Compendium for Early Career Researchers in Mathematics Education.

• Superior document: ICME-13 Monographs
• Author: Kaiser, Gabriele.
• TeilnehmendeR: Presmeg, Norma.
• Place / Publishing House: Cham : : Springer International Publishing AG,, 2019.; Ã2019.
• Year of Publication: 2019
• Edition: 1st ed.
• Language: English
• Series: ICME-13 Monographs
• Physical Description: 1 online resource (528 pages)

Table of Contents

Intro -- Preface -- Contents -- Contributors -- Empirical Methods -- 1 Argumentation Analysis for Early Career Researchers -- Abstract -- 1.1 Toulmin's Functional Model of Argumentation -- 1.2 Local and Global Arguments -- 1.3 Reconstructing Arguments in Classrooms -- 1.3.1 Reconstructing the Sequencing and Meaning of Classroom Talk -- 1.3.2 Turn by Turn Analyses -- 1.3.3 Analysing Arguments and Argumentation Structures -- 1.3.3.1 Functional Reconstruction of Local Arguments -- 1.3.3.2 Functional Reconstruction of Intermediate Argumentation Streams -- 1.3.3.3 Reconstructing the Argumentation Structure of Proving Processes in Class -- 1.4 Comparing Argumentation Structures and Revealing Their Rationale -- 1.4.1 Knipping's French-German Comparison -- 1.4.1.1 The Source-Structure -- 1.4.1.2 The Reservoir-Structure -- 1.4.1.3 Comparison -- 1.4.2 Knipping and Reid's Spiral Versus Source Comparison -- 1.4.2.1 Spiral-Structure -- 1.4.2.2 Comparison -- 1.4.3 Abductions in the Reservoir-Structure Versus Ms James' Lesson -- 1.4.4 Shinno's Research -- 1.4.5 Cramer's Comparisons -- 1.4.6 Potari and Psycharis' Comparisons -- 1.4.7 Papadaki, Reid and Knipping's Comparisons -- 1.5 Concluding Remarks -- References -- 2 Topic-Specific Design Research: An Introduction -- Abstract -- 2.1 Introduction -- 2.2 What Is Design Research? -- 2.2.1 Dual Aims and Common Characteristics -- 2.2.2 General Structure of a Design Experiment -- 2.2.3 Differences Between Various Design Research Approaches -- 2.2.4 Striving for Topic-Specific Design Research Rather Than Only Generic Educational Design Research -- 2.3 Learning from Examples of Topic-Specific Design Research -- 2.3.1 Exploratory Design Research-An Example Project for Instantaneous Speed in Grade 5 -- 2.3.2 Structuring Learning Trajectories-An Example Project on Exponential Growth for Grade 10 -- 2.4 Looking Back.

2.4.1 When Is Topic-Specific Design Research a Suitable Methodology? -- 2.4.2 Meeting Major Methodological Concerns -- References -- 3 A Naturalistic Paradigm: An Introduction to Using Ethnographic Methods for Research in Mathematics Education -- Abstract -- 3.1 Introduction -- 3.2 A Naturalistic Paradigm -- 3.2.1 An Ethnographic Stance -- 3.2.2 Ecological Validity -- 3.2.3 Context -- 3.3 Research Design Issues for Ethnographic Data Collection -- 3.4 Video as an Ethnographic Research Methodology -- 3.4.1 Advantages and Disadvantages of Using Video Data -- 3.4.2 Transcription and Translation as Theory -- 3.4.3 Analysing Mathematical Activity -- 3.5 Analyzing Mathematical Activity Using a Naturalistic Paradigm and Ethnographic Methods -- 3.5.1 An Ethno-Mathematical Perspective as an Example of an Ethnographic Stance -- 3.5.2 Two Studies as Examples of Using an Ethnographic Stance and Designing Ecologically Valid Tasks -- 3.6 Learning to Use Ethnographic Methods -- References -- 4 An Introduction to Grounded Theory with a Special Focus on Axial Coding and the Coding Paradigm -- Abstract -- 4.1 Introduction -- 4.2 A Short Positioning of Grounded Theory -- 4.2.1 What Is Grounded Theory? -- 4.2.2 What Kind of Research Questions Are Appropriate for a Grounded Theory Study? -- 4.3 A Short Introduction to the Methods and Techniques of Grounded Theory -- 4.3.1 Theoretical Sensitivity and Sensitizing Concepts -- 4.3.2 Interdependence of Data Collection, Analysis, and Development of Theory -- 4.3.3 Data Analysis -- 4.3.3.1 Open Coding -- 4.3.3.2 Axial Coding -- 4.3.3.3 Selective Coding -- 4.3.3.4 Memos and Diagrams -- 4.4 The Role of Theory Within Grounded Theory and the Coding Paradigm -- 4.4.1 Examples from Studies in Which the Coding Paradigm Was Changed -- 4.4.1.1 A Modification of the Coding Paradigm from the Perspective of Learning and Educational Theory.

