Mathematical Modelling: From Theory to Practice PDF
Preview Mathematical Modelling: From Theory to Practice
MATHEMATICAL MODELLING From Theory to Practice 8935_9789814546911_tp.indd 1 15/12/14 9:35 am SERIES ON MATHEMATICS EDUCATION Series Editors: Mogens Niss (Roskilde University, Denmark) Lee Peng Yee (Nanyang Technological University, Singapore) Jeremy Kilpatrick (University of Georgia, USA) Published Vol. 1 How Chinese Learn Mathematics Perspectives from Insiders Edited by: L. Fan, N.-Y. Wong, J. Cai and S. Li Vol. 2 Mathematics Education The Singapore Journey Edited by: K. Y. Wong, P. Y. Lee, B. Kaur, P. Y. Foong and S. F. Ng Vol. 4 Russian Mathematics Education History and World Significance Edited by: A. Karp and B. R. Vogeli Vol. 5 Russian Mathematics Education Programs and Practices Edited by A. Karp and B. R. Vogeli Vol. 7 Mathematics Education in Korea Volume 1: Curricular and Teaching and Learning Practices Edited by Jinho Kim, Inki Han, Joongkwoen Lee and Mangoo Park Vol. 8 Mathematical Modelling From Theory to Practice Edited by N. H. Lee and D. K. E. Ng Vol. 9 Primary Mathematics Standards for Pre-Service Teachers in Chile A Resource Book for Teachers and Educators By P. Felmer, R. Lewin, S. Martínez, C. Reyes, L. Varas, E. Chandía, P. Dartnell, A. López, C. Martínez, A. Mena, A. Ortíz, G. Schwarze and P. Zanocco Vol. 10 Mathematics and Its Teaching in the Southern Americas Edited by H. Rosario, P. Scott and B. R. Vogeli Forthcoming Vol. 3 Lesson Study Challenges in Mathematics Education Edited by M. Inprasitha, M. Isoda, B.-H. Yeap and P. Wang-Iverson Vol. 6 How Chinese Teach Mathematics Perspectives from Insiders Edited by L. Fan, N.-Y. Wong, J. Cai and S. Li Elizabeth - Mathematical modelling.indd 1 11/12/2014 9:01:23 AM Series on Mathematics Education Vol. 8 MATHEMATICAL MODELLING From Theory to Practice Edited by Lee Ngan Hoe Ng Kit Ee Dawn National Institute of Education, Nanyang Technological University, Singapore World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI 8935_9789814546911_tp.indd 2 15/12/14 9:35 am Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE Library of Congress Cataloging-in-Publication Data Lee, Ngan Hoe. Mathematical modelling : from theory to practice / Lee Ngan Hoe, National Institute of Education, Nanyang Technological University, Singapore, Ng Kit Ee Dawn, National Institute of Education, Nanyang Technological University, Singapore. pages cm. -- (Series on mathematics education ; volume 8) Includes bibliographical references. ISBN 978-9814546911 (hardcover : alk. paper) 1. Mathematics--Study and teaching (Secondary) 2. Mathematics teachers--Training of. 3. High school teachers--Training of. I. Ng, Kit Ee Dawn. II. Title. QA11.2.L445 2015 510.71'25957--dc23 2014045571 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Copyright © 2015 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. Typeset by Stallion Press Email: [email protected] Printed in Singapore Elizabeth - Mathematical modelling.indd 2 11/12/2014 9:01:23 AM December 16, 2014 10:3 9in x 6in Mathematical Modelling: From Theory to Practice b1645-fm AUTHORS’BIOGRAPHY ANGKengChengiscurrentlyanAssociateProfessorandtheHeadofthe Mathematics and Mathematics Education academic group at the National InstituteofEducation,Singapore.HeobtainedhisPhDinAppliedMathe- matics from the University of Adelaide, Australia. His research interests includecomputationalmethodsinpartialdifferentialequations,numerical analysis,andtheteachingandlearningofmathematicalmodelling. Raymond BROWN is an Associate Professor and the Deputy Head of School,Learning&Teaching,intheSchoolofEducationandProfessional Studies at Griffith University, Australia. Recently, his research has been concernedwithprovidinginsightsintohowsocialprocessesinteractatthe individualandsmallgrouplevelstomotivateandguidestudentsto‘speak’ and‘act’asmathematicianswhenengagedinMathematicalModelling. CHANChunMingEric(PhD)isalecturerwiththeMathematicsandMath- ematicsEducationAcademicGroup,NationalInstituteofEducation,Singa- pore.Helecturesonprimarymathematicseducationinthepre-serviceand in-service programmes. He is the author of several mathematics resource books(primarylevels)andisalsotheco-authoroftheTargetingMathseries. CHENG Lu Pien, received her PhD in Mathematics Education from the University of Georgia, United States in 2006. She is anAssistant Profes- sorwiththeMathematicsandMathematicsEducationAcademicGroupat