This book contains suggestions for and reflections on the teaching, learning and assessing of mathematical modelling and applications in a rapidly changing world, including teaching and learning environments. It addresses all levels of education from universities and technical colleges to secondary and primary schools. Sponsored by the International Community of Teachers of Mathematical Modelling and Applications (ICTMA), it reflects recent ideas and methods contributed by specialists from 30 countries in Africa, the Americas, Asia, Australia and Europe. Inspired by contributions to the Fourteenth Conference on the Teaching of Mathematical Modelling and Applications (ICTMA14) in Hamburg, 2009, the book describes the latest trends in the teaching and learning of mathematical modelling at school and university including teacher education. The broad and versatile range of topics will stress the international state-of-the-art on the following issues:
Theoretical reflections on the teaching and learning of modelling
Modelling competencies
Cognitive perspectives on modelling
Modelling examples for all educational levels
Practice of modelling in school and at university level
Practices in Engineering and Applications
Applications and modelling and their learning and teaching in school and university have become a prominent topic in the last decades in view of the world-wide importance of the usage of mathematics in science, technology and everyday life. Trends in Teaching and Learning of Mathematical Modelling provides the reader ship with an overview on the newest international trends and developments on the teaching and learning of modelling from various theoretical and practical perspectives.
Recenzijas
"ICTMA14 was inspiring and as a first-time participant, I immediately felt that I was a part of this stimulating group."
Usha Kotelawala (New York State University, USA)
"The conference provided the participants with a comprehensive and multi-faceted overview of the state-of-the-art of mathematical modelling in school and university, both as regards developmental practice and research."
Mogens Niss (Roskilde University, Denmark)
"I was able to understand how the Brazilian approach to modeling contrast with the other ones practiced all over the world."
Marcelo Borba (Rio Claro, Brazil)
Series Preface: Gabriele Kaiser and Gloria Stillman.
Chapter 1: Trends
in Teaching and Learning of Mathematical Modelling (ICTMA14) Preface :
Gabriele Kaiser, Werner Blum, Rita Borromeo Ferri, Gloria Stillman.- Part
I: Modelling from Primary to Upper Secondary School: Findings of Empirical
Research.
Chapter 2: Modelling from Primary to Upper Secondary School:
Findings of Empirical Research Overview: Thomas Lingefjärd.
Chapter 3:
Can Modelling be Taught and Learnt? Some Answers from Empirical Research:
Werner Blum.
Chapter 4: Can Modelling Be Taught and Learnt? A Commentary:
Marcelo C. Borba.
Chapter 5: Upper Secondary Students' Handling of
Real-World Contexts: Andreas Busse.
Chapter 6: Word Problem Classification:
A Promising Modelling Task at the Elementary Level: Dirk de Bock, Kim
Vleugels, and Lieven Verschaffel.
Chapter 7 : Understanding and Promoting
Mathematical Modeling Competencies: An Applied Perspective: George Ekol.-
Chapter 8: Secondary Teachers Beliefs About Teaching Applications - Design
and Selected Results of a Qualitative Case Study: Frank Förster.
Chapter 9:
Secondary Teachers Beliefs on Modelling in Geometry and Stochastics: Boris
Girnat and Andreas Eichler.
Chapter 10: Examining Mathematising Activities
in Modelling Tasks with a Hidden Mathematical Character:Roxana Grigoras, Fco.
Javier Garcķa, and Stefan Halverscheid.
Chapter 11: The Sun Hour Project:
Thomas Lingefjärd and Stephanie Meier.
Chapter 12: Mathematical Knowledge
Application and Student Difficulties in a Design-Based Interdisciplinary
Project: Kit Ee Dawn Ng.
Chapter 13: Evaluation of Teaching Activities with
Multi-Variable Functions in Context: Yoshiki Nisawa and Seiji Moriya.-
Chapter 14: Mathematical Modelling in Secondary Education: A Case Study: José
Ortiz and Aldora Dos Santos.
Chapter 15: Students Overcoming Blockages While
Building A Mathematical Model: Exploring A Framework : Sanne Schaap, Pauline
Vos, and MartinGoedhart.
Chapter 16: What Did Taiwan Mathematics Teachers
Think of Model-Eliciting Activities And Modeling Teaching? : Shih-Yi Yu and
Ching-Kuch Chang.- Part II: Looking Deeper into Modelling Processes: Studies
with a Cognitive Perspective.
