Practice-Oriented Research in Tertiary Mathematics Education

• Intro -- Contents -- Chapter 1: Practice-Oriented Research in Tertiary Mathematics Education -- An Introduction -- 1.1 Context of This Book -- 1.2 Overall Structure of the Book -- 1.2.1 Section 1: Research on the Secondary-Tertiary Transition -- 1.2.2 Section 2: Research on University Students´ Mathematical Practices -- 1.2.3 Section 3: Research on Teaching and Curriculum Design -- 1.2.4 Section 4: Research on University Students´ Mathematical Inquiry -- 1.2.5 Section 5: Research on Mathematics for Non-specialists -- References -- Part I: Research on the Secondary-Tertiary Transition -- Chapter 2: Emotions in Self-Regulated Learning of First-Year Mathematics Students -- 2.1 Introduction: The Transition from School to University in Mathematics -- 2.2 Theory -- 2.2.1 Self-Regulated Learning in Undergraduate Mathematics -- 2.2.2 Achievement Emotions and Control-Value Theory -- 2.2.3 An Integrated Model of Achievement Emotions and Self-Regulated Learning -- 2.3 Research Interest and Research Questions -- 2.4 Methods and Research Design -- 2.4.1 Institutional Context of the Study -- 2.4.2 Data Collection -- 2.4.3 Data Analysis -- 2.5 Results -- 2.5.1 Joy, Relief, Anxiety, and Hopelessness in the First Year of Study -- 2.5.2 The Roles of Perceived Control and Subjective Values in the Emergence of Joy, Relief, Anxiety, and Hopelessness -- 2.5.3 Joy, Relief, Anxiety, Hopelessness, and Self-Regulated Learning -- 2.6 Discussion -- 2.6.1 Discussion of Results -- 2.6.2 Implications, Limitations, and Outlook -- References -- Chapter 3: The Unease About the Mathematics-Society Relation as Learning Potential -- 3.1 Prelude -- 3.2 Subject-Scientific Approach -- 3.2.1 Fundamental Assumptions and Subject-Scientific Categories -- 3.2.2 Subject-Scientific Understanding of Learning -- 3.3 Unease to Be Identified as a Mathematician (Only).
• 3.3.1 Against Being Identified as Becoming a Constricted One-Track-Specialist -- 3.3.2 Against Being Identified as Just Being Mathematically Able -- 3.3.3 Interlude -- 3.4 Belief Research -- 3.4.1 Change of Teacher Beliefs -- 3.4.2 In-/Consistencies Between Teacher Beliefs and Teaching Practices -- 3.5 Current Trends in Belief Research from a Subject-Scientific Perspective -- 3.6 Discussion -- References -- Chapter 4: Collaboration Between Secondary and Post-secondary Teachers About Their Ways of Doing Mathematics Using Contexts -- 4.1 Introduction -- 4.2 The Secondary to Postsecondary Transition in Mathematics -- 4.2.1 A Need for Dialogue Between Secondary and Postsecondary Teachers -- 4.2.2 The Use of Contexts in Mathematics and the Secondary to Postsecondary Transition -- 4.2.3 Research Questions -- 4.3 The Theoretical Perspective -- 4.4 Methodology -- 4.4.1 An Investigation in Two Phases -- 4.4.2 The Dialogue Organized Around a Reflexive Activity -- 4.4.3 The Overall Analytical Process -- 4.5 Results -- 4.5.1 Phase 1: Two Territories Established Around the Use of Contexts -- 4.5.1.1 Secondary Level Territory: Contextual Mathematics -- Three Specificities to Characterize the Territory at the Secondary Level -- 4.5.1.2 The Territory of Postsecondary Mathematics: Illustrated Mathematics -- Four Specificities to Characterize the Territory at the Postsecondary Level -- 4.5.2 Phase 2: A Process of Rapprochement Between Levels -- 4.5.2.1 Moment 1: Explaining Their Respective Ways of Doing -- 4.5.2.2 Moment 2: The Establishment of Common Elements -- 4.5.2.3 Moment 3: Revisiting One´s Territory in Light of the Other -- 4.5.2.4 Moment 4: Joint Planning -- 4.6 Conclusion -- References -- Chapter 5: Framing Goals of Mathematics Support Measures -- 5.1 Supporting Students in the Secondary-Tertiary Transition and the WiGeMath Project.
• 5.2 Development of the Goal Categories in the WiGeMath Framework -- 5.2.1 The Underlying Concept of Theory-Driven Evaluation -- 5.2.2 The Purpose of a Framework Model for Goal Categories -- 5.2.3 Main Steps in Developing the Model -- 5.2.4 Presentation of the Goal Categories -- 5.2.4.1 Educational Goals -- 5.2.4.2 System-Related Goals -- 5.3 Using the Goal Categories of the Framework to Compare Measures -- 5.3.1 Background and Methods -- 5.3.2 Pre-University Bridging Courses -- 5.3.3 Redesigned Lectures -- 5.3.4 Mathematics Learning Support Centres -- 5.3.5 Comparing Different Types of Measures -- 5.4 Discussion -- 5.4.1 The Framework Model -- 5.4.2 Using the Framework Model to Evaluate Measures -- 5.4.3 Further Use of the Framework Model -- Appendix -- References -- Part II: Research on University Students´ Mathematical Practices -- Chapter 6: ``It Is Easy to See´´: Tacit Expectations in Teaching the Implicit Function Theorem -- 6.1 