Practice-Oriented Research in Tertiary Mathematics Education

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
10.6.6 Conclusions
References
Chapter 11: Proving and Defining in Mathematics Two Intertwined Mathematical Practices
11.1 Introduction
11.2 Defining to be Able to Prove - The Case of Irrational Numbers
11.2.1 Defining Irrational Numbers by Cuts (Dedekind, 1872)
11.2.2 Defining Rational Numbers as Fundamental Sequences (Cantor, 1872)
11.2.3 Impact of the Way of Defining Real Numbers on Proving
11.2.4 A Didactic Situation to Address Issues Related to -Completeness Versus -Incompleteness
11.3 Enumeration, Infinite Sets, and Diagonal Proofs
11.3.1 How to Define Infinite Sets?
11.4 Infinite Sets as Non-finite Sets
11.5 Infinite Sets as Violating the Principle the ``Whole is Greater Than the Part.´´
11.5.1 Impact of the Ways of Defining on Proving That a Set Is Infinite
11.6 How Big Is Infinity?
11.6.1 The Diagonal Proof That Is Denumerable
11.6.2 The Diagonal Proof That Is Not Denumerable
11.7 Didactic Implications
11.8 Conclusion
Appendix
References
Part III: Research on Teaching and Curriculum Design
Chapter 12: Developing Mathematics Teaching in University Tutorials: An Activity Perspective
12.1 Introduction
12.2 Practice-Oriented/Close-to-Practice Research
12.3 Our Use of Activity Theory
12.4 Meaning Making
12.5 Methodology
12.5.1 Analysis of Data
12.6 Analysis of Dialogue in Key Episodes
12.6.1 Tutoring for Students´ Meaning-Making - Actions and Goals
12.6.2 The Practice of Tutoring - Summary of Tutorial - Key Points
12.6.3 The Episodes and the Grounded Analysis
12.6.4 Synthesizing/Exposing: Building on Students´ Solutions to Present the General Solution Method - (Episode 5)
12.6.5 The Tensions Manifested in the Three Episodes
12.7 Analyzing the Episodes from an Activity Theory Perspective
12.8 In Conclusion
References
Chapter 13: Lecture Notes Design by Post-secondary Instructors: Resources and Priorities
13.1 Theoretical Tools
13.2 Methods
13.2.1 The Textbooks
13.2.2 Participants
13.2.3 Data Collected
13.2.4 Analysis
13.3 Results
13.3.1 Maps
13.3.2 Resources
13.3.3 Lecture Notes
13.3.4 Instrumentation and Instrumentalization of the Resources
13.4 Discussion and Conclusion
References
Chapter 14: Creating a Shared Basis of Agreement by Using a Cognitive Conflict
14.1 The `Flow of a Proof´ and Its Rhetorical Features
14.2 Theoretical Framework - The New Rhetoric
14.3 Cognitive Conflict and Mathematics Education
14.4 The Study
14.4.1 Objectives
14.4.2 Setting
14.4.3 Analysis
14.4.3.1 Interviews Analysis
14.4.3.2 PNR Analysis
14.5 Findings
14.5.1 Findings from the Lecturer Interviews
14.5.2 Scope and Organization of the Lesson
14.5.3 Analysis of an Episode from Module V - Cognitive Conflict, and Dissociation
14.6 Discussion and Implications
References
Chapter 15: Teaching Mathematics Education to Mathematics and Education Undergraduates
15.1 Mathematics Education Courses in the University Curriculum
15.2 Challenges in the Transition from Studies in Mathematics or Education to Mathematics Education
15.3 Theoretical Underpinnings of Undergraduate RME Course Design
15.4 Design, Delivery and Assessment of Two RME Courses
15.4.1 The BMath Course
15.4.2 The BEd Course
15.5 The Interplay of Research and Practice in Welcoming Two Different Communities of Learners - from Mathematics and from Edu...
References
Chapter 16: Inquiry-Oriented Linear Algebra: Connecting Design-Based Research and Instructional Change Research in Curriculum ...
