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Mathematical modelling is often spoken of as a way of life, referring to habits of mind and to dependence on the power of mathematics to describe, explain, predict and control real phenomena. This book aims to encourage teachers to provide opportunities for students to model a variety of real phenomena appropriately matched to students’ mathematical backgrounds and interests from early stages of mathematical education. Habits, misconceptions, and mindsets about mathematics can present obstacles to university students’ acceptance of a ‘‘models-and-modelling perspective’’ at this stage of mathematics education. Without prior experience in building, interpreting and applying mathematical models, many students may never come to view and regard modelling as a way of life. The book records presentations at the ICTMA 11 conference held in Milwaukee, Wisconsin in 2003.
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ICTMA 11 MATHEMATICAL MODELLING: A WAY OF LIFE Omnia apud me mathematica fiunt. With me everything turns into mathematics. Rene Descartes ABOUT THE EDITORS Susan J. Lamon, Professor in the Department of Mathematics, Statistics, and Computer Science at Marquette University, earned her Master of Science and PhD degrees from the University of Wisconsin-Madison. Her research, a combination of mathematics and cognitive science, uses modelling activities to study the development of rational number concepts and proportional reasoning. She works on numerous state and national projects to improve the teaching and assessment of mathematics, and currently serves on the executive board of ICTMA. Willard A. Parker earned his PhD from the University of Oregon, taught in the Department of Mathematics at Kansas State University for 28 years, and now teaches at Marquette University. His research interests include abstract harmonic analysis, the history of mathematics, and mathematics education. He has worked to improve school mathematics at the local, state, and national levels and has served as a governor of the Mathematical Association of America. S. Ken Houston, Professor of Mathematical Studies in the School of Computing and Mathematics, University of Ulster, gained his BSc Honours and PhD degrees at Queens University, Belfast. He is a long-standing member and current president of ICTMA and he serves on national committees in the UK and Ireland. He has a strong interest in all aspects of teaching, learning, and assessing mathematical modelling, and in innovative methods for preparing students to pursue careers in applied mathematics. IIleTMA 11 The Eleventh International Conference on the Teaching of Mathematical Modelling and Applications MATHEMATICAL MODELLING: A WAY OF LIFE Edited by Susan J. Lamon Willard A. Parker Ken Houston Horwood Publishing Chichester 2003 First published in 2003 by HORWOOD PUBLISHING LIMITED Coli House, Westergate, Chichester, West Sussex, P020 6QL England COPYRIGHT NOTICE All Rights Reserved, No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the permission of Horwood Publishing Limited. © Horwood Publishing Limited, 2003 British Library Cataloguing in Publication Data A catalogue record of this book is available from the British Library. ISBN 1-904275-03-6 Printed in Great Britain by Antony Rowe Limited. Table of Contents ICTMA Publications viii ix Preface Section A: Modelling in the Elementary School Mathematical Modelling With Young Learners Lyn English, Queensland University of Technology, Australia 2 Modelling in Elementary School: Helping Young Students to See the World Mathematically Susan 1. La