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Format: 1 online resource (270 pages)

Edition: 1st ed.

ISBN: 9783030149314

Series Statement: ICME-13 Monographs

Note: 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.

Additional Edition: Print version: Stillman, Gloria Ann Lines of Inquiry in Mathematical Modelling Research in Education Cham : Springer International Publishing AG,c2019 ISBN 9783030149307

Language: English

Subjects: Education , Mathematics

Keywords: Electronic books. ; Aufsatzsammlung ; Konferenzschrift ; Aufsatzsammlung ; Konferenzschrift

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Format: 1 Online-Ressource (259 p.)

ISBN: 9783030149314

Series Statement: ICME-13 Monographs

Content: This open access book is based on selected presentations from Topic Study Group 21: Mathematical Applications and Modelling in the Teaching and Learning of Mathematics at the 13th International Congress on Mathematical Education (ICME 13), held in Hamburg, Germany on July 24–31, 2016. It contributes to the theory, research and teaching practice concerning this key topic by taking into account the importance of relations between mathematics and the real world. Further, the book addresses the “balancing act” between developing students’ modelling skills on the one hand, and using modelling to help them learn mathematics on the other, which arises from the integration of modelling into classrooms. The contributions, prepared by authors from 9 countries, reflect the spectrum of international debates on the topic, and the examples presented span schooling from years 1 to 12, teacher education, and teaching modelling at the tertiary level. In addition the book highlights professional learning and development for in-service teachers, particularly in systems where the introduction of modelling into curricula means reassessing how mathematics is taught. Given its scope, the book will appeal to researchers and teacher educators in mathematics education, as well as pre-service teachers and school and university educators

Note: English

Language: English

URL: kostenfrei

UID:

Format: 1 online resource (x, 259 pages) : , illustrations (some color)

ISBN: 9783030149314 , 3030149315

Series Statement: ICME-13 monographs,

Content: This open access book is based on selected presentations from Topic Study Group 21: Mathematical Applications and Modelling in the Teaching and Learning of Mathematics at the 13th International Congress on Mathematical Education (ICME 13), held in Hamburg, Germany on July 24-31, 2016. It contributes to the theory, research and teaching practice concerning this key topic by taking into account the importance of relations between mathematics and the real world. Further, the book addresses the "balancing act" between developing students' modelling skills on the one hand, and using modelling to help them learn mathematics on the other, which arises from the integration of modelling into classrooms. The contributions, prepared by authors from 9 countries, reflect the spectrum of international debates on the topic, and the examples presented span schooling from years 1 to 12, teacher education, and teaching modelling at the tertiary level. In addition the book highlights professional learning and development for in-service teachers, particularly in systems where the introduction of modelling into curricula means reassessing how mathematics is taught. Given its scope, the book will appeal to researchers and teacher educators in mathematics education, as well as pre-service teachers and school and university educators

Note: Includes index. , Series Preface Gabriele Kaiser Preface ContentsChapter 1 State of the Art on Mathematical Modelling in Mathematics Education -- Lines of InquiryGloria A. Stillman Chapter 2 Towards a Framework for a Dialectical Relationship between Pedagogical Practice and ResearchJussara de Loiola Araújo Chapter 3 Interplay between Research and Development of Teaching Practices in Mathematical ModellingMorten Blomhöj Chapter 4 Establishing the Construct: Task Context Jill Brown Chapter 5 Approaches to Investigating Complex Dynamical SystemsFrance Caron and Miroslav Lovric Chapter 6 Precision, Priorities, and Proxies in Mathematical ModellingJennifer Czocher Chapter 7 A Modelling Perspective on Students' Reasoning: From a Mathematical Model to a Motion Model Angeles Dominguez and Jorge de la Garza Chapter 8 Teachers as Learners: Understanding and Valuing Mathematical Modelling through Professional Development Elizabeth W. Fulton, Megan H. Wickstrom, Elizabeth A. Burroughs, and Mary Alice Carlson Chapter 9 Assessing Sub-Competencies of Mathematical Modelling with the Help of Item Response Theory -- Presentation of a New Test InstrumentCorinna Hertleif, Catharina Adamek and Gilbert Greefrath Chapter 10 The Influence of Technology on the Mathematical Modelling of Physical PhenomenaMiriam Ortega and Luis Puig Chapter 11 Adapting a Cognitive Tool for Representing Prospective and Practicing Teachers' Interpretations of Students' Modelling Activities Juhaina Awawdeh Shahbari and Michal Tabach Chapter 12 Heuristic Strategies in Modelling ProblemsPeter Stender Chapter 13 The Impact of Task Authenticity on Students' Mathematical Modelling Process Dung Tran, An Nguyen, Duyen Nguyen, Giang-Nguyen T. Nguyen and Phuong Ta Chapter 14 Children with Mathematical Difficulties Cope with Modelling Tasks: The Case of SamiIbtisam Abedelhalek Zubi and Irit Peled Chapter 15 Data modelling Djorde Kadijevich Chapter 16 Conclusions and Future Lines of Inquiry in Mathematical Modelling Research in Education Toshikazu Ikeda and Jill Brown Refereeing process & reviewersIndex.