4.4.1.2 Personal Meaning When Dealing with Mathematics in a School Context -- 4.4.1.3 Learning Mathematics with Textbooks -- 4.5 Concluding Remarks -- References -- 5 Interactional Analysis: A Method for Analysing Mathematical Learning Processes in Interactions -- Abstract -- 5.1 Introduction -- 5.2 Mathematics Learning from an Interactionist Perspective -- 5.3 Theory Development in Interpretive Research -- 5.4 Basic Concepts: The Negotiation of Mathematical Meaning -- 5.5 Interactional Analysis -- 5.5.1 Setting of the Interactional Unit -- 5.5.2 Structure of the Interactional Unit -- 5.5.3 Displaying Transcript of Selected Sequence -- 5.5.4 General Description of Selected Sequence -- 5.5.5 Detailed Sequential Interpretation of Individual Utterances -- 5.5.6 Turn-by-Turn Analysis -- 5.5.7 Summary of the Interpretation -- 5.6 Conclusion -- Appendix -- References -- 6 Planning and Conducting Mixed Methods Studies in Mathematics Educational Research -- Abstract -- 6.1 Introduction -- 6.2 Methodological Background of Mixed Methods Research -- 6.2.1 What Is Mixed Methods Research? -- 6.2.2 What Kind of Research Questions Does Mixed Methods Research Require? -- 6.2.3 What Is the Purpose of Doing MMR? And Why Should I Choose This Methodological Approach? -- 6.3 Special Features of MMR in Mathematics Education -- 6.4 Choosing a Research Design -- 6.5 Mixed Data Analysis: Integrating Qualitative and Quantitative Findings-Joint Displays -- 6.6 Methodological Challenges for MMR -- 6.7 Summary: How to Conduct a Mixed Methods Study -- References -- 7 The Research Pentagon: A Diagram with Which to Think About Research -- Abstract -- 7.1 Introduction -- 7.2 The Research Pentagon Embedded in Research as an Inquiry Practice -- 7.3 The Research Pentagon as a Model for Practicing Research -- 7.3.1 Hidden Views on Formulas.

7.3.2 Language Demands in Qualitative Calculus -- 7.4 The Research Pentagon Illustrating a Case of Networking of Theories -- 7.4.1 Abstraction in Context (AiC) -- 7.4.2 Interest-Dense Situations (IDS) -- 7.4.3 Comparing and Contrasting the Two Theories -- 7.4.4 A Case of Networking Between AiC and IDS -- 7.4.5 Reflecting on the Case Study -- 7.5 What Is Networking of Theories About? -- 7.6 Final Comments -- Acknowledgements -- Appendix -- References -- 8 Qualitative Text Analysis: A Systematic Approach -- Abstract -- 8.1 Introduction: Qualitative and Quantitative Data -- 8.2 Key Points of Qualitative Content Analysis -- 8.3 The Analysis Process in Detail -- 8.4 Summary and Conclusions -- References -- 9 Problematising Video as Data in Three Video-based Research Projects in Mathematics Education -- Abstract -- 9.1 Introduction -- 9.2 Video-Based Research in Education -- 9.3 Three Research Projects in Mathematics Education Employing Video -- 9.3.1 The Learner's Perspective Study (LPS) -- 9.3.2 The Social Unit of Learning Project -- 9.3.3 The International Classroom Lexicon Project (The Lexicon Project) -- 9.4 Ontological Grounding in Terms of Researcher Role and Status of the Video in Each Project -- 9.4.1 The Ontological Grounding of the Three Metaphors -- 9.5 The Co-determining Nature of the Role of the Researcher and the Status of the Video Material -- 9.6 The Role of the Researcher and the Status of the Video Material in the Three Projects -- 9.7 Implications -- References -- Important Mathematics Educational Themes -- 10 Approaching Proof in the Classroom Through the Logic of Inquiry -- Abstract -- 10.1 Introduction -- 10.2 Argumentations and Proofs: Education to Rationality as a Learning Goal in Secondary School -- 10.3 The Theoretical Basis of Our Proposal -- 10.3.1 The Model of Stephen E. Toulmin -- 10.3.2 The Logic of Inquiry by Jaako Hintikka.

10.4 Educating to Rationality Through an Inquiring-Game Activity -- 10.5 Discussion -- Acknowledgements -- References -- 11 A Friendly Introduction to "Knowledge in Pieces": Modeling Types of Knowledge and Their Roles in Learning -- Abstract -- 11.1 Introduction -- 11.1.1 Overview -- 11.1.2 Empirical Methods -- 11.2 Two Models: Illustrative Data and Analysis -- 11.2.1 Intuitive Knowledge -- 11.2.2 Scientific Concepts -- 11.3 Examples in Mathematics -- 11.3.1 The Law of Large Numbers -- 11.3.2 Understanding Fractions -- 11.3.3 Conceptual and Procedural Knowledge in Strategy Innovation -- 11.3.4 Other Examples -- 11.4 Cross-Cutting Themes -- 11.4.1 Continuity or Discontinuity in Learning -- 11.4.2 Understanding Representations -- References -- 12 Task Design Frameworks in Mathematics Education Research: An Example of a Domain-Specific Frame for Algebra Learning with Technological Tools -- Abstract -- 12.1 Introduction -- 12.2 Brief History of the Emergence of Design-Related Theoretical Work from the 1960s Onward -- 12.2.1 Influences from Psychology -- 12.2.2 Early Design Initiatives of the Mathematics Education Research Community -- 12.2.3 The 1990s and Early 2000s: Development of Design Experiments -- 12.2.4 From Early 2000 Onward -- 12.2.5 A Key Issue -- 12.3 A Conceptualization of Current Theoretical Frameworks and Principles for Task Design in Mathematics Education Research -- 12.3.1 Introduction -- 12.3.2 Grand Theoretical Frames -- 12.3.3 Intermediate Level Frames -- 12.3.4 Domain-Specific Frames -- 12.4 A Domain-Specific Frame for the CAS-Supported Co-emergence of Technique and Theory within the Activity of Algebraic Factorization -- 12.4.1 The Theoretical Underpinnings of the Design Study -- 12.4.2 The Implementation of the Design Study -- 12.4.3 Theorizing Resulting from the Implementation of the Proving Phase of the Design Study.

12.5 Concluding Remarks.