Mathematics Teachers as designers: an international perspective

Chair: Birgit Pepin Eindhoven University of Technology, NL Panel: Michele Artigue Verônica Gitirana Binyan Xu Takeshi Miyakawa Kenneth Ruthven

Structure of the session •  Introduction(bythechair)(10minutes)•  EachpanelparticipantanswersthefollowingthreeW-questions(approx.10minuteseach):– Whyareteacherdesignactivitiesrelevant?Whywouldtheydesign?

– Whatwouldteachersdesign?Whatarethemostinteresting/challengingdesigntasks?

– Howwouldteachersdesign?Whatsortsofdesignapproacheswouldtheyuse,andunderwhichconditions?

•  PlenaryDiscussion(30minutes)

Teacher Design Capacity (Pepin, Gueudet, & Trouche 2017)

•  Agoal,orpoint/sofreference,forthedesign•  Asetofdesignprinciples:(a)firm/robustand(atthesametime)(b)didacticallyflexible

•  “Reflection-in-action”typeof(oftenimplicit)understandings

Michèle Artigue Université Paris-Diderot France

Some contextual characteristics •  TheIREMnetworkand

thespecificityofthisstructureinwhichmixedthematicgroupsdevelopadesignactivity.

•  ThefactthatdesignisconsideredanormalteacheractivityintheFrencheducationsystem.

•  Thediversityofexistingresourcesandsourcesforthese.

Why, What, and How?

•  Answersdependontheexactmeaninggivento‘designactivity’.

•  IadoptawidevisioninlinewithDAD,includinginitanyformofcombination,complementation,andredesignofexistingresources(design/Design).

•  Withinthisvision,thisisclearthatteachersdodesign.

Why? Whatneedsdoteacherdesignanswer?Whatdoesthisdesignoffermoreglobally,beyondansweringteachers’personalneeds?

Externalresourcesthatteachersaccessalwaysaresomekindsofgenericobjects

Adaptationwhennotatallanticipatedmustbemadeonthespot,whichissourceofworkoverloadandcounter-productivedidacticdecisions

Teachers’designactivity,ifcarefullysupported,canbeanessentialcomponentoftheirprofessionaldevelopment

Teachers’experienceandspecificexpertiseisnecessaryindesignteams

What?

Whatwouldteachersdesign?Whywouldwelimittheextensionofteacherdesign?

Whatarethemostinteresting/challengingtasks?Interesting/challengingforwhom?Theindividualteacher?Somecollective(s)hebelongsto?Others?

SomeexamplesofchallengingdesignactivitiesinmyrecentIREMactivities:•  designingforrealinterdisciplinary

projects,takingintoaccountthesystemicconditionsandconstraints;

•  designingsequencesoftaskscombiningtheprogressionofmathematicsknowledgeandthatofmoretransversalcompetences,suchasmodelling.

How? •  TheICMI-Study22bookmakesclearthediversityof

possibleanswerstothisquestion.

•  IntheFrenchdidacticculture,TDSandnowATDwiththeconceptofSRP,themodelofdidacticalengineering,obviouslyinfluencethevisionofpossibleanswers.

•  Personally,andcertainlyduetomyIREMexperience,Iamespeciallysensitive:–  totheaffordancesofcollective,iterativeandreflective

designforteachers;–  totheimportanceofdesigningsequencesprovidinga

teachingprogression,andtakinginchargethedifferentmomentsofthestudyprocess;

–  tothedifficultiesthatwestillmeetathavingresearchknowledgetakenintoconsideration.

The design double-bind?

Kenneth Ruthven, University of Cambridge UK

Apossbileimage?

