Mathematical Modelling and Applications

1. Crossing Boundaries in Mathematical Modelling and Applications Educational Research and Practice
Gloria Ann Stillman, Werner Blum, Gabriele Kaiser

Part I. New Approaches in Research, Teaching and Practice from Crossing Boundaries

2. Mathematical Modelling with Increasing Learning Aids: A Video Study
Deike S. Alfke

3. Modelling with Statistical Data: Characterisation of Student Models
Àngels Aymerich, Núria Gorgorió, Lluís Albarracín

4. How Teachers Can Promote Mathematising by Means of Mathematical City Walks
Nils Buchholtz

5. L’Hospital’s Weight Problem: Testing the Boundaries Between Mathematics and Physics and Between Application and Modelling
France Caron, Kathleen Pineau

6. Representations of Modelling in Mathematics Education
Helen M. Doerr, Jonas B. Ärlebäck, Morten Misfeldt

7. The Primacy of ‘Noticing’: A Key to Successful Modelling
Peter Galbraith, Gloria Ann Stillman, Jill P. Brown

8. Combining Models Related to Data Distribution Through Productive Experimentation
Takashi Kawakami

9. Reconciling Intuitions and Conventional Knowledge: The Challenge of Teaching and Learning Mathematical Modelling
Azita Manouchehri, Stephen T. Lewis

10. A Modelling Perspective in Designing Teacher Professional Learning Communities
Nicholas Mousoulides, Marilena Nicolaidou, Maria Evagorou

11. Mathematical Modelling and Proof by Recurrence: An Analysis from a Wittgensteinian Perspective
Bárbara Nilvada Palharini, Emerson Tortola, Lourdes Maria Werle Almeida

12. Quality Criteria for Mathematical Models in Relation to Models’ Purposes: Their Usefulness in Engineering Education
Jacob Perrenet, Bert Zwaneveld, Kees Overveld, Tijn Borghuis

13. Ethnomodelling as the Mathematization of Cultural Practices
Milton Rosa, Daniel Clark Orey

14. Enabling Anticipation Through Visualisation in Mathematising Real-World Problems in a Flipped Classroom
Gloria Ann Stillman

15. Measuring Metacognitive Modelling Competencies
Katrin Vorhölter

Part II. Researching Boundaries in Mathematical Modelling Education

16. The Mathematical Modelling Competencies Required for Solving Engineering Statics Assignments
Burkhard Alpers

17. Pre-service Teachers’ Levels of Reflectivity After Mathematical Modelling Activities with High School Students
Rita Borromeo Ferri

18. Context and Understanding: The Case of Linear Models
Jill P. Brown

19. Difficulties in Teaching Modelling: A French-Spanish Exploration
Richard Cabassut, Irene Ferrando

20. How Students Connect Mathematical Models to Descriptions of Real-World Situations
Dirk Bock, Nele Veracx, Wim Dooren

21. Mathematical Modelling Strategies and Attitudes of Third Year Pre-service Teachers
Rina Durandt, Gerrie J. Jacobs

22. Exploring the Notion of Mathematical Literacy in Curricula Documents
Peter Frejd, Vincent Geiger

23. Design and Implementation of a Tool for Analysing Student Products When They Solve Fermi Problems
César Gallart, Irene Ferrando, Lluís M. García-Raffi, Lluís Albarracín, Núria Gorgorió

24. Implementing Modelling into Classrooms: Results of an Empirical Research Study
Jana Kreckler

25. A Commognitive Perspective on Pre-service Secondary Teachers’ Content Knowledge in Mathematical Modelling
Joo Young Park

26. Mathematics Teachers’ Learning at the Boundaries of Teaching and Workplace
Giorgos Psycharis, Despina Potari

27. Case Study of Pre-service Teacher Education for Mathematical Modelling and Applications Connecting Paintings with Mathematics
Akihiko Saeki, Masafumi Kaneko, Daisuke Saito

