Introduction: Conceptualizing Argumentation, Justification, and Proof in Mathematics Education |
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1 | (12) |
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Part I Argumentation, Justification and Proof in an Elementary Classroom |
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Overview of the Elementary Level Data |
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13 | (6) |
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Argumentation in the Context of Elementary Grades: The Role of Participants, Tasks, and Tools |
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19 | (16) |
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Justification in the Context of Elementary Grades: Justification to Develop and Provide Access to Mathematical Reasoning |
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35 | (14) |
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Proof in the Context of Elementary Grades: A Multimodal Approach to Generalization and Proof in Elementary Grades |
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49 | (16) |
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On the Meanings of Argumentation, Justification, and Proof: General Insights from Analyses of Elementary Classroom Episodes |
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65 | (10) |
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Part II Argumentation, Justification and Proof in a Middle Grades Classroom |
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Overview of Middle Grades Data |
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75 | (4) |
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Argumentation in the Middle Grades: Exploring a Teacher's Support of Collective Argumentation |
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79 | (16) |
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Carlos Nicolas Gomez Marchant |
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Justification in the Context of Middle Grades: A Process of Verification and Sense-Making |
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95 | (14) |
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Proof in the Context of Middle Grades: Can We Label Middle School Arguments as Proof with a Capital P? |
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109 | (20) |
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Argumentation, Justification, and Proof in Middle Grades: A Rose by Any Other Name |
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129 | (10) |
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Part III Argumentation, Justification and Proof in High School Mathematics |
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Overview of High School-Level Data |
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139 | (6) |
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Argumentation in the Context of High School Mathematics: Examining Dialogic Aspects of Argumentation |
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145 | (14) |
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Justification in the Context of High School: Co-constructing Content and Process |
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159 | (18) |
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Proof in the Context of High School: A First Approach Through Discussion, with Occasions and Missed Opportunities |
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177 | (18) |
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Reasoning Is in the Eye of the Lens-Holder: Observations Made Through the Lenses of Justification, Argumentation, and Proof at the High School Level |
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195 | (16) |
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Part IV Argumentation, Justification and Proof at the Tertiary Level |
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Overview of Tertiary Level Data |
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211 | (8) |
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Argumentation in the Context of Tertiary Mathematics: A Case Study of Classroom Argumentation and the Role of Instructor Moves |
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219 | (20) |
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Justification in the Context of Tertiary Mathematics: Undergraduate Students Exploring the Properties and Relations of the Dihedral Group |
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239 | (12) |
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Proof in the Context of Tertiary Mathematics: Undergraduate Inquiry-Based Learning in Abstract Algebra as a Precursor to Mathematical Proof |
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251 | (14) |
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Mathematics Educators as Polymaths, Brokers, and Learners: Commentary on the Tertiary Chapters on Argumentation, Justification, and Proof |
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265 | (12) |
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Part V Lenses on Researching Argumentation, Justification and Proof Across the Grade Levels |
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Participation in Argumentation: Teacher and Student Roles Across the Grades |
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277 | (10) |
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Justification Across the Grade Bands |
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287 | (12) |
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Lens, Blinders, or Kaleidoscope? Using a Definition of Proof to Make Sense of Classroom Activity |
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299 | (14) |
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Conclusion: Considering the Consequences of Our Conceptions of Argumentation, Justification, and Proof |
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313 | (12) |
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Index |
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325 | |