Trends in Teaching and Learning of Mathematical Modelling

1. Trends in Teaching and Learning of Mathematical Modelling – Preface
Gabriele Kaiser, Werner Blum, Rita Borromeo Ferri, Gloria Stillman

2. Modelling from Primary to Upper Secondary School: Findings of Empirical Research – Overview
Thomas Lingefjärd

3. Can Modelling Be Taught and Learnt? Some Answers from Empirical Research
Werner Blum

4. “Can Modelling Be Taught and Learnt?” – A Commentary
Marcelo C. Borba

5. Upper Secondary Students’ Handling of Real-World Contexts
Andreas Busse

6. Word Problem Classification: A Promising Modelling Task at the Elementary Level
Wim Dooren, Dirk Bock, Kim Vleugels, Lieven Verschaffel

7. Understanding and Promoting Mathematical Modelling Competencies: An Applied Perspective
George Ekol

8. Secondary Teachers’ Beliefs About Teaching Applications – Design and Selected Results of a Qualitative Case Study
Frank Förster

9. Secondary Teachers’ Beliefs on Modelling in Geometry and Stochastics
Boris Girnat, Andreas Eichler

10. Examining Mathematising Activities in Modelling Tasks with a Hidden Mathematical Character
Roxana Grigoraş, Fco. Javier Garcia, Stefan Halverscheid

11. The Sun Hour Project
Thomas Lingefjärd, Stefanie Meier

12. Mathematical Knowledge Application and Student Difficulties in a Design-Based Interdisciplinary Project
Kit Ee Dawn Ng

13. Evaluation of Teaching Activities with Multi-Variable Functions in Context
Yoshiki Nisawa, Seiji Moriya

14. Mathematical Modelling in Secondary Education: A Case Study
José Ortiz, Aldora Dos Santos

15. Students Overcoming Blockages While Building a Mathematical Model: Exploring a Framework
Sanne Schaap, Pauline Vos, Martin Goedhart

16. What Did Taiwan Mathematics Teachers Think of Model-Eliciting Activities and Modelling Teaching?
Shih-Yi Yu, Ching-Kuch Chang

17. Looking Deeper into Modelling Processes: Studies with a Cognitive Perspective – Overview
Susana Carreira

18. Applying Metacognitive Knowledge and Strategies in Applications and Modelling Tasks at Secondary School
Gloria Stillman

19. Effective Mathematical Modelling without Blockages – A Commentary
Rita Borromeo Ferri

20. Modelling Tasks: Insight into Mathematical Understanding
Jill P. Brown, Ian Edwards

21. Mathematical Modelling of Daily Life in Adult Education: Focusing on the Notion of Knowledge
Susana Carreira, Nélia Amado, Filipa Lecoq

22. Students’ Modelling Routes in the Context of Object Manipulation and Experimentation in Mathematics
Susana Carreira, Ana Margarida Baioa

23. Engineering Model Eliciting Activities for Elementary School Students
Nicholas G. Mousoulides, Lyn D. English

24. Project Modelling Routes in 12–16-Year-Old Pupils
Manuel Sol, Joaquin Giménez, Núria Rosich

25. Mathematical Modelling in Teacher Education – Overview
Jill P. Brown

26. Models and Modelling Perspectives on Teaching and Learning Mathematics in the Twenty-First Century
Helen M. Doerr, Richard Lesh

27. Mathematical Modelling in a Distance Course for Teachers
Maria Salett Biembengut, Thaís Mariane Biembengut Faria

28. In-Service and Prospective Teachers’ Views About Modelling Tasks in the Mathematics Classroom – Results of a Quantitative Empirical Study
Sebastian Kuntze

29. Pre-service Secondary Mathematics Teachers’ Affinity with Using Modelling Tasks in Teaching Years 8–10
Gloria Stillman, Jill P. Brown

30. Using Technologies: New Possibilities of Teaching and Learning Modelling – Overview
Gilbert Greefrath

31. Factors Affecting Teachers’ Adoption of Innovative Practices with Technology and Mathematical Modelling
Vince Geiger

32. Modelling Considering the Influence of Technology
Gilbert Greefrath, Hans-Stefan Siller, Jens Weitendorf

33. Improving Learning in Science and Mathematics with Exploratory and Interactive Computational Modelling
Rui Gomes Neves, Jorge Carvalho Silva, Vítor Duarte Teodoro

