x

• Series Preface; Gabriele Kaiser and Gloria Stillman.- Helena Wessels – Her ‘Life Story’; Dirk Wessels.- 1. Sense-Making in Mathematical Modelling and Applications Educational Research and Practice; Gloria Stillman, Gabriele Kaiser, and Erna Lampen.- Part I Innovative Approaches in Modelling Educational Research and Teaching.- 2. Connections of Science Capital and the Teaching and Learning of Mathematical Modelling - an Introduction; Pauline Vos, Paul Hernandez-Martinez and Peter Frejd.- 3. Teachers’ Possibilities to Generate Science Capital for Modelling; Peter Frejd.- 4. Science Capital, Habitus and Mathematical Modelling Practices in the Field of University Education; Paul Hernandez-Martinez.- 5. On Science Museums, Science Capital and the Public Understanding of Mathematical Modelling; Pauline Vos.- 6. Working as a Cross-Institutional Collaborator Network to Develop Enhanced Analyses of Learners' Models and Modelling; Corey Brady, Jeffrey A. McLean, Hyunyi Jung, Aran W. Glancy and Ángeles Domínguez.- 7. Mapping Shifting Discourses in Classroom Talk Through Indexical Discourse Analysis: From the World of Mathematics to the World of Work; Stephen T. Lewis and Azita Manouchehri.- 8. Joy of Mathematical Modelling: A Forgotten Perspective?; Yuriy Rogovchenko, Olov Viirman and Stephanie Treffert-Thomas.- 9. Re-Signifying Function Concept: A Mixed Methods Study to Understand the Contributions of the Dialogic Approach of Ethnomodelling; Milton Rosa, Daniel Clark Orey and Diego Pereira de Oliveira Cortes.- Part II Research into or Evaluation of, Teaching Practice in Mathematical Modelling Education.- 10. Sense-Making with the Mathematical Modelling Process: Developing a Framework for Faculty Practice; Todd Abel, Mary Elizabeth Searcy and Tracie McLemore Salinas.- 11. Mathematical Modelling with a Solution Plan – An Intervention Study about the Development of Grade 9 Students’ Modelling Competencies; Catharina Adamek.- 12. A case study of the tensions and challenges arising as an upper secondary teacher designs and implements a model development sequence on statistics; Jonas Bergman Ärlebäck.- 13. Year 6 Students’ Gradual Identification of Mathematical Models of Average Speed when Making Sense of ‘Walking’; Takashi Kawakami, Shigekazu Komeda and Akihiko Saeki.- 14. A Time-Based Measurement of the Intensity of Difficulties in the Modelling Process; Heiner Klock and Hans-Stefan Siller.- 15. Deepening and Expanding Mathematical Models of Speed in Relation to Walking: The Case of Year 8 Students; Shigekazu Komeda, Takashi Kawakami, Masafumi Kaneko and Takashi Yamaguchi.- 16. Facilitating Modelling Activities in a Grade 5 Classroom; Azita Manouchehri, Mehmet Bekdemir  and Xiangquan Yao.- 17. Mathematical Modelling as a Learning Environment to Transform a Street Activity into a Sport Practice; Daniel Clark Orey, Milton Rosa and Rogério Braga Soares.- 18. Co-development of engineering technician and mathematical modelling competencies; Lidamaride Villiers and Dirk Wessels.- Part III Pedagogical Issues for Teachers and Teacher Educators Using Mathematical Modelling and Applications.- 19. Sensemaking in Modelling Tasks - What Can We Learn From Other Domains?; Piera Biccard.- 20. The Deployment of Mathematics in Areas other than Those Normally Associated with Mathematical Modelling and the Applications of Mathematics; Cyril Julie.- 21. Rising to the Challenge: Promoting Mathematical Modelling as Real-World Problem Solving; Peter Galbraith, Derek Holton and Ross Turner.- 22. Mathematics Trails and Learning Barriers; Iwan Gurjanow and Matthias Ludwig.- 23. Validating with the Use of a Dynamic Geometry Software; Corinna Hankeln.- 24. Using a Mathematical Modelling Activity to Assist Students to Make Sense of a Limit Theorem in Trigonometry; Toshikazu Ikeda and Max Stephens.