Mathematical Modelling and Applications: Crossing and Researching Boundaries in Mathematics Education

Front Matter ....Pages i-xi
 Crossing Boundaries in Mathematical Modelling and Applications Educational Research and Practice  (Gloria Ann Stillman, Werner Blum, Gabriele Kaiser)....Pages 1-22
Front Matter ....Pages 23-23
 Mathematical Modelling with Increasing Learning Aids: A Video Study  (Deike S. Alfke)....Pages 25-35
 Modelling with Statistical Data: Characterisation of Student Models  (Àngels Aymerich, Núria Gorgorió, Lluís Albarracín)....Pages 37-47
 How Teachers Can Promote Mathematising by Means of Mathematical City Walks  (Nils Buchholtz)....Pages 49-58
 L’Hospital’s Weight Problem: Testing the Boundaries Between Mathematics and Physics and Between Application and Modelling  (France Caron, Kathleen Pineau)....Pages 59-69
 Representations of Modelling in Mathematics Education  (Helen M. Doerr, Jonas B. Ärlebäck, Morten Misfeldt)....Pages 71-81
 The Primacy of ‘Noticing’: A Key to Successful Modelling  (Peter Galbraith, Gloria Ann Stillman, Jill P. Brown)....Pages 83-94
 Combining Models Related to Data Distribution Through Productive Experimentation  (Takashi Kawakami)....Pages 95-105
 Reconciling Intuitions and Conventional Knowledge: The Challenge of Teaching and Learning Mathematical Modelling  (Azita Manouchehri, Stephen T. Lewis)....Pages 107-116
 A Modelling Perspective in Designing Teacher Professional Learning Communities  (Nicholas Mousoulides, Marilena Nicolaidou, Maria Evagorou)....Pages 117-127
 Mathematical Modelling and Proof by Recurrence: An Analysis from a Wittgensteinian Perspective  (Bárbara Nilvada Palharini, Emerson Tortola, Lourdes Maria Werle de Almeida)....Pages 129-139
 Quality Criteria for Mathematical Models in Relation to Models’ Purposes: Their Usefulness in Engineering Education  (Jacob Perrenet, Bert Zwaneveld, Kees van Overveld, Tijn Borghuis)....Pages 141-152
 Ethnomodelling as the Mathematization of Cultural Practices  (Milton Rosa, Daniel Clark Orey)....Pages 153-162
 Enabling Anticipation Through Visualisation in Mathematising Real-World Problems in a Flipped Classroom  (Gloria Ann Stillman)....Pages 163-173
 Measuring Metacognitive Modelling Competencies  (Katrin Vorhölter)....Pages 175-185
Front Matter ....Pages 187-187
 The Mathematical Modelling Competencies Required for Solving Engineering Statics Assignments  (Burkhard Alpers)....Pages 189-199
 Pre-service Teachers’ Levels of Reflectivity After Mathematical Modelling Activities with High School Students  (Rita Borromeo Ferri)....Pages 201-210
 Context and Understanding: The Case of Linear Models  (Jill P. Brown)....Pages 211-221
 Difficulties in Teaching Modelling: A French-Spanish Exploration  (Richard Cabassut, Irene Ferrando)....Pages 223-232
 How Students Connect Mathematical Models to Descriptions of Real-World Situations  (Dirk De Bock, Nele Veracx, Wim Van Dooren)....Pages 233-242
 Mathematical Modelling Strategies and Attitudes of Third Year Pre-service Teachers  (Rina Durandt, Gerrie J. Jacobs)....Pages 243-253
 Exploring the Notion of Mathematical Literacy in Curricula Documents  (Peter Frejd, Vincent Geiger)....Pages 255-263
 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)....Pages 265-275
 Implementing Modelling into Classrooms: Results of an Empirical Research Study  (Jana Kreckler)....Pages 277-287
 A Commognitive Perspective on Pre-service Secondary Teachers’ Content Knowledge in Mathematical Modelling  (Joo Young Park)....Pages 289-299
 Mathematics Teachers’ Learning at the Boundaries of Teaching and Workplace  (Giorgos Psycharis, Despina Potari)....Pages 301-312
