Browsing by Subject "mathematical knowledge for teaching"
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Item Mathematical Knowledge for Teaching Proof in Secondary Mathematics Teacher Preparation(2020-07) Graif, FosterProof is considered foundational for mathematical understanding and has received increased attention in mathematics education over the last two decades. This mixed methods research study explores opportunities to develop mathematical knowledge for teaching proof during secondary mathematics teacher preparation. I used the mathematical knowledge for teaching proof framework (Lesseig, 2011) to develop a survey distributed to secondary mathematics methods instructors. This survey provided data pertaining to each instructor’s learning goals around proof and instructional strategies they use to support opportunities to develop their teacher candidates’ mathematical knowledge for teaching proof. In addition, interviews were conducted with five participants to provide further details on their survey responses and their instructional strategies. The responses related to learning goals were often focused on providing opportunities to develop common content knowledge for proof. The findings also indicated that factors such as educational level and departmental assignment were not associated with providing opportunities intended to support the development of mathematical knowledge for teaching proof. Instead, a teacher educator’s approach towards proof in their methods course(s) is influenced by their view of what counts as proof. This view varied across all participants and is not unlike the variation discovered in previous research. Further research must explore reasonable expectations for what counts as proof at the secondary level and must identify specific strategies for drawing connections between common content knowledge for proof and the work of teaching.Item Recognizing Mathematical Opportunities in Student Thinking by Preservice Teachers(2019-11) Carlovsky, JamesThis research study was an investigation of 63 preservice teachers’ recognizing classroom students’ mathematical opportunities in student thinking. These preservice teachers watched video case studies of elementary math classrooms as presented to them during a college mathematics and pedagogy hybrid course. I use the conceptual framework of the Mathematical Opportunity in Student Thinking (MOST) research team (Leatham, Peterson, Stockero, & Van Zoest, 2015) as the framework for what specifically is recognized within a classroom setting. This research contributes to the understanding of preservice teachers’ recognition and noticing of student thinking within mathematical classroom events. What makes this project unique is that it primarily looked at how a preservice teacher’s mathematical knowledge for teaching helped to inform the specifics of what those preservice teachers noticed within a lesson. The preservice teachers’ written accounts indicated that a majority felt that a MOST event often occurred. Across the preservice teacher interpretation of their noticings, four important themes emerged as catalysts for MOST events: teacher actions, student actions, group work itself, and the mathematical tasks chosen. Implications for mathematics educators and educational researchers about preservice teacher noticing activities as well as moments of learning are discussed. Keywords: mathematical opportunity in student thinking, elementary mathematics preservice teachers, mathematical knowledge for teaching, noticing student mathematical thinking, moments of learning