- 25. Exploring Habits and Habitus of Biomedical Students with Modelling Tasks; Hanti Kotze.- 26. Metacognitive Strategies in Group Work in Mathematical Modelling Activities – the Students’ Perspective; Alexandra Krüger, Katrin Vorhölter and Gabriele Kaiser.- 27. Fostering Students´ Construction of Meaningfulness of Mathematics with Mathematical Modelling Problems; Katrin Vorhölter and Björn Schwarz.- 28. Teachers’ Perspectives on Students’ Metacognitive Strategies During Mathematical Modelling Processes – a Case Study; Lisa Wendt, Katrin Vorhölter and Gabriele Kaiser.- Part IV Assessment of Mathematical Modelling in Schools.- 29. Cognitive Diagnostic Modelling for Mathematical Modeling Assessment; Cigdem Alagoz and Celil Ekici.- 30. Occurrences of Mathematical Modelling Competencies in the Nationally-set Examination for Mathematical Literacy in South Africa; Mbulelo Bali, Cyril Julie, and Monde Mbekwa.- 31. Expectations for Challenge in Modelling and its Assessment; Jill Brown.- 32. Modelling Tasks in Central Examinations Based on the Example of Austria; Hans-Stefan Siller and Gilbert Greefrath.- Part V Applicability at Different Levels ofSchooling and University.- 33. Characterising Modelling Competency in Students’ Projects: Experiences from a Natural Science Bachelor Program; Morten Blomhøj.- 34. From Royaumont to Lyon: Applications and Modelling During the Sixties; Dirk De Bock and Bert Zwaneveld.- 35. Interactive Case Practice Teaching on Mathematical Modelling Course; Xiaojun Duan, Dan Wang and Mengda Wu.- 36. Pre-service Teachers’ Sense Making of Mathematical Modelling through a Design-Based Research Strategy; Rina Durandt and Geoffrey V. Lautenbach.- 37. Mathematical Modelling: A ‘Growing Tree’ for Creative and Flexible Thinking in Pre-service Mathematics Teachers; Rajendran Govender.- 38. Implementation of teacher trainings to promote action orientated and interdisciplinary modeling projects; Jean-Marie Lantau, Martin Bracke, Wolfgang Bock, and Patrick Capraro.- 39. Using Mathematical Modelling in the Teaching and Learning of Mathematical Literacy: Perspectives on the South African Context; Duncan Mhakure.- 40A Lecturer’s View on Teaching Mathematical Modelling; Kerri Spooner.- Part VI Examples of Modelling and Applications in Practice.- 41. Embodied Phenomenology in Mathematical Modeling of Sailing for Integrated STEM Learning; Celil Ekici and Cigdem Alagoz.- 42. Algebra Students Build Stock/Flow Models to Study Non-linear, Dynamic, Feedback System Problems; Diana M. Fisher.- Index.

x

• Series Preface; Gabriele Kaiser and Gloria Stillman.- Helena Wessels – Her ‘Life Story’; Dirk Wessels.- 1. Sense-Making in Mathematical Modelling and Applications Educational Research and Practice; Gloria Stillman, Gabriele Kaiser, and Erna Lampen.- Part I Innovative Approaches in Modelling Educational Research and Teaching.- 2. Connections of Science Capital and the Teaching and Learning of Mathematical Modelling - an Introduction; Pauline Vos, Paul Hernandez-Martinez and Peter Frejd.- 3. Teachers’ Possibilities to Generate Science Capital for Modelling; Peter Frejd.- 4. Science Capital, Habitus and Mathematical Modelling Practices in the Field of University Education; Paul Hernandez-Martinez.- 5. On Science Museums, Science Capital and the Public Understanding of Mathematical Modelling; Pauline Vos.- 6. Working as a Cross-Institutional Collaborator Network to Develop Enhanced Analyses of Learners' Models and Modelling; Corey Brady, Jeffrey A. McLean, Hyunyi Jung, Aran W. Glancy and Ángeles Domínguez.- 7. Mapping Shifting Discourses in Classroom Talk Through Indexical Discourse Analysis: From the World of Mathematics to the World of Work; Stephen T. Lewis and Azita Manouchehri.- 8. Joy of Mathematical Modelling: A Forgotten Perspective?; Yuriy Rogovchenko, Olov Viirman and Stephanie Treffert-Thomas.