Compendium for Early Career Researchers in Mathematics Education.
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Superior document: | ICME-13 Monographs |
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TeilnehmendeR: | |
Place / Publishing House: | Cham : : Springer International Publishing AG,, 2019. Ã2019. |
Year of Publication: | 2019 |
Edition: | 1st ed. |
Language: | English |
Series: | ICME-13 Monographs
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Online Access: | |
Physical Description: | 1 online resource (528 pages) |
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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.