PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Abstract algebra and secondary school mathematics: Identifying mathematical connections in textbooks
Page: 238
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 learning abstract algebra for the first time often struggle to relate the new abstract concepts to previously learned concepts found in secondary school mathematics. In this study, I examined nine undergraduate abstract algebra textbooks to elaborate on the mathematical connections explicitly stated in the textbooks between abstract algebra and secondary school mathematics concepts, and categorized them according to an analytic framework based on categories of mathematical connections found in previous literature. In this report, I discuss three specific categories of connections: comparison through common features, generalization, and hierarchical or inclusion. I found that the connection types discussed in textbooks differ from past literature that highlight connections related to abstract algebra as generalization of school algebra.