- 9. Re-Signifying Function Concept: A Mixed Methods Study to Understand the Contributions of the Dialogic Approach of Ethnomodelling; Milton Rosa, Daniel Clark Orey and Diego Pereira de Oliveira Cortes.- Part II Research into or Evaluation of, Teaching Practice in Mathematical Modelling Education.- 10. Sense-Making with the Mathematical Modelling Process: Developing a Framework for Faculty Practice; Todd Abel, Mary Elizabeth Searcy and Tracie McLemore Salinas.- 11. Mathematical Modelling with a Solution Plan – An Intervention Study about the Development of Grade 9 Students’ Modelling Competencies; Catharina Adamek.- 12. A case study of the tensions and challenges arising as an upper secondary teacher designs and implements a model development sequence on statistics; Jonas Bergman Ärlebäck.- 13. Year 6 Students’ Gradual Identification of Mathematical Models of Average Speed when Making Sense of ‘Walking’; Takashi Kawakami, Shigekazu Komeda and Akihiko Saeki.- 14. A Time-Based Measurement of the Intensity of Difficulties in the Modelling Process; Heiner Klock and Hans-Stefan Siller.- 15. Deepening and Expanding Mathematical Models of Speed in Relation to Walking: The Case of Year 8 Students; Shigekazu Komeda, Takashi Kawakami, Masafumi Kaneko and Takashi Yamaguchi.- 16. Facilitating Modelling Activities in a Grade 5 Classroom; Azita Manouchehri, Mehmet Bekdemir  and Xiangquan Yao.- 17. Mathematical Modelling as a Learning Environment to Transform a Street Activity into a Sport Practice; Daniel Clark Orey, Milton Rosa and Rogério Braga Soares.- 18. Co-development of engineering technician and mathematical modelling competencies; Lidamaride Villiers and Dirk Wessels.- Part III Pedagogical Issues for Teachers and Teacher Educators Using Mathematical Modelling and Applications.- 19. Sensemaking in Modelling Tasks - What Can We Learn From Other Domains?; Piera Biccard.- 20. The Deployment of Mathematics in Areas other than Those Normally Associated with Mathematical Modelling and the Applications of Mathematics; Cyril Julie.- 21. Rising to the Challenge: Promoting Mathematical Modelling as Real-World Problem Solving; Peter Galbraith, Derek Holton and Ross Turner.- 22. Mathematics Trails and Learning Barriers; Iwan Gurjanow and Matthias Ludwig.- 23. Validating with the Use of a Dynamic Geometry Software; Corinna Hankeln.- 24. Using a Mathematical Modelling Activity to Assist Students to Make Sense of a Limit Theorem in Trigonometry; Toshikazu Ikeda and Max Stephens.- 25. Exploring Habits and Habitus of Biomedical Students with Modelling Tasks; Hanti Kotze.- 26. Metacognitive Strategies in Group Work in Mathematical Modelling Activities – the Students’ Perspective; Alexandra Krüger, Katrin Vorhölter and Gabriele Kaiser.- 27. Fostering Students´ Construction of Meaningfulness of Mathematics with Mathematical Modelling Problems; Katrin Vorhölter and Björn Schwarz.- 28. Teachers’ Perspectives on Students’ Metacognitive Strategies During Mathematical Modelling Processes – a Case Study; Lisa Wendt, Katrin Vorhölter and Gabriele Kaiser.- Part IV Assessment of Mathematical Modelling in Schools.- 29. Cognitive Diagnostic Modelling for Mathematical Modeling Assessment; Cigdem Alagoz and Celil Ekici.- 30. Occurrences of Mathematical Modelling Competencies in the Nationally-set Examination for Mathematical Literacy in South Africa; Mbulelo Bali, Cyril Julie, and Monde Mbekwa.- 31. Expectations for Challenge in Modelling and its Assessment; Jill Brown.- 32. Modelling Tasks in Central Examinations Based on the Example of Austria; Hans-Stefan Siller and Gilbert Greefrath.- Part V Applicability at Different Levels ofSchooling and University.- 33. Characterising Modelling Competency in Students’ Projects: Experiences from a Natural Science Bachelor Program; Morten Blomhøj.