Conceptions and consequences of mathematical argumentation, justification, and proof

著者

    • Bieda, Kristen
    • Conner, AnnaMarie
    • Kosko, Karl W.
    • Staples, Megan

書誌事項

Conceptions and consequences of mathematical argumentation, justification, and proof

Kristen N. Bieda ... [et al.], editors

（Research in mathematics education / series editors, Jinfa Cai, James Middleton）

Springer, c2022

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注記

Other editors: AnnaMarie Conner, Karl W. Kosko, Megan Staples

Includes bibliographical references and index

内容説明・目次

内容説明

This book aims to advance ongoing debates in the field of mathematics and mathematics education regarding conceptions of argumentation, justification, and proof and the consequences for research and practice when applying particular conceptions of each construct. Through analyses of classroom practice across grade levels using different lenses - particular conceptions of argumentation, justification, and proof - researchers consider the implications of how each conception shapes empirical outcomes. In each section, organized by grade band, authors adopt particular conceptions of argumentation, justification, and proof, and they analyse one data set from each perspective. In addition, each section includes a synthesis chapter from an expert in the field to bring to the fore potential implications, as well as new questions, raised by the analyses. Finally, a culminating section considers the use of each conception across grade bands and data sets.

目次

Table of Contents Introduction: Conceptualizing Argumentation, Justification, and Proof in Mathematics Education Megan Staples & AnnaMarie Conner Part 1: Argumentation, Justification and Proof in an Elementary Classroom Overview of the Elementary Level Data Karl W. Kosko Argumentation in the Elementary Grades: The Role of Participants, Tasks, and Tools Chepina Rumsey, Ian Whitacre, Sebnem Atabas,& Jessica L. Smith Justification in the Elementary Grades: Justification to Develop and Provide Access to Mathematical Reasoning Eva Thanheiser & Amanda Sugimoto Proof in the Elementary Grades: A Multimodal Approach to Generalization and Proof Candace Walkington & Dawn Woods On the Meanings of Argumentation, Justification, and Proof: General Insights from Analyses of Elementary Classroom Episodes Andreas J. Stylianides & Gabriel J. Stylianides Part 2: Argumentation, Justification and Proof in a Middle Grades Classroom Overview of Middle Level Data Megan Staples Argumentation in the Middle Grades: Exploring a Teacher's Support of Collective Argumentation Carolos Nicolas Gomez, Stacy R. Jones, & Hilary Tanck Justification in the Middle Grades: A Process of Verification and Sense-Making Kristin Lesseig & Jerilynn Lepak Proof in the Middle Grades: Can we Label Middle Grades Arguments as Proof with a Capital P? David A. Yopp, Rob Ely, Anne E. Adams, & Annelise W. Nielsen Argumentation, Justification, and Proof in Middle School: A Rose by Any Other Name Eric Knuth, Orit Zaslavsky, & Hangil Kim Part 3: Argumentation, Justification and Proof in High School Mathematics Overview of High School Level Data AnnaMarie Conner Argumentation in the Context of High School Mathematics: Examining Dialogic Aspects of Argumentation Markus Hahkioeniemi Justification in the Context of High School Mathematics: Co-Constructing Content and Process Jill Newton Proof in the Context of High School Mathematics: A First Approach through Discussion, with Occasions and Missed Opportunities Francesca Morselli Reasoning is in the Eye of the Lens-Holder: Observations Made through the Lenses of Justification, Argumentation, and Proof at the High School Level Michelle Cirillo & Dana C. Cox Part 4: Argumentation, Justification and Proof at the Tertiary Level Overview of Tertiary Level Data David Plaxco Argumentation in the Context of Tertiary Mathematics: A Case Study of Classroom Argumentation and the Role of Instructor Moves David Plaxco & Megan Wawro Justification in the Context of Tertiary Mathematics: Undergraduate Students Exploring the Properties and Relations of the Dihedral Group Shiv Smith Karunakaran & Mariana Levin Proof in the Context of Tertiary Mathematics: Undergraduate Inquiry-Based Learning in Abstract Algebra as a Precursor to Mathematical Proof Timothy Fyukawa-Connelly & Sera Karahoca Mathematics Educators as Polymaths, Brokers, and Learners: Commentary on the Tertiary Chapters on Argumentation, Justification, and Proof Paul Christian Dawkins Part 5: Lenses on Researching Argumentation, Justification and Proof Across the Grade Levels Participation in Argumentation: Teacher and Student Roles across the Grades AnnaMarie Conner Justification Across the Grade Bands Amy Ellis, Megan Staples, & Kristen N. Bieda Lens, Blinders, or Kaleidoscope? Using a Definition of Proof to Make Sense of Classroom Activity Sean Larsen & Tenchita Alzaga Elizondo Conclusion: Considering the Consequences of Our Conceptions of Argumentation, Justification, and Proof Karl W. Kosko & Kristen N. Bieda

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