| Description |
1 online resource |
| Series |
Research in mathematics education |
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Research in mathematics education
|
| 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 |
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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 |
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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 |
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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 |
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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 |
| 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 such advanced mathematics is unrelated to their future professional work in the classroom. This edited volume elaborates on some of the connections between abstract algebra and secondary mathematics, including why and in what ways they may be important for secondary teachers. Notably, the volume disseminates research findings about how secondary teachers engage with, and make sense of, abstract algebra ideas, both in general and in relation to their own teaching, as well as offers itself as a place to share practical ideas and resources for secondary mathematics teacher preparation and professional development. Contributors to the book are scholars who have both experience in the mathematical preparation of secondary teachers, especially in relation to abstract algebra, as well as those who have engaged in related educational research. The volume addresses some of the persistent issues in secondary mathematics teacher education in connection to advanced mathematics courses, as well as situates and conceptualizes different ways in which abstract algebra might be influential for teachers of algebra. Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers is a productive resource for mathematics teacher educators who teach capstone courses or content-focused methods courses, as well as for abstract algebra instructors interested in making connections to secondary mathematics." |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Algebra, Abstract -- Study and teaching (Secondary)
|
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Mathematics -- Study and teaching (Secondary)
|
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Mathematics teachers -- Training of.
|
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MATHEMATICS -- Algebra -- Intermediate.
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Mathematics -- Study and teaching (Secondary)
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Mathematics teachers -- Training of
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| Form |
Electronic book
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| ISBN |
9783319992143 |
|
3319992147 |
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