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E-grāmata: Mathematical Modelling and Applications: Crossing and Researching Boundaries in Mathematics Education

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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.

1 Crossing Boundaries in Mathematical Modelling and Applications Educational Research and Practice
1(24)
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
25(12)
Deike S. Alfke
3 Modelling with Statistical Data: Characterisation of Student Models
37(12)
Angels Aymerich
Nuria Gorgorio
Lluis Albarracin
4 How Teachers Can Promote Mathematising by Means of Mathematical City Walks
49(10)
Nils Buchholtz
5 L'Hospital's Weight Problem: Testing the Boundaries Between Mathematics and Physics and Between Application and Modelling
59(12)
France Caron
Kathleen Pineau
6 Representations of Modelling in Mathematics Education
71(12)
Helen M. Doerr
Jonas B. Arleback
Morten Misfeldt
7 The Primacy of `Noticing': A Key to Successful Modelling
83(12)
Peter Galbraith
Gloria Ann Stillman
Jill P. Brown
8 Combining Models Related to Data Distribution Through Productive Experimentation
95(12)
Takashi Kawakami
9 Reconciling Intuitions and Conventional Knowledge: The Challenge of Teaching and Learning Mathematical Modelling
107(10)
Azita Manouchehri
Stephen T. Lewis
10 A Modelling Perspective in Designing Teacher Professional Learning Communities
117(12)
Nicholas Mousoulides
Marilena Nicolaidou
Maria Evagorou
11 Mathematical Modelling and Proof by Recurrence: An Analysis from a Wittgensteinian Perspective
129(12)
Barbara Nilvada Palharini
Emerson Tortola
Lourdes Maria Werle de Almeida
12 Quality Criteria for Mathematical Models in Relation to Models' Purposes: Their Usefulness in Engineering Education
141(12)
Jacob Perrenet
Bert Zwaneveld
Kees van Overveld
Tijn Borghuis
13 Ethnomodelling as the Mathematization of Cultural Practices
153(10)
Milton Rosa
Daniel Clark Orey
14 Enabling Anticipation Through Visualisation in Mathematising Real-World Problems in a Flipped Classroom
163(12)
Gloria Ann Stillman
15 Measuring Metacognitive Modelling Competencies
175(14)
Katrin Vorholter
Part II Researching Boundaries in Mathematical Modelling Education
16 The Mathematical Modelling Competencies Required for Solving Engineering Statics Assignments
189(12)
Burkhard Alpers
17 Pre-service Teachers' Levels of Reflectivity After Mathematical Modelling Activities with High School Students
201(10)
Rita Borromeo Ferri
18 Context and Understanding: The Case of Linear Models
211(12)
Jill P. Brown
19 Difficulties in Teaching Modelling: A French-Spanish Exploration
223(10)
Richard Cabassut
Irene Ferrando
20 How Students Connect Mathematical Models to Descriptions of Real-World Situations
233(10)
Dirk De Bock
Nele Veracx
Wim Van Dooren
21 Mathematical Modelling Strategies and Attitudes of Third Year Pre-service Teachers
243(12)
Rina Durandt
Gerrie J. Jacobs
22 Exploring the Notion of Mathematical Literacy in Curricula Documents
255(10)
Peter Frejd
Vincent Geiger
23 Design and Implementation of a Tool for Analysing Student Products When They Solve Fermi Problems
265(12)
Cesar Gallart
Irene Ferrando
Lluis M. Garcfa-Raffi
Lluis Albarraci'n
Nuria Gorgorio
24 Implementing Modelling into Classrooms: Results of an Empirical Research Study
277(12)
Jana Kreckler
25 A Commognitive Perspective on Pre-service Secondary Teachers' Content Knowledge in Mathematical Modelling
289(12)
Joo Young Park
26 Mathematics Teachers' Learning at the Boundaries of Teaching and Workplace
301(12)
Giorgos Psycharis
Despina Potari
27 Case Study of Pre-service Teacher Education for Mathematical Modelling and Applications Connecting Paintings with Mathematics
313(12)
Akihiko Saeki
Masafumi Kaneko
Daisuke Saito
28 Inquiry and Modelling in a Real Archaeological Context
325(12)
Gemma Sala Sebastia
Vicenc Font Moll
Joaquim Gimenez Rodriguez
Berta Barquero Farras
29 Students' Overreliance on Linearity in Economic Applications: A State of the Art
337(14)
Daam Van Reeth
Dirk De Bock
Part III Pedagogical Issues for Teachers and Teacher Educators Using Mathematical Modelling and Applications
30 Teaching Modelling and Systemic Change
351(20)
Hugh Burkhardt
Malcolm Swan
31 Mathematical Modelling as a Professional Activity: Lessons for the Classroom
371(18)
Peter Frejd
32 Modelling Task Design: Science Teachers' View
389(10)
Carolina Guerrero-Ortiz
Jaime Mena-Lorca
33 Modelling as Interactive Translations Among Plural Worlds: Experimental Teaching Using the Night-Time Problem
399(12)
Toshikazu Ikeda
Max Stephens
34 The Dual Modelling Cycle Framework: Report on an Australian Study
411(10)
Janeen Lamb
Akio Matsuzaki
Akihiko Saeki
Takashi Kawakami
35 Implementing Mathematical Modelling: The Challenge of Teacher Educating
421(12)
Azita Manouchehri
36 The Velocity Concept: The History of Its Modelling Development
433(10)
Regina Dorothea Moeller
37 Developing a Mathematical Modelling Task for All Students
443(12)
Edel Reilly
38 The Hidden Benefits of Mathematical Modelling for Students with Disabilities
455(12)
Rina Scott-Wilson
Dirk Wessels
Helena M. Wessels
Estelle Swart
39 Scaffolding Complex Modelling Processes: An In-Depth Study
467(12)
Peter Stender
Nadine Krosanke
Gabriele Kaiser
40 Long-Term Development of How Students Interpret a Model: Complementarity of Contexts and Mathematics
479(12)
Pauline Vos
Gerrit Roorda
41 Exploring Aspects of Creativity in Mathematical Modelling
491(12)
Helena M. Wessels
42 Mathematical Modelling in Dutch Textbooks: Is It Genuine Mathematical Modelling?
503(14)
Bert Zwaneveld
Jacob Perrenet
Kees van 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
517(12)
Peter Frejd
Jonas B. Arleback
44 Modelling and Simulation with the Help of Digital Tools
529(12)
Gilbert Greefrath
Hans-Stefan Siller
45 Mathematical Modelling for Engineering Diploma Students: Perspectives on Visualisation
541(12)
Hanti Kotze
Gerrie J. Jacobs
Erica D. Spangenberg
46 Interactive Diagrams Used for Collaborative Learning Concerning Mathematical Models of Motion
553(12)
Elena Naftaliev
47 Using Modelling and Tablets in the Classroom to Learn Quadratic Functions
565(12)
Miriam Ortega
Luis Puig
48 Mathematical Modelling in a Long-Distance Teacher Education in Brazil: Democratizing Mathematics
577(12)
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
589(12)
Piera Biccard
Dirk Wessels
50 Assessing Mathematizing Competences Through Multiple-Choice Tasks: Using Students' Response Processes to Investigate Task Validity
601(14)
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
615(12)
Irene Grafenhofer
Hans-Stefan Siller
52 Authentic Mathematical Modelling Experiences of Upper Secondary School: A Case Study
627(12)
Kerri Spooner
Refereeing Process 639(2)
Index 641