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Exploring Advanced Mathematics Courses and Content for Secondary Mathematics Teachers

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Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers

Part of the book series: Research in Mathematics Education ((RME))

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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Notes

  1. 1.

    Although not the focus of the chapters in this section, for those interested in how an abstract algebra course might draw on guided reinvention as a means to model inquiry-oriented instruction in undergraduate mathematics education, see also: Larsen (2009); Larsen, Johnson, and Weber (2013); and Weber and Larsen (2008).

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Authors and Affiliations

  1. Department of Mathematics, Science and Technology, Teachers College, Columbia University, New York, NY, USA

    Nicholas H. Wasserman

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  1. Department of Mathematics, Science and Technology, Teachers College, Columbia University, New York, NY, USA

    Nicholas H. Wasserman

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Wasserman, N.H. (2018). Exploring Advanced Mathematics Courses and Content for Secondary Mathematics Teachers. In: Wasserman, N. (eds) Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-99214-3_1

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  • DOI: https://doi.org/10.1007/978-3-319-99214-3_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99213-6

  • Online ISBN: 978-3-319-99214-3

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