Teacher design

•  [We]regard“design”asthepracticeofdesigningforteaching,asinlessonpreparation(thatisdesignbeforeenactment),aswellasinteaching,whatwelabeledas“design-in-use”thathappensduringenactmentoftheresources/materials

•  [A]ccordingtoBrown(2009)teachers’pedagogicaldesigncapacity(PDC)isthecapacitytoutilizeandtransformexistingcurricularresourceseffectively,andtodesign/createnewmaterials,forthepurposeofeffectivemathematicsinstruction

(Pepin,Gueudet&Trouche,2017)

Double bind

•  asituationinwhichapersonisconfrontedwithtwoirreconcilabledemandsorachoicebetweentwoundesirablecoursesofaction

Freedom, workload and retention: National survey of mathematics teachers

•  Likelihoodofremaininginteachingassociatedwith:–  Levelofsatisfactionwithworkinghours(r=.22)–  Levelofsatisfactionwithfreedomtoteach(r=.22)

(NFER,2006)

0% 20% 40% 60% 80%100%

Freedomtoteachinthewayyouchoose

Thehoursyouspendworking

1Verydissatisfied

2

3

4

5Verysatisfied

The design double-bind

•  Teachersatisfactionderivesfrom–  Exercisingfreedomtoteachasyouchoose(i.e.undertakingteacherdesign)

–  Havingreasonableworkinghours•  However(giventhenumberoflessonsthatteachersare

expectedtoteacheachday,aswellastheotherdutiesthattheyarerequiredtofulfill)thisproducesadouble-bind,wherein:–  Exercisingfreedomtoteachasyouchoose(i.e.undertakingteacherdesign)increasesworkinghourstoanunreasonablelevel

Teacher design •  Howmuch?

–  Teachersshouldbeexpectedtoengageindesignonlytosuchanextentthattheirworkloadremainsreasonable

•  Why?–  Thosedesignactivitiesthatteachersdoundertakeshould:

–  Increasethesatisfactionthattheyderivefromteaching–  Clearlyhelpimprovethequalityoftheirteaching

•  What?–  Whatevercanbeshowntosatisfythecriteriaabove

•  How?–  Howevercanbeshowntosatisfythecriteriaabove

Takeshi Miyakawa Joetsu University of Education Japan

Resource design

•  Who?–  Ingeneral,teachersshouldnotbeexpectedtodesigntheirowncurricularresources

–  Suchresourcesshouldbedesignedbyhighlyskilledteams,includingmemberswhohaverelevantteachingexperienceandwhohaveparticularexpertiserelevanttothecurricularaimsoftheresources

–  Atthesametime,suchresourcesshouldbetrialledbyordinaryteachers,refinedinthelightofinsightsgainedthroughsuchtrialling,andshowntobeeffectiveinasuitablywiderangeofcircumstances,beforebeinggenerallydistributed

Why are teacher design activities relevant? •  Inordinaryteaching

– Useoftextbook– Rolesofteachers:teacherdesignervsteacherfreetextbook

•  Professionaldevelopment– LessonStudyinJapan– Practiceresearch(oractionresearch)

What would teachers design?

•  FromJapaneseperspective– Taskdesign– Lessondesign

•  FromATDperspective– Levelsofdidacticcodetermination(cf.Chevallard,2002)

– “Thematicconfinement”(cf.Barbéetal,2005)

CivilisationSociety

School

PedagogyDiscipline

DomainSector

Theme

Subject

How would teachers design? •  LessonStudyinJapan

Discussion of task in a small group

Task design Lesson design and writing of a lesson plan

Discussion of lesson plan in a bigger group

Trials in class

Open lesson

Discussion of a lesson

Writing of a report

Collectifwork

Individualwork

1monthormore

Binyan Xu East China Normal University China

– Whyareteacherdesignactivitiesrelevant?Whywouldtheydesign?(BinyanXu)

•  InChina,ateacherplaysmultiplerolesinschool– Doteaching– Doresearch– Doconsulting–  Lifelonglearner

EducationalTasks:Todevelopstudents’abilitytoanalyseandsolveproblems,tobuildtheselfconfidence、selfesteemofstudents….

