Exploring Mathematical Connections Preservice Teachers Make Between Abstract Algebra and Secondary Mathematics: Implications for Learning and Teaching

Abstract algebra has been identified as an important course for preservice secondary mathematics teachers because much of the abstract algebra content is connected to, and thus relevant for, secondary mathematics teaching (Wasserman et al., 2017). However, many preservice teachers do not recognize the usefulness of an undergraduate abstract algebra course and see no relation between abstract algebra and secondary school mathematics (Christy & Sparks, 2015; Ticknor, 2012). While much of the research regarding preservice teachers making connections to secondary school mathematics in abstract algebra has been conducted in courses designed for preservice teachers, the research suggests that most universities with teacher preparation programs do not offer such a course (Blair et al., 2013; Hoffman, 2017). Research in this area has the potential to not only impact the teaching and learning of abstract algebra, but also mathematics teacher preparation. This multi-stage, exploratory qualitative study investigated what connections abstract algebra faculty identify as important, how they incorporate those connections into their instruction, and what activities help preservice teachers make mathematical connections between abstract algebra and secondary school mathematics. Throughout the study, situated cognition (Boaler, 2000; Ticknor, 2012; Wasserman et al., 2017) provided a theoretical lens for data collection and analysis. During Stage One I investigated what was currently happening in abstract algebra courses required of preservice teachers across the country by distributing a Qualtrics survey to abstract algebra faculty at 75 institutions. Using data from Stage One, I created and implemented instructional tasks situated in a secondary teaching context in a single section of introductory abstract algebra required of future teachers. During this second stage I explored what mathematical connections preservice teachers were able to make to secondary school mathematics while enrolled in abstract algebra through course observations, interviews, and written responses to the instructional tasks. The results suggest that the implementation of short instructional tasks that provide explicit opportunities for students to make connections between abstract algebra and secondary school mathematics can help preservice teachers understand why abstract algebra is a required course. In fact, providing these opportunities can help preservice teachers see the concepts of abstract algebra as valuable tools for their future teaching careers. The results also suggest that if students have the opportunity to make these mathematical connections there is potential to positively impact their learning in the abstract algebra course; however, further research is needed to confirm these findings