Advancing and Consolidating Mathematical Modelling: Research from ICME-14

Series Preface
Contents
List of Contributors
Part I Overview
1 Advancing Mathematical Modelling and Applications Educational Research and Practice
1.1 Introduction
1.2 Overviewing Mathematical Modelling in Education
1.3 Learning Mathematical Modelling at School
1.4 Mathematical Modelling at University
1.5 Teacher Education in Mathematical Modelling
1.6 Teaching Mathematical Modelling at School
1.7 Discussion
1.8 Final Reflections and Outlook for Future Work
References
2 Survey of Interdisciplinary Aspects of the Teaching and Learning of Mathematical Modelling in Mathematics Education
2.1 Introduction
2.2 Relations Between Mathematics and the Real World
2.3 Methodology
2.4 Major Findings and Threads
2.4.1 A Well-Understood Relation Between Mathematics and the Real World Underpinning Interdisciplinary Work
2.4.2 Interdisciplinary Teams in Mathematics Education Research and Teaching Related to the Real World
2.4.3 Issues and Challenges Around Relationships Among Mathematical Modelling, Mathematics, the Real World and Interdisciplinarity
2.4.4 Mathematical Modelling and STEM Integration
2.5 Final Reflections
References
3 Diversity of Perspectives on Mathematical Modelling: A Review of the International Landscape
3.1 Introduction
3.2 Selected Systematic Reviews of Mathematical Modelling
3.3 Methodology
3.4 Findings
3.4.1 Classification by Modelling Perspectives
3.5 Conclusions
References
Part II Mathematical Modelling at School
4 Student Presentations of Mathematical Modelling Solutions as a Setting for Fostering Reflective Discourse
4.1 Purpose of the Study and Related Literature
4.1.1 Framing Modelling as a Context for Meaningful Mathematical Activity
4.1.2 Reification: A Signature of Meaningful Mathematical Activity
4.1.3 Opportunities for Reification in a Social Context: Reflective Discourse
4.1.4 Research Question
4.2 Methods
4.3 Findings
4.3.1 Shift in MEA #1: Identifying Critical “Wrinkles” in the Problem
4.3.2 Shift in MEA #2: Making Connections Across Mathematisations
4.3.3 Shift in MEA #3: Attending to How Key Concepts Are Operationalised
4.4 Discussion, Limitations, and Directions for Future Research
References
5 Students’ Processing Types in a Computer-Based Learning Environment for Mathematical Modelling
5.1 Introduction
5.2 Theoretical Background
5.2.1 Computer-Based Learning Environments
5.2.2 Self-Regulated Learning
5.2.3 CBLEs, Self-Regulated Learning and Mathematical Modelling
5.3 Materials and Methods
5.3.1 Research Questions
5.3.2 Methodology
5.4 Results
5.4.1 Modelling Performance and Extracted Variables
5.4.2 Processing Types
5.5 Discussion of Results
5.6 Conclusion
References
6 The Impact of Real-World Mathematical Modelling Problems on Students’ Beliefs About the Nature of Mathematics
6.1 Introduction
6.2 Students’ Beliefs and Mathematical Modelling
6.3 IMMC and Selection Process in Chile
6.4 Methodology
6.5 Results
6.6 Discussion and Conclusion
References
7 Study of a Problem-Solving Activity Using the Extended Mathematical Working Space Framework
7.1 Introduction
7.2 Theoretical Framework
7.3 Methodology
7.4 Results
7.5 Conclusion
References
8 Assessment of the Competency of Grade Four Students in Mathematical Modelling: An Example from One City in China
8.1 Introduction
8.2 Theoretical Framework
8.2.1 Mathematical Modelling
8.2.2 Mathematical Modelling Competency
8.2.3 Assessment of Mathematical Modelling Competency
8.3 Research Questions
8.4 Method
8.4.1 Participants and Data Collection
8.4.2 Measures
8.4.3 Data Analysis
8.5 Results
8.5.1 The Mathematical Modelling Competency of Grade Four Students
8.5.2 The Relationship Between Students’ Mathematical Modelling and Mathematics Competency
8.6 Discussion and Limitations
8.6.1 The Mathematical Modelling Competency of Grade Four Students Needs to Be Improved
8.6.2 Applied Mathematics Should Be Paid Special Attention to in Mathematics Teaching
8.6.3 Limitations
8.7 Conclusion
References
Part III Mathematical Modelling at University
9 Learning of Linear Transformations Involving Mathematical Modelling Supported by Technology: A Study with Undergraduate Students
9.1 Introduction
9.2 Studies Addressing Modelling and Technology Use in Learning Linear Transformations
9.3 Modelling Supported by Technology and Potential Difficulties
9.4 Methodology
9.4.1 Context, Participants and Research Questions
9.4.2 The Modelling Task (in Two Versions)
9.4.3 Data Collection and Analysis
9.5 Results
9.5.1 General Characteristics of Students’ Models
9.5.2 The Case of Group S4
9.5.3 The Case of Group Z7
9.6 Conclusions
References
10 Validating a Multiple-Choice Modelling Competencies Assessment
10.1 Introduction
10.2 Conceptual and Assessment Frameworks
10.3 Prior Work on Multiple-Choice Instrument Development
10.3.1 Item Creation Approach
10.3.2 Response Process Validity
10.3.3 Relations to Other Measures
10.4 Methods
10.5 Results and Discussion
10.5.1 Interpretation of Rasch Analysis
10.5.2 Difficulty Analysis for Existing Items from the Literature
10.5.3 Discussion
10.6 Conclusions
References
11 A Mathematical Modelling Project with Biology Undergraduates: Using Activity Theory to Understand Tensions
