Mathematical Modelling in Education Research and Practice Cultural, Social and Cognitive Influences

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.

Series Preface, Gabriele Kaiser and Gloria Stillman.- Chapter 1 Cultural, Social, Cognitive and Research Influences on Mathematical Modelling Education: Perspectives and Future Prospects, Gloria Stillman, Werner Blum, and Maria Salett Biembengut.- Part I Innovative Practices in Modelling Education Research and Teaching.- Chapter 2 Mathematical Modelling as a Strategy for Building-up Systems of Knowledge in Different Cultural Environments, Ubiratan D’Ambrosio.- Chapter 3 The Meaning of the Problem in a Mathematical Modelling Activity, Lourdes Maria Werle de Almeida and Karina Alessandra Pessoa da Silva.- Chapter 4 Extending the Reach of the Models and Modelling Perspective: A Course-Sized Research Site, Corey Brady, Richard Lesh and Serife Sevis.- Chapter 5 Prescriptive Modelling – Challenges and Opportunities, Mogens Niss.- Chapter 6 An Approach to Theory Based Modelling Tasks, Xenia-Rosemary Reit and Matthias Ludwig.- Chapter 7 Facilitating Mathematisation in Modelling by Beginning Modellers in Secondary School, Gloria Ann Stillman, Jill P. Brown and Vince Geiger.- Chapter 8 Authenticity in extra-curricular mathematics activities; researching authenticity as a social construct, Pauline Vos.- Chapter 9 The Teaching Goal and Oriented Learning of Mathematical Modelling courses, Mengda Wu, Dan Wang and Xiaojun Duan.- Part II Research into, or Evaluation of, Teaching and Learning.- Chapter 10 Modelling Competencies–Past Development and Further Perspectives, Gabriele Kaiser and Susanne Brand.- Chapter 11 How to Support Teachers to Give Feedback to Modelling Tasks Effectively? Results from a Teacher-Training-Study in the Co2CA Project, Michael Besser, Werner Blum and Dominik Leiss.- Chapter 12 A Reflection on Mathematical Modelling and Applications as a Field of Research: Theoretical Orientation and Diversity, Vince Geiger and Peter Frejd.- Chapter 13 Problem Solving Methods for Mathematical Modelling, Gilbert Greefrath.- Chapter 14 ImprovingMathematical Modelling by Fostering Measurement Sense: An Intervention Study with Pre-service Mathematics Teachers, Maike Hagena.- Chapter 15 How do Students Share and Refine Models through Dual Modelling Teaching: The Case of Students who do not Solve Independently, Takashi Kawakami^, Akihiko Saeki and Akio Matsuzaki.- Chapter 16 Exploring Interconnections between Real-World and Application Tasks: Case Study from Singapore, Dawn Ng and Gloria Ann Stillman.- Chapter 17 Mathematical Modelling Tasks and the Mathematical Thinking of Students, Bárbara Nilvada Palharini, Alvim Sousa Robim and Lourdes Maria Werle de Almeida.- Chapter 18 Measurement of Area and Volume in an Authentic Context: An Alternative Learning Experience through Mathematical Modelling, Santiago Manuel Rivera Quiroz , Sandra Milena Londoño Orrego and Carlos Mario Jaramillo López.- Chapter 19 Mathematical Modelling and Culture – An Empirical Study, Jhony Alexander Villa-Ocha and Mario J. Berrío.- Chapter 20 Mathematical Modelling of a Social Problem in Japan: The Income and Expenditure of an Electric Power Company, Noboru Yoshimura.- Part III Pedagogical Issues for Teaching and Learning.- Chapter 21 The Place of Mathematical Modelling in the System of Mathematics Education: Perspective and Prospect , Henry O.Pollak.- Chapter 22 Moving within a Mathematical Modelling Map, Rita Borromeo Ferri.- Chapter 23 Negotiating the Use of Mathematics in a Mathematical Modelling Project, Jussara de Loiola Araújo and Ilaine da Silva Campos.- Chapter 24 Moving Beyond a Single Modelling Activity, Jonas B Ärlebäck and Helen M. Doerr.- Chapter 25 The Possibility of Interdisciplinary Integration through Mathematical Modelling of Optical Phenomena, Jennifer Barboza, Luana Bassani, Luciano Lewandoski, and Lucilaine Abitante.