**Series Preface: **Gabriele Kaiser and Gloria Stillman

Chapter 1 **Mathematical Modelling:** **Connecting to Teaching and Research Practices – the impact of globalisation: **Gloria Stillman, Gabriele Kaiser,** **Werner Blum, and Jill Brown

**Part I Innovative Practices in Modelling Education Research and Teaching**

Chapter 2 **From Conference to Community: An ICTMA Journey—***The Ken Houston Inaugural Lecture: *Peter Galbraith

Chapter 3 **Modelling from the Perspective of Commognition – An Emerging Framework: **Jonas Bergman Ärlebäck and Peter Frejd

Chapter 4 **Should Interpretation Systems be Considered to be Models if They only Function Implicitly?: **Rita Borromeo Ferri and Richard Lesh

Chapter 5 **Mathematical Modelling, Mathematical Content and Tensions in Discourses: **Andréia Maria Pereira de Oliveira and Jonei Cerqueira Barbosa

Chapter 6 **Ethnomodelling as a Methodology for Ethnomathematics: **Milton Rosa and Daniel Clark Orey

Chapter 7 **Dual Modelling Cycle Framework for Responding to the Diversities of Modellers: **Akihiko Saeki and Akio Matsuzaki

Chapter 8 **The Eyes to See: Theoretical Lenses for Mathematical Modelling Research: **Nils Buchholtz

Chapter 9 **Strässer’s Didactic Tetrahedron as a Basis for Theorising Mathematical Modelling Activity within Social Contexts: **Vince Geiger

Chapter 10 **Ethnomodelling as a Research Lens on Ethnomathematics and Modelling: **Milton Rosa and Daniel Clark Orey

**Part II Research into, or Evaluation of, Teaching Practice**

Chapter 11 **Real-life Modelling within a Traditional Curriculum: Lessons from a Singapore Experience: **Ang Keng Cheng

Chapter 12 **Students’ Mathematical Learning in Modelling Activities: **Morten Blomhøj and Tinne Hoff Kjeldsen

Chapter 13 **Students' Designing an Ideal Tourism Route as Mathematical Modelling: **Chan Chun Ming Eric

Chapter 14 **Comparison of Mathematical Modelling Skills of Secondary and Tertiary Students: **Juntao Fu and Jinxing Xie

Chapter 15 **Taking Advantage of Incidental School Events to Engage with the Applications of Mathematics: The Case of Surviving the Reconstruction: **Vince Geiger, Merrilyn Goos, and Shelley Dole

Chapter 16 **The Development of Modelling Competencies by Year 9 Students: Effects of a Modelling Project: **Susanne Grünewald

Chapter 17 **Evidence of a Dual Modelling Cycle: Through a Teaching Practice Example for Pre-service Teachers: **Akio Matsuzaki and Akihiko Saeki

Chapter 18 **Considering Multiple Solutions for Modelling Problems – Design and First Results from the MultiMa-Project: **Stanislaw Schukajlow and André Krug

Chapter 19 **Challenges in Modelling Challenges: Intents and Purposes: **Gloria Stillman, Jill Brown, and Peter Galbraith

Chapter 20 **Mathematical Modelling of a Real-world Problem: The Decreasing Number of Bluefin Tuna: **Akira Yanagimoto and Noboru Yoshimura

Chapter 21 **Mathematical Modelling of a Social Problem: Pension Tax Issues: **Noboru Yoshimura and Akira Yanagimoto

**Part III Pedagogical Issues for Teaching and Learning**

Chapter 22 **Pedagogical Reflections on the Role of Modelling in Mathematics Instruction: **Toshikazu Ikeda

Chapter 23 **Complex Modelling Problems in Co-Operative, Self-directed Learning Environments: **Gabriele Kaiser and Peter Stender

Chapter 24 **Inducting Year 6 Students into “a Culture of Mathematising as a Practice”: **Jill Brown

Chapter 25 **A Whole Week of Modelling – Examples and Experiences of Modelling for Students in Mathematics Education: **Nils Buchholtz and Sarah Mesrogli

Chapter 26 **Teachers’ Self-Perceptions of their Pedagogical Content Knowledge Related to Modelling – An Empirical Study with Austrian Teachers: **Sebastian Kuntze, Hans-Stefan Siller, and Christiane Vogl