Introduction -- 6.2 Theoretical Framework and Research Questions -- 6.3 Context of the Study -- 6.4 Mathematical Analysis of Student Tasks in the Exercise Class -- 6.5 Methodology -- 6.6 Results -- Students´ Solutions and Reflections -- 6.7 Results -- Interviews with Teachers -- 6.8 Conclusions and Further Perspectives -- References -- Chapter 7: University Students´ Development of (Non-)Mathematical Practices: The Case of a First Analysis Course -- 7.1 Introduction -- 7.2 Theoretical Framework -- 7.2.1 Mathematical and Non-Mathematical Practices -- 7.2.2 The Progressive Development of Practices -- 7.3 Methodology -- 7.4 Results -- 7.4.1 Suggested Practice Associated with T2 -- 7.4.2 Practices Enacted by Participants for Solving T2 -- 7.4.2.1 The Identification of T2 with a Type of Task and Technique -- 7.4.2.2 The Implementation of a Technique to Accomplish T2 -- 7.4.2.3 The Explanation of a Technique for Accomplishing T2.
• 7.5 Discussion -- 7.5.1 Answer to the Research Questions and Contribution of the Study to Research in University Mathematics Education -- 7.5.2 Limitations and Directions for Future Research -- References -- Chapter 8: The Mathematical Practice of Learning from Lectures: Preliminary Hypotheses on How Students Learn to Understand Def... -- 8.1 Introduction -- 8.2 Literature Review -- 8.2.1 What Do We Mean by Learning from Lectures? -- 8.2.2 Research on Lecturing in Advanced Mathematics -- 8.2.3 The Inadequacy of a Transmission Model of Learning -- 8.2.4 The Importance of Modeling During Lectures -- 8.2.5 Goals of This Chapter -- 8.3 Data and Analysis -- 8.3.1 A Data Corpus of Lectures in Advanced Mathematics -- 8.3.2 Analysis -- 8.4 Results -- 8.4.1 When Learning a Definition, One Should Justify Why the Definition Has Desirable Attributes -- 8.4.2 When a New Definition Is Proposed, One Should Actively Explore the Definition -- 8.4.3 When a New Definition Is Provided, One Should Exemplify this Definition in Many Ways -- 8.4.4 How Should Students Study New Definitions That Are Presented in Lectures? -- 8.5 Discussion -- References -- Chapter 9: Supporting Students in Developing Adequate Concept Images and Definitions at University: The Case of the Convergenc... -- 9.1 Introduction and Overview -- 9.2 Theoretical Background and Literature Review -- 9.3 Research Questions -- 9.4 Context of the Study -- 9.5 The Design of the Initial Learning Environment -- 9.5.1 The Set of Examples and Non-examples and Its Anticipated Use -- 9.5.2 The Initial Task Formulation -- 9.5.3 Anticipated Obstacles and Prepared Support -- 9.6 Design of the Study, Sample, Collected Data, Methods of Data Analysis -- 9.6.1 Instructional Design of the Workshop -- 9.6.2 Iterative Analysis from the Perspective of Design Research -- 9.7 Results.
• 9.7.1 Changes in the Set of Examples/Non-examples and the Anticipated Use -- 9.7.2 Changes in the Prepared Support for the Second Cycle Based on Retrospective Analysis of Cycle 1 -- 9.7.3 Changes in the Prepared Support for the Third Cycle Based on Retrospective Analysis of Cycle 2 -- 9.7.4 Changes in the Task Formulation -- 9.8 Discussion -- References -- Chapter 10: Investigating High School Graduates´ Basis for Argumentation: Considering Local Organisation, Epistemic Value, and... -- 10.1 Introduction -- 10.2 Theoretical Background -- 10.2.1 Set of Accepted Statements, Local Organisation, and the Basis for Argumentation -- 10.2.2 The Epistemic Value of Statements -- 10.2.3 Toulmin´s Model for Structuring Argumentation -- 10.2.4 Basis for Argumentation, Local Organisation, and Epistemic Value -- 10.2.5 Findings from the Literature -- 10.3 Research Questions -- 10.4 Methodology -- 10.4.1 Research Instruments -- 10.4.1.1 Task Analysis and Expected Solution -- 10.4.1.2 Construction of the Interview Guide -- 10.4.2 Procedure -- 10.4.3 Piloting the Research Instrument -- 10.4.4 Data Collection -- 10.4.5 Data Analysis -- 10.5 Results -- 10.5.1 Results concerning the Elements of the Basis for Argumentation used in the Proof Constructions -- 10.5.2 Results concerning the Embeddedness of the Statements used in a Local Organisation -- 10.5.3 Results concerning the Epistemic Value Assigned to the Statements, Rules, and Definitions used -- 10.5.4 Results on the Effects of Epistemic Values on the Conclusion´s Modal Qualifier -- 10.6 Discussion -- 10.6.1 Elements of the Basis for Argumentation used in the Proof Constructions -- 10.6.2 Statements Embedded in a Local Organisation -- 10.6.3 The Epistemic Value Assigned to the Statements and Definitions used -- 10.6.4 Effects of Epistemic Values on the Conclusions´ Modal Qualifier -- 10.6.5 Limitations.

Klassifikation

QA10.92-20 (LCC)

507.11 (DDC)

Epabu (kssb/8 (machine generated))