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E-book: Mathematical Modelling in Education Research and Practice: Cultural, Social and Cognitive Influences

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In this volume cultural, social and cognitive influences on the research and teaching of mathematical modelling are explored from a variety of theoretical and practical perspectives. The authors of the current volume are all members of the International Community of Teachers of Mathematical Modelling and Applications, the peak research body in this field. A distinctive feature of this volume is the high number of authors from South American countries. These authors bring quite a different perspective to modelling than has been showcased in previous books in this series, in particular from a cultural point of view. As well as recent international research, there is a strong emphasis on pedagogical issues including those associated with technology and assessment, in the teaching and learning of modelling. Applications at various levels of education are exemplified. The contributions reflect common issues shared globally and represent emergent or on-going challenges.

1 Cultural, Social, Cognitive and Research Influences on Mathematical Modelling Education
1(34)
Gloria Ann Stillman
Werner Blum
Maria Salett Biembengut
Part I Innovative Practices in Modelling Education Research and Teaching
2 Mathematical Modelling as a Strategy for Building-Up Systems of Knowledge in Different Cultural Environments
35(10)
Ubiratan D'Ambrosio
3 The Meaning of the Problem in a Mathematical Modelling Activity
45(10)
Lourdes Maria Werle de Almeida
Karina Alessandra Pessoa da Silva
4 Extending the Reach of the Models and Modelling Perspective: A Course-Sized Research Site
55(12)
Corey Brady
Richard Lesh
Serife Sevis
5 Prescriptive Modelling -- Challenges and Opportunities
67(14)
Mogens Niss
6 An Approach to Theory Based Modelling Tasks
81(12)
Xenia-Rosemarie Reit
Matthias Ludwig
7 Facilitating Mathematisation in Modelling by Beginning Modellers in Secondary School
93(12)
Gloria Ann Stillman
Jill P. Brown
Vince Geiger
8 Authenticity in Extra-curricular Mathematics Activities: Researching Authenticity as a Social Construct
105(10)
Pauline Vos
9 The Teaching Goal and Oriented Learning of Mathematical Modelling Courses
115(14)
Mengda Wu
Dan Wang
Xiaojun Duan
Part II Research into, or Evaluation of, Teaching and Learning
10 Modelling Competencies: Past Development and Further Perspectives
129(22)
Gabriele Kaiser
Susanne Brand
11 How to Support Teachers to Give Feedback to Modelling Tasks Effectively? Results from a Teacher-Training-Study in the Co2CA Project
151(10)
Michael Besser
Werner Blum
Dominik Leiss
12 A Reflection on Mathematical Modelling and Applications as a Field of Research: Theoretical Orientation and Diversity
161(12)
Vince Geiger
Peter Frejd
13 Problem Solving Methods for Mathematical Modelling
173(12)
Gilbert Greefrath
14 Improving Mathematical Modelling by Fostering Measurement Sense: An Intervention Study with Pre-service Mathematics Teachers
185(10)
Maike Hagena
15 How Do Students Share and Refine Models Through Dual Modelling Teaching: The Case of Students Who Do Not Solve Independently
195(12)
Takashi Kawakami
Akihiko Saeki
Akio Matsuzaki
16 Exploring Interconnections Between Real-World and Application Tasks: Case Study from Singapore
207(12)
Kit Ee Dawn Ng
Gloria Ann Stillman
17 Mathematical Modelling Tasks and the Mathematical Thinking of Students
219(10)
Barbara Palharini
Lourdes Maria Werle de Almeida
18 Measurement of Area and Volume in an Authentic Context: An Alternative Learning Experience Through Mathematical Modelling
229(12)
Santiago Manuel Rivera Quiroz
Sandra Milena Londono Orrego
Carlos Mario Jaramillo Lopez
19 Mathematical Modelling and Culture: An Empirical Study
241(10)
Jhony Alexander Villa-Ochoa
Mario J. Berrio
20 Mathematical Modelling of a Social Problem in Japan: The Income and Expenditure of an Electric Power Company
251(14)
Noboru Yoshimura
Part III Pedagogical Issues for Teaching and Learning
21 The Place of Mathematical Modelling in the System of Mathematics Education: Perspective and Prospect
265(12)
Henry O. Pollak
22 Moving Within a Mathematical Modelling Map
277(6)
Rita Borromeo Ferri
23 Negotiating the Use of Mathematics in a Mathematical Modelling Project
283(10)
Jussara de Loiola Araujo
Ilaine da Silva Campos
24 Moving Beyond a Single Modelling Activity
293(12)
Jonas B. Arleback
Helen M. Doerr
25 The Possibility of Interdisciplinary Integration Through Mathematical Modelling of Optical Phenomena
305(12)
Jennifer Valleriano Barboza
Luana Tais Bassani
Luciano Lewandoski Alvarenga
Lucilaine Goin Abitante
26 Activation of Student Prior Knowledge to Build Linear Models in the Context of Modelling Pre-paid Electricity Consumption
317(10)
Jose Luis Bossio Velez
Sandra Milena Londono Orrego
Carlos Mario Jaramillo Lopez
27 Mathematical Modellers' Opinions on Mathematical Modelling in Upper Secondary Education
327(12)
Peter Frejd
28 Modelling, Education, and the Epistemic Fallacy
339(12)
Peter Galbraith
29 Reconsidering the Roles and Characteristics of Models in Mathematics Education
351(12)
Toshikazu Ikeda
Max Stephens
30 Developing Statistical Numeracy: The Model Must Make Sense
363(12)
