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A qualifying paper submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Math, Science, Technology, and Engineering Education. Abstract: The purpose of this review is to build a foundation from which to consider the relationships among the professional development activities of middle and secondary school mathematics teachers, the mathematical understanding ... read moreand pedagogical content knowledge of the teachers, and the mathematical understanding of their students. The goal is to enable investigation of the following questions: What are the relationships among: (i) a teacher's understanding in combinatorics; (ii) the teacher's pedagogical content knowledge in combinatorics; (iii) their students' understanding in combinatorics? Specifically, what is the relationship between the ways in which a teacher is able to solve and explain introductory problems in combinatorics and the ways in which their students respond to similar problems? Are there connections between a teacher's mathematical understanding and their students' mathematical understanding?read less
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