This study explores the complex relationship between teachers understandings of mathematics and their classroom practices. The study details students engagement in a segment of a university course designed to position pre-service teachers to develop a coherent understanding of functions as covariation of quantities. With regards to this instruction, this study was guided by two research questions that dealt with understanding (a) the pre-service teachers mathematical development and then (b) how the pre-service teachers emerging understanding of function as covariation impact how they envision and enact instruction, with particular emphasis on the pre-service teachers ability to orchestrate conceptual conversations about significant mathematical ideas.
Analyses highlight the fact that one teaches what they know pre-service teachers particular understandings of mathematical content have a significant impact on their pedagogical conceptualizations of the content. It is these pedagogical conceptualizations of content and the related images that serve to guide the pre-service teachers decisions and instructional actions. The study concludes with suggestions for ways in which appropriate pedagogical conceptualizations of the content might be developed.
| Identifer | oai:union.ndltd.org:VANDERBILT/oai:VANDERBILTETD:etd-06272005-212328 |
| Date | 18 July 2005 |
| Creators | Silverman, Jason |
| Contributors | Patrick W. Thompson, Kay J. McClain, Rogers P. Hall, Philip S. Crooke, III |
| Publisher | VANDERBILT |
| Source Sets | Vanderbilt University Theses |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.library.vanderbilt.edu/available/etd-06272005-212328/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Vanderbilt University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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