The level of challenge, or cognitive demand, of the tasks students solve is the foundation for their learning opportunities in mathematics classrooms. Unfortunately, it is difficult for teachers to effectively use cognitively demanding tasks (CDTs). I seek to understand how to support and improve mathematics teachers enactment of CDTs at scale. The purpose of this three-paper dissertation is to address some of the key unresolved questions and to set a direction for future research.
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In paper 1, based on a comprehensive literature review, I identify 13 potentially relevant factors and elaborate a method for building on results from small-scale studies to better understand the enactment of CDTs across large samples of teachers.
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Paper 2 investigates how teachers mathematical knowledge for teaching and their beliefs about teaching and learning mathematics are related to their enactment of CDTs. I found that aspects of teachers knowledge and beliefs are interconnected and are significantly related to their enactment of CDTs.
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Paper 3 investigates changes in teachers enactment of CDTs over time and whether their interactions with colleagues (e.g., work with a math coach, advice-seeking interactions) are related to these changes. I found that the mere occurrence of interactions was generally not sufficient to support teachers development, and expertise available within interactions did not influence the productivity of those interactions. However, advice-seeking interactions were significantly related to teachers development. Further, the lack of expertise within interactions might have contributed to these findings.
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These three studies suggest that there is much more to be understood about supporting teachers enactment of CDTs. There is, however, evidence that teachers mathematical knowledge for teaching and their beliefs about teaching and learning mathematics are integral to their enactment of CDTs, and that they are interrelated. In addition, it is clear that in designing supports for teachers enactment of CDTs, schools and districts should go beyond policies that provide only opportunities for interaction, and should specifically plan productive activities and enhance the available expertise within those interactions.
| Identifer | oai:union.ndltd.org:VANDERBILT/oai:VANDERBILTETD:etd-06072013-080515 |
| Date | 15 July 2013 |
| Creators | Garrison, Anne Louisa |
| Contributors | Ilana S. Horn, Paul A. Cobb, Marcy Singer-Gabella, Thomas M. Smith |
| 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-06072013-080515/ |
| 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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