PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
Impact of abstract algebra knowledge on the teaching and learning of secondary mathematics
Page: 481
This study explores how in- and pre-service teachers make connections between advanced mathematics, specifically abstract algebra, and secondary mathematics. To better understand these connections, we draw on three areas of research: mathematical knowledge for teaching (e.g., Ball, Thames, & Phelps, 2008), mathematical practices (e.g., Council of Chief State School Officers [CCSSO], 2010; RAND, 2003) and habits of mind (e.g., Cuoco, Goldenberg, & Mark, 1996). In order to investigate how exposure to and instruction in abstract algebra impact the way teachers understand secondary mathematics and approach instruction, this study utilizes two main frameworks. To characterize mathematics understanding, we used the action, process, object, and schema (APOS) framework (Asiala, 1997). To unpack approaches to discussion, we use the construct of knowledge of content and teaching, part of pedagogical content knowledge in mathematical knowledge for teaching (Ball, Thames, & Phelps, 2008). Our analysis uncovered two broad themes related to understanding and approach to instruction— understanding and interpreting inverse, and use of mathematical language.