Chapter 17: Looking Deeper into Modelling
Processes: Studies with a Cognitive Perspective Overview: Susana
Carreira.
Chapter 18: Applying Metacognitive Knowledge and Strategies in
Applications and Modelling Tasks at Secondary School: Gloria Stillman.-
Chapter 19: Effective Mathematical Modelling without Blockages A Reaction
on some Theoretical and Practical Ideas A Commentary.- Rita Borromeo
Ferri.
Chapter 20: Modelling Tasks: Insight into Mathematical Understanding:
Jill P. Brown and Ian Edwards.
Chapter 21: Mathematical Modelling of Daily
Life in Adult Education: Focusing on the Notion of Knowledge: Susana
Carreira, Nélia Amado, and Filipa Lecoq.
Chapter 22: Students Modeling
Routes in the Context of Object Manipulation and Experimentation in
Mathematics: Susana Carreira and Ana Margarida Baioa.
Chapter 23:
Engineering Model Eliciting Activities for Elementary School Students:
Nicolas G. Mousoulides and Lyn D. English.
Chapter 24: Project Modelling
Routes in 12 to 16-year-old Pupils: Manuel Sol, Joaquin Giménez and Nśria
Rosich.- Part III: Modelling in Teacher Education.
Chapter 25: Modelling in
Teacher Education Overview: Jill P. Brown.
Chapter 26: Models and
Modelling: Perspectives on Teaching and Learning Mathematics for the 21st
Century: Helen Doerr and Richard Lesh.
Chapter 27: Mathematical Modelling in
a Distance Course for Teachers: Maria Salett Biembengut Hein and Thaķs
Mariane Biembengut Faria.
Chapter 28: In-service and Prospective Teachers
Views about Modelling Tasks in the Mathematics Classroom Results of a
Quantitative Empirical Study: Sebastian Kuntze.
Chapter 29: Pre-service
Secondary Mathematics Teachers Affinity with using Modelling Tasks
inTeaching Years 8-10: Gloria Stillman and Jill P. Brown. Part IV: Using
Technologies: New Possible Ways of Learning and Teaching Modelling.
Chapter
30: Using Technologies: New Possible Ways of Learning and Teaching Modelling
Overview: Gilbert Greefrath.
Chapter 31: Factors Affecting Teachers
Adoption of Innovative Practices with Technology and Mathematical Modelling:
Vince Geiger.
Chapter 32: Modelling Considering the Influence of Technology:
Gilbert Greefrath, Hans-Stefan Siller, and Jens Weitendorf.
Chapter 33:
Improving Learning in Science and Mathematics with Exploratory and
Interactive Computational Modelling: Rui Gomes Neves, Jorge Carvalho Silva,
and Vķtor Duarte Teodoro.- Part V: Modelling Competency: Learning, Applying
and Developing Competencies.
Chapter 34: Modelling Competency: Learning,
Applying and Developing Competencies Overview: Morten Blomhųj.
Chapter
35.
Drivers for Mathematical Modelling: Pragmatism in Practice: Christopher
Haines.
Chapter 36: Identifying Drivers for Mathematical Modelling A
Commentary: Katja Maaß .
Chapter 37: Documenting the Development of
Modelling Competencies of Grade 7 Mathematics Students: Piera Biccard and
Dirk Wessels.
Chapter 38: Students Reflections in Mathematical Modelling
Projects: Morten Blomhųj and Tinne Hoff Kjeldsen.
Chapter 39: From Data to
Functions: Connecting Modeling Competencies and Statistical Literacy: Joachim
Engel and Sebastian Kuntze.
Chapter 40: First Results from a Study
Investigating Swedish Upper Secondary Students Mathematical Modelling
Competencies: Peter Frejd and Jonas Bergman Ärlebäck.
Chapter 41: Why Cats
Happen to Fall From the Sky or On Good and Bad Models: Hans-Wolfgang Henn.-
Chapter 42: Assessing Modelling Competencies Using a Multidimensional
IRT-Approach: Luzia Zöttl.- Part VI: Modelling in Tertiary Education.-
Chapter 43: Modelling in Tertiary Education - Overview : Peter Galbraith.-
Chapter 44: The MathematicalExpertise of Mechanical Engineers Taking and
Processing Measurements: Burkhard Alpers.
Chapter 45: Mathematical Modelling
Skills and Creative Thinking Levels: An Experimental Study: Qi Dan and
Jinxing Xie.
Chapter 46: Modelling the Evolution of the Belgian Population
Using Matrices, Eigenvalues and Eigenvectors: Johan Deprez.
