Preface	6
	References	11
	Contents	14
	Part I: Grounded Theory Methodology	17
	Chapter 1: Grounded Theory Methods	18
	1.1 The Development of “Grounded Theory”	18
	1.1.1 Overview of Research Processes	19
	1.2 Place of Literature Review in Grounded Theory	20
	1.3 Data Analysis: Open Coding	21
	1.4 Memoing	22
	1.4.1 Writing Memos and Using Diagrams	22
	1.4.2 Using Computer Programs	23
	1.5 Intermediate Coding and the Use of a Coding Paradigm	24
	1.5.1 Heuristic Concepts	25
	1.5.2 Coding for Process	25
	1.6 Delimiting the Study	27
	1.6.1 Theoretical Sampling and Saturation	27
	1.6.2 Core Category	28
	1.7 Theoretical Integration	28
	1.7.1 Sorting Memos	29
	1.7.2 Validating the Theory	30
	1.8 Interpretive Frameworks	30
	1.8.1 Pragmatism	31
	1.8.2 Corbin and Strauss Circa 2008: Pragmatism and Symbolic Interactionism	32
	1.8.3 Constructivist Grounded Theory	33
	1.8.4 Situational Analysis	33
	1.9 End Comment	35
	References	35
	Chapter 2: To See the Wood for the Trees: The Development of Theory from Empirical Interview Data Using Grounded Theory	37
	2.1 Background and Focus of the Study	38
	2.2 Realization of the Study	39
	2.3 Theoretical Sensitivity and Sensitizing Concepts	42
	2.4 Interdependence of Data Collection, Analysis, and Development of Theory	42
	2.5 Data Analysis	47
	2.5.1 Open Coding	48
	2.5.2 Axial Coding	49
	2.5.3 Exemplary Illustration of Open and Axial Coding Using Memos and Diagrams	50
	2.5.4 Selective Coding	58
	2.6 Going Beyond Grounded Theory	59
	2.7 Conclusion	60
	References	60
	Part II: Approaches to Reconstructing Argumentation	63
	Chapter 3: Methods for Reconstructing Processes of Argumentation and Participation in Primary Mathematics Classroom Interaction	64
	3.1 Introduction	65
	3.2 The Concepts of Argumentation and Participation	65
	3.2.1 The Example “Thirteen Pearls”	67
	3.2.1.1 The Transcript	67
	3.2.1.2 Analyses of the Scene	68
	The Analysis of Argumentation	68
	The Analysis of Participation	70
	3.2.2 The Example of “Mister X”	74
	3.2.2.1 The Transcript	74
	3.2.2.2 The Analyses of the Scene	75
	The Analysis of Argumentation	75
	The Analysis of Participation	78
	3.2.3 Comparison of the Results of the Analyses of the Two Scenes	78
	3.3 Some Theoretical Remarks	81
	3.3.1 Further Research on the “Production-Design” in Mathematics Classes	82
	3.3.2 More Complexly Structured Argumentations	82
	Appendix: Transcripts and Rules of Transcription	83
	Thirteen Pearls	83
	Mister X	84
	Rules of Transcription	85
	References	86
	Chapter 4: Reconstructing Argumentation Structures: A Perspective on Proving Processes in Secondary Mathematics Classroom Interactions	88
	4.1 Introduction	88
	4.2 The Importance of Understanding Proving Practices in the Classroom	90
	4.3 Approaches to Describing Arguments	92
	4.3.1 The Inadequacy of Logical Analysis for Reconstructing Proving Processes in Classrooms	92
	4.3.2 Toulmin’s Functional Model of Argument	93
	4.3.3 Local and Global Arguments	95
	4.4 A Method for Reconstructing Arguments in Classrooms	96
	4.4.1 Reconstructing the Sequencing and Meaning of Classroom Talk	97
	4.4.1.1 Layout of Episodes	97
	4.4.1.2 Turn by Turn Analyses	98
	4.4.2 Analyzing Arguments and Argumentation Structures	99
	4.4.2.1 Functional Reconstruction of the Argumentation	99
	4.4.2.2 Reconstructing the Argumentation Structure of Proving Processes in Class	102
	4.4.3 Comparing Global Argumentation Structures	104