- 34. From Royaumont to Lyon: Applications and Modelling During the Sixties; Dirk De Bock and Bert Zwaneveld.- 35. Interactive Case Practice Teaching on Mathematical Modelling Course; Xiaojun Duan, Dan Wang and Mengda Wu.- 36. Pre-service Teachers’ Sense Making of Mathematical Modelling through a Design-Based Research Strategy; Rina Durandt and Geoffrey V. Lautenbach.- 37. Mathematical Modelling: A ‘Growing Tree’ for Creative and Flexible Thinking in Pre-service Mathematics Teachers; Rajendran Govender.- 38. Implementation of teacher trainings to promote action orientated and interdisciplinary modeling projects; Jean-Marie Lantau, Martin Bracke, Wolfgang Bock, and Patrick Capraro.- 39. Using Mathematical Modelling in the Teaching and Learning of Mathematical Literacy: Perspectives on the South African Context; Duncan Mhakure.- 40A Lecturer’s View on Teaching Mathematical Modelling; Kerri Spooner.- Part VI Examples of Modelling and Applications in Practice.- 41. Embodied Phenomenology in Mathematical Modeling of Sailing for Integrated STEM Learning; Celil Ekici and Cigdem Alagoz.- 42. Algebra Students Build Stock/Flow Models to Study Non-linear, Dynamic, Feedback System Problems; Diana M. Fisher.- Index.

x

• Series Preface; Gabriele Kaiser and Gloria Stillman.- Helena Wessels – Her ‘Life Story’; Dirk Wessels.- 1. Sense-Making in Mathematical Modelling and Applications Educational Research and Practice; Gloria Stillman, Gabriele Kaiser, and Erna Lampen.- Part I Innovative Approaches in Modelling Educational Research and Teaching.- 2. Connections of Science Capital and the Teaching and Learning of Mathematical Modelling - an Introduction; Pauline Vos, Paul Hernandez-Martinez and Peter Frejd.- 3. Teachers’ Possibilities to Generate Science Capital for Modelling; Peter Frejd.- 4. Science Capital, Habitus and Mathematical Modelling Practices in the Field of University Education; Paul Hernandez-Martinez.- 5. On Science Museums, Science Capital and the Public Understanding of Mathematical Modelling; Pauline Vos.- 6. Working as a Cross-Institutional Collaborator Network to Develop Enhanced Analyses of Learners' Models and Modelling; Corey Brady, Jeffrey A. McLean, Hyunyi Jung, Aran W. Glancy and Ángeles Domínguez.- 7. Mapping Shifting Discourses in Classroom Talk Through Indexical Discourse Analysis: From the World of Mathematics to the World of Work; Stephen T. Lewis and Azita Manouchehri.- 8. Joy of Mathematical Modelling: A Forgotten Perspective?; Yuriy Rogovchenko, Olov Viirman and Stephanie Treffert-Thomas.- 9. Re-Signifying Function Concept: A Mixed Methods Study to Understand the Contributions of the Dialogic Approach of Ethnomodelling; Milton Rosa, Daniel Clark Orey and Diego Pereira de Oliveira Cortes.- Part II Research into or Evaluation of, Teaching Practice in Mathematical Modelling Education.- 10. Sense-Making with the Mathematical Modelling Process: Developing a Framework for Faculty Practice; Todd Abel, Mary Elizabeth Searcy and Tracie McLemore Salinas.- 11. Mathematical Modelling with a Solution Plan – An Intervention Study about the Development of Grade 9 Students’ Modelling Competencies; Catharina Adamek.- 12. A case study of the tensions and challenges arising as an upper secondary teacher designs and implements a model development sequence on statistics; Jonas Bergman Ärlebäck.- 13. Year 6 Students’ Gradual Identification of Mathematical Models of Average Speed when Making Sense of ‘Walking’; Takashi Kawakami, Shigekazu Komeda and Akihiko Saeki.- 14. A Time-Based Measurement of the Intensity of Difficulties in the Modelling Process; Heiner Klock and Hans-Stefan Siller.- 15. Deepening and Expanding Mathematical Models of Speed in Relation to Walking: The Case of Year 8 Students; Shigekazu Komeda, Takashi Kawakami, Masafumi Kaneko and Takashi Yamaguchi.