16.1 Background Theory and Literature
16.1.1 Realistic Mathematics Education
16.1.2 Inquiry-Oriented Instruction
16.1.3 Instructional Change at the University Level
16.2 The Design Research Spiral
16.2.1 Design Phase
16.2.2 PTE Phase
16.2.3 CTE Phase
16.2.4 OWG Phase
16.2.5 Web Phase
16.3 Discussion
References
Chapter 17: Profession-Specific Curriculum Design in Mathematics Teacher Education: Connecting Disciplinary Practice to the Le...
17.1 Profession-Specific Teaching Designs: Introducing Theory Elements for Reflecting on Design and Content Decisions
17.1.1 Facets of Teacher Knowledge as Categorial and Normative Theory Elements
17.1.2 Learning Abstract Algebra: What We Learn from Previous Research for Answering How-Questions
17.1.3 Learning Abstract Algebra: What We Learn from Previous Research for Answering What-Questions
17.2 Design Principles and Design Elements for Enhancing Profession-Specificity in an Abstract Algebra Class for Prospective T...
17.2.1 First Design Experiment Cycle
17.2.2 Second Design Experiment Cycle: Scaffolding Guided Reinvention and Noticing Connections
17.3 Outlook on the Third Cycle and Discussion
References
Chapter 18: Drivers and Strategies That Lead to Sustainable Change in the Teaching and Learning of Calculus Within a Networked...
18.1 Introduction
18.2 Theoretical Background
18.3 Methods
18.4 Findings and Results
18.4.1 California State University East Bay (CSUEB)
18.4.1.1 Shared Tools and Resources
18.4.1.2 Professional Development
18.4.1.3 Policies and Structures
18.4.1.4 Networking
18.4.2 Kennesaw State University (KSU)
18.4.2.1 Shared Tools and Resources
18.4.2.2 Professional Development
18.4.2.3 Policies and Structures
18.4.2.4 Networking
18.4.3 The Ohio State University (OSU)
18.4.3.1 Shared Tools and Resources
18.4.3.2 Professional Development
18.4.3.3 Policies and Structures
18.4.3.4 Networking
18.5 Reflections and Synthesis
18.5.1 Shared Tools and Resources
18.5.2 Professional Development
18.5.3 Policies and Structures
18.5.4 Networking
18.6 Implications and Limitations
References
Part IV: Research on University Students´ Mathematical Inquiry
Chapter 19: Real or Fake Inquiries? Study and Research Paths in Statistics and Engineering Education
19.1 Introduction
19.2 Theoretical Framework, Research Questions and Empirical Methodology
19.3 An SRP in Elasticity
19.4 An SRP in Statistics
19.5 Conclusions and New Open Questions
19.5.1 The Choice of the Generating Question and the Curriculum Constraint
19.5.2 Taking Q Seriously and Creating Adidacticity During the Inquiry Process
19.5.3 Changing the Generating Question or Changing the Situation in Which It Arises?
19.5.4 The Inclusion of TDS Notions into ATD Analyses
References
Chapter 20: Fostering Inquiry and Creativity in Abstract Algebra: The Theory of Banquets and Its Reflexive Stance on the Struc...
