TABLE OF CONTENTS
Preface v
MODEL TRANSITIONS IN A REAL WORLD v
ICTMA12 - THE CONFERENCE vii
ICTMA xi
ICTMA Books xii
Acknowledgements xiii
Section 1: Models and Modelling in Reality 1
1.1 Communicating big themes in applied mathematics 2
Julian Hunt FRS, University College, London, UK
1.2 Economic modelling: Theory, reality, uncertainty and 25
decision-making
Kate Barker, Bank of England, UK
Section 2: Modelling Constructs in Education 43
2.1 Dreaming a 'possible dream': More windmills to conquer 44
Peter Galbraith, University of Queensland, Australia
2.2 Modelling in class: What do we want the students 63
to learn?
Katja Maaß, University of Education, Freiburg, Germany
2.3 Learning by constructing and sharing models 79
Celia Hoyles and Richard Noss, Institute of Education, University of London, UK
Section 3: Recognising Modelling Competencies 89
3.1 Exemplar models: Expert-novice student behaviours 90
Rosalind Crouch, University of Hertfordshire
and Christopher Haines, City University, London, UK
3.2 A teaching experiment in mathematical modelling 101
Toshikazu Ikeda, Yokohama National University, Japan
Max Stephens, University of Melbourne, Australia
and Akio Matsuzaki, Tsukuba University, Japan
3.3 Modelling and modelling competencies in school 110
Gabriele Kaiser, University of Hamburg, Germany
3.4 Exploring university students' competencies in modelling 120
France Caron and Jacques Bélair, Université de Montréal, Canada
3.5 Facilitating middle secondary modelling competencies 130
Peter Galbraith, University of Queensland, Australia
Gloria Stillman and Jill Brown, University of Melbourne
and Ian Edwards, Luther College, Melbourne, Australia
3.6 Assessing mathematical modelling competency 141
Tomas Højgaard Jensen, The Danish University of Education, Denmark
3.7 A stochastic model for the modelling process 149
Michael Voskoglou, Higher Technological Educational Institute, Patras, Greece
3.8 Assessing progress in mathematical modelling 158
John Izard, RMIT University, Melbourne, Australia
3.9 An introduction to CUMCM
Qiyuan Jiang and Jinxing Xie, Tsinghua University, China 168
and Qixiao Ye, Beijing Institute of Technology, China
Section 4: Everyday Aspects of Modelling 'Literacy' 176
4.1 Functional mathematics and teaching modelling 177
Hugh Burkhardt, University of Nottingham, UK
4.2 Modelling and the critical use of mathematics 187
Jussara de Loiola Araújo, Universidade Federal de Minas Gerais (UFMG), Brazil
4.3 Learners’ context preferences and mathematical literacy 195
Cyril Julie, University of the Western Cape, South Africa
4.4 ‘Real world’ interactions for adult basic numeracy tutors 203
Yvonne Hillier, City University, London, UK
4.5 Math modelling: What skills do employers want in industry? 212
ManMohan Sodhi and Byung-Gak Son, City University, London, UK
Section 5: Cognitive Perspectives on Modelling 221
5.1 How do students and teachers deal with modelling problems? 222
Werner Blum and Dominik Leiß, University of Kassel, Germany
5.2 Teacher-student interactions in mathematical modelling 232
Jonei Cerqueira Barbosa, State University of Feira de Santana, Brazil
5.3 Mathematical modelling: A teachers' training study 241
José Ortiz, University of Carabobo, Venezuela,
Luis Rico and Enrique Castro, University of Granada, Spain
5.4 Mathematics in the physical sciences: Multiple perspectives 250
Geoff Wake and Graham Hardy, University of Manchester, UK
5.5 Modelling problems from a cognitive perspective 260
Rita Borromeo Ferri, University of Hamburg, Germany
5.6 An explorative study on realistic mathematical modelling 271
Cinzia Bonotto, University of Padova, Italy