34. Modelling Competency: Teaching, Learning and Assessing Competencies – Overview
Morten Blomhøj

35. Drivers for Mathematical Modelling: Pragmatism in Practice
Christopher Haines

36. Identifying Drivers for Mathematical Modelling – A Commentary
Katja Maaß

37. Documenting the Development of Modelling Competencies of Grade 7 Mathematics Students
Piera Biccard, Dirk C. J. Wessels

38. Students’ Reflections in Mathematical Modelling Projects
Morten Blomhøj, Tinne Hoff Kjeldsen

39. From Data to Functions: Connecting Modelling Competencies and Statistical Literacy
Joachim Engel, Sebastian Kuntze

40. First Results from a Study Investigating Swedish Upper Secondary Students’ Mathematical Modelling Competencies
Peter Frejd, Jonas Bergman Ärlebäck

41. Why Cats Happen to Fall from the Sky or on Good and Bad Models
Hans-Wolfgang Henn

42. Assessing Modelling Competencies Using a Multidimensional IRT Approach
Luzia Zöttl, Stefan Ufer, Kristina Reiss

43. Modelling in Tertiary Education – Overview
Peter Galbraith

44. The Mathematical Expertise of Mechanical Engineers: Taking and Processing Measurements
Burkhard Alpers

45. Mathematical Modelling Skills and Creative Thinking Levels: An Experimental Study
Qi Dan, Jinxing Xie

46. Modelling the Evolution of the Belgian Population Using Matrices, Eigenvalues and Eigenvectors
Johan Deprez

47. Modelling and the Educational Challenge in Industrial Mathematics
Matti Heilio

48. Modelling of Infectious Disease with Biomathematics: Implications for Teaching and Research
Sergiy Klymchuk, Ajit Narayanan, Norbert Gruenwald, Gabriele Sauerbier, Tatyana Zverkova

49. Using Response Analysis Mapping to Display Modellers’ Mathematical Modelling Progress
Akio Matsuzaki

50. Modelling Examples and Modelling Projects – Overview
Hugh Burkhardt

51. Modelling Chemical Equilibrium in School Mathematics with Technology
Mette Andresen, Asbjoern Petersen

52. Real-World Modelling in Regular Lessons: A Long-Term Experiment
Martin Bracke, Andreas Geiger

53. Modelling Tasks at the Internet Portal “Program for Gifted”
Matthias Brandl

54. Modelling at Primary School Through a French–German Comparison of Curricula and Textbooks
Richard Cabassut, Anke Wagner

55. Modifying Teachers’ Practices: The Case of a European Training Course on Modelling and Applications
Fco. Javier García, Luisa Ruiz-Higueras

56. Google’s PageRank: A Present-Day Application of Mathematics in the Classroom
Hans Humenberger

57. Authentic Modelling Problems in Mathematics Education
Gabriele Kaiser, Björn Schwarz, Nils Buchholtz

58. Using Modelling Experiences to Develop Japanese Senior High School Students’ Awareness of the Interrelations between Mathematics and Science
Tetsushi Kawasaki, Seiji Moriya

59. Stochastic Case Problems for the Secondary Classroom with Reliability Theory
Usha Kotelawala

60. LEMA – Professional Development of Teachers in Relation to Mathematical Modelling
Katja Maaß, Johannes Gurlitt

61. Modelling in the Classroom: Obstacles from the Teacher’s Perspective
Barbara Schmidt

62. Teachers’ Professional Learning: Modelling at the Boundaries
Geoff D. Wake

63. Theoretical and Curricular Reflections on Mathematical Modelling – Overview
Pauline Vos

64. Making Connections Between Modelling and Constructing Mathematics Knowledge: An Historical Perspective
Toshikazu Ikeda, Max Stephens

65. Practical Knowledge of Research Mathematicians, Scientists, and Engineers About the Teaching of Modelling
Jeroen Spandaw

66. Evolution of Applications and Modelling in a Senior Secondary Curriculum
Gloria Stillman, Peter Galbraith

67. Sense of Reality Through Mathematical Modelling
Jhony Alexander Villa-Ochoa, Carlos Mario Jaramillo López

68. What Is ‘Authentic’ in the Teaching and Learning of Mathematical Modelling?
Pauline Vos

Keywords: Education, Mathematics Education, Mathematical Modeling and Industrial Mathematics