- 16. Facilitating Modelling Activities in a Grade 5 Classroom; Azita Manouchehri, Mehmet Bekdemir  and Xiangquan Yao.- 17. Mathematical Modelling as a Learning Environment to Transform a Street Activity into a Sport Practice; Daniel Clark Orey, Milton Rosa and Rogério Braga Soares.- 18. Co-development of engineering technician and mathematical modelling competencies; Lidamaride Villiers and Dirk Wessels.- Part III Pedagogical Issues for Teachers and Teacher Educators Using Mathematical Modelling and Applications.- 19. Sensemaking in Modelling Tasks - What Can We Learn From Other Domains?; Piera Biccard.- 20. The Deployment of Mathematics in Areas other than Those Normally Associated with Mathematical Modelling and the Applications of Mathematics; Cyril Julie.- 21. Rising to the Challenge: Promoting Mathematical Modelling as Real-World Problem Solving; Peter Galbraith, Derek Holton and Ross Turner.- 22. Mathematics Trails and Learning Barriers; Iwan Gurjanow and Matthias Ludwig.- 23. Validating with the Use of a Dynamic Geometry Software; Corinna Hankeln.- 24. Using a Mathematical Modelling Activity to Assist Students to Make Sense of a Limit Theorem in Trigonometry; Toshikazu Ikeda and Max Stephens.- 25. Exploring Habits and Habitus of Biomedical Students with Modelling Tasks; Hanti Kotze.- 26. Metacognitive Strategies in Group Work in Mathematical Modelling Activities – the Students’ Perspective; Alexandra Krüger, Katrin Vorhölter and Gabriele Kaiser.- 27. Fostering Students´ Construction of Meaningfulness of Mathematics with Mathematical Modelling Problems; Katrin Vorhölter and Björn Schwarz.- 28. Teachers’ Perspectives on Students’ Metacognitive Strategies During Mathematical Modelling Processes – a Case Study; Lisa Wendt, Katrin Vorhölter and Gabriele Kaiser.- Part IV Assessment of Mathematical Modelling in Schools.- 29. Cognitive Diagnostic Modelling for Mathematical Modeling Assessment; Cigdem Alagoz and Celil Ekici.- 30. Occurrences of Mathematical Modelling Competencies in the Nationally-set Examination for Mathematical Literacy in South Africa; Mbulelo Bali, Cyril Julie, and Monde Mbekwa.- 31. Expectations for Challenge in Modelling and its Assessment; Jill Brown.- 32. Modelling Tasks in Central Examinations Based on the Example of Austria; Hans-Stefan Siller and Gilbert Greefrath.- Part V Applicability at Different Levels ofSchooling and University.- 33. Characterising Modelling Competency in Students’ Projects: Experiences from a Natural Science Bachelor Program; Morten Blomhøj.- 34. From Royaumont to Lyon: Applications and Modelling During the Sixties; Dirk De Bock and Bert Zwaneveld.- 35. Interactive Case Practice Teaching on Mathematical Modelling Course; Xiaojun Duan, Dan Wang and Mengda Wu.- 36. Pre-service Teachers’ Sense Making of Mathematical Modelling through a Design-Based Research Strategy; Rina Durandt and Geoffrey V. Lautenbach.- 37. Mathematical Modelling: A ‘Growing Tree’ for Creative and Flexible Thinking in Pre-service Mathematics Teachers; Rajendran Govender.- 38. Implementation of teacher trainings to promote action orientated and interdisciplinary modeling projects; Jean-Marie Lantau, Martin Bracke, Wolfgang Bock, and Patrick Capraro.- 39. Using Mathematical Modelling in the Teaching and Learning of Mathematical Literacy: Perspectives on the South African Context; Duncan Mhakure.- 40A Lecturer’s View on Teaching Mathematical Modelling; Kerri Spooner.- Part VI Examples of Modelling and Applications in Practice.- 41. Embodied Phenomenology in Mathematical Modeling of Sailing for Integrated STEM Learning; Celil Ekici and Cigdem Alagoz.- 42. Algebra Students Build Stock/Flow Models to Study Non-linear, Dynamic, Feedback System Problems; Diana M. Fisher.- Index.