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 DAmbrosio.
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 CompetenciesPast 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, Bįrbara 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 Londońo Orrego and
Carlos Mario Jaramillo López.
Chapter 19 Mathematical Modelling and Culture
An Empirical Study, Jhony Alexander Villa-Ocha and Mario J. Berrķo.-
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 Araśjo 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 Londońo 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 Fįtima 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 Rodrķguez 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 Jśnior, Joćo Frederico da Costa
Azevedo Meyer, Deive Barbosa Alves, Fernando da Costa Barbosa, Mįrio 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, Otįvio Roberto Jacobini and Maria Lścia Lorenzetti
Wodewotzki.
Chapter 43 Models and Modelling in an Integrated Physics and
Mathematics Course, Angeles Domķnguez, 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 Rodrķguez
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.