Language: English

DOI: 10.1007/978-3-030-14931-4

URL: ProQuest Ebook Central

URL: SpringerLink

UID:

Format: 1 online resource (X, 259 p. 60 illus., 27 illus. in color.)

Edition: 1st ed. 2019.

ISBN: 3-030-14931-5

Series Statement: ICME-13 Monographs,

Content: This open access book is based on selected presentations from Topic Study Group 21: Mathematical Applications and Modelling in the Teaching and Learning of Mathematics at the 13th International Congress on Mathematical Education (ICME 13), held in Hamburg, Germany on July 24–31, 2016. It contributes to the theory, research and teaching practice concerning this key topic by taking into account the importance of relations between mathematics and the real world. Further, the book addresses the “balancing act” between developing students’ modelling skills on the one hand, and using modelling to help them learn mathematics on the other, which arises from the integration of modelling into classrooms. The contributions, prepared by authors from 9 countries, reflect the spectrum of international debates on the topic, and the examples presented span schooling from years 1 to 12, teacher education, and teaching modelling at the tertiary level. In addition the book highlights professional learning and development for in-service teachers, particularly in systems where the introduction of modelling into curricula means reassessing how mathematics is taught. Given its scope, the book will appeal to researchers and teacher educators in mathematics education, as well as pre-service teachers and school and university educators.

Note: Preface -- Chapter 1. State of the Art on Mathematical Modelling in Mathematics Education – Lines of Inquiry -- Chapter 2. Towards a Framework for a Dialectical Relationship between Pedagogical Practice and Research -- Chapter 3. Interplay between Research and Development of Teaching Practices in Mathematical Modelling -- Chapter 4. Establishing the Construct: Task Context -- Chapter 5. Approaches to Investigating Complex Dynamical Systems -- Chapter 6. Precision, Priorities, and Proxies in Mathematical Modelling -- Chapter 7. A Modelling Perspective on Students’ Reasoning: From a Mathematical Model to a Motion Model -- Chapter 8. Teachers as Learners: Understanding and Valuing Mathematical Modelling through Professional Development -- Chapter 9. Assessing Sub-Competencies of Mathematical Modelling with the Help of Item Response Theory – Presentation of a New Test Instrument -- Chapter 10. The Influence of Technology on the Mathematical Modelling of Physical Phenomena -- Chapter 11. Adapting a Cognitive Tool for Representing Prospective and Practicing Teachers' Interpretations of Students' Modelling Activities -- Chapter 12. Heuristic Strategies in Modelling Problems -- Chapter 13. The Impact of Task Authenticity on Students’ Mathematical Modelling Process -- Chapter 14. Children with Mathematical Difficulties Cope with Modelling Tasks: The Case of Sami -- Chapter 15. Data modelling -- Chapter 16. Conclusions and Future Lines of Inquiry in Mathematical Modelling Research in Education -- Index. , English

Additional Edition: ISBN 3-030-14930-7

Language: English

DOI: 10.1007/978-3-030-14931-4

UID:

Format: 1 online resource (X, 259 p. 60 illus., 27 illus. in color.)

Edition: 1st ed. 2019.

