In recent years, the field of mathematics education has advocated for an expanded view of what it means to know mathematics and participate in mathematics as a practice. Here, I present three papers that describe my investigations of how students participate in the important mathematical practice of defining. The first paper consists of a review of research about how K-16 students participated in establishing and refining mathematical definitions. Analysis of the forms of activity revealed by this research led to the construction of a synthetic framework to more closely describe the practice of defining, which I termed Aspects of Definitional Practice. These aspects included asking definitional questions, constructing and/or evaluating examples, and constructing definitional explanations or arguments. In the second paper, the Aspects framework served as a lens for investigating how defining was initially established in one middle school classroom. The analysis focused on how defining was realized in interactions among students and between the teacher and students. The third paper describes how students participation in Aspects of Definitional Practice developed over time, and how change in participation influenced the development of mathematical knowledge. Collectively, the three papers provide: (a) an analytic and theoretical framework for examining the mathematical practice of defining as it might be constituted in classrooms; (b) an analysis of the initial establishment of this form of practice as instantiated in interaction among students and their teacher; and (c) an investigation of how knowledge, practice and the interactions that contribute to their co-constitution develop and change over time.
| Identifer | oai:union.ndltd.org:VANDERBILT/oai:VANDERBILTETD:etd-11302012-143043 |
| Date | 15 December 2012 |
| Creators | Kobiela, Marta Anna |
| Contributors | Richard Lehrer, Leona Schauble, Ilana Horn, Philip Crooke |
| 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-11302012-143043/ |
| 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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