Abstract algebra and secondary school mathematics
Suominen, Ashley Luan
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Many stakeholders concur that secondary teacher preparation programs should include study of abstract algebraic structures, and most certification programs require an abstract algebra course for prospective mathematics teachers. However, research has shown that undergraduate students struggle to understand fundamental concepts and, upon completion of the course, are unable to articulate connections between abstract algebra and secondary school mathematics. This three-part study involved a textbook analysis, the creation of a comprehensive connections list, and a series of expert interviews. In the textbook analysis, I examined nine introductory abstract algebra textbooks to elaborate the mathematical connections that authors explicitly mentioned between concepts found in abstract algebra and secondary school mathematics. I identified any potential connections made in the text, categorizing them according to five types: alternative or equivalent representations, comparison through common features, generalization, hierarchical relationship, and real-world application. I then interviewed 13 mathematicians and mathematics educators involved in abstract algebra teaching and research to understand how they describe connections between abstract algebra and secondary mathematics. Participants’ descriptions of connections reflected their experiences with the secondary curriculum and differed according to their individual conceptualizations of abstract algebra. That is, participants prioritized different sets of connections based on their views of abstract algebra. Identifying and characterizing the connections between abstract algebra concepts and secondary school mathematics concepts offers abstract algebra professors, in particular, additional knowledge that can be used to enhance undergraduate students’ understandings of abstract algebra in addition to providing the vocabulary to discuss these connections.