(International Perspectives on the Teaching and Learning of Mathematical Modelling)
Gloria Ann Stillman, Gabriele Kaiser, Werner Blum e Jill P. Brown
Springer | 2013 | 612 páginas | pdf | 9 Mb
This book provides readers with an overview of recent international research and developments in the teaching and learning of modelling and applications from a variety of theoretical and practical perspectives. There is a strong focus on pedagogical issues for teaching and learning of modelling as well as research into teaching and practice. The teaching of applications of mathematics and mathematical modelling from the early years through primary and secondary school and at tertiary level is rising in prominence in many parts of the world commensurate with an ever-increasing usage of mathematics in business, the environment, industry and everyday life. The authors are all members of the International Community of Teachers of Mathematical Modelling and Applications and important researchers in mathematics education and mathematics. The book will be of interest to teachers, practitioners and researchers in universities, polytechnics, teacher education, curriculum and policy
Contents
1 Mathematical Modelling: Connecting to Teaching and Research Practices – The Impact of Globalisation…. 1
Gloria Ann Stillman, Gabriele Kaiser, Werner Blum, and Jill P. Brown
Part I Innovative Practices in Modelling Education Research and Teaching
2 From Conference to Community: An ICTMA Journey—The Ken Houston Inaugural Lecture …. 27
Peter Galbraith
3 Modelling from the Perspective of Commognition – An Emerging Framework….. 47
Jonas Bergman Ärlebäck and Peter Frejd
4 Should Interpretation Systems Be Considered to Be Models if They Only Function Implicitly?…. 57
Rita Borromeo Ferri and Richard Lesh
5 Mathematical Modelling, Mathematical Content and Tensions in Discourses …… 67
Andréia Maria Pereira de Oliveira and Jonei Cerqueira Barbosa
6 Ethnomodelling as a Methodology for Ethnomathematics …… 77
Milton Rosa and Daniel Clark Orey
7 Dual Modelling Cycle Framework for Responding to the Diversities of Modellers….. 89
Akihiko Saeki and Akio Matsuzaki
8 The Eyes to See: Theoretical Lenses for Mathematical Modelling Research…… 101
Nils Buchholtz
9 Strässer’s Didactic Tetrahedron as a Basis for Theorising Mathematical Modelling Activity Within Social Contexts…. 107
Vince Geiger
10 Ethnomodelling as a Research Lens on Ethnomathematics and Modelling ….. 117
Milton Rosa and Daniel Clark Orey
Part II Research into, or Evaluation of, Teaching Practice
11 Real-Life Modelling Within a Traditional Curriculum: Lessons from a Singapore Experience …. 131
Ang Keng Cheng
12 Students’ Mathematical Learning in Modelling Activities ….. 141
Morten Blomhøj and Tinne Hoff Kjeldsen
13 Students’ Designing an Ideal Tourism Route as Mathematical Modelling …. 153
Chan Chun Ming Eric
14 Comparison of Mathematical Modelling Skills of Secondary and Tertiary Students …. 165
Juntao Fu and Jinxing Xie
15 Taking Advantage of Incidental School Events to Engage with the Applications of Mathematics: The Case of Surviving the Reconstruction…….. 175
Vince Geiger, Merrilyn Goos, and Shelley Dole
16 The Development of Modelling Competencies by Year 9 Students: Effects of a Modelling Project….. 185
Susanne Grünewald
17 Evidence of a Dual Modelling Cycle: Through a Teaching Practice Example for Pre service Teachers….. 195
Akio Matsuzaki and Akihiko Saeki
18 Considering Multiple Solutions for Modelling Problems – Design and First Results from the MultiMa-Project…. 207
Stanislaw Schukajlow and André Krug
19 Challenges in Modelling Challenges: Intents and Purposes … 217
Gloria Ann Stillman, Jill P. Brown, and Peter Galbraith
20 Mathematical Modelling of a Real-World Problem: The Decreasing Number of Bluefi n Tuna … 229
Akira Yanagimoto and Noboru Yoshimura
21 Mathematical Modelling of a Social Problem: Pension Tax Issues …. 241
Noboru Yoshimura and Akira Yanagimoto
Part III Pedagogical Issues for Teaching and Learning
22 Pedagogical Refl ections on the Role of Modelling in Mathematics Instruction ….. 255
Toshikazu Ikeda
23 Complex Modelling Problems in Co-operative, Self-Directed Learning Environments ….. 277