- Chapter 26 Activation of Student Prior Knowledge to Build Linear Models in the Context of Modelling Pre-paid Electricity Consumption, José Luis Bossio Vélez,Sandra Milena Londoño Orrego, and Carlos Mario Jaramillo López.- Chapter 27 Mathematical Modellers’ Opinions on Mathematical Modelling in Upper Secondary Education, Peter Frejd.- Chapter 28 Modelling, Education, and the Epistemic Fallacy, Peter Galbraith.- Chapter 29 Reconsidering the Roles and Characteristics of Models in Mathematics Education, Toshikazu Ikeda and Max Stephens.- Chapter 30 Developing Statistical Numeracy: The Model Must Make Sense, Janeen Lamb and Jana Visnovska.- Chapter 31 Mathematical Modelling and Cognitive Load Theory: Approved or Disapproved? Jacob Perrenet and Bert Zwaneveld.- Chapter 32 Social-Critical Dimension of Mathematical Modelling, Milton Rosa and Daniel Clark Orey.- Chapter 33 Pedagogical Practices of Reflective Mathematical Modelling, Morgana Scheller, Paula Andrea Grawieski Civiero, and Fátima Peres Zago de Oliveira.- Chapter 34 Context Categories in Mathematical Modelling in Fundamentals of Calculus Teaching, Mara Kessler Ustra and Sandro Rogério Vargas Ustra.- Chapter 35 Applied Mathematical Problem Solving – Principles for Designing Small Realistic Problems, Dag Wedelin and Tom Adawi.- Part IV Influences of Technologies.- Chapter 36 Visualisation Tactics for Solving Real World Tasks, Jill Brown.- Chapter 37 Developing Modelling Competencies through the Use of Technology, Ruth Rodríguez Gallegos and Samantha Quiroz Rivera.- Chapter 38 Model Analysis with Digital Technology – a “Hybrid Approach”, Débora da Silva Soares.- Chapter 39 Collective Production with Mathematical Modelling in Digital Culture, Arlindo José de Souza Júnior, João Frederico da Costa Azevedo Meyer, Deive Barbosa Alves, Fernando da Costa Barbosa, Mário Lucio Alexandre, Douglas Carvalho de Menezes and Douglas Marin.- Part V Assessment in Schools and Universities.- Chapter 40 Learners’ Dealing with a Financial Applications-like Problem in a High-stakes School-leaving Mathematics Examination, Cyril Julie.- Chapter 41 Evidence ofReformulation of Situation Models: Modelling Tests before and after a Modelling Class for Lower Secondary School Students, Akio Matsuzaki and Masafumi Kaneko.- Part VI Applicability at Different Levels of Schooling, Vocational Education, and in Tertiary Education.- Chapter 42 Mathematical Modelling in the Teaching of Statistics in Undergraduate Courses, Celso Ribeiro Campos, Denise Helena Lombardo Ferreira, Otávio Roberto Jacobini and Maria Lúcia Lorenzetti Wodewotzki.- Chapter 43 Models and Modelling in an Integrated Physics and Mathematics Course, Angeles Domínguez, Jorge de la Garza, and Genaro Zavala.- Chapter 44 Research-based Modelling Teaching Activities: A case of Mathematical Positioning with GNSS, Xiaojun Duan , Dan Wang, and Mengda Wu.- Chapter 45 Mathematical Texts in a Mathematical Modelling Learning Environment in Primary School, Ana Virginia de Almeida Luna, Elizabeth Goumes Souza and Larissa Borges de Souza Lima.- Chapter 46 A Differential Equations Course for Engineers through Modelling and Technology, Ruth Rodríguez Gallegos.- Chapter 47 Contributions of Mathematical Modelling in Education of Youth and Adults, Jonson Ney Dias da Silva, Taise Sousa Santana and Carlos Henrique Carneiro.- Chapter 48 Pre-service Mathematics Teachers’ Experiences in Modelling Projects from a Socio-critical Modelling Perspective, Mónica E. Villarreal, Cristina B. Esteley and Silvina Smith.- Chapter 49 A Mathematical Modelling Challenge Program for J.H.S. Students in Japan, Akira Yanagimoto, Tetsushi Kawasaki and Noboru Yoshimura.- Part VII Modelling and Applications in the Lived Environment.- Chapter 50 Modelling the Wall: The Mathematics of the Curves on the Wall of Colégio Arquidiocesano in Ouro Preto, Daniel Orey and Milton Rosa.- List of Corresponding Authors.- Refereeing Process.- Index.