Mathematical knowledge for teaching proof Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/j38608975

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  • The purpose of this study was to detail mathematical knowledge that supports the work of teaching proof and to investigate how such knowledge is evidenced in professional development (PD). To advance the construct of mathematical knowledge for teaching (MKT) in the context of proof, I developed a framework of MKT for proof by documenting classroom proof activity and student and teachers' understanding of proof in coordination with Ball and colleagues' (2008) domains of teacher knowledge. The framework specifies ways in which teachers hold their knowledge of proof across domains of common and specialized content knowledge as well as knowledge of students and teaching. This MKT for proof framework supported an empirical study of teachers' proof activity within an existing PD project, Researching Mathematics Leader Learning (RMLL). Specifically, this dissertation details teachers' work on two proof-related tasks in RMLL seminars and subsequent PD sessions case study teachers enacted. Findings indicate how the two tasks engaged teachers in different though complementary aspects of MKT for proof. These findings resulted in the refinement of the MKT for proof framework and demonstrated its utility in linking PD activities to domains of teacher knowledge. For example, activities in which participants were prompted to compare or evaluate justifications afforded opportunities to develop specialized knowledge of proof representations and argument structures. Comparing the use of the same tasks across seminars and PD enactments allowed for a more detailed description of MKT for proof afforded by each task. This comparison highlighted how the specific goals and context of these PD sessions led to the foregrounding of different aspects of MKT for proof. For example, knowledge of proof and students (e.g. considering algebraic representations that might be accessible to students) was more evident when tasks were linked to particular grade level concerns. PD is a primary means for teachers to both enhance their own understanding of proof and to develop the knowledge and skills needed to engage students in rich proof experiences (Knuth, 2002; Sowder, 2007). This study offers significant insights on how PD might support such learning and provides a valuable analytic tool for further investigation of mathematical knowledge specifically useable in teaching proof.
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