	4.4.3.1 Source-Structure	105
	4.4.3.2 Spiral-Structure	106
	4.4.3.3 Comparing Source-and-Spiral Argumentation Structures	109
	4.5 Conclusion	111
	References	112
	Part III: Ideal Type Construction	115
	Chapter 5: Empirically Grounded Building of Ideal Types. A Methodical Principle of Constructing Theory in the Interpretative Research in Mathematics Education	116
	5.1 Introduction	116
	5.2 Theories and Their Significance	117
	5.3 The Notion of Theory in Interpretative Mathematics Education Research	119
	5.4 Theory-Developing Research	120
	5.5 Looking Back: The Roots of the Ideal Type Concept	122
	5.6 Ideal Type Construction: Method of Everyday Understanding	126
	5.7 Empirically Based Ideal Type Construction: A New Beginning	131
	5.8 Ideal Type Construction in Research of Mathematics Education	132
	5.8.1 Ideal Type Construction by Idealizing of Prototypes	132
	5.8.2 Ideal Type Construction: Principle of Factual Theory Construction	134
	5.8.3 A Model of Polar Ideal-Type Construction	135
	5.8.4 Construction of Epistemic Action Types	137
	5.8.5 Construction of Production Types	138
	5.8.6 Ideal Type Construction with Ideal Types	140
	5.9 Summary and Conclusion	142
	References	143
	Chapter 6: How Ideal Type Construction Can Be Achieved: An Example	147
	6.1 Introduction	147
	6.2 Methodological and Theoretical Considerations	148
	6.3 Example: Constructing Ideal Types of Epistemic Processes	150
	6.3.1 Step 1: Re-constructing the Cases Illustrated by an Epistemic Process as a Case for Ideal Type Construction	150
	6.3.1.1 Approaching the Empirical Case with Peirce’s Sign Concept	150
	6.3.1.2 The Epistemic Actions of Gathering and Connecting Mathematical Meanings	152
	6.3.1.3 The Epistemic Action of Structure-Seeing	155
	6.3.1.4 Representing the Course of the Epistemic Process	156
	6.3.1.5 A Pictograph Representing the Phase Structure	158
	6.3.2 Step 2: Grouping the Cases	158
	6.3.3 Step 3: Building Ideal Types	160
	6.3.4 Step 4: Building Theoretical Knowledge	161
	6.4 What Can Be Learnt from This Example?	162
	Appendix: Transcription Key	163
	References	163
	Part IV: Semiotic Research	165
	Chapter 7: The Question of Method in a Vygotskian Semiotic Approach	166
	7.1 Introduction	167
	7.2 Method as the Central Problem of Scientific Inquiry	168
	7.3 A Vygotskian Semiotic Approach	170
	7.3.1 Knowledge	171
	7.3.2 Learning	173
	7.4 The Methodology of Our Semiotic Approach	174
	7.5 Multi-Semiotic Analysis: An Example Concerning Pattern Generalization	178
	7.5.1 Words-Gesture Combinations in the Production of a Factual Generalization	179
	7.5.2 Words, Gesture and Rhythm: Refining the Generalization	184
	7.6 Concluding Remarks	187
	References	189
	Part V: A Theory on Abstraction and Its Methodology	192
	Chapter 8: The Nested Epistemic Actions Model for Abstraction in Context: Theory as Methodological Tool and Methodological Tool as Theory	193
	8.1 Theory	194
	8.2 The AiC Methodology	197
	8.2.1 Design for Abstraction	198
	8.2.2 A Priori Analysis	198
	8.2.3 Data Collection and Preliminary Analysis	200
	8.2.4 Need	201
	8.2.5 Analysis According to the RBC-Model	202
	8.2.6 Consolidation	205
	8.2.7 Who Is Constructing?	206
	8.3 A Focus Group in a Classroom as an Example	206
	8.3.1 Design for Abstraction	207
	8.3.2 A Priori Analysis	209
	8.3.3 Data Collection and Preliminary Analysis	211
	8.3.4 Analysis According to the RBC-Model, Including Need and Consolidation	211