Gabriele Kaiser and Peter Stender
24 Inducting Year 6 Students into “A Culture of Mathematising as a Practice” ….. 295
Jill P. Brown
25 A Whole Week of Modelling – Examples and Experiences of Modelling for Students in Mathematics Education…. 307
Nils Buchholtz and Sarah Mesrogli
26 Teachers’ Self-Perceptions of Their Pedagogical Content Knowledge Related to Modelling – An Empirical Study with Austrian Teachers …… 317
Sebastian Kuntze, Hans-Stefan Siller, and Christiane Vogl
27 A Cross-Sectional Study About Modelling Competency in Secondary School …. 327
Matthias Ludwig and Xenia-Rosemarie Reit
28 Teacher Readiness in Mathematical Modelling: Are There Differences Between Pre-service and In-Service Teachers?… 339
Kit Ee Dawn Ng
29 Exploring the Relationship Between Mathematical Modelling and Classroom Discourse …. 349
Trevor Redmond, Raymond Brown, and Joanne Sheehy
30 The Role of Textbooks in Developing a Socio- critical Perspective on Mathematical Modelling in Secondary Classrooms … 361
Gloria Ann Stillman, Jill P. Brown, Rhonda Faragher, Vince Geiger, and Peter Galbraith
31 Pre-service Secondary School Teachers’ Knowledge in Mathematical Modelling – A Case Study …. 373
Tan Liang Soon and Ang Keng Cheng
32 How Students Connect Descriptions of Real- World Situations to Mathematical Models in Different Representational Modes .. 385
Wim Van Dooren, Dirk De Bock, and Lieven Verschaffel
33 Pre-service Teacher Learning for Mathematical Modelling ….. 395
Mark Winter and Hamsa Venka
34 Initial Perspectives of Teacher Professional Development on Mathematical Modelling in Singapore: Conceptions of Mathematical Modelling ……. 405
Chan Chun Ming Eric
35 Initial Perspectives of Teacher Professional Development on Mathematical Modelling in Singapore: Problem Posing and Task Design …. 415
Lee Ngan Hoe
36 Initial Perspectives of Teacher Professional Development on Mathematical Modelling in Singapore: A Framework for Facilitation……. 427
Kit Ee Dawn Ng
37 Teacher Professional Development on Mathematical Modelling: Initial Perspectives from Singapore …. 437
Vince Geiger
Part IV Influences of Technologies
38 Reality Based Test Tasks with Digital Tools at Lower Secondary ……. 445
Gilbert Greefrath and Michael Rieß
39 On Comparing Mathematical Models and Pedagogical Learning ……. 457
Janeen Lamb and Jana Visnovska
Part V Assessment in Schools
40 Formative Assessment in Everyday Teaching of Mathematical Modelling: Implementation of Written and Oral Feedback to Competency- Oriented Tasks…… 469
Michael Besser, Werner Blum, and Malte Klimczak
41 Assessment of Modelling in Mathematics Examination Papers: Ready-Made Models and Reproductive Mathematising ……. 479
Pauline Vos
Part VI Applicability at Different Levels of Schooling, Vocational Education, and in Tertiary Education
42 Complex Modelling in the Primary and Middle School Years: An Interdisciplinary Approach ….. 491
Lyn D. English
43 Modelling in Brazilian Mathematics Teacher Education Courses …… 507
Maria Salett Biembengut
44 The Development of Mathematical Concept Knowledge and of the Ability to Use This Concept to Create a Model … 517
César Cristóbal-Escalante and Verónica Vargas-Alejo
45 Problem Posing: A Possible Pathway to Mathematical Modelling ….. 527
Ann Downton
46 A Study of the Effectiveness of Mathematical Modelling of Home Delivery Packaging on Year 12 Students’ Function Education .. 537
Tetsushi Kawasaki and Yoshiki Nisawa
47 How to Introduce Mathematical Modelling in Industrial Design Education? …… 551
Geert Langereis, Jun Hu, and Loe Feijs
48 Rationality of Practice and Mathematical Modelling – On Connections, Conflicts, and Codifications ……. 563
Lars Mouwitz
49 Extending Model Eliciting Activities (MEAs) Beyond Mathematics Curricula in Universities …. 573
Mark Schofield
50 Building Awareness of Mathematical Modelling in Teacher Education: A Case Study in Indonesia …… 583
Wanty Widjaja
Part VII Modelling and Applications in Business and the Lived Environment
51 Mathematics and the Pharmacokinetics of Alcohol …… 597
Michael Jennings and Peter Adams
52 Beyond the Modelling Process: An Example to Study the Logistic Model of Customer Lifetime Value in Business Marketing …… 607
Issic K.C. Leung.