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Compendium for Early Career Researchers in Mathematics Education.

Bibliographic Details
Main Author: Kaiser, Gabriele.
Other Authors: Presmeg, Norma.
Format: eBook
Language:English
Published: Cham : Springer International Publishing AG, 2019.
Edition:1st ed.
Series:ICME-13 Monographs
Subjects:
Electronic books.
Online Access:Click to View
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.

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