 Case Study of Pre-service Teacher Education for Mathematical Modelling and Applications Connecting Paintings with Mathematics  (Akihiko Saeki, Masafumi Kaneko, Daisuke Saito)....Pages 313-323
 Inquiry and Modelling in a Real Archaeological Context  (Gemma Sala Sebastià, Vicenç Font Moll, Joaquim Giménez Rodríguez, Berta Barquero Farràs)....Pages 325-335
 Students’ Overreliance on Linearity in Economic Applications: A State of the Art  (Daam Van Reeth, Dirk De Bock)....Pages 337-347
Front Matter ....Pages 349-349
 Teaching Modelling and Systemic Change  (Hugh Burkhardt, Malcolm Swan)....Pages 351-370
 Mathematical Modelling as a Professional Activity: Lessons for the Classroom  (Peter Frejd)....Pages 371-388
 Modelling Task Design: Science Teachers’ View  (Carolina Guerrero-Ortiz, Jaime Mena-Lorca)....Pages 389-398
 Modelling as Interactive Translations Among Plural Worlds: Experimental Teaching Using the Night-Time Problem  (Toshikazu Ikeda, Max Stephens)....Pages 399-409
 The Dual Modelling Cycle Framework: Report on an Australian Study  (Janeen Lamb, Akio Matsuzaki, Akihiko Saeki, Takashi Kawakami)....Pages 411-419
 Implementing Mathematical Modelling: The Challenge of Teacher Educating  (Azita Manouchehri)....Pages 421-432
 The Velocity Concept: The History of Its Modelling Development  (Regina Dorothea Moeller)....Pages 433-442
 Developing a Mathematical Modelling Task for All Students  (Edel Reilly)....Pages 443-453
 The Hidden Benefits of Mathematical Modelling for Students with Disabilities  (Rina Scott-Wilson, Dirk Wessels, Helena M. Wessels, Estelle Swart)....Pages 455-465
 Scaffolding Complex Modelling Processes: An In-Depth Study  (Peter Stender, Nadine Krosanke, Gabriele Kaiser)....Pages 467-477
 Long-Term Development of How Students Interpret a Model: Complementarity of Contexts and Mathematics  (Pauline Vos, Gerrit Roorda)....Pages 479-489
 Exploring Aspects of Creativity in Mathematical Modelling  (Helena M. Wessels)....Pages 491-501
 Mathematical Modelling in Dutch Textbooks: Is It Genuine Mathematical Modelling?  (Bert Zwaneveld, Jacob Perrenet, Kees van Overveld, Tijn Borghuis)....Pages 503-514
Front Matter ....Pages 515-515
 Initial Results of an Intervention Using a Mobile Game App to Simulate a Pandemic Outbreak  (Peter Frejd, Jonas B. Ärlebäck)....Pages 517-527
 Modelling and Simulation with the Help of Digital Tools  (Gilbert Greefrath, Hans-Stefan Siller)....Pages 529-539
 Mathematical Modelling for Engineering Diploma Students: Perspectives on Visualisation  (Hanti Kotze, Gerrie J. Jacobs, Erica D. Spangenberg)....Pages 541-551
 Interactive Diagrams Used for Collaborative Learning Concerning Mathematical Models of Motion  (Elena Naftaliev)....Pages 553-563
 Using Modelling and Tablets in the Classroom to Learn Quadratic Functions  (Miriam Ortega, Luis Puig)....Pages 565-575
 Mathematical Modelling in a Long-Distance Teacher Education in Brazil: Democratizing Mathematics  (Daniel Clark Orey, Milton Rosa)....Pages 577-586
Front Matter ....Pages 587-587
 Six Principles to Assess Modelling Abilities of Students Working in Groups  (Piera Biccard, Dirk Wessels)....Pages 589-599
 Assessing Mathematizing Competences Through Multiple-Choice Tasks: Using Students’ Response Processes to Investigate Task Validity  (Brikena Djepaxhija, Pauline Vos, Anne Berit Fuglestad)....Pages 601-611
Front Matter ....Pages 613-613
 How to Build a Hydrogen Refuelling Station Infrastructure in Germany: An Interdisciplinary Project Approach for Mathematics Classrooms  (Irene Grafenhofer, Hans-Stefan Siller)....Pages 615-625
 Authentic Mathematical Modelling Experiences of Upper Secondary School: A Case Study  (Kerri Spooner)....Pages 627-637
Back Matter ....Pages 639-647