	8.3.4.1 Episode 1: Constructing EP	211
	8.3.4.2 Episode 2: Partially Constructing ECE and ESS	213
	8.3.4.3 Episode 3: The differences’ Task (Task 2)	216
	8.3.5 Additional Methodological Comments	218
	8.3.5.1 Knowledge Construction and Social Interaction	218
	8.3.5.2 Tools as Contextual Elements in Knowledge Construction	218
	8.3.5.3 Revision of the Instructional Design on the Basis of RBC Analysis	219
	8.4 The Relationship of Theory and Methodology in AiC	219
	References	223
	Part VI: Networking of Theories	226
	Chapter 9: Advancing Research by Means of the Networking of Theories	227
	9.1 Introduction	227
	9.1.1 The Evolution of Networking	228
	9.1.2 Why Networking?	228
	9.2 Language for Networking	229
	9.2.1 The Semiosphere	229
	9.2.2 The Essence of Networking and Its Limits	229
	9.3 Methodological Considerations	230
	9.3.1 Networking Strategies: The Spectrum of Networking Theories	230
	9.3.2 Cross-Methodologies for Networking	231
	9.4 Different Cases of Networking	232
	9.5 Methodological Reflections: Difficulties That Accompany the Networking	234
	9.6 Benefits of Networking: Advancing Research by Means of the Networking of Theories	235
	References	235
	Chapter 10: A Cross-Methodology for the Networking of Theories: The General Epistemic Need (GEN) as a New Concept at the Boundary of Two Theories	239
	10.1 Introduction	239
	10.1.1 Abstraction in Context	240
	10.1.2 The Theory of Interest-Dense Situations	241
	10.1.3 General Description of the Cross-Methodology of Networking the Two Theories	242
	10.2 An Illustrative Example: Investigating the General Epistemic Need	243
	10.2.1 The Task and Its Setting	244
	10.2.2 Beginning a Cross-Analysis	245
	10.2.3 Separate Analysis from the AiC-View	247
	10.2.4 A Re-Analysis from the IDS-View and Its Results	249
	10.3 Methodological Reflections About the Networking Process	253
	Transcription Key	254
	References	255
	Part VII: Multi-Level-Analysis	257
	Chapter 11: Understanding Learning Across Lessons in Classroom Communities: A Multi-leveled Analytic Approach	258
	11.1 A Conceptual Framework for Analyzing the Generation of Common Ground	259
	11.1.1 Core Constructs	260
	11.1.2 The Reproduction and Alteration of a Common Ground: An Illustrative Exchange	261
	11.1.3 Analyzing Common Ground at Collective and Individual Levels	264
	11.1.3.1 The Collective Level	264
	11.1.3.2 The Individual Level	266
	Microgenesis	268
	Ontogenesis	270
	Sociogenesis	271
	The Interplay Between Micro-, Onto-, and Sociogenetic Developments in Collective Activities	273
	11.1.3.3 A Final Note on Collective and Individual Activity	274
	11.2 An Illustration of Empirical Techniques: The Learning Mathematics Through Representations Project	275
	11.2.1 Empirical Techniques Used to Inform Design Choices for the LMR Lesson Sequence	275
	11.2.1.1 Preliminaries	275
	11.2.1.2 Empirical Techniques and Design Choices	277
	Interview Studies	277
	Tutorial Studies	282
	Classroom Studies	285
	Preliminary Classroom Studies	285
	LMR Classroom Studies: Preliminary Lessons and Their Iterative Refinement	286
	Support for Use of the Lesson Sequence with New Teachers	287
	Efficacy study	287
	Student Assessment Instrument	287
	Student Assessments and Growth	288
	11.2.2 The Complete Lesson Series	288
	11.2.2.1 Supports for a Common Ground of Talk and Action with Shifting Lesson Topics	290
	Ordering of Lesson Topic	291
