Impact of Abstract Algebra on Teachers’ Understanding of and Approaches to Instruction in Solving Equations

Abstract

Every 5 years, the College Board of the Mathematical Sciences (CBMS) executes a national survey of undergraduate mathematical and statistical sciences in 2- and 4-year colleges and universities. The 2010 report stated that among 4-year institutions with secondary pre-service teaching certification programs, 89% of all mathematics departments require their students to take modern algebra (Blair et al., Statistical abstract of undergraduate programs in the mathematical sciences in the United States: Fall 2010 CBMS survey. American Mathematical Society, Providence, RI, 2013). Professional mathematics societies, such as the Mathematics Association of America, also advocate that future high school mathematics teachers take advanced courses, such as abstract algebra. Despite this requirement and advocacy, there is a need for more research on how knowledge of mathematical content is employed in teaching practice, as well as how secondary teachers view their university courses as relevant to their teaching (Zazkis and Leikin, Mathematical Thinking and Learning 12:263–281, 2010). This chapter presents results from a study investigating how a professional development workshop focused on abstract algebra impacted teachers’ understanding of secondary mathematics. After presenting the nature of the workshop and discussing the design and redesign of the workshop materials, we discuss how teachers’ involvement affected their mathematical understandings, as well as their views on how they might teach students about particular content. Specifically, we describe how instruction in and exposure to the abstract algebraic structures of groups, rings, and fields influenced teachers’ understanding of and approaches to teaching students about the mathematical properties used to solve equations in secondary algebra classrooms.