Concepts for in-service teacher education Deliverable 4.3

This project has been funded with support from the European Commission.This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

Concepts for In-Service Mathematics Teacher Education:

Examples from Europe Stefan Zehetmeier, Manfred Piok, Karin Höller, Petar Kenderov, Toni Chehlarova, Evgenia Sendova, Carolin Gehring, Volker Ulm

1 Introduction1

Teachers are considered to play a central rolewhenaddressingprofessionaldevelopmentpro‐grammes:“Teachersarenecessarilyatthecenterofreform,fortheymustcarryoutthedemandsofhighstandards intheclassroom”(Garet,Porter,Desimone,Birman,&Yoon,2001,p.916).Ingvar‐son,Meiers,andBeavis(2005)sumup:“Profes‐sional development for teachers is now recog‐nisedasavitalcomponentofpoliciestoenhancethe quality of teaching and learning in ourschools.Consequently,thereisincreasedinterestin research that identifies features of effectiveprofessionallearning”(p.2).Inthepast20years,newlyemergingchallengesfortheteachingprofessionhaveresultedinanin‐creaseddemandforcorresponding(new)profes‐sionalcompetencesandanadequateframework(Posch,Rauch&Mayr2009).Untilthe1990s,theroleofteacherswasmostlylimitedtoofferingpre‐determinedcontentsinamannerthatisasclearandillustrativeaspossi‐ble, toensuringdisciplineandassessingperfor‐mance. This “static” culture of school‐basedteachingand learninghascomeunderpressurein recent years, both with regard to stu‐dent/teacher interaction and how classroomwork is defined in substantive terms. Increas‐ingly,thenormsapplicableatschoolareatvari‐ancewith thewealthofextramuralexperienceschildren and adolescents gather. As a conse‐quence, thereareeffortsto furtherdevelopandinstildynamicmomentumintothestaticcultureofteachingandlearning.The conditions of work and employment havechanged:Graduatesareincreasinglyexpectedtohavemulti‐functionalskills.Theyshouldbeabletoperformconceptual,planningandsupervisorytasks.Higherdemandsarebeingplacedinterms

1ThisintroductionisbasedonRauch,Zehetmeier&Erlacher(2014)andZehetmeier,Rauch&Schuster(inpreparation).

ofaself‐reliantdesignofworkprocesses.Andul‐timately–duetothegrowingcomplexityofworksettings– teamworkhasgained increasing im‐portance.Requirementssuchasthesehavecre‐ated a demand for what has been called “dy‐namic”skills,forself‐reliance,independentman‐agementanduseofknowledge,andasenseofre‐sponsibility.Thesocialisationwhichchildrenandadolescentshaveexperiencedbeforetheyenrolatschoolhasalteredsignificantlyinthepast30years.Familiestendtohavefewerchildren,whilsttheindividualchildplaysamorecentralrole.Therelationshipofparentsandchildrenhasshiftedtoonethatre‐volvesaroundpartnership.Whatisallowedandwhatisforbiddenismoreandmoretheoutcomeof a negotiating process between children andparents.Itiswiththisbackgroundofexperiencesthat children and adolescents come to school,projectingitontothisinstitution.Astheprevail‐ingworkcultureatschoolrestsonasocialmodelinwhichchildrenandadolescