Assessing productivity of secondary mathematics’ discussions and activities

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 this thesis 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 applied this framework to analyze recorded data from my instruction in a secondary classroom as a pre-service secondary mathematics educator. After teaching my lessons, I reflected on the effectiveness of the tasks and discussions I facilitated in the classroom in regards to productive struggle. I then analyzed the discussions and activities according to a three tier model reflecting cognitive demand and progress in doing mathematics. This analytical framework for productivity of mathematics’ discussions and tasks is applicable at a large scale level when evaluating the effectiveness of instructional practices and/or curricular resources for secondary mathematics.