28. Inquiry and Modelling in a Real Archaeological Context
Gemma Sala Sebastià, Vicenç Font Moll, Joaquim Giménez Rodríguez, Berta Barquero Farràs

29. Students’ Overreliance on Linearity in Economic Applications: A State of the Art
Daam Reeth, Dirk Bock

Part III. Pedagogical Issues for Teachers and Teacher Educators Using Mathematical Modelling and Applications

30. Teaching Modelling and Systemic Change
Hugh Burkhardt, Malcolm Swan

31. Mathematical Modelling as a Professional Activity: Lessons for the Classroom
Peter Frejd

32. Modelling Task Design: Science Teachers’ View
Carolina Guerrero-Ortiz, Jaime Mena-Lorca

33. Modelling as Interactive Translations Among Plural Worlds: Experimental Teaching Using the Night-Time Problem
Toshikazu Ikeda, Max Stephens

34. The Dual Modelling Cycle Framework: Report on an Australian Study
Janeen Lamb, Akio Matsuzaki, Akihiko Saeki, Takashi Kawakami

35. Implementing Mathematical Modelling: The Challenge of Teacher Educating
Azita Manouchehri

36. The Velocity Concept: The History of Its Modelling Development
Regina Dorothea Moeller

37. Developing a Mathematical Modelling Task for All Students
Edel Reilly

38. The Hidden Benefits of Mathematical Modelling for Students with Disabilities
Rina Scott-Wilson, Dirk C. J. Wessels, Helena M. Wessels, Estelle Swart

39. Scaffolding Complex Modelling Processes: An In-Depth Study
Peter Stender, Nadine Krosanke, Gabriele Kaiser

40. Long-Term Development of How Students Interpret a Model: Complementarity of Contexts and Mathematics
Pauline Vos, Gerrit Roorda

41. Exploring Aspects of Creativity in Mathematical Modelling
Helena M. Wessels

42. Mathematical Modelling in Dutch Textbooks: Is It Genuine Mathematical Modelling?
Bert Zwaneveld, Jacob Perrenet, Kees Overveld, Tijn Borghuis

Part IV. Influences of Technologies on Modelling and Applications

43. Initial Results of an Intervention Using a Mobile Game App to Simulate a Pandemic Outbreak
Peter Frejd, Jonas B. Ärlebäck

44. Modelling and Simulation with the Help of Digital Tools
Gilbert Greefrath, Hans-Stefan Siller

45. Mathematical Modelling for Engineering Diploma Students: Perspectives on Visualisation
Hanti Kotze, Gerrie J. Jacobs, Erica D. Spangenberg

46. Interactive Diagrams Used for Collaborative Learning Concerning Mathematical Models of Motion
Elena Naftaliev

47. Using Modelling and Tablets in the Classroom to Learn Quadratic Functions
Miriam Ortega, Luis Puig

48. Mathematical Modelling in a Long-Distance Teacher Education in Brazil: Democratizing Mathematics
Daniel Clark Orey, Milton Rosa

Part V. Assessment of Mathematical Modelling in Schools

49. Six Principles to Assess Modelling Abilities of Students Working in Groups
Piera Biccard, Dirk Wessels

50. Assessing Mathematizing Competences Through Multiple-Choice Tasks: Using Students’ Response Processes to Investigate Task Validity
Brikena Djepaxhija, Pauline Vos, Anne Berit Fuglestad

Part VI. Applicability at Different Levels of Schooling

51. How to Build a Hydrogen Refuelling Station Infrastructure in Germany: An Interdisciplinary Project Approach for Mathematics Classrooms
Irene Grafenhofer, Hans-Stefan Siller

52. Authentic Mathematical Modelling Experiences of Upper Secondary School: A Case Study
Kerri Spooner

53. Erratum
Gloria Ann Stillman, Werner Blum, Gabriele Kaiser

Avainsanat: Education, Mathematics Education, Learning & Instruction, Teaching and Teacher Education, Educational Technology