Janeen Lamb
Jana Visnovska
31 Mathematical Modelling and Cognitive Load Theory: Approved or Disapproved?
375(10)
Jacob Perrenet
Bert Zwaneveld
32 Social-critical Dimension of Mathematical Modelling
385(12)
Milton Rosa
Daniel Clark Orey
33 Pedagogical Actions of Reflective Mathematical Modelling
397(10)
Morgana Scheller
Paula Andrea Grawieski Civiero
Fatima Peres Zago de Oliveira
34 Context Categories in Mathematical Modelling in Fundamentals of Calculus Teaching
407(10)
Mara Kessler Ustra
Sandro Rogerio Vargas Ustra
35 Applied Mathematical Problem Solving: Principles for Designing Small Realistic Problems
417(14)
Dag Wedelin
Tom Adawi
Part IV Influences of Technologies
36 Visualisation Tactics for Solving Real World Tasks
431(12)
Jill P. Brown
37 Developing Modelling Competencies Through the Use of Technology
443(10)
Ruth Rodriguez Gallegos
Samantha Quiroz Rivera
38 Model Analysis with Digital Technology: A "Hybrid Approach"
453(12)
Debora da Silva Soares
39 Collective Production with Mathematical Modelling in Digital Culture
465(12)
Arlindo Jose de Souza Junior
Joao Frederico da Costa Azevedo Meyer
Deive Barbosa Alves
Fernando da Costa Barbosa
Mario Lucio Alexandre
Douglas Carvalho de Menezes
Douglas Marin
Part V Assessment in Schools and Universities
40 Learners' Dealing with a Financial Applications-Like Problem in a High-Stakes School-Leaving Mathematics Examination
477(10)
Cyril Julie
41 Evidence of Reformulation of Situation Models: Modelling Tests Before and After a Modelling Class for Lower Secondary School Students
487(14)
Akio Matsuzaki
Masafumi Kaneko
Part VI Applicability at Different Levels of Schooling, Vocational Education, and in Tertiary Education
42 Mathematical Modelling in the Teaching of Statistics in Undergraduate Courses
501(12)
Celso Ribeiro Campos
Denise Helena Lombardo Ferreira
Otavio Roberto Jacobini
Maria Lucia Lorenzetti Wodewotzki
43 Models and Modelling in an Integrated Physics and Mathematics Course
513(10)
Angeles Dominguez
Jorge de la Garza
Genaro Zavala
44 Research-Based Modelling Teaching Activities: A Case of Mathematical Positioning with GNSS
523(12)
Xiaojun Duan
Dan Wang
Mengda Wu
45 Mathematical Texts in a Mathematical Modelling Learning Environment in Primary School
535(10)
Ana Virginia de Almeida Luna
Elizabeth Gomes Souza
Larissa Borges de Souza Lima
46 A Differential Equations Course for Engineers Through Modelling and Technology
545(12)
Ruth Rodriguez Gallegos
47 Contributions of Mathematical Modelling in Education of Youth and Adults
557(10)
Jonson Ney Dias da Silva
Taise Sousa Santana
Carlos Henrique Carneiro
48 Pre-service Mathematics Teachers' Experiences in Modelling Projects from a Socio-critical Modelling Perspective
567(12)
Monica E. Villarreal
Cristina B. Esteley
Silvina Smith
49 A Mathematical Modelling Challenge Program for J.H.S. Students in Japan
579(14)
Akira Yanagimoto
Tetsushi Kawasaki
Noboru Yoshimura
Part VII Modelling and Applications in the Lived Environment
50 Modelling the Wall: The Mathematics of the Curves on the Wall of Colegio Arquidiocesano in Ouro Preto
593(12)
Daniel Clark Orey
Milton Rosa
Refereeing Process 605(2)
Index 607