Teaching Mathematical Modelling: Connecting to Research and Practice

✍ Scribed by Gloria Ann Stillman, Gabriele Kaiser (auth.), Gloria Ann Stillman, Gabriele Kaiser, Werner Blum, Jill P. Brown (eds.)

• Publisher: Springer Netherlands
• Year: 2013
• Tongue: English
• Leaves: 612
• Series: International Perspectives on the Teaching and Learning of Mathematical Modelling
• Edition: 1
• Category: Library

✦ Synopsis

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.​

✦ Table of Contents

Front Matter....Pages i-xvi
Mathematical Modelling: Connecting to Teaching and Research Practices – The Impact of Globalisation....Pages 1-24
Front Matter....Pages 25-25
From Conference to Community: An ICTMA Journey— The Ken Houston Inaugural Lecture ....Pages 27-45
Modelling from the Perspective of Commognition – An Emerging Framework....Pages 47-56
Should Interpretation Systems Be Considered to Be Models if They Only Function Implicitly?....Pages 57-66
Mathematical Modelling, Mathematical Content and Tensions in Discourses....Pages 67-76
Ethnomodelling as a Methodology for Ethnomathematics....Pages 77-88
Dual Modelling Cycle Framework for Responding to the Diversities of Modellers....Pages 89-99
The Eyes to See: Theoretical Lenses for Mathematical Modelling Research....Pages 101-106
Strässer’s Didactic Tetrahedron as a Basis for Theorising Mathematical Modelling Activity Within Social Contexts....Pages 107-116
Ethnomodelling as a Research Lens on Ethnomathematics and Modelling....Pages 117-127
Front Matter....Pages 129-129
Real-Life Modelling Within a Traditional Curriculum: Lessons from a Singapore Experience....Pages 131-140
Students’ Mathematical Learning in Modelling Activities....Pages 141-151
Students’ Designing an Ideal Tourism Route as Mathematical Modelling....Pages 153-163
Comparison of Mathematical Modelling Skills of Secondary and Tertiary Students....Pages 165-173
Taking Advantage of Incidental School Events to Engage with the Applications of Mathematics: The Case of Surviving the Reconstruction....Pages 175-184
The Development of Modelling Competencies by Year 9 Students: Effects of a Modelling Project....Pages 185-194
Evidence of a Dual Modelling Cycle: Through a Teaching Practice Example for Pre-service Teachers....Pages 195-205
Considering Multiple Solutions for Modelling Problems – Design and First Results from the MultiMa-Project....Pages 207-216
Challenges in Modelling Challenges: Intents and Purposes....Pages 217-227
Mathematical Modelling of a Real-World Problem: The Decreasing Number of Bluefin Tuna....Pages 229-239
Front Matter....Pages 129-129
Mathematical Modelling of a Social Problem: Pension Tax Issues....Pages 241-251
Front Matter....Pages 253-253
Pedagogical Reflections on the Role of Modelling in Mathematics Instruction....Pages 255-275
Complex Modelling Problems in Co-operative, Self-Directed Learning Environments....Pages 277-293
Inducting Year 6 Students into “A Culture of Mathematising as a Practice”....Pages 295-305
A Whole Week of Modelling – Examples and Experiences of Modelling for Students in Mathematics Education....Pages 307-316
Teachers’ Self-Perceptions of Their Pedagogical Content Knowledge Related to Modelling – An Empirical Study with Austrian Teachers....Pages 317-326
A Cross-Sectional Study About Modelling Competency in Secondary School....Pages 327-337
Teacher Readiness in Mathematical Modelling: Are There Differences Between Pre-service and In-Service Teachers?....Pages 339-348
Exploring the Relationship Between Mathematical Modelling and Classroom Discourse....Pages 349-360
The Role of Textbooks in Developing a Socio-critical Perspective on Mathematical Modelling in Secondary Classrooms....Pages 361-371
Pre-service Secondary School Teachers’ Knowledge in Mathematical Modelling – A Case Study....Pages 373-383
How Students Connect Descriptions of Real-World Situations to Mathematical Models in Different Representational Modes....Pages 385-393
Pre-service Teacher Learning for Mathematical Modelling....Pages 395-404
Initial Perspectives of Teacher Professional Development on Mathematical Modelling in Singapore: Conceptions of Mathematical Modelling....Pages 405-413
Initial Perspectives of Teacher Professional Development on Mathematical Modelling in Singapore: Problem Posing and Task Design....Pages 415-425
Initial Perspectives of Teacher Professional Development on Mathematical Modelling in Singapore: A Framework for Facilitation....Pages 427-436
Teacher Professional Development on Mathematical Modelling: Initial Perspectives from Singapore....Pages 437-442
Front Matter....Pages 443-443
Reality Based Test Tasks with Digital Tools at Lower Secondary....Pages 445-456
On Comparing Mathematical Models and Pedagogical Learning....Pages 457-466
Front Matter....Pages 467-467
Formative Assessment in Everyday Teaching of Mathematical Modelling: Implementation of Written and Oral Feedback to Competency-Oriented Tasks....Pages 469-478
Front Matter....Pages 467-467
Assessment of Modelling in Mathematics Examination Papers: Ready-Made Models and Reproductive Mathematising....Pages 479-488
Front Matter....Pages 489-489
Complex Modelling in the Primary and Middle School Years: An Interdisciplinary Approach....Pages 491-505
Modelling in Brazilian Mathematics Teacher Education Courses....Pages 507-516
The Development of Mathematical Concept Knowledge and of the Ability to Use This Concept to Create a Model....Pages 517-526
Problem Posing: A Possible Pathway to Mathematical Modelling....Pages 527-536
A Study of the Effectiveness of Mathematical Modelling of Home Delivery Packaging on Year 12 Students’ Function Education....Pages 537-549
How to Introduce Mathematical Modelling in Industrial Design Education?....Pages 551-561
Rationality of Practice and Mathematical Modelling – On Connections, Conflicts, and Codifications....Pages 563-572
Extending Model Eliciting Activities (MEAs) Beyond Mathematics Curricula in Universities....Pages 573-581
Building Awareness of Mathematical Modelling in Teacher Education: A Case Study in Indonesia....Pages 583-593
Front Matter....Pages 595-595
Mathematics and the Pharmacokinetics of Alcohol....Pages 597-606
Beyond the Modelling Process: An Example to Study the Logistic Model of Customer Lifetime Value in Business Marketing....Pages 607-617
Back Matter....Pages 619-627

✦ Subjects

Mathematics Education; Applications of Mathematics; Learning & Instruction