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Researchers (such as Tallman, 2015; Thompson, 1993, 1994, 2011) have argued for and demonstrated the importance of students’ attention to quantities and quantitative relationships in learning key ideas in grade school and undergraduate mathematics. In this talk I will discuss how work in quantitative reasoning, as well as constructs such as such as speaking with meaning (Clark, Moore, & Carlson, 2008), informed a professional development intervention that resulted in supporting a teacher’s increased attention to her students’ thinking while planning and delivering lessons. Insights from this study led to the development of the construct emergent symbol meaning relating to students’ expectations for the meanings conveyed through algebraic formulas and expressions. I will elaborate on this construct during the presentation and share data from a second study that helped to refine its definition and demonstrate its importance in student learning of key ideas in grade school and undergraduate mathematics.
Alan O’Bryan is a Senior Research Analyst in the School of Mathematical and Statistical Sciences at Arizona State University. He is a researcher working with Project Pathways, a research-based curriculum and professional development support study that (1) seeks to unpack and make explicit the key meanings students need to develop to prepare them for Calculus, (2) designs, tests, and refines course materials to support students in constructing these key meanings, and (3) develops and refines professional training systems to support instructors in using the materials and shifting their teaching to focus on student thinking. Alan is currently studying the meanings student construct in online courses designed to support similar learning goals as the Pathways materials and how to design key features of these courses to best leverage advantages of the online environment.