Chapter 47:
Modelling and the Educational Challenge in Industrial Mathematics: Matti
Heilio.
Chapter 48:Modelling of Infectious Disease with Biomathematics:
Implications for Teaching and Research: Norbert Gruenwald, Gabriele
Sauerbier, Ajit Narayanan, Sergiy Klymchuk, and Tatyana Zverkova.
Chapter
49: Using Response Analysis Mapping to Display Modellers Mathematical
Modelling Progress: Akio Matsuzaki.- Part VII: Modelling Examples and
Modelling Projects: Concrete Cases.
Chapter 50: Modelling Examples and
Modelling Projects: Concrete Cases Overview: Hugh Burkhardt.
Chapter
51: The Mathematical Expertise of Mechanical Engineers Taking and
Processing Measurements: Mette Andresen and Asbjoern Petersen.
Chapter 52:
Real-World Modelling in Regular Lessons: A Long-Term Experiment: Martin
Bracke and Andreas Geiger.
Chapter 53: Modelling Tasks at the Internet
Portal Program for Gifted: Matthias Brandl.
Chapter 54: Modelling at
Primary School Through a French-German Comparison of Curricula and Textbooks:
Richard Cabassut and Anke Wagner.
Chapter 55: Modifying Teachers Practices:
The Case of a European Training Course on Modelling and Applications: Javier
Garcķa and Luisa Ruiz-Higueras.
Chapter 56: Googles PageRank A Present
Day Application of Mathematics in Classroom: Hans Humenberger.
Chapter 57:
Authentic Modelling Problems in Mathematics Education: Gabriele Kaiser,
Björn Schwarz, and Nils Buchholtz.
Chapter 58: Using Modelling Experiences
to Develop Japanese Senior High School Students' Awareness of the
Interrelations between Mathematics and Science: Tetsushi Kawasaki and
SeijiMoriya.
Chapter 59: Stochastic Case Problems for the Secondary
Classroom with Reliability Theory : Usha Kotelawala.
Chapter 60: LEMA
Professional Development of Teachers in Relation to Mathematical Modelling:
atja Maaß and Johannes Gurlitt .
Chapter 61: Modelling in the Classroom
Obstacles from the Teachers Perspective: Barbara Schmidt.
Chapter 62:
Teachers Professional Learning: Modelling at the Boundaries: Geoff Wake.-
Part VIII: Theoretical and Curricular Reflections on Modelling.
Chapter 63:
Theoretical and Curricular Reflections on Modelling Overview: Pauline Vos.-
Chapter 64: Making Connections between Modelling and Constructing Mathematics
Knowledge: An Historical Perspective: Toshikazu Ikeda and Max Stephens.-
Chapter 65: Practical Knowledge of Research Mathematicians, Scientists and
Engineers about the Teaching of Modelling: Jeroen Spandaw.
Chapter 66:
Evolution of Applications and Modelling in a Senior Secondary Curriculum:
Gloria Stillman and Peter Galbraith.
Chapter 67: Sense of Reality Through
Mathematical Modeling: Jhony A.Villa-Ochoa and Carlos M. Jaramillo L.-
Chapter 68: What is Authentic in the Teaching and Learning of Mathematical
Modelling?: Pauline Vos
Gabriele Kaiser is a Professor of Mathematics Education at the University of Hamburg. She holds a masters degree as a teacher for mathematics and humanities and completed her doctorate in mathematics education on applications and modelling. She is Editor-in-Chief of ZDM The International Journal on Mathematics Education (formerly Zentralblatt fuer Didaktik der Mathematik) and since July 2007 she serves as president of the International Community of Teachers of Modelling and Applications (ICTMA), an ICMI affiliated Study Group.
Werner Blum is a Professor of Mathematics Education at the University of Kassel. He got a Ph.D. in Pure Mathematics in 1970 from the University of Karlsruhe. His main research areas include empirical studies into the teaching and learning of mathematics and the professional knowledge of mathematics teachers, national and international comparative studies (especially PISA), quality development in mathematics teaching as well as applications and modelling in mathematics education.
Rita Borromeo Ferri is a Guest Professor of Mathematics Education at the University of Hamburg. She holds a masters degree as a teacher for mathematics and geography and completed her doctorate in mathematics education on mathematical thinking styles and her post-doc study on applications and modelling. She taught several years in school and got a teaching award of the Faculty of Education at University of Hamburg.
