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Title page for ETD etd-06072013-080515


Type of Document Dissertation
Author Garrison, Anne Louisa
URN etd-06072013-080515
Title Understanding Teacher and Contextual Factors that Influence the Enactment of Cognitively Demanding Mathematics Tasks
Degree PhD
Department Learning, Teaching and Diversity
Advisory Committee
Advisor Name Title
Paul A. Cobb Committee Chair
Ilana S. Horn Committee Member
Marcy Singer-Gabella Committee Member
Thomas M. Smith Committee Member
Keywords
  • teaching
  • teacher learning
  • teacher networks
  • math coach
Date of Defense 2013-05-13
Availability unrestricted
Abstract
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.

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.

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.

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.

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.

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