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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Connecting abstract algebra to secondary mathematics, for secondary mathematics teachers. Cham, Switzerland : Springer, 2018 (OCoLC)1044855934 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

ISBN: | 9783319992143 3319992147 |

OCLC Number: | 1082677190 |

Description: | 1 online resource |

Contents: | Intro; Foreword; Acknowledgments; Contents; List of Contributors; External Chapter Reviewers; About the Authors; 1 Exploring Advanced Mathematics Courses and Contentfor Secondary Mathematics Teachers; Introduction; Background for the Edited Volume; Ostensible Benefits in Studying Advanced Mathematics; Are These Ostensible Benefits Realized by Secondary Teachers?; What Are Potential Explanations for Why Benefits Are Not Being Realized?; Points of Connection to Secondary Teaching; Content Connections; Disciplinary Practice Connections; Classroom Teaching Connections Modeled Instruction ConnectionsA Few Remarks; Introduction to Sections and Chapters in the Edited Volume; Exploring Students' Learning of Abstract Algebra Concepts; Exploring Content Connections to Secondary Mathematics; Exploring Approaches to Secondary Teacher Education via Disciplinary Practice Connections; Exploring Approaches to Secondary Teacher Education via Classroom Teaching Connections; References; Part I Exploring Students' Learning of Abstract Algebra Concepts Closely Connected to Secondary Mathematics 2 Connecting the Group Theory Concept Assessment to Core Concepts at the Secondary LevelIntroduction; Literature and Theoretical Perspective; Conceptual Understanding in Group Theory; Core Concepts: Binary Operation and Function; Function Concept Image Components; Binary Operation Concept Image Components; Function and Binary Operation from the Secondary Level to Abstract Algebra; Instrument and Methods; Research Questions; Task Performance Results; Functions; Meanings and Metaphors of Function: Machines and Collapsing; Properties of Function: Injective Representation of Function: Symbolic and Function DiagramsConclusion; Binary Operation; Meaning and Metaphors of Binary Operation: Operator Symbol, Input/Output, and Weighting; Properties of Binary Operation: Binary, Commutative, and Associative; Representation of Binary Operation: Symbolic Forms and Tables; Conclusion; Discussion of Opportunities for Backward Transfer; Moving Students Beyond Surface Level Form of BinaryOperation; Developing a Conceptual Understandingof the Associative Property; Distinguishing Between Constants and Variables Understanding the Implications and the Nonnecessity of Functions Being InjectiveDeveloping Flexibility in Moving Between and Leveraging Alternate Function Representations: Function Diagrams; Backward Transfer Conclusion; Conclusion; References; 3 Monster-Barring as a Catalyst for Bridging Secondary Algebra to Abstract Algebra; Introduction; Literature and Theoretical Framing; Effective Ways of Understanding; A Hypothesis for How Students Might Achieve Such a Way of Understanding; Methods; Participants; Data Collection and Analysis; Instructional Tasks; Results |

Series Title: | Research in mathematics education. |

### Abstract:

Secondary mathematics teachers are frequently required to take a large number of mathematics courses - including advanced mathematics courses such as abstract algebra - as part of their initial teacher preparation program and/or their continuing professional development.
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