Trends In Teaching And Learning Of Mathematical Modelling

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

This survey provides an overview of the German discussion on modelling and applications in schools. It considers the development from the beginning of the 20th century to the present, and discusses the term “mathematical model” as well as different representations of the modelling process as modelling cycles. Different trends in the historical and current debate on applications and modelling can be differentiated as perspectives of modelling. Modelling is now one of the six general mathematical competencies defined in the educational standards for mathematics introduced in Germany in 2003, and there have been several initiatives to implement modelling in schools, as well as a whole range of empirical research projects focusing on teachers or students in modelling processes. As a special kind for implementing modelling into school, modelling weeks and days carried out by various German universities have been established.

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. The comprehensive overview on the most recent empirical research reflecting the development and promotion of modelling competencies at various age levels allows insight into possible affective and cognitive blockages and barriers for students modelling processes and its teaching. The papers on the usage of technology describe new possibilities, how the usage of technology can inspire the teaching and learning of modelling. International modelling projects offer chances and possibilities to enrich the teaching and learning of mathematical modelling at secondary and tertiary level and describe challenging modelling examples and their possible usage in school and university. The necessary change of teacher education towards an inclusion of mathematical modelling is reflected from different perspectives and challenging examples are given. The contributing authors are influential members of the group International Community of Teachers of Modelling and Applications and important researchers in mathematics and mathematics education. The book will be of interest to mathematics educators, teacher educators, researchers, education administrators, curriculum developers, teachers and student teachers.

This book documents the journey undertaken by educators from the Mathematics and Mathematics Education (MME) Academic Group in the National Institute of Education (NIE) and Singapore schools during a Mathematical Modelling Outreach (MMO) event in June 2010 under the guidance of renowned experts in the field of mathematical modelling. The main goal of MMO was to reach out to Singapore primary and secondary schools and introduce the potentials of mathematical modelling as a platform for eliciting mathematical thinking, communication, and reasoning among students. This book contributes to the expanding literature on mathematical modelling by offering voices from the Singaporean context. It suggests how theoretical perspectives on mathematical modelling can be transformed into actual practice in schools, all within the existing infrastructure of the current Singapore mathematics curriculum. More importantly, the book provides documentary evidence on how plans put in place through MMO in 2010 have since been realised. The publication of this book is hence timely at this juncture. Not only does the book record how MMO was among the first pebbles launched into the pond, it also serves as a bridge over which educators can stand upon to view how the ripple effect had developed from the initial MMO pebble and the directions it may continue to extend. Perhaps in the process, other ripples in the teaching, learning, and research of mathematical modelling can be created. Contents:Introduction: Mathematical Modelling Outreach in Singapore (NG Kit Ee Dawn and LEE Ngan Hoe)Setting the Stage for Mathematical Modelling in Schools:Promotion of Mathematical Modelling Competencies in the Context of Modelling Projects (Gabriele KAISER and Susanne GRÜNEWALD)Problem Finding and Problem Posing for Mathematical Modelling (Gloria STILLMAN)Mathematical Modelling in Singapore Schools: A Framework for Instruction (ANG Keng Cheng)Mathematical Modelling in Australia (Vincent GEIGER)Mathematical Modelling in Japan (Toshikazu IKEDA)Fostering Mathematical Modelling in Schools:Learning through Modelling in the Primary Years (Lyn D ENGLISH)Fostering Mathematical Modelling in Secondary Schools (Gloria STILLMAN)Mathematical Modelling — An Example from an Inter-School Modelling Challenge (Raymond BROWN, Trevor REDMOND, Joanne SHEEHY and Dawn LANG)Mathematical Learning through Modelling Tasks:Learning through "Designing a Café" (YEO Kai Kow Joseph)Learning through "Plane Punctuality" (HO Weng Kin)Learning through "Mobile Phone Plan" (CHENG Lu Pien and CHUA Kwee Gek)Learning through "The Best Paper Plane" (SOON Wan Mei Amanda, CHIOK Hwee Fen and KONG May Hua Maybelline)Learning through "Designing a Tent" (HO Siew Yin)Learning through "Dream Home" (CHAN Chun Ming Eric)Learning through "The Unsinkable Titanic" (JAGUTHSING Dindyal and FOO Him Ho) Readership: Graduate students and researchers in mathematics education; mathematics educators. Keywords:Mathematical Modelling;Mathematical Modelling in Singapore;Modelling Competencies;Model-Eliciting Tasks;Modelling Research;Modelling Projects;Theoretical Perspectives on Mathematical Modelling;Modelling framework;Teacher Education in Mathematical ModellingKey Features:This book discusses the use of mathematical modelling activities for teaching and learning in Singapore classrooms, drawing upon experiences from other countriesIt provides focused discussions on the practicalities of conducting modelling activities in the classroom based on actual implementation in the Singapore context, drawing on the Singapore Mathematics Curriculum and other curriculaIt also proposes the way forward in addressing the issue of mathematical modelling for teacher education and curricula planning in the Singapore context

Modeling Students’ Mathematical Modeling Competencies offers welcome clarity and focus to the international research and professional community in mathematics, science, and engineering education, as well as those involved in the sciences of teaching and learning these subjects.

This book takes stock of the state of affairs of the teaching and learning of mathematical modelling with regard to research, development and practice. It provides a conceptual framework for mathematical modelling in mathematics education at all education levels, as well as the background and resources for teachers to acquire the knowledge and competencies that will allow them to successfully include modelling in their teaching, with an emphasis on the secondary school level. Mathematics teachers, mathematics education researchers and developers will benefit from this book. Expertly written and researched, this book includes a comprehensive overview of research results in the field, an exposition of the educational goals associated with modelling, the essential components of modelling competency and an extensive discussion of didacticopedagogical challenges in modelling. Moreover, it offers a wide variety of illuminating cases and best-practice examples in addition to insights into the focal points for future research and practice. The Learning and Teaching of Mathematical Modelling is an invaluable resource for teachers, researchers, textbook authors, secondary school mathematics teachers, undergraduate and graduate students of mathematics as well as student teachers.

This survey provides an overview of the German discussion on modelling and applications in schools. It considers the development from the beginning of the 20th century to the present, and discusses the term "mathematical model" as well as different representations of the modelling process as modelling cycles. Different trends in the historical and current debate on applications and modelling can be differentiated as perspectives of modelling. Modelling is now one of the six general mathematical competencies defined in the educational standards for mathematics introduced in Germany in 2003, and there have been several initiatives to implement modelling in schools, as well as a whole range of empirical research projects focusing on teachers or students in modelling processes. As a special kind for implementing modelling into school, modelling weeks and days carried out by various German universities have been established. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.

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.