the National Institute of Education, Singapore. She specialises in mathe- matics education courses for primary school teachers. Her research inter- ests include the professional development of primary school mathematics teachers,toolsandprocessesinmathematicseducationprogrammesforpre- serviceteachers,andchildren’sthinkinginthemathematicsclassrooms. CHUA Kwee Gek was a teaching fellow and lecturer with the Mathe- maticsandMathematicsEducationAcademicGroup,NationalInstituteof Education,Singapore.ShehasheldthepositionsofDepartmentHeadand v December 16, 2014 10:3 9in x 6in Mathematical Modelling: From Theory to Practice b1645-fm vi MathematicalModelling:FromTheorytoPractice Mathematics and Research and Evaluation Officer at the Singapore Min- istry of Education. Currently, she is a part-time mathematics tutor and an external mentor for the Ministry’s Improve Confidence andAchievement inNumeracyproject. LynD.ENGLISHisaProfessorofmathematicseducationattheQueens- landUniversityofTechnology.Herareasofresearchincludemathematical modelling,mathematicalreasoningandproblemsolving,engineeringedu- cation,andstatisticalliteracy.LynisaFellowofTheAcademyoftheSocial Sciences in Australia and is founding Editor of the international journal, MathematicalThinkingandLearning. VinceGEIGERisanAssociateProfessorintheFacultyofEducationatAus- tralianCatholicUniversity,Australia.HeiscurrentlyanAssociate-Editorof theMathematicsEducationResearchJournal.VinceisalsoaformerSec- retary of the Mathematics Education Research Group of Australasia and a Past President of the Australian Association of Mathematics Teachers. His research interests include mathematical modelling, numeracy, the use ofdigitaltoolsinmathematicsteachingandlearning,andtheprofessional learningofmathematicsteachers. Susanne GRUENEWALD studied mathematics and history to become a teacherattheUniversityofHamburg,Germany.Sheholdsamasterdegree in education. Currently she is completing her PhD at the University of Hamburgonempiricalresearchinmathematicalmodelling. HOFooHimwasateachingfellowfortheMathematicsandMathematics EducationAcademic Group of the National Institute of Education, Singa- pore.Hisacademicaffiliationsareasfollows:MSc(SystemsandControl), University of Sheffield, United Kingdom; BSc (Maths) National Univer- sity of Singapore, Singapore; Diploma in Education, National Institute of Education,Singapore. HOSiewYiniscurrentlyaPost-DoctoralFellowattheFacultyofEducation, Science,Technology and Mathematics, University of Canberra,Australia. She holds a PhD in mathematics education from the National Institute of Education, Singapore. Her research interest is in visualisation and teacher education. December 16, 2014 10:3 9in x 6in Mathematical Modelling: From Theory to Practice b1645-fm Authors’Biography vii HOWengKiniscurrentlyanAssistantProfessorattheAcademicGroupof MathematicsandMathematicsEducation,NationalInstituteofEducation, Singapore. He holds a PhD in Computer Science from the University of Birmingham,UnitedKingdom.Hisresearchinterestisintheoreticalcom- puter science, mathematics and mathematics education. For mathematics education,heisparticularlyinterestedintheuseofhistoryofmathematics andinformationtechnologyintheteachingandlearningofmathematicsin secondaryschools. ToshikazuIKEDAisaProfessorinmathematicseducationattheFacultyof EducationandHumanSciencesofYokohamaNationalUniversityinJapan. HehasbeenoneofthemembersoftheInternationalExecutiveCommittee of International Community of Teachers of Mathematical Modelling and Applications since 2005. Further, from 2010, he is one of the members of MathematicsExpertGroupforPISA2012. JAGUTHSING Dindyal is currently anAssociate Professor at the Mathe- maticsandMathematicsEducationAcademicGroup,NationalInstituteof Education,Singapore.HeholdsaPhDinMathematicsEducationfromthe Illinois State University, United States. His research interest is in various aspectsofmathematicseducationincludingmathematicalproblemsolving, internationalstudies,teachereducationandalgebraicthinking. GabrieleKAISERhasbeenaProfessorofmathematicseducationattheFac- ultyofEducationoftheUniversityofHamburg,Germanysince1998.Her areas of research include modelling and applications, international com- parative studies, gender and cultural aspects in mathematics education as well as teacher education. Her latest project deals with teacher education under an international perspective. She is a prolific writer and since 2005 she has served as Editor-in-Chief of ZDM - The International Journal on MathematicsEducation.ShehasservedasthePresidentoftheInternational CommunityofTeachersofMathematicalModellingandApplications.Cur- rentlysheisconvenorofthe13thInternationalCongressonMathematical Education. Dawn LANG was Principal ofA.B. Paterson College from 1994 to 2011. SheisamemberoftheBoardofIndependentSchoolsQueenslandandchairs the Block GrantAuthority. Dawn organises and implements programmes December 16, 2014 10:3 9in x 6in Mathematical Modelling: From Theory to Practice b1645-fm viii MathematicalModelling:FromTheorytoPractice fornewprincipalsaswellasTheMiddleManagersasLeadersProgramme fortheQueenslandEducationLeadershipInstitute. LEENganHoeisanAssistantProfessorattheNationalInstituteofEduca- tion,Singapore.HeholdsaPhDinEducationfromNanyangTechnological University, Singapore. His publication and research interests include the teachingandlearningofmathematicsatprimaryandsecondarylevels,cov- ering areas such as mathematics curriculum development, metacognition andmathematicalproblemsolving/modelling,technologyandmathematics education,andtextbooksandmathematicseducation. NG Kit Ee Dawn is a lecturer in the Mathematics and Mathematics Edu- cationAcademic Group at the National Institute of Education, Singapore. She holds a PhD in mathematics education from The University of Mel- bourne,Australia. She is involved in teacher professional development at bothprimaryandsecondarylevels.Herresearchinterestsincludetheuseof contextualised tasks in the teaching and learning of mathematics and fos- teringstudents’mathematicalthinkingandmetacognition. TrevorREDMONDhasbeenalearnerandteacherofmathematicsformany years.Heusesmathematicalmodellingtodevelopinstudentsaninterestof makingmathematicsthroughmakingitrelevanttothem.Heisinterestedin seeingstudentsdeveloptheirmathematicalunderstandingandthinking.He conceptualisedandhascoordinatedtheA.B.PatersonCollegeMathematical ModellingForumandChallengefromitsinception.TrevorisnowtheHead ofMathematicsatSomervilleHouse,agirls’schoolinBrisbane,Australia. JoanneSHEEHYhasbeentheHeadofmathematicsforthepastdecadeand anadvocate,supporterandmentoroftheA.B.PatersonCollegeMathemat- icalModellingForumandChallenge.Sheseesthathavinganunderstanding ofmathematicalmodellingassistsstudentstogenerateresilienceinsolving problems,allowsthemtoaccessproblemsandbecomebetterthinkers. SOON Wan Mei Amanda is an Assistant Professor in the Mathematics and Mathematics Education Academic Group at the National Institute of Education in Singapore. She received her PhD in mathematics from the National University of Singapore. Her main research interests include the December 16, 2014 10:3 9in x 6in Mathematical Modelling: From Theory to Practice b1645-fm Authors’Biography ix pricingofmultipleproductsandtheteachingandlearningofmathematical modelling,inparticularwithdifferentialequations. GloriaSTILLMANisanAssociateProfessorattheAustralianCatholicUni- versity,Australia. Currently, she holds two positions as the Deputy Head ofEducationintheFacultyofEducationandArts(Victoria)aswellasthe Head of Education in the Faculty of Education andArts (Ballarat) at her university. She has a PhD in mathematics education from the University ofQueensland,Australia.Hercurrentmajorresearchinterestisinteaching andassessingmathematicalmodellinginsecondaryschools.Sheisapro- lific writer who has published extensively in areas such as metacognition, applications and modelling, curriculum development and teacher educa- tion.SheisnowthePresidentoftheInternationalCommunityofTeachers ofMathematicalModellingandApplications. YEOKaiKowJosephisafacultymemberintheMathematicsandMathe- matics EducationAcademic Group at the National Institute of Education, Singapore. As a teacher educator, he is involved in training pre-service and in-service mathematics teachers at primary and secondary levels and hasalsoconductednumerousprofessionaldevelopmentcoursesforteach- ers in Singapore and overseas. Before joining the National Institute of Education in 2000, he held the post ofVice Principal and Head of Math- ematics Department in secondary schools. His research interests include mathematicalproblemsolvingintheprimaryandsecondarylevels,mathe- matics pedagogical content knowledge of teachers, mathematics teaching inprimaryschoolsandmathematicsanxiety.
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