	Definitions and Principles	291
	Cuisenaire™ Rods (C-Rods)	294
	Recurrent Lesson Structure	295
	11.2.3 Empirical Techniques Used to Analyze the Reproduction and Alteration of a Common Ground of Talk and Action in a Classroom Community	296
	11.2.3.1 Empirical Techniques: Data Collection	296
	Video Records (of Lessons)	297
	Assessment of Integers and Fractions Knowledge	297
	After Class Interviews	298
	Sociogram	298
	Teacher Interviews	298
	11.2.3.2 Empirical Techniques: Data Reduction and Analytic Approach	299
	Collective Level: A Focus on Emergent Norms in the Classroom Community	301
	Sociomathematical Norm #1. Use Definitions to Support Your Ideas: Especially When Explaining Thinking or Justifying Reasoning	302
	Sociomathematical Norm #2. When Definitions Are Used, Connect Them to a Particular Problem Context and/or to Other Definitions	304
	Individual Level: A Focus on the Microgenesis, Ontogenesis, and Sociogenesis of Form-Function Relations	306
	Microgenesis: Empirical Techniques and the Unit Interval	307
	Ontogenesis: Empirical Techniques and the Unit Interval	308
	After Class Interviews: Ravena’s After Class Interview and Shifts in Thinking Through the Lesson	309
	Student Assessment Instrument to Document Longer-Term Ontogenetic Shifts: Pre-, Interim-, Post-, and Final Assessments	310
	Sociogenesis: Empirical Techniques and the Unit Interval	313
	Documenting Shifts in the Distributions of Form-Function Relations	314
	Explaining Shifts in the Distributions of Form-Function Relations	316
	11.3 Final Thoughts and Next Steps	318
	References	321
	Part VIII: Mixed Methods	324
	Chapter 12: The Combination of Qualitative and Quantitative Research Methods in Mathematics Education: A “Mixed Methods” Study on the Development of the Professional Knowledge of Teachers	325
	12.1 Introduction	326
	12.2 “Mixed Methods”: Challenging the Qualitative-­Quantitative Divide in Social and Educational Research	327
	12.3 The Dispute About “Quan” and “Qual” and Mixed Methods in Research on Mathematics Education	329
	12.4 Basic Methodological Concepts of Method Integration	333
	12.4.1 Combination of Methods and Techniques During Data Collection and Analysis	333
	12.4.2 Integration of Methodological Approaches Within one Research Design	334
	12.5 Capabilities and Functions of Mixed Methods Designs	337
	12.5.1 Strengths and Challenges of Quantitative Methods	337
	12.5.2 Strengths and Challenges of Qualitative Methods	340
	12.5.3 Types of Mixed Methods Designs and Their Function in the Research Process	342
	12.6 An Example of a Mixed Methods Research Design in Mathematics Education	344
	12.6.1 Research Purpose and Mixed Methods Design of the TEDS-Telekom Study	344
	12.6.2 The Quantitative Sub-Study	346
	12.6.3 The Qualitative Sub-Study	349
	12.6.4 Triangulation in the Mixed Methods Design: Relating Quantitative and Qualitative Findings to Each Other	351
	12.7 Different Functions of Mixed Methods Designs: An Overview	357
	References	359
	Part IX: Qualitative Content Analysis	366
	Chapter 13: Qualitative Content Analysis: Theoretical Background and Procedures	367
	13.1 Methodological Background of Qualitative Content Analysis	367
	13.2 Development and Definition of Content Analysis	369
	13.3 Basics of Qualitative Content Analysis	371
	13.3.1 Embedding of the Material Within the Communicative Context	371
	13.3.2 Systematic, Rule-Bound Procedure	371
	13.3.3 Categories as the Focus of Analysis	372
	13.3.4 Object Reference in Place of Formal Techniques	373
	13.3.5 Pilot Testing of the System of Categories and the Content Analytical Rules	373
	13.3.6 Theory-Guided Character of the Analysis	374
	13.3.7 Integrating Quantitative Steps of Analysis	374
	13.3.8 Quality Criteria	374
	13.4 Basic Procedures or Techniques of Qualitative Content Analysis	375
	13.4.1 Inductive Category Formation	376
	13.4.2 Deductive Category Assignment (Structuring)	378
	13.5 Final Appraisal of the Qualitative Content Analysis	380
	References	381
	Chapter 14: A Study on Professional Competence of Future Teacher Students as an Example of a Study Using Qualitative Content Analysis	383
	14.1 Introduction	383
	14.2 Theoretical Framework and Research Question of the Study	384
	14.3 Why Was Qualitative Content Analysis Chosen?	385
	14.4 How Was Qualitative Content Analysis Used in This Study?	389
	14.5 Summary	399
	References	399
	Part X: Triangulation and Cultural Studies	402
	Chapter 15: The Contemporary Importance of Triangulation in a Post-Positivist World: Examples from the Learner’s Perspective Study	403
	15.1 Introduction	404
	15.2 Triangulation	406
	15.3 Research as the Mobilization of Bias	409
	15.3.1 Mathematics Teaching	409
	15.3.2 Chinese Learners’ Paradox	410
	15.3.3 National Pedagogies	410
	15.3.4 Research Design Characteristics	410
	15.4 Characteristic Features of the Hong Kong LPS Research Implementation	411
	15.5 Triangulation and Acts of Cross-Cultural Comparison	413
	15.5.1 Lesson Patterns or Lesson Structure	414
	15.5.2 The Hong Kong Investigation of Lesson Structure	416
	15.5.3 Contrasting the Enactment of “Lesson Events” Across Different Cultural Systems	418
	15.5.3.1 The Learning Task: One Example of a Lesson Event	420
	15.6 Conclusion	422
	References	423
	Part XI: Design Research as a Research Methodology	426
	Chapter 16: An Introduction to Design-Based Research with an Example From Statistics Education	427
	16.1 Theory of Design-Based Research	427
	16.1.1 Purpose of the Chapter	427
	16.1.2 Characterizing Design-Based Research	428
	16.1.2.1 Integration of Design and Research	428
	16.1.2.2 Predictive and Advisory Nature of DBR	428
	16.1.2.3 The Role of Hypotheses and the Engineering Nature of DBR	429
	16.1.2.4 Open and Interventionist Nature of DBR	430
	16.1.2.5 Comparison of DBR with Randomized Controlled Trials (RCT)	431
	16.1.2.6 Comparison of DBR with Action Research	433
	16.1.2.7 Names and History of DBR	434
	16.1.2.8 Theory Development in Design-Based Research	435
	16.1.2.9 Summary of Key Characteristics of Design-Based Research	435
	16.1.3 Hypothetical Learning Trajectory (HLT)	436
	16.1.3.1 HLT in the Design Phase	437
	16.1.3.2 HLT in Teaching Experiment	437
	16.1.3.3 HLT in the Retrospective Analysis	438
	16.1.4 Phases in DBR	439
	16.1.4.1 Phase 1: Preparation and Design	439
	16.1.4.2 Phase 2: Teaching Experiment	439
	16.1.4.3 Retrospective Analysis	440
	16.1.5 Validity and Reliability	441
	16.1.5.1 Internal Validity	442
	16.1.5.2 External Validity	442
	16.1.5.3 Internal Reliability	443
	16.1.5.4 External Reliability	443
	16.2 Example of Design-Based Research	443
	16.2.1 Relevance and Aim	444
	16.2.2 Research Question	444
	16.2.3 Orienting Framework: Diagrammatic Reasoning	445
	16.2.4 Domain-Specific Framework for Action: Realistic Mathematics Education (RME)	446
	16.2.5 Methods	447
	16.2.6 HLT and Retrospective Analysis	450
	16.2.6.1 Analysis of the First Phase of Growing a Sample	452
	16.2.6.2 Analysis of the Second Phase of Growing a Sample	454
	16.2.6.3 Analysis of the Third Phase of Growing a Sample	456
	16.2.7 Reflection on the Example	458
	16.2.8 Final Remarks	459
	Appendix: Structure of a DBR Project with Illustrations	459
	References	461
	Chapter 17: Perspectives on Design Research: The Case of Didactical Engineering	465
	17.1 Introduction	465
	17.2 Didactical Engineering: An Historical Review	466
	17.3 Didactical Engineering as a Research Methodology	469
	17.3.1 Preliminary Analyses	470
	17.3.2 Conception and a Priori Analysis	471
	17.3.3 Realization, Observation and Data Collection	472
	17.3.4 A Posteriori Analysis and Validation	472
	17.3.5 The Nature of the Results	473
	17.3.6 Didactical Engineering and Design-Based Research	474
	17.4 Two Particular Examples	475
	17.4.1 A Paradigmatic Example: The Extension of the Field of Numbers by G. and N. Brousseau	475
	17.4.1.1 Preliminary Analyses	476
	17.4.1.2 Conception and Analysis a Priori	476
	17.4.1.3 Realization, Data Collection, a Posteriori Analysis, Validation and Further Outcomes	478
	17.4.2 An Example of Didactical Engineering Combining the Theory of Didactical Situations with Semiotic Perspectives	480
	17.4.2.1 Preliminary Analyses	480
	17.4.2.2 Conception and Analysis a Priori	481
	17.4.2.3 Data Collection, a Posteriori Analysis and Validation	483
	17.5 Some Recent Developments of Didactical Engineering	488
	17.5.1 Didactical Engineering and the Anthropological Theory of Didactics	488
	17.5.2 Research and Development: Didactical Engineering of Second Generation	490
	17.6 Conclusion	491
	References	492
	Chapter 18: Educational Design Research to Support System-Wide Instructional Improvement	495
	18.1 The United States Context	497
	18.2 An Orienting Vision of High-Quality Mathematics Instruction	498
	18.3 Design Studies to Investigate and Support System-Wide Improvement in Mathematics Instruction	499
	18.4 Developing Initial Conjectures	500
	18.5 Recruiting Collaborating Educational Systems	502
	18.6 Using an Interpretive Framework to Assess Designed and Implemented Improvement Strategies	503
	18.7 New Positions	504
	18.8 Learning Events	505
	18.8.1 Intentional Learning Events	505
	18.8.2 Incidental Learning Events	506
	18.9 New Organizational Routines	507
	18.10 New Tools	507
	18.11 Summary	509
	18.12 Conducting Design, Analysis and Feedback Cycles	509
	18.12.1 Documenting Current Instructional Improvement Strategies	510
	18.12.2 Documenting How Instructional Improvement Strategies Are Implemented	513
	18.12.3 Sharing Findings and Recommendations with System Leaders	514
	18.12.4 Assessing the Influence of Recommendations on Collaborating System’s Instructional Improvement Strategies	517
	18.13 Testing and Revising Conjectures that Comprise a Theory of Action for System-Wide Instructional Improvement	519
	18.14 Findings About the Districts’ Instructional Improvement Strategies	519
	18.15 Research Literature	519
	18.16 Retrospective Analyses	520
	18.17 MIST’s Current Theory of Action for Instructional Improvement in Middle-Grades Mathematics	520
	18.18 Conclusion	522
	References	523
	Part XII: Final Considerations	529
	Chapter 19: Looking Back	530
	References	533
	Bibliography	534
	Author Index	573
	Subject Index	580