Interdisciplinary Mathematics Education: The State of the Art and Beyond PDF
Preview Interdisciplinary Mathematics Education: The State of the Art and Beyond
ICME-13 Monographs Brian Doig · Julian Williams · David Swanson · Rita Borromeo Ferri · Pat Drake Editors Interdisciplinary Mathematics Education The State of the Art and Beyond ICME-13 Monographs Series editor Gabriele Kaiser, Faculty of Education, Didactics of Mathematics, Universität Hamburg, Hamburg, Germany Each volume in the series presents state-of-the art research on a particular topic in mathematics education and reflects the international debate as broadly as possible, while also incorporating insights into lesser-known areas of the discussion. Each volumeisbasedonthediscussionsandpresentationsduringtheICME-13conference and includes the best papers from one of the ICME-13 Topical Study Groups, DiscussionGroupsorpresentationsfromthethematicafternoon. More information about this series at http://www.springer.com/series/15585 Brian Doig Julian Williams (cid:129) (cid:129) David Swanson Rita Borromeo Ferri (cid:129) (cid:129) Pat Drake Editors Interdisciplinary Mathematics Education The State of the Art and Beyond Editors BrianDoig Julian Williams Faculty of Arts andEducation EllenWilkinson Building Deakin University TheUniversity of Manchester Victoria, VIC,Australia Manchester, UK DavidSwanson Rita BorromeoFerri ManchesterInstitute of Education Institut für Mathematik TheUniversity of Manchester UniversitätKassel Manchester, UK Kassel, Hessen,Germany PatDrake Victoria University Melbourne, VIC,Australia ISSN 2520-8322 ISSN 2520-8330 (electronic) ICME-13 Monographs ISBN978-3-030-11065-9 ISBN978-3-030-11066-6 (eBook) https://doi.org/10.1007/978-3-030-11066-6 LibraryofCongressControlNumber:2018966113 ©TheEditor(s)(ifapplicable)andTheAuthor(s)2019.Thisbookisanopenaccesspublication. 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ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Contents 1 Introduction to Interdisciplinary Mathematics Education. . . . . . . . 1 Brian Doig and Julian Williams Part I Conceptualising and Theorising Interdisciplinarity in Research, Policy and Practice Julian Williams 2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Julian Williams 3 Theoretical Perspectives on Interdisciplinary Mathematics Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Julian Williams and Wolff-Michael Roth 4 Integration from a Commognitive Perspective: An Experience with Mathematics and Music Students . . . . . . . . . . . . . . . . . . . . . . 35 M. Alicia Venegas-Thayer 5 Challenges and Opportunities for a STEM Interdisciplinary Agenda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Russell Tytler, Gaye Williams, Linda Hobbs and Judy Anderson Part II Focus on Cross-Cutting Skills: A Glass Half-Full? Pat Drake 6 Introduction: A Glass Half Full? . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Pat Drake 7 Developing Mathematical Reasoning Using a STEM Platform . . . . 93 Andrzej Sokolowski 8 Quantitative Reasoning and Its Rôle in Interdisciplinarity . . . . . . . 113 Robert Mayes v vi Contents 9 Modelling and Programming of Digital Video: A Source for the Integration of Mathematics, Engineering, and Technology . . . . . . . 135 Carlos A. LópezLeiva, Marios S. Pattichis and Sylvia Celedón-Pattichis Part III Case Studies in Inter-Disciplinarity: Mathematics as Tool and Mathematics as (Conscious) Generalisation David Swanson 10 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 David Swanson 11 Mathematics in an Interdisciplinary STEM Course (NLT) in The Netherlands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Nelleke den Braber, Jenneke Krüger, Marco Mazereeuw and Wilmad Kuiper 12 Maths Adds up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Maite Gorriz and Santi Vilches 13 The Successful Students STEM Project: A Medium Scale Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 Linda Hobbs, Brian Doig and Barry Plant 14 “Draw What You See” Transcending the Mathematics Classroom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 Signe E. Kastberg, Rachel Long, Kathleen Lynch-Davis and Beatriz S. D’Ambrosio 15 Inter-disciplinary Mathematics: Old Wine in New Bottles? . . . . . . 245 Brian Doig and Wendy Jobling Part IV Teacher Education and Teacher Development Rita Borromeo Ferri 16 Teacher Education and Teacher Development . . . . . . . . . . . . . . . . 259 Rita Borromeo Ferri 17 Inclusion of Interdisciplinary Approach in the Mathematics Education of Biology Trainee Teachers in Slovakia . . . . . . . . . . . . 263 Ivana Boboňová, Soňa Čeretková, Anna Tirpáková and Dagmar Markechová 18 Creating Academic Teacher Scholars in STEM Education by Preparing Preservice Teachers as Researchers . . . . . . . . . . . . . 281 Jennifer Wilhelm and Molly H. Fisher Contents vii Part V Conclusion to Interdisciplinary Mathematics Education Brian Doig 19 Conclusion to Interdisciplinary Mathematics Education. . . . . . . . . 