PlayingtheserolesRealizingeducationaltasks

Structuredknowledge

Sequenceoflearningtask

Creativestrategy

Evaluationofprocess

Adjustmentofprocess/strategy

ReflectsomeNaturesofDesign

– Whatwouldteachersdesign?Microlevel:–  learningtargetsofeachlesson–  Sequenceofmathematicstasks–  Assessmenttools–  Lessonplan

•  Macrolevel:–  Teachingresearchproposefocusedonpracticesproblems–  OnlinewholeLearningplan(学案)–  Professionaldevelopmentprogram

•  Whatarethemostinteresting/challengingdesigntasks?– Tasksthatarousestudents’interestingandexploration(HPMperspectives)

– Taskthateliminatestudents’misunderstanding(variation)

– Taskthatpresentinter-relationbetweenmathematicsandothersubjects(STEM)

•  Howwouldteachersdesign?Whatsortsofdesignapproacheswouldtheyuse,andunderwhichconditions?

Actioneducation-designresearch

•  Actioneducationoffersoneeffectivewayforteachersandresearcherstocollaborate,sothattheymayimprovethemselvesthroughlearningfromeachother.Thiscontributestotheresolutionofthe“missingparadigm”inteachers’professionallearningandtothedesignofmoreeffectiveandrealisticlearningprogrammes.

•  ActionEducationusesthe“scientificdiscoverytheory”andfeedbackmechanisminthedevelopmentalprocess.Teachersagreetotryatheory-basedideafromtheresearchers,withthehelpofawell-establishedmechanismforcollectingfeedbacksystematicallyandregularly.Intheprocessofdecisionmakingthereisstronginteractionbetweenexperienceandtheory,whichinformeachother.

The procedure of the model of Action Education is as follows.

•  Step1.Agroupofteachersinvitesoneortworesearcherstostudyrelatedmaterialsandsharetheirviewsandexperiencewiththeaimofenrichingteachers’professionalknowledgeofeducationaltheory.Theycanchooseaspecificlessonasacasefordiscussioninordertolookforwaystoimprovetheirpedagogicalskills.

•  Step2.Colleaguesandresearchersparticipateinobservationoftherevisedlesson,reflectontheeffectivenessofthislesson,andmakeamendmentstothelessonplan.

•  Step3.Therevisedlessonisimplementedandisfollowedbypost-lessondiscussionandtheteacher’sreflectivewritingontheprocess.Suchaprocessisrepeatedseveraltimesineachschooltermsoastosetupaknowledgebasefor“actioneducation”.

Teacher as designer of curriculum materials: some contributions from Brazil

Verônica Gitirana LEMATEC – EDUMATEC Federal University of Pernambuco, Brazil FinancialSupport

Questions

Teachers’documentationgenesis–Gueudet,Pepin&Trouche(2012)In-serviceandpreserviceteachers’trainingCurriculumergonomic–Chopinetal(toappear)

Whyareteacherdesignactivitiesrelevant?

Whatwouldteachersdesign:actions,orartefacts?Whatarethemostinteresting/challengingdesigntasks?Howwouldteachersdesign?Whatsortsofdesignapproacheswouldtheyuse?Wouldtheydesignindividually,orcollectively?Underwhichconditions?Short-term,orlong-term?

Iwillpointoutsomeinterestingdesigntasks,thatinvolvesdesigncurricularmaterials,andactions,onhowtouseit.

Itwasinspiredoninstructionaldesigntogetherwithreflectivemethodology(fromDAD),inacollectiveprocessofdesignforlong-term.

Brazilian social and cultural diversity

Cultural and social diversity

Inequality on Regional distribution

Curriculum Ergonomic

Howtohaveeffectiveusecurriculummaterialinthisculturalandsocialdiversitywithinequalityofrichnessdistribution?Remillard(2018)-ALookacrossCulturalBoundariesTheimportanceofteachers’knowledgeabout:•  students’knowledgeandbehavior;•  students’socialreality–relevantproblems;•  students’timetodoeachtask;•  schoolcommunity.