20.1 Introduction
20.2 Inquiry and Creativity in Abstract Algebra Teaching and Learning
20.2.1 Inquiry
20.2.2 Creativity
20.2.3 The Objects-Structures Dialectic
20.3 The Theory of Banquets: A Didactic Engineering
20.3.1 Mathematical Presentation of the Theory of Banquets
20.3.2 A Priori Analysis of the Classification Tasks
20.4 Learning Affordances of the Theory of Banquets
20.4.1 What Is a Banquet? Students´ Creative Processes in Making Sense of a Formal System of Axioms
20.4.2 What Does It Mean to Classify Banquets? Students´ Creative Processes in Developing a Structuralist Point of View
20.5 Conclusion and Perspectives
References
Chapter 21: Following in Cauchy´s Footsteps: Student Inquiry in Real Analysis
21.1 Introduction
21.2 Context and Brief Description of the Instructional Sequence
21.2.1 Intermediate Value Theorem as Starting Point
21.2.2 Context: The Course and the Participating Students
21.2.3 Starting Point and Cauchy´s Proof of IVT
21.2.4 Data Analysis
21.3 Classroom Inquiry: From the Bisection Method to Least Upper Bounds
21.3.1 Developing a Shared Understanding of the Two Approximation Methods
21.3.2 Connecting the Approximation Method to Formal Mathematical Language and Notation
21.3.3 Eliciting Student Reasoning: Conjectures About Sequences Generated by the Bisection Method
21.3.4 Building on Students´ Ways of Reasoning: General Conjectures About Sequence Convergence
21.3.5 Building on Students´ Ways of Reasoning: Investigating the False General Conjectures
21.3.6 Building on Students´ Ways of Reasoning: Investigating the True General Conjecture
21.3.7 Generating Student Ways of Reasoning: Brainstorming Why the Least Upper Bound Will Be the Limit
21.4 Conclusion
References
Chapter 22: Examining the Role of Generic Skills in Inquiry-Based Mathematics Education - The Case of Extreme Apprenticeship
22.1 Introduction
22.2 Generic Skills and Their Role in Mathematics Curricula
22.3 Extreme Apprenticeship, a Form of Inquiry-Based Mathematics Education
22.4 Research Problem and Hypotheses
22.5 Method
22.6 Context and Sources
22.7 Results
22.7.1 Generic Skills as Learning Objectives
22.7.2 Communicating the Generic Skills
22.7.3 Interplay of Objectives, Methods and Assessment
22.7.4 Programme-Level Development
22.8 Concluding Remarks
References
Chapter 23: On the Levels and Types of Students´ Inquiry: The Case of Calculus
23.1 Introduction
23.2 Theoretical Background and Framework
23.3 The Levels of Inquiry in Calculus Textbooks
23.3.1 The Structured and Guided Inquiries
23.3.2 The Confirmation and Open Inquiries: Two Extremes
23.4 Additional Types of Activities That Promote Students´ Inquiry
23.4.1 Classifying Mathematical Objects
23.4.2 Interpreting Multiple Representations
23.4.3 Evaluating Mathematical Statements
23.4.4 Creating Problems
23.4.5 Analysing Reasoning and Solutions
23.4.6 Different Types of Activities and Milieu Construction
23.5 Concluding Discussion
References
Chapter 24: From ``Presenting Inquiry Results´´ to ``Mathematizing at the Board as Part of Inquiry´´: A Commognitive Look at F...
24.1 Introduction
24.2 Boards, Inquiry, and Mathematics
24.3 Mathematizing at the Board from the Commognitive Standpoint
24.3.1 Commognition in a Nutshell
24.3.2 Mathematizing at the Board
24.4 From a Broad Practice to More Focused Routines
24.4.1 Chalk Talk
24.4.2 Audience
24.4.3 What Is Said and What Is Written
24.5 Illustrations
24.5.1 Jonah´s Proof
24.5.1.1 Coordinating Between Written and Oral Narratives
24.5.1.2 Accounting for the Audience
24.5.1.3 Meta-Mathematizing
24.5.2 Virginia´s Proof
24.5.2.1 Coordinating Between Written and Oral Narratives
24.5.2.2 Accounting for the Audience
24.5.2.3 Meta-Mathematizing
24.6 Summary
References
Chapter 25: Preservice Secondary School Teachers Revisiting Real Numbers: A Striking Instance of Klein´s Second Discontinuity
25.1 Introduction
25.2 Formulating Klein´s Double Discontinuity Within the ATD
25.3 Real Numbers in Capstone Mathematics for Future High School Teachers
25.4 Context of the Capstone Course UvMat and Methodology for the Case Study
25.5 Student Work on the Task T
25.6 Students´ Perceptions
25.7 Discussion and Conclusions
References
Part V: Research on Mathematics for Non-specialists
Chapter 26: Challenges for Research on Tertiary Mathematics Education for Non-specialists: Where Are We and Where Are We to Go?
