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This book is Volume 8 in the Series on Mathematics Education publications showcasing different themes and trends in mathematics research and practice around the world. This volume features mathematical modelling. It discusses links between theoretical underpinnings of mathematical modelling and various practices in different education systems, with particular emphasis in the Singapore context. In addition, the book documents two events organised by the Mathematics and Mathematics Education Academic Group of the National Institute of Education in June 2010: The Mathematical Modelling Outreach (MMO) and The 2nd Lee Peng Yee Symposium (LPYS). Pre-service teachers, experienced teachers and school students engaged in mathematical modelling processes during the two events. Teaching ideas, learning activities and alternative modes of evaluating the students' learning based on the Singapore Mathematics Curriculum are also presented in this volume.