Connecting abstract algebra to secondary mathematics, for secondary mathematics teachers. (2018)

• Record Type: Book
• 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
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 512/.02; Algebra, Abstract -- Study and teaching (Secondary); Mathematics -- Study and teaching (Secondary); Mathematics teachers -- Training of; MATHEMATICS / Algebra / Intermediate; Mathematics -- Study and teaching (Secondary); Mathematics teachers -- Training of; Mathematics Education; Learning & Instruction; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783319992143; 3319992147
• Related ISBNs: 3319992139; 9783319992136
• Notes: Note: Includes bibliographical references and index.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.