Chapter 27 **A Cross-Sectional Study about Modelling Competency in Secondary School: **Matthias Ludwig and Xenia-Rosemarie Reit

Chapter 28** Teacher Readiness in Mathematical Modelling: Are there Differences between Pre-service and In-service Teachers? **Kit Ee Dawn Ng

Chapter 29 **Exploring the Relationship between Mathematical Modelling and Classroom Discourse: **Trevor Redmond, Raymond Brown, and Joanne Sheehy

Chapter 30 **The Role of Textbooks in Developing a Socio-critical Perspective on Mathematical Modelling**** in Secondary Classrooms: **Gloria Stillman, Jill P Brown, Rhonda Faragher, Vince Geiger and Peter Galbraith

Chapter 31 **Pre-service Secondary School Teachers’ Knowledge in Mathematical Modelling – A Case Study: **Tan Liang Soon and Ang Keng Cheng

Chapter 32 **How Students Connect Descriptions of Real-world Situations to Mathematical Models in Different Representational Modes: **Wim Van Dooren, Dirk De Bock, and Lieven Verschaffel

Chapter 33 **Pre-service Teacher Learning for Mathematical Modelling: **Mark Winter

Chapter 34 **Initial Perspectives of Teacher Professional Development on Mathematical Modelling in Singapore: Problem Posing and Task Design: **Lee Ngan Hoe

Chapter 35 **Initial Perspectives of Teacher Professional Development on Mathematical Modelling in Singapore: Conceptions of Mathematical Modelling: **Chan Chun Ming Eric

Chapter 36 **Initial Perspectives of Teacher Professional Development on Mathematical Modelling in Singapore: A Framework for Facilitation: **Kit Ee Dawn Ng

Chapter 37 **Teacher Professional Development on Mathematical Modelling: Initial Perspectives from Singapore: **Vince Geiger

**Part IV Influences of Technologies**

Chapter 38 **Reality Based Test Tasks with Digital Tools at Lower Secondary: **Gilbert Greefrath and Michael Rieß

Chapter 39 **On Comparing Mathematical Models and Pedagogical Learning: **Janeen Lamb and Jana Visnovska

**Part V Assessment in Schools**

Chapter 40 **Formative Assessment in Everyday Teaching of Mathematical Modelling: Implementation of Written and Oral Feedback to Competency-Oriented Tasks: **Michael Besser, Werner Blum, and Malte Klimczak

Chapter 41 **Assessment of Modelling in Mathematics Examination Papers: Ready-made Models and Reproductive Mathematising: **Pauline Vos

**Part VI Applicability at Different Levels of Schooling, Vocational Education, and in Tertiary Education**

Chapter 42 **Complex Modelling in the Primary and Middle School Years: An Interdisciplinary Approach: **Lyn D. English

Chapter 43 **Modelling in Brazilian Mathematics Teacher Education Courses: **Maria Salett Biembengut

Chapter 44 **The Development of Mathematical Concept Knowledge and of the Ability to use this Concept to Create a Model: **César Cristóbal Escalante and Verónica Vargas Alejo

Chapter 45 **Problem Posing: A Possible Pathway to Mathematical Modelling: **Ann Downton

Chapter 46 **A Study of the Effectiveness of Mathematical Modelling of Home: Delivery Packaging on Year 12 Students' Function Education: **Tetsushi Kawasaki and Yoshiki Nisawa

Chapter 47 **How to Introduce Mathematical Modelling in Industrial Design Education? **Geert Langereis, Jun Hu, and Loe Feijs

Chapter 48 **Rationality of Practice and Mathematical Modelling – On Connections, Conflicts, and Codifications: **Lars Mouwitz

Chapter 49 **Extending Model Eliciting Activities (MEAs) beyond Mathematics Curricula in Universities: **Mark Schofield

Chapter 50 **Building Awareness of Mathematical Modelling in Teacher Education: A Case Study in Indonesia: **Wanty Widjaja

**Part VII Modelling and Applications in Business and the Lived Environment**

Chapter 51: **Mathematics and the Pharmacokinetics of Alcohol: **Michael Jennings and Peter Adams. - Chapter 52 **Beyond the Modelling Process: An Example to Study the Logistic Model of Customer Lifetime Value in Business Marketing: **Issic K. C. Leung

**List of Corresponding Authors**

Refereeing Process

Index