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Connecting abstract algebra to secondary mathematics, for secondary mathematics teachers.

Publisher: Cham, Switzerland : Springer, 2018.
Series: Research in mathematics education.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
"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. The content areas of advanced and secondary mathematics are closely connected. Yet, despite this connection many secondary teachers insist that  Read more...
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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  Read more...

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