26.1 Introduction
26.2 A Historical Perspective
26.2.1 A First Historical Lens: The École Polytechnique
26.2.2 A Second Historical Lens: CIEM/ICMI Studies
26.3 Mathematics Education for Non-specialists Through the Lens of the Encyclopaedia of Mathematics Education
26.4 Mathematical Training for Non-specialists from an Institutional Perspective
26.4.1 Selected Theoretical Elements of the ATD
26.4.2 Mathematical Praxeologies in Workplaces
26.4.3 Mathematics and Major Discipline Courses
26.4.4 Didactic Proposals for Mathematical Training for Non-specialists
26.5 Conclusion
References
Chapter 27: Mathematics in the Training of Engineers: Contributions of the Anthropological Theory of the Didactic
27.1 Introduction
27.2 Problems with Mathematics Courses for Engineers
27.3 Some Key Notions from ATD
27.4 Practices in Engineering Courses
27.5 SRPs in Engineering Programs
27.5.1 Epistemological Tools for Designing and Managing an SRP: An Example in Statistics
27.5.2 Teaching Formats of SRPs and Their Ecology: Two Examples of Engineering Courses
27.6 Conclusions
References
Chapter 28: Modifying Exercises in Mathematics Service Courses for Engineers Based on Subject-Specific Analyses of Engineering...
28.1 Introduction
28.2 Theoretical Perspective and Previous Research
28.2.1 Concepts of the Anthropological Theory of the Didactic
28.2.2 Mathematical Practices in Signal Theory
28.2.2.1 Amplitude Modulation and the Role of Complex Numbers in Electrical Engineering and in Mathematics Service Courses
28.2.2.2 ATD Analyses of the Lecturer´s Sample Solution and Student Solutions
28.3 From Analyses of Engineering Mathematical Practices to Modifying Exercises in Mathematics Service Courses
28.4 Discussion
Appendix: Exercise with Lecturer Sample Solution
References
Chapter 29: Learning Mathematics in a Context of Electrical Engineering
29.1 Introduction
29.2 Background and Context of the Study
29.3 Theory and Methodology
29.4 Previous Relevant Research
29.5 Analysis of Data
29.5.1 Example: An Electric Circuit
29.5.2 Opportunities for Connections
29.6 Discussion
References
Chapter 30: Towards an Institutional Epistemology
30.1 Introduction
30.2 Theoretical Framework
30.3 From Mathematics to Land Surveying, an Example of Transpositive Effects
30.4 Aspects of an Industrial Epistemology
30.4.1 General Conditions and Constraints
30.4.2 Measurement System Analysis
30.4.3 Process Capability Analysis
30.5 Making the PageRank Algorithm Intelligible
30.6 Conclusion
References
Chapter 31: Concept Images of Signals and Systems: Bringing Together Mathematics and Engineering
31.1 Background
31.2 Literature Review
31.2.1 Engineering and Mathematics
31.2.2 Use of Representations as Contexts
31.3 Signals and Systems Courses in Engineering
31.4 Interviews and Analysis
31.5 Signals and Systems Concept Image and Conceptual Problems
31.5.1 Concept Image for Signals and Systems
31.6 Analysis of Concept Inventory Questions
31.6.1 Students´ Descriptions of Frequency
31.6.2 Connections Between Graphical and Symbolic Contexts
31.6.3 Applications and the Concept Image
31.7 Discussion
31.8 Limitations
31.9 Conclusion
References
Chapter 32: Analyzing the Interface Between Mathematics and Engineering in Basic Engineering Courses
32.1 Introduction
32.2 Theoretical Backgrounds
32.2.1 Different Mathematical Practices and Disparities in Mathematics and Engineering Courses
32.2.2 Conceptions of Mathematical Modeling
32.2.3 Conceptions of Problem-Solving
32.2.4 Conceptualizations About the Use of Mathematics in Physics