ISBN: 3-030-14931-5

Series Statement: ICME-13 Monographs,

Content: This open access book is based on selected presentations from Topic Study Group 21: Mathematical Applications and Modelling in the Teaching and Learning of Mathematics at the 13th International Congress on Mathematical Education (ICME 13), held in Hamburg, Germany on July 24–31, 2016. It contributes to the theory, research and teaching practice concerning this key topic by taking into account the importance of relations between mathematics and the real world. Further, the book addresses the “balancing act” between developing students’ modelling skills on the one hand, and using modelling to help them learn mathematics on the other, which arises from the integration of modelling into classrooms. The contributions, prepared by authors from 9 countries, reflect the spectrum of international debates on the topic, and the examples presented span schooling from years 1 to 12, teacher education, and teaching modelling at the tertiary level. In addition the book highlights professional learning and development for in-service teachers, particularly in systems where the introduction of modelling into curricula means reassessing how mathematics is taught. Given its scope, the book will appeal to researchers and teacher educators in mathematics education, as well as pre-service teachers and school and university educators.

Note: Preface -- Chapter 1. State of the Art on Mathematical Modelling in Mathematics Education – Lines of Inquiry -- Chapter 2. Towards a Framework for a Dialectical Relationship between Pedagogical Practice and Research -- Chapter 3. Interplay between Research and Development of Teaching Practices in Mathematical Modelling -- Chapter 4. Establishing the Construct: Task Context -- Chapter 5. Approaches to Investigating Complex Dynamical Systems -- Chapter 6. Precision, Priorities, and Proxies in Mathematical Modelling -- Chapter 7. A Modelling Perspective on Students’ Reasoning: From a Mathematical Model to a Motion Model -- Chapter 8. Teachers as Learners: Understanding and Valuing Mathematical Modelling through Professional Development -- Chapter 9. Assessing Sub-Competencies of Mathematical Modelling with the Help of Item Response Theory – Presentation of a New Test Instrument -- Chapter 10. The Influence of Technology on the Mathematical Modelling of Physical Phenomena -- Chapter 11. Adapting a Cognitive Tool for Representing Prospective and Practicing Teachers' Interpretations of Students' Modelling Activities -- Chapter 12. Heuristic Strategies in Modelling Problems -- Chapter 13. The Impact of Task Authenticity on Students’ Mathematical Modelling Process -- Chapter 14. Children with Mathematical Difficulties Cope with Modelling Tasks: The Case of Sami -- Chapter 15. Data modelling -- Chapter 16. Conclusions and Future Lines of Inquiry in Mathematical Modelling Research in Education -- Index. , English

Additional Edition: ISBN 3-030-14930-7

Language: English

DOI: 10.1007/978-3-030-14931-4

UID:

Format: 1 online resource (X, 259 p. 60 illus., 27 illus. in color.)

Edition: 1st ed. 2019.

ISBN: 3-030-14931-5

Series Statement: ICME-13 Monographs,

Content: This open access book is based on selected presentations from Topic Study Group 21: Mathematical Applications and Modelling in the Teaching and Learning of Mathematics at the 13th International Congress on Mathematical Education (ICME 13), held in Hamburg, Germany on July 24–31, 2016. It contributes to the theory, research and teaching practice concerning this key topic by taking into account the importance of relations between mathematics and the real world. Further, the book addresses the “balancing act” between developing students’ modelling skills on the one hand, and using modelling to help them learn mathematics on the other, which arises from the integration of modelling into classrooms. The contributions, prepared by authors from 9 countries, reflect the spectrum of international debates on the topic, and the examples presented span schooling from years 1 to 12, teacher education, and teaching modelling at the tertiary level. In addition the book highlights professional learning and development for in-service teachers, particularly in systems where the introduction of modelling into curricula means reassessing how mathematics is taught. Given its scope, the book will appeal to researchers and teacher educators in mathematics education, as well as pre-service teachers and school and university educators.