In-service teacher training Project - Game with recycle material in Mathematic Education Gitiranaetal(2013)-ProjectwithSecretaryofEducationIn-serviceteachertrainingproject2835teachers,whoteachmath.Activitiesdevelopedintheproject:•  Re-designamathgameusingwaste;•  Designactivitiescontextualized

withinthegame;•  Designamodellinglessonbasedon

constructingthegamewithwaste;•  Testitwithpupils;•  Writeatextaboutthemathgame;•  Publishtheresults;•  Trainothersteacherstouseit.

Pre-service teacher training project

Gitirana,V.ProjectoftheStageSenioryearTrouche,Rodrigues,Lucena,BellemainAprojectofpre-servicemathteachertraining–15students,workinginfourmathgamere-design.Activities:•  Constructamapofresource•  Playingwithmathgameandanalyzemath

mobilized;•  Re-designamathgame;•  Describeit;•  Testit;•  Investigateitsuse;•  Writeaboutthisinvestigationonweb-

base(web-doc);•  Sharethegameandtheresults,as

productandasaresearchactionintheweb.

AtwoyearsProject.

InitialTeachers’Education

Documen-tationgenesis

Collabora-tiveWork

Design/Beingauthor

Research

Web-doc

Publish/Share

Principles

Dothetaskassimpleaspossible

Immersion

Contentmobilized

Playingwithamathgame

Difficultyonidentifyingmathonplaying

Prototype

Createcurricularmaterial(CM)

Recreateamathgame

Testwithspecialists

AnalyzethecontextofCM

Testthegamewithcolleagues

Obstaclesonludicaspects/board

Resourcetransparence

Relateplaystrategy/mathknowledge

Testinclass

Analyzedidacticaspects

Testthegameinaclass

Pupils’playsrevealplaystrategy/Knowledge

Discovernewcontentsmobilized

Mapp of prospective teachers’ documentation

Design

Teacherstraining

Session

Mathknowledge

Motivation

Context/game

Curricularmaterial

Mapp of prospective teachers’ documentation

Analyzetheresults

Analyzeandwritetheexperience

Writeabouttheexperience

Roleofcurricularresources–ident.Pupils’difficulties

Flexibilitymathcontent/schoolgrade

Students’voicesandstrategies

Obstaclesonludicaspects/board

Redesign Documenttheproduct

Writeaboutdidacticaspects

Organizetheweb-doctoshare

ArguebasedondataPredictnewstrategies

Share

Discussabouttheirmathgame

PresenttheirWDinthecourse

Ownrequesttodoanothertestinclass

Design

TeacherTraining

Session

Mathknowledge

Motivation

Context/game

Curricularmaterial

Conclusions

Whyareteacherdesignactivitiesrelevant?

TeacherdesignactivitiesisrelevantinculturalandsocialdiversitycountryasinBrazil,becauseweneedteachersflexibilitytorecreateactivitiesadequatetotheirculturalandsocialcontext.Integratingtheactor(teacher)whoknowsbetterdidacticvariablesoftheirownstudents–motivation,times,previousknowledge,andallthevariablesoftheirownwork.

Conclusions

Whyareteacherdesignactivitiesrelevant?

Itshowedtobearelevantsetofactivitiesforteacherstraining–redesignamathgame,write,test,redesign,investigate,andpublish,inalong-termdesignprocess,because:•  Beinganauthorisamoment:tobeinvolvedinareflect;toshortenthe

timetheyconsidersomeimportantresourcesintheirdocumentation,suchaspupils’voicesandobservingtheirstrategiesasaresourcetorethinkteachingaspects;

•  Itshowedtobeana-didacticalsituationforteachers’training–theyassumeastheirproduct,andthewaytheyperceiveit’swelldoneornot.

•  Libertytothink,creativitytoinnovate,self-confidence;•  Changetheirbehaviorrelatingtotheerror.Theystartedtospeakabout

theirownerrorortheabsenceofknowledge.

Plenary Discussion