32.3 Synthesis of Frameworks with a View Towards the Electrotechnical Tasks
32.4 Research Questions
32.5 Methodology and Data Collection
32.5.1 Overview
32.5.2 Goals and Methods for Interviewing EE Experts About the Tasks
32.5.3 Methods for Developing the Student-Expert-Solution
32.6 The Exercise on Oscillating Current as an Example and Its Solution Outline for the First Two Subtasks
32.6.1 The Subtasks B1 and B2 and the Official Solution Outline
32.6.2 Summary of the SES of Subtasks B1 and B2
32.7 Development of the Student Expert Solution for Exercise B3: Setting Up the Differential Equation)
32.7.1 Official Solution Outline of Subtask B3
32.7.2 SES1 Object-Level: Extended Structured Solution Outline, Knowledge from EE-Theory Relevant for the Solving Process
32.7.3 SES1 Meta-Level: Viewing the Solution According to the Theoretical Approaches and Identifying Cognitive Resources
32.7.4 Developing SES2 of B3 Based on the Expert Interviews
32.8 Development of the Student Expert Solution for Exercise B4 (the Solving of the Differential Equation)
32.8.1 Official Solution Outline
32.8.2 SES1 Object-Level: Extended Structured Solution Outline, Knowledge from EE-Theory Relevant for the Solving Process
32.8.3 SES1 Meta-Level: Structuring the Solution According to the Theoretical Approaches and Identifying Cognitive Resources
32.8.4 Developing SES2 to B4, Based on the Expert Interviews
32.9 Summary and Outlook
References
Chapter 33: Tertiary Mathematics Through the Eyes of Non-specialists: Engineering Students´ Experiences and Perceptions
33.1 Introduction - Students´ Perceptions and the Curriculum
33.2 Theoretical Horizon - Mathematics as a Service Subject, Disintegrated Practice and the Position of Engineering Students
33.3 Research Questions, Context and Data
33.4 Findings
33.4.1 Recognising a ``Mathematics Text´´
33.4.2 The Usefulness and Role of Mathematics
33.4.2.1 General Mathematico-Logical Thinking
33.4.2.2 Schema for Learning
33.4.2.3 Ways of Thinking for Systematic Problem-Solving
33.4.2.4 Understanding of the Mathematical Underpinnings of Activities at Work Place
33.4.2.5 Understanding of Mathematical Underpinnings of Other Academic Subjects
33.4.2.6 Applications of Mathematics at Workplace
33.4.2.7 Applications of Mathematics in Other Academic Subjects
33.4.3 Ways of Studying Mathematics Compared to the Other Subjects
33.4.3.1 Knowledge Structures, Criteria for Accomplishment and Intellectual Demands
33.4.3.2 Forms and Habits of Working and Thinking, and Their Appreciation
33.4.3.3 Investment of Time and Effort, and the Worth of Credit Points
33.5 Discussion
References
Chapter 34: Early Developments in Doctoral Research in Norwegian Undergraduate Mathematics Education
34.1 Examples of Doctoral Research in RUME Supported by MatRIC
34.1.1 Researching Flipped Classroom Approaches by Helge Fredriksen
34.1.2 Researching Online and Blended Learning Approaches in Mathematics for Engineering Students by Shaista Kanwal
34.1.3 Researching Learning with a Visualisation and Simulation Program by Ninni Marie Hogstad
34.1.4 Researching Economics Students´ Performance in Mathematics by Ida Landgärds
34.1.5 Researching the Development of Mathematical Competency of Biology Students by Yannis Liakos
34.1.6 Researching Biology Students´ Use of Mathematics by Floridona Tetaj
34.1.7 Researching Relationships Between Prior Knowledge, Self-Efficacy and Approaches to Learning Mathematics of Engineering ...
34.2 Conclusion
References