Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers pp 1-15 | Cite as

# Exploring Advanced Mathematics Courses and Content for Secondary Mathematics Teachers

## Abstract

Over the past century, mathematicians and mathematics educators have explored various ways in which abstract algebra is related to school mathematics. These have included Felix Klein's work as a mathematician—in which his synthesis of the study of geometry through abstract algebraic structures has proved influential on our approach to teaching secondary students geometry even today; his work as a mathematics teacher educator—famous for his observation of the ``double—discontinuity'' that secondary teachers face in their mathematical preparation; the provocative and controversial New Math curricular reforms in the 1960s in the USA, which reorganized and restructured the content of school mathematics to be more in accord with formal set theory and the study of algebraic structures; and various studies about, and investigations of, teachers' (advanced) mathematical knowledge in relation to their practices in the classroom and their student's outcomes. These efforts, and others, have considered the connection between school mathematics and the study of the abstract algebra structures they comprise.

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