5.7 Student reasoning when models and reality conflict 281
Jerry Legé, California State University, Fullerton, USA
5.8 The concept of the derivative in modelling and applications 288
Gerrit Roorda, Pauline Vos and Martin Goedhart, University of Groningen, The Netherlands
5.9 Inequalities as modelling tools in computing applications 294
Sergei Abramovich, State University of New York at Potsdam, USA
Section 6: The Practice of Modelling 303
6.1 Integration of energy issues in mathematics classrooms 304
Astrid Brinkmann, Berufskolleg Iserlohn, University of Dortmund
and Klaus Brinkmann, University of Trier, Umwelt Campus, Birkenfeld, Germany
6.2 Models of ecology in teaching engineering mathematics 314
Norbert Gruenwald and Gabriele Sauerbier,
Wismar University of Technology, Germany,
Tatyana Zverkova, Odessa National University, Ukraine
and Sergiy Klymchuk, Auckland University of Technology, New Zealand
6.3 Modelling as an integrated part of the class on calculus 323
Adolf Johannes Riede, Ruprecht-Karls-Universität, Heidelberg, Germany
6.4 Case study: Leak detection in a pipeline 332
Andrei Kolyshkin, Riga Technical University, Latvia
6.5 Discrete and continuous models for the evolution of 340
lizard populations
Michael Jones and Arup Mukherjee, Montclair State University, New Jersey, USA
6.6 Modelling and problem solving in billiards 349
Burkhard Alpers, Aalen University of Applied Sciences: Germany
6.7 The lottery of Casanova 359
Hans-Wolfgang Henn and Andreas Büchter, University of Dortmund, Germany
6.8 Model transitions in the real world: The Catwalk problem 368
Thomas Lingefjärd and Mikael Holmquist, Gothenburg University, Sweden
6.9 Fractal image compression 377
Franceso Leonetti, University of L’Aquila, Italy
6.10 Modelling heat flow in work rolls 386
Leticia Corral, Instituto Tecnológico de Cd. Cuauhtémoc, Chihuahua, Mexico,
Rafael Colás, UANL, San Nicolás de los Garza, Mexico and Antonino Hernández,
Centro de Investigación en Materiales
Avanzados, Chihuahua, México
6.11 Applications of modelling in engineering and technology 395
Sanowar Khan, Kenneth Grattan and Ludwik Finkelstein, City University, London, UK
Section 7: Behaviours in Engineering and Applications 405
7.1 Mathematics in architecture education 406
Igor Verner and Sarah Maor, Technion – Israel Institute of Technology
7.2 Modelling in Engineering: Advantages and difficulties 415
Maria Salett Biembengut and Nelson Hein, Universidade Regional de Blumenau, Brazil
7.3 Modelling: Difficulties for novice engineering students 424
Marta Anaya, María Inés Cavallaro and María Cristina Domínguez,
University of Buenos Aires, Argentina
7.4 Integration of applications in the Technion calculus course 433
Shuki Aroshas, Igor Verner and Abraham Berman, Technion – Israel Institute of Technology
7.5 Mathematical modelling modules for calculus teaching 443
Qiyuan Jiang and Jinxing Xie, Tsinghua University, China
and Qixiao Ye, Beijing Institute of Technology, China
7.6 An experimental approach to teaching modelling 451
Ken Houston and Mark McCartney, University of Ulster, UK
7.7 Modelling for pre-service teachers 458
Susann Mathews and Michelle Reed, Wright State University, Dayton, Ohio, USA
7.8 The Finnish Network for mathematical modelling 465
Robert Piché, Seppo Pohjolainen, Kari Suomela, Kirsi Silius and
Anne-Maritta Tervakari, Tampere University of Technology, Finland
7.9 Learning environment through modelling and computing 473
Regina Lino Franchi, Methodist University of Piracicaba, Brazil
7.10 Modelling is for reasoning 480
Luís Soares Barbosa and Maria Helena Martinho, Minho University, Braga, Portugal
Authors’ contact email addresses 490