299 Brian Doig and Julian Willams Chapter 1 Introduction to Interdisciplinary Mathematics Education BrianDoigandJulianWilliams Abstract The purpose of this chapter is to preface, and introduce, the content of this book, but also to help clarify concepts and terms addressed, set the stage by summarisingourpreviouswork,andissuesomecaveatsaboutourlimitations.We will close with a discussion of the mathematics in Interdisciplinary Mathematics Education(IdME),whichweseeasalacunaintheliterature,andeveninthisbook. · · · Keywords Interdisciplinary Mathematics Education Introduction 1.1 OriginsandContextofThisVolume The origins of this book emerged after some of us were invited to lead a Topic StudyGroup(TSG-22)attheInternationalConferenceonMathematicsEducation inHamburgin2016(ICME-13).InitiallythesuggestionwasforatopiconScience, Technology,EngineeringandMathematics(STEM)education,atopicthathasbeen increasinglyprominentineducationalpolicy,andpractice,inthelastdecade.How- ever,wepreferredtogototheconceptof‘interdisciplinarity’asthefocusofinterest forseveralreasons.First,whilemuchSTEM-relatedworkdoesinvolveinterdisci- plinarity,muchdoesnot—ithademergedasafundingpriority,andisoftenrelated moretopoliticalandeconomicexpediencies,thantoeducationalprinciples.Second, muchSTEMworkdoeslittletoemphasisemathematics,andwhenitdoesso,itdoes notalwaysrelatethemathematicstotheotherdisciplinesorsubjectsinvolved.Third, much good interdisciplinary mathematics involves non-STEM disciplines, and we wantedtoincludethearts,music,andotherdisciplinesthatmightbeexcludedfrom STEM.Finally,however,wehopedthat“Interdisciplinarymathematicseducation” wouldincludemuchSTEMwork,andevenmostofSTEMwork,thatmightbeof contemporaryinterest. B.Doig DeakinUniversity,Melbourne,Australia B J.Williams( ) UniversityofManchester,ManchesterM139PL,UK e-mail:[email protected] ©TheAuthor(s)2019 1 B.Doigetal.(eds.),InterdisciplinaryMathematicsEducation, ICME-13Monographs,https://doi.org/10.1007/978-3-030-11066-6_1 2 B.DoigandJ.Williams 1.2 TheStateoftheArtin2016:WhatNext? PriortotheICME-13conference,theorganiserswereinvitedtoproduceaStateof theart inthetopic,whichwaspublishedimmediatelypriortotheconference,and isavailablefreelyon-line(see,Williamsetal.,2016).Thisprovidedthebaselevel ofknowledgethatallpapersinTopicGroup22builton,andmanyofthechapters inthisbookrefertoit,soitisworthsummarisingsomeofitskeypointshere. IntheStateoftheart,theauthorsmakeclearthatpreviousresearchinthetopic suffersfromseveralkeyproblems,orevenflaws.First,thereisconfusionoverthe key concepts and terms, making it hard for research to become cumulative. Much ofthewritinginthetopicassumesthatadisciplineequates withaschoolcurricu- lumsubject,andthatanyformofcollaboration,orintegration,betweensubjectsis therefore ‘interdisciplinary’, whereas, we prefer to use the term ‘curriculum inte- gration’ or ‘subject integration’ in such cases, unless there is, also, a clear case of interdisciplinarity,i.e.ofdistinctdisciplinesworkingtogether atsomelevel(more ofthese‘levels’later).TheStateoftheartaddressedthisconcern,andthisisfurther developed in this book, particularly in the first section. However, we will have to facethefactthattheterm‘discipline’hasmultipleuses,meaningsomewhatdiffer- ent, though overlapping, things inside academia, and outside it in workplaces. In places such as health services, for example, multi-disciplinary teams tend to refer toteams involving distinct professions; someof which may arguably have an aca- demicdiscipline,ortwo,intheirbackgroundtraining,buttheacademicdisciplines involved do not determine the profession. The inter-professional education being promotedtheredoes,however,engagewithmanyoftheissuesinvolvedinacademic ‘interdisciplinarity’,then,buttheconceptsinvolvedaredifferent. Second, the practices involved in schools and tertiary institutions that are quite reasonablydescribedasinterdisciplinary,maytakeanumberofforms,andempirical researchesintothesepracticesdonotoftenmakeclearwhatformtheyarestudying. Again, this makes accumulation of knowledge difficult, and meta-analyses almost impossible. A particular concern comes when these practices are studied empiri- cally, using measurements of learning outcomes; the learning out-comes rarely, in fact,correspondwiththeinterdisciplinarylearningoutcomesthatmighthavebeen anticipatedorthatmotivatedthepracticeinthefirstplace.Studiesthatusetraditional testscoresinmathematicsasanoutcomemeasure,forexample,mightproducedis- appointing findings, because the traditional measures are not designed to measure whatinterdisciplinarypracticesaredesignedtodevelopinlearners. Nevertheless, empirical studies have consistently shown that the raft of school practices,calledinterdisciplinary,havepositiveimpactinatleastonerespect—that istheattitudesofteachersandlearnerstotheseinnovativepractices,whichusually involve the disciplines being called upon to help learners solve problems in some sort of inquiry classroom practice. It is difficult to extract this dimension, which also is clearly present in the mathematical modelling literature, from the fact of interdisciplinarityassuch.
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