives and asked to produce graphs that represented their images--their unique internal representations. Their attempts to provide external representations of their images provided the data for the study. The purposes of the study are two-fold: (1) to contrast the different mathematical understandings of these two students that have been revealed as a result of analyses of their graphic constructs for the derivative function and (2) to present the consequences of an instructional strategy based on graphic representation for functions and derivatives. / The study demonstrates that graphic instructional representations for functions and their derivatives, and students' concomitant images, have the potential for producing a richer understanding than that achieved by analytic study alone. Stimulated by graphic instructional representations, students form and can utilize mental images to construct understanding of the calculus derivative and to demonstrate their unique internal mathematical representations. / Source: Dissertation Abstracts International, Volume: 55-07, Section: A, page: 1859. / Major Professor: Kenneth L. Shaw. / Thesis (Ph.D.)--The Florida State University, 1994.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_77182 |
| Contributors | Aspinwall, Leslie Nolan., Florida State University |
| Source Sets | Florida State University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | 365 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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