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.