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Lines of Inquiry in Mathematical Modelling Research in Education.

Bibliographic Details
Main Author: Stillman, Gloria Ann.
Other Authors: Brown, Jill P.
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
  • 1 State of the Art on Modelling in Mathematics Education-Lines of Inquiry
  • 1.1 What Is Mathematical Modelling?
  • 1.1.1 An Example from Teacher Education
  • 1.2 Real-World Applications and Mathematical Modelling in Curricula
  • 1.3 What Do We Know?
  • 1.3.1 Theoretical Focuses-Lines of Inquiry
  • 1.3.2 Empirical Lines of Inquiry
  • 1.4 Future Directions
  • 1.5 Final Considerations
  • References
  • 2 Toward a Framework for a Dialectical Relationship Between Pedagogical Practice and Research
  • 2.1 Introduction: Setting the Scene and Presenting the Objective
  • 2.2 Pedagogical Practice|Research
  • 2.2.1 An Example
  • 2.3 Teacher|Researcher
  • 2.3.1 Aspect 1: From Researcher to Teacher
  • 2.3.2 Aspect 2: Research Participants Are Students, so the Researcher Is the Teacher
  • 2.3.3 Aspect 3: The Teacher Acts on Her Own Initiative
  • 2.3.4 Aspect 4: The Teacher's Reflections Favouring the Performance of the Researcher
  • 2.4 Students|Participants
  • 2.5 Final Remarks
  • References
  • 3 Towards Integration of Modelling in Secondary Mathematics Teaching
  • 3.1 Introduction
  • 3.2 Learning Mathematics Through Modelling in Practice
  • 3.3 Modelling Dynamical Phenomena
  • 3.3.1 The Morning Shower
  • 3.3.2 The 100 m Sprint
  • 3.4 Conclusion
  • References
  • 4 Real-World Task Context: Meanings and Roles
  • 4.1 Introduction
  • 4.2 Method
  • 4.2.1 Journal Selection
  • 4.2.2 Initial Analysis
  • 4.2.3 Detailed and In-Depth Analyses
  • 4.3 Content Analysis: ESM
  • 4.3.1 Initial Analysis and Sample Selection
  • 4.3.2 Detailed Analysis
  • 4.3.3 In-Depth Analysis of the ESM Sample
  • 4.4 Content Analysis: JRME
  • 4.4.1 Initial Analysis and Sample Selection
  • 4.4.2 Detailed Analysis
  • 4.4.3 In-Depth Analysis of JRME Sample
  • 4.5 Content Analysis: MTL
  • 4.5.1 Initial Analysis and Sample Selection
  • 4.5.2 Detailed Analysis.
  • 4.5.3 In-Depth Analysis of MTL Sample
  • 4.6 Content Analysis: JMB
  • 4.6.1 Initial Analysis and Sample Selection
  • 4.6.2 Detailed Analysis
  • 4.6.3 In-Depth Analysis of the JMB Sample
  • 4.7 Discussion: Looking Across the Samples
  • 4.8 Concluding Remarks
  • Appendix/Online Supplementary Material
  • References
  • 5 Approaches to Investigating Complex Dynamical Systems
  • 5.1 Introduction
  • 5.2 The Experiment
  • 5.3 Habits of Mind at Play
  • 5.4 Modelling Complex Systems
  • 5.4.1 Functions and Differential Equations
  • 5.4.2 System Dynamics Software
  • 5.4.3 Cellular Automata
  • 5.4.4 Agent-Based Models
  • 5.5 Discussion
  • 5.5.1 Epistemological Issues
  • 5.5.2 Interdisciplinary Collaborations
  • 5.5.3 Technology and Computational Thinking
  • 5.5.4 Curriculum and Mathematical Content
  • 5.6 Conclusion
  • References
  • 6 Precision, Priority, and Proxies in Mathematical Modelling
  • 6.1 Introduction
  • 6.2 Empirical and Theoretical Background
  • 6.3 Methods
  • 6.3.1 Data Collection
  • 6.3.2 Data Analysis
  • 6.4 Results
  • 6.5 Interpretation and Discussion
  • 6.6 Limitations, Future Directions and Recommendations
  • References
  • 7 Teachers as Learners: Engaging Communities of Learners in Mathematical Modelling Through Professional Development
  • 7.1 Introduction
  • 7.2 Perspectives and Stance on Modelling Professional Development
  • 7.2.1 Preparing Teachers as Modellers
  • 7.2.2 Preparing Teachers to Teach Modelling
  • 7.3 Theoretical Framework: Mathematical Modelling as a Community of Practice
  • 7.4 Setting and Method
  • 7.4.1 Data Collection
  • 7.4.2 Data Analysis
  • 7.5 Results
  • 7.5.1 The Lunch Planning Task
  • 7.5.2 The Pizza Party Task
  • 7.5.3 City Park Ice Rink Design Task
  • 7.5.4 Looking Across Tasks
  • 7.6 Discussion and Implications
  • 7.7 Conclusion
  • References.
  • 8 Assessing Sub-competencies of  Mathematical Modelling-Development of a New Test Instrument
  • 8.1 Theoretical Background
  • 8.1.1 Mathematical Modelling Competency
  • 8.1.2 Assessment of Modelling Competencies
  • 8.2 Methods
  • 8.2.1 Item Construction
  • 8.2.2 Testing of Items
  • 8.2.3 Combining Items into a Test
  • 8.2.4 Methods of Data Collection
  • 8.2.5 Statistical Analyses to Answer the Research Questions
  • 8.3 Results
  • 8.4 Summary and Discussion
  • References
  • 9 The Influence of Technology on the Mathematical Modelling of Physical Phenomena
  • 9.1 Introduction
  • 9.2 Theoretical Framework
  • 9.3 The Research Study
  • 9.3.1 Participants and Teaching Methodology
  • 9.3.2 Data Analysis and Research Method
  • 9.4 Design of the Teaching Experiments
  • 9.5 Implementation of Teaching Experiments
  • 9.6 Results
  • 9.6.1 Choosing References in Video Physics®
  • 9.6.2 Interpretation of the Models
  • 9.7 Discussion and Conclusions
  • References
  • 10 Adopting the Modelling Cycle for Representing Prospective and Practising Teachers' Interpretations of Students' Modelling Activities
  • 10.1 Introduction
  • 10.2 Theoretical Background
  • 10.2.1 Modelling
  • 10.2.2 Teachers' Knowledge About Modelling
  • 10.3 Method
  • 10.3.1 Participants and Procedure
  • 10.3.2 Modelling Activities During the Intervention
  • 10.3.3 Sneaker Activity
  • 10.3.4 Analyses of Students' Modelling Activity
  • 10.3.5 Data Analysis of the First and Second Reports
  • 10.4 Findings
  • 10.4.1 Participants' Descriptions of Students' Modelling Process in R1 and R2
  • 10.5 Discussion and Conclusion
  • References
  • 11 Heuristic Strategies as a Toolbox in Complex Modelling Problems
  • 11.1 Theoretical Framework
  • 11.1.1 Teacher Activities to Promote Independent Student Action
  • 11.1.2 Heuristic Strategies
  • 11.2 The Study
  • 11.2.1 Modelling Days.
  • 11.2.2 Modelling: Roundabout Versus Traffic Light
  • 11.2.3 Empirical Survey
  • 11.3 Results
  • 11.3.1 Using Heuristic Strategies in Modelling Problems
  • 11.3.2 Results Referring to the Modelling Cycle and Observations in the Empirical Research
  • 11.4 Summary and Conclusions
  • References
  • 12 Modelling Tasks and Students with Mathematical Difficulties
  • 12.1 Theoretical Background
  • 12.2 Method
  • 12.3 Findings
  • 12.3.1 Sami's Pre-test in Modelling Competencies
  • 12.3.2 Sami's Performance and Role During the Task Sequence
  • 12.3.3 Sami's Progress in Mathematical Knowledge
  • 12.4 Discussion
  • 12.5 Conclusion
  • Appendix 1
  • Appendix 2
  • References
  • 13 Conclusions and Future Lines of Inquiry in Mathematical Modelling Research in Education
  • 13.1 Mathematical Modelling: What Lines of Inquiry?
  • 13.1.1 Goal, or Purpose, of Mathematical Modelling
  • 13.2 Theoretical Lines of Inquiry
  • 13.2.1 Prescriptive Modelling
  • 13.2.2 Modelling Frameworks and Modelling Cycles
  • 13.2.3 Modelling Competence and Competencies
  • 13.3 Empirical Lines of Inquiry
  • 13.3.1 Focus on the Modeller
  • 13.3.2 Focus on Teachers of Modelling
  • 13.3.3 Focus on Modelling Task
  • 13.3.4 Affordances of Technology-Rich Teaching and Learning Environments
  • 13.3.5 Verification and Validation
  • 13.4 Future Lines of Inquiry
  • 13.5 Conclusion
  • References
  • Refereeing Process
  • Index
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