Learning Mathematical Practices to Connect Abstract Algebra to High School Algebra

Abstract

Making connections between advanced mathematical content, such as abstract algebra, and the mathematics of the school curriculum is a critical component of the mathematical education of future secondary teachers. In this chapter, I argue that engagement in mathematical practices (e.g., constructing arguments, attending to precision) can serve as a link for preservice teachers from their study of abstract algebra to the content they will teach as high school teachers. Using a multiple case study approach, I describe how four preservice teachers had opportunities to learn to engage in mathematical practices in their abstract algebra course. Participants were taking an abstract algebra course specifically designed for future teachers. Data sources include video records from the abstract algebra course and problem-solving interviews with each participant before and after the course. Each participant showed improvement in their mathematical practice engagement and reflected on how valuable a focus on mathematical practices would be in their teaching. These findings demonstrate the key role that mathematical practices play in the preparation of future teachers. There are valuable implications for the design of content courses for teachers and for the ongoing research into connections between advanced mathematics and the school curriculum.