Conceptions and consequences of mathematical argumentation, justification, and proof / Kristen N. Bieda, AnnaMarie Conner, Karl W. Kosko, Megan Staples, editors.

Format:

Book

Contributor:

Bieda, Kristen, editor.

Conner, AnnaMarie, editor.

Kosko, Karl W., editor.

Staples, Megan, editor.

Series:

Research in mathematics education (Springer (Firm)) 2570-4737

Research in mathematics education, 2570-4737

Language:

English

Subjects (All):

Mathematics--Study and teaching.

Mathematics.

Proof theory.

Syllogism.

Mathematics teachers--Training of.

Mathematics teachers.

Genre:

Electronic books.

Physical Description:

1 online resource : illustrations (some color).

Place of Publication:

Cham : Springer, [2022]

Summary:

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.

Contents:

Introduction: Conceptualizing Argumentation, Justification, and Proof in Mathematics Education

Part 1: Argumentation, Justification and Proof in an Elementary Classroom

Overview of the Elementary Level Data

Argumentation in the Elementary Grades: The Role of Participants, Tasks, and Tools

Justification in the Elementary Grades: Justification to Develop and Provide Access to Mathematical Reasoning

Proof in the Elementary Grades: A Multimodal Approach to Generalization and Proof

On the Meanings of Argumentation, Justification, and Proof: General Insights from Analyses of Elementary Classroom Episodes

Part 2: Argumentation, Justification and Proof in a Middle Grades Classroom

Overview of Middle Level Data

Argumentation in the Middle Grades: Exploring a Teacher's Support of Collective Argumentation

Justification in the Middle Grades: A Process of Verification and Sense-Making

Proof in the Middle Grades: Can we Label Middle Grades Arguments as Proof with a Capital P?

Argumentation, Justification, and Proof in Middle School: A Rose by Any Other Name

Part 3: Argumentation, Justification and Proof in High School Mathematics

Overview of High School Level Data

Argumentation in the Context of High School Mathematics: Examining Dialogic Aspects of Argumentation

Justification in the Context of High School Mathematics: Co-Constructing Content and Process

Proof in the Context of High School Mathematics: A First Approach through Discussion, with Occasions and Missed Opportunities

Reasoning is in the Eye of the Lens-Holder: Observations Made through the Lenses of Justification, Argumentation, and Proof at the High School Level

Part 4: Argumentation, Justification and Proof at the Tertiary Level

Overview of Tertiary Level Data

Argumentation in the Context of Tertiary Mathematics: A Case Study of Classroom Argumentation and the Role of Instructor Moves

Justification in the Context of Tertiary Mathematics: Undergraduate Students Exploring the Properties and Relations of the Dihedral Group

Proof in the Context of Tertiary Mathematics: Undergraduate Inquiry-Based Learning in Abstract Algebra as a Precursor to Mathematical Proof

Mathematics Educators as Polymaths, Brokers, and Learners: Commentary on the Tertiary Chapters on Argumentation, Justification, and Proof

Part 5: Lenses on Researching Argumentation, Justification and Proof Across the Grade Levels

Participation in Argumentation: Teacher and Student Roles across the Grades

Justification Across the Grade Bands

Lens, Blinders, or Kaleidoscope? Using a Definition of Proof to Make Sense of Classroom Activity

Conclusion: Considering the Consequences of Our Conceptions of Argumentation, Justification, and Proof.

Notes:

Includes index.

Online resource; title from PDF title page (SpringerLink, viewed March 10, 2022).

Other Format:

Print version:

ISBN:

9783030800086

3030800083

OCLC:

1302308634

Access Restriction:

Restricted for use by site license.