11.1 Introduction
11.2 Activity Theory
11.3 Contradictions and Development
11.4 Planning and Organisation of a MM Project
11.5 Contextualisation of the Activity System
11.6 Methodology
11.7 Identification of Tensions
11.8 Contradictions and Expansive Learning
References
12 Seeing the Forest for the Trees: Investigating Students’ Data Moves in a Citizen Science Based Model-Eliciting Activity
12.1 Purpose of the Study and Related Literature
12.1.1 Models and Modelling Perspective
12.1.2 Data Moves
12.1.3 Monitor My Maple
12.2 Methods
12.2.1 Model-Eliciting Activity
12.2.2 Data Analysis
12.3 Findings
12.3.1 Filtering for Convenience
12.3.2 Filtering for Robustness
12.3.3 Filtering with Purpose
12.4 Discussion and Conclusion
References
Part IV Teacher Education in Mathematical Modelling
13 Pre-service Teachers’ Knowledge and Noticing Competencies for Teaching Mathematical Modelling Regarding Students’ Use of Metacognitive Strategies
13.1 Introduction
13.2 Theoretical Framework
13.2.1 Competencies for Teaching Mathematical Modelling
13.2.2 Metacognitive Strategies in Modelling Processes
13.3 Research Questions
13.4 Study Design and Methods
13.4.1 Design of the Study
13.4.2 Instruments
13.4.3 Sample
13.4.4 Modelling Seminar
13.4.5 Data Analysis
13.5 Results
13.5.1 Pre-Service Teachers’ Knowledge About Metacognitive Modelling Strategies
13.5.2 Pre-service Teachers’ Noticing Competencies Regarding Metacognitive Modelling Strategies
13.5.3 Relation of Pre-service Teachers’ Knowledge and Noticing Competencies
13.6 Conclusion, Limitations and Looking Ahead
References
14 Using an Assessment for Learning Framework to Support Pre-service Teachers’ Mathematical Modelling Activities
14.1 Introduction
14.1.1 Mathematical Modelling
14.1.2 Mathematical Modelling Assessment
14.1.3 Assessment for Learning
14.1.4 Modelling Activities
14.2 The Study
14.2.1 Research Design
14.2.2 Data Gathering and Analysis
14.3 Results
14.4 Discussion and Conclusion
References
15 In-Service Teachers’ Transformation of a Mathematised Task into Modelling Tasks
15.1 Introduction
15.2 A Framework for Describing and Analysing Teachers’ Activities to Design and Implement Modelling Tasks
15.3 Method
15.3.1 Participants and Teacher Educators
15.3.2 Design of the PD Program
15.3.3 Overview of the Implementation of Modules 3.1–3.3
15.3.4 Data Collection and Analysis
15.4 Results
15.4.1 Mr B’s Selection and Analysis of the Mathematised Task at the Beginning of Module 3.1
15.4.2 Transformation and Improvement of the Modelling Tasks of Mr A and Mr B Through Module 3
15.4.3 Final Lesson Plan for the Modelling Lesson at the End of Module 3.3
15.4.4 Changes in Teachers’ Modelling Tasks Through Module 3
15.5 Discussion and Conclusion
References
16 Pre-service Teachers’ Self-Efficacy for Teaching Mathematical Modelling
16.1 Introduction
16.2 Theoretical Background
16.2.1 Modelling Competence
16.2.2 Professional Competence
16.2.3 Test Instrument for Self-Efficacy
16.3 Research Question
16.4 Research Design
16.4.1 Treatment Design: Teaching–Learning Laboratories
16.4.2 Data Acquisition and Analysis
16.5 Results
16.6 Discussion
References
17 A Case Study of Pre-service Teachers’ Task Design and Implementation for a Mathematical Modelling Lesson Sequence in Project-Based Instruction
17.1 Introduction
17.2 Theoretical Framework for Project-Based Modelling Lesson Plans and Implementation
17.3 Method
17.3.1 The Case
17.3.2 PBI Lessons
17.4 Results
17.5 Discussion and Conclusion
References
Part V Teaching Mathematical Modelling
18 The Relationships Between Statistics, Statistical Modelling and Mathematical Modelling
18.1 Introduction
18.2 Background
18.2.1 Statistics and Modelling from a Statistical Perspective
18.2.2 Statistics as a Discipline from a Mathematical Perspective
18.2.3 Mathematics vs. Statistics—Differences and Commonalities Focusing on the Notion and Role of Modelling in the Disciplines and in Education
18.3 Towards a Framework Conceptualising the Relationships Between Statistics, Statistical Modelling and Mathematical Modelling
18.3.1 Recent Research Focusing on Aspects Integrating Statistical and Mathematical Modelling
18.4 Rationales for Statistical Modelling in Education Research from a Mathematical Modelling Perspective
18.5 Conclusion, Suggestions and Outlook
References
19 The Dialogic Approach of Ethnomodelling and Its Cultural Dynamics
19.1 Initial Considerations
19.2 Ethnomodelling
19.3 Ethnomodels of Measuring Plots of Land
19.3.1 Area of Plots of Land with Three Corners: Cubação of Land with Triangular Shapes
19.3.2 Four Corners Plot Land Area: Cubação with Quadrilateral Shapes
19.3.3 Some Considerations About Brazilian Plot of Land (Cubação)
19.4 Final Considerations
References
20 Methods for Teaching Modelling Problems
20.1 Introduction
20.2 Guidance as a Key Principle of Instructional and Constructional Approaches to Learning
20.2.1 Categorisation of Teaching Methods
20.2.2 Direct Instruction
20.2.3 Teaching Methods Oriented Towards Students’ Self-Regulation
20.3 Methods for Teaching Modelling Problems
20.4 Consequences and Outlook
References
Refereeing Process
Index