Lines of Inquiry in Mathematical Modelling Research in Education.

• Superior document: ICME-13 Monographs
• Author: Stillman, Gloria Ann.
• TeilnehmendeR: Brown, Jill P.
• Place / Publishing House: Cham : : Springer International Publishing AG,, 2019.; ©2019.
• Year of Publication: 2019
• Edition: 1st ed.
• Language: English
• Series: ICME-13 Monographs
• Physical Description: 1 online resource (270 pages)

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 -- Blank Page -- Blank Page -- Blank Page -- Blank Page -- Blank Page -- Blank Page.