Conceptions and consequences of mathematical argumentation, justification, and proof / / edited by Kristen N. Bieda, [and three others]

• Pubblicazione: Cham, Switzerland : , : Springer, , [2022]; ©2022
• Descrizione fisica: 1 online resource (331 pages)
• Disciplina: 510.71
• Soggetto topico: Mathematics - Study and teaching; Ensenyament de la matemàtica
• Soggetto genere / forma: Llibres electrònics
• Persona (resp. second.): BiedaKristen
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Foreword -- Acknowledgments -- Contents -- Contributors -- Introduction: Conceptualizing Argumentation, Justification, and Proof in Mathematics Education -- Conceptions of Argumentation, Justification, and Proof in the Literature -- Argumentation -- Justification -- Proof -- Charges Given to Authors/Synthesizers -- Organization of This Volume -- References -- Part I: Argumentation, Justification and Proof in an Elementary Classroom -- Overview of the Elementary Level Data -- Ms. Kirk's Lesson -- Description of the Lesson -- Conclusion -- References -- Argumentation in the Context of Elementary Grades: The Role of Participants, Tasks, and Tools -- Introduction -- Arguments and Argumentation -- Argumentation in the Classroom -- Mathematical Content for Argumentation -- Brief Summary of the Lesson -- Analyzing the Lesson Transcript -- The Role of Definitions, Established Facts, and Common Language -- The Role of Participants (Teacher and Students) -- The Role of the Task -- The Role of the Tool in Terms of Evidence and Potential Connections -- Discussion -- The Role of Definitions and Common Language -- The Role of Participants -- The Role of the Task -- The Role of Tools -- Conclusion -- References -- Justification in the Context of Elementary Grades: Justification to Develop and Provide Access to Mathematical Reasoning -- Role of Justification in the Mathematics Classroom -- Student Justifications and Justification Tasks -- Potential Relationships Between Justification and Equity -- Summary -- Methods -- The Nature of the Tasks -- Students' Justifications -- Providing Access to Participation Through Justification -- Discussion -- References -- Proof in the Context of Elementary Grades: A Multimodal Approach to Generalization and Proof in Elementary Grades -- Introduction -- Theoretical Framework -- Definition of Proof. ; Generalization and Proof -- The Multimodal Nature of Proof -- Modal-Specific Epistemological Commitments and Generalization -- Method -- Data Analysis and Findings -- Excerpt 1: Defining the Equals Sign -- Summary -- Multimodality -- Excerpt 2: Discussion of 14 + 3 = 15 + 2 -- Summary -- Generalization -- Multimodality -- Excerpt 3: Jacob's Proof of 40 + 9 = 27 + 22 -- Summary -- Generalization -- Multimodality -- Discussion -- Conclusion -- References -- On the Meanings of Argumentation, Justification, and Proof: General Insights from Analyses of Elementary Classroom Episodes -- References -- Part II: Argumentation, Justification and Proof in a Middle Grades Classroom -- Overview of Middle Grades Data -- References -- Argumentation in the Middle Grades: Exploring a Teacher's Support of Collective Argumentation -- Exploring Collective Argumentation in the Mathematics Classroom -- Teacher Support for Collective Argumentation Framework -- Methodology -- Limitations -- Data Analysis Procedures -- Results -- Episode of Argumentation and Teacher Support -- Directly Contributing an Argumentation Component -- Asking Questions Prompting an Argumentation Component -- Other Supportive Actions -- What We Learned from Mr. MC's Facilitation of Argumentation -- Conclusion: Larger Spheres of Argumentation -- Appendix A: Sample from Spreadsheet Deconstructing Argument -- References -- Justification in the Context of Middle Grades: A Process of Verification and Sense-Making -- Theoretical Framework -- Literature Review -- The Teacher's Role in Promoting Justification -- Justification as a Learning Practice -- Method -- Results -- Justification Process -- Factors That Shaped the Justification Process -- Task as Written and Setup -- Task as Implemented -- Discussion -- What Might Students Be Learning About the Justification Process? -- Conclusion -- References. ; Proof in the Context of Middle Grades: Can We Label Middle School Arguments as Proof with a Capital P? -- Introduction -- Reframing the Definition of Proof for the Current Context -- Methods -- Findings -- Classroom Episode -- Students' Written Work -- Summary -- Is a Proof Accessible to This Classroom Community? -- Data from Another Project -- Conclusion -- References -- Argumentation, Justification, and Proof in Middle Grades: A Rose by Any Other Name -- Introduction -- The Task and Its Possibilities -- Potential Proving-Related Activities -- Potential Instructional Goals -- Framing Matters -- Capturing the Breadth of Proving-Related Activity -- References -- Part III: Argumentation, Justification and Proof in High School Mathematics -- Overview of High School-Level Data -- Overview of the Data -- Part 1 -- Part 2 -- Argumentation in the Context of High School Mathematics: Examining Dialogic Aspects of Argumentation -- Introduction -- Conceptual Framework -- Students' Dialogic and Justifying Moves -- Communicative Approaches and Structuring Argumentation -- Methods -- Results -- Students' Dialogic and Justifying Moves -- Structuring Argumentation and Using Communicative Approaches -- Discussion -- Dialogic Argumentation and Teacher Support -- Dialogic Argumentation in Studying Mathematical Argumentation -- References -- Justification in the Context of High School: Co-constructing Content and Process -- Introduction -- Theoretical Perspectives -- Methods -- Findings -- How Were Norms for Justification Enacted and Co-constructed? -- Which Mathematical Ideas Were Justified, and Which Mathematical Ideas Were Left Unjustified? -- To What Extent Were the Members of the Classroom Community Convinced by the Justifications Provided? -- Discussion -- References. ; Proof in the Context of High School: A First Approach Through Discussion, with Occasions and Missed Opportunities -- Introduction and Background -- Method -- Results -- Analysis of the Task -- Analysis of the Class Discussion -- Part 1: Discovering the Formula -- Part 2: Constructing Triangles -- Part 3: Towards a Formula (Again) -- Discussion -- Conclusions -- References -- Reasoning Is in the Eye of the Lens-Holder: Observations Made Through the Lenses of Justification, Argumentation, and Proof at the High School Level -- Introduction -- Defining and Framing Different Forms of Reasoning -- The Research Questions and Their Influence -- Framing of the Task and the Classroom Activities on Days 1 and 2 -- A Series of Commonly Analyzed Episodes -- Key Episode 1: Discussion of Solution to the Day 1 Task (Lines 1-35) -- Key Episode 2: Dividing a Quadrilateral into Triangles (Lines 111-130) -- Key Episode 3: Returning to the Day 1 Function (Lines 247-272) -- Looking Across the Key Episodes -- Considering the Non-common (Gray) Episodes -- Concluding Discussion -- References -- Part IV: Argumentation, Justification and Proof at the Tertiary Level -- Overview of Tertiary Level Data -- The Mathematics Involved in the Lesson -- Outline of the Class Discussion with Selected Excerpts of Transcript -- Conclusion -- References -- Argumentation in the Context of Tertiary Mathematics: A Case Study of Classroom Argumentation and the Role of Instructor Moves -- Theoretical Frameworks and Analysis Methods -- Results -- Vignette 1: How to Fill in the Cayley Table -- Vignette 2: Leveraging Specific Activity Toward General Discussion About Associativity -- Vignette 3: Instructor Solicits More Rules, but These Are Specific to the Relationships Between R and F as Symmetries of a Triangle -- Vignette 4: Demonstrating the New Rule and Moving Toward Incorporation of New Rules. ; Discussion -- References -- Justification in the Context of Tertiary Mathematics: Undergraduate Students Exploring the Properties and Relations of the Dihedral Group -- Introduction -- Defining and Operationalizing Justification -- Context for the Data Provided to Us -- Research Questions -- Method of Analysis -- Results -- Category 1: Perceptual Pattern Recognition Justifications -- Category 2: Recounting of Process Justifications -- Category 3: Mathematically Rationalized Justifications -- A Note Regarding Source of Justifications in the Classroom -- Discussion -- References -- Proof in the Context of Tertiary Mathematics: Undergraduate Inquiry-Based Learning in Abstract Algebra as a Precursor to Mathematical Proof -- Methods -- Data and Results -- Discussion -- References -- Mathematics Educators as Polymaths, Brokers, and Learners: Commentary on the Tertiary Chapters on Argumentation, Justification, and Proof -- Mathematics Educators as Polymaths: Definitions Have Natural Histories -- Mathematics Educators as Brokers: Adapting Definitions to Balance Obligations -- Brokers Between Mathematics Instruction and Mathematics Research -- Brokers Between Mathematics Education and Psychology -- Brokers Between Researchers and Instructors -- Mathematics Educators as Learners: Accumulating Knowledge of Complex Phenomena -- References -- Part V: Lenses on Researching Argumentation, Justification and Proof Across the Grade Levels -- Participation in Argumentation: Teacher and Student Roles Across the Grades -- Opening Spaces for Student Agency and Ownership -- Responding to Others' Ideas by Building and Critiquing -- Multiple Frameworks for Teacher Actions -- Considering Argumentation as Larger than Mathematics -- Consequences of the Definition -- Concluding Thoughts -- References -- Justification Across the Grade Bands -- Introduction. ; Using the Definition of Justification.
• Titolo autorizzato: Conceptions and Consequences of Mathematical Argumentation, Justification, and Proof
• ISBN: 3-030-80008-3
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910551839503321
• Lo trovi qui: Univ. Federico II
• Serie: Research in Mathematics Education