Mathematical Modelling And Applications: Crossing And Researching Boundaries In Mathematics Education (international Perspectives On The Teaching And Learning Of Mathematical Modelling)

Annotation This volume documents on-going research and theorising in the sub-field of mathematics education devoted to the teaching and learning of mathematical modelling and applications. Mathematical modelling provides a way of conceiving and resolving problems in the life world of people whether these range from the everyday individual numeracy level to sophisticated new problems for society at large. Mathematical modelling and real world applications are considered as having potential for multi-disciplinary work that involves knowledge from a variety of communities of practice such as those in different workplaces (e.g., those of educators, designers, construction engineers, museum curators) and in different fields of academic endeavour (e.g., history, archaeology, mathematics, economics). From an educational perspective, researching the development of competency in real world modelling involves research situated in crossing the boundaries between being a student engaged in modelling or mathematical application to real word tasks in the classroom, being a teacher of mathematical modelling (in or outside the classroom or bridging both), and being a modeller of the world outside the classroom. This is the focus of many of the authors of the chapters in this book. All authors of this volume are members of the International Community of Teachers of Mathematical Modelling (ICTMA), the peak research body into researching the teaching and learning of mathematical modelling at all levels of education from the early years to tertiary education as well as in the workplace 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