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Assessing productivity of secondary mathematics' discussions and activities

Johnson, Taylor
Students’ discussions about and engagement with mathematics largely shape their conceptualizations and dispositions towards learning and doing mathematics. It is crucial for educators, particularly at the secondary level, to facilitate discussions and activities that not only engage students, but support their development of productive reasoning. The purpose of the proposed research is to create a theoretical framework “assessing productivity” of discussions and activities based on related literature and empirical research. This framework will be used to analyze various aspects of students’ participation in classroom instruction, such as the students’ mathematical thinking and the prior knowledge required to meaningfully engage in the lesson. The goal of the research is to discern how to promote students’ understanding at a deeper level than memorizing facts and becoming fluent with procedures. I intend to apply this framework to analyze previously recorded data collected by my research mentor of a pre-service mathematics educator’s instruction in a secondary classroom. After the initial teaching videos were recorded, the participant went through a series of interviews where she noted moments of high quality instruction and room for improvement within her lessons that were recorded. The participant’s personal assessment and reflection of her own teaching will then be compared with my analysis of the discussions and activities that were productive in the lessons. I expect the analytical framework I propose to develop to be suitable for application at a large scale level when evaluating the effectiveness of instructional practices and/or curricular resources for secondary mathematics.