Note: Preface -- Chapter 1. State of the Art on Mathematical Modelling in Mathematics Education – Lines of Inquiry -- Chapter 2. Towards a Framework for a Dialectical Relationship between Pedagogical Practice and Research -- Chapter 3. Interplay between Research and Development of Teaching Practices in Mathematical Modelling -- Chapter 4. Establishing the Construct: Task Context -- Chapter 5. Approaches to Investigating Complex Dynamical Systems -- Chapter 6. Precision, Priorities, and Proxies in Mathematical Modelling -- Chapter 7. A Modelling Perspective on Students’ Reasoning: From a Mathematical Model to a Motion Model -- Chapter 8. Teachers as Learners: Understanding and Valuing Mathematical Modelling through Professional Development -- Chapter 9. Assessing Sub-Competencies of Mathematical Modelling with the Help of Item Response Theory – Presentation of a New Test Instrument -- Chapter 10. The Influence of Technology on the Mathematical Modelling of Physical Phenomena -- Chapter 11. Adapting a Cognitive Tool for Representing Prospective and Practicing Teachers' Interpretations of Students' Modelling Activities -- Chapter 12. Heuristic Strategies in Modelling Problems -- Chapter 13. The Impact of Task Authenticity on Students’ Mathematical Modelling Process -- Chapter 14. Children with Mathematical Difficulties Cope with Modelling Tasks: The Case of Sami -- Chapter 15. Data modelling -- Chapter 16. Conclusions and Future Lines of Inquiry in Mathematical Modelling Research in Education -- Index. , English

Additional Edition: ISBN 3-030-14930-7

Language: English

DOI: 10.1007/978-3-030-14931-4

UID:

Format: X, 259 p. 60 illus., 27 illus. in color. , online resource.

Edition: 1st ed. 2019.

ISBN: 9783030149314

Series Statement: ICME-13 Monographs,

Content: This open access book is based on selected presentations from Topic Study Group 21: Mathematical Applications and Modelling in the Teaching and Learning of Mathematics at the 13th International Congress on Mathematical Education (ICME 13), held in Hamburg, Germany on July 24–31, 2016. It contributes to the theory, research and teaching practice concerning this key topic by taking into account the importance of relations between mathematics and the real world. Further, the book addresses the “balancing act” between developing students’ modelling skills on the one hand, and using modelling to help them learn mathematics on the other, which arises from the integration of modelling into classrooms. The contributions, prepared by authors from 9 countries, reflect the spectrum of international debates on the topic, and the examples presented span schooling from years 1 to 12, teacher education, and teaching modelling at the tertiary level. In addition the book highlights professional learning and development for in-service teachers, particularly in systems where the introduction of modelling into curricula means reassessing how mathematics is taught. Given its scope, the book will appeal to researchers and teacher educators in mathematics education, as well as pre-service teachers and school and university educators.

Note: Preface -- Chapter 1. State of the Art on Mathematical Modelling in Mathematics Education – Lines of Inquiry -- Chapter 2. Towards a Framework for a Dialectical Relationship between Pedagogical Practice and Research -- Chapter 3. Interplay between Research and Development of Teaching Practices in Mathematical Modelling -- Chapter 4. Establishing the Construct: Task Context -- Chapter 5. Approaches to Investigating Complex Dynamical Systems -- Chapter 6. Precision, Priorities, and Proxies in Mathematical Modelling -- Chapter 7. A Modelling Perspective on Students’ Reasoning: From a Mathematical Model to a Motion Model -- Chapter 8. Teachers as Learners: Understanding and Valuing Mathematical Modelling through Professional Development -- Chapter 9. Assessing Sub-Competencies of Mathematical Modelling with the Help of Item Response Theory – Presentation of a New Test Instrument -- Chapter 10. The Influence of Technology on the Mathematical Modelling of Physical Phenomena -- Chapter 11. Adapting a Cognitive Tool for Representing Prospective and Practicing Teachers' Interpretations of Students' Modelling Activities -- Chapter 12. Heuristic Strategies in Modelling Problems -- Chapter 13. The Impact of Task Authenticity on Students’ Mathematical Modelling Process -- Chapter 14. Children with Mathematical Difficulties Cope with Modelling Tasks: The Case of Sami -- Chapter 15. Data modelling -- Chapter 16. Conclusions and Future Lines of Inquiry in Mathematical Modelling Research in Education -- Index.

In: Springer eBooks

Additional Edition: Printed edition: ISBN 9783030149307

Additional Edition: Printed edition: ISBN 9783030149321

Additional Edition: Printed edition: ISBN 9783030149338

Language: English

DOI: 10.1007/978-3-030-14931-4

URL: https://doi.org/10.1007/978-3-030-14931-4