Mathematical Modelling: From Theory to Practice

254 Pages·2015·5.087 MB·English

by  Lee Ngan Hoe, Ng Kit Ee Dawn (eds.)

MATHEMATICAL
MODELLING
From Theory to Practice
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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
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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
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Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy
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Typeset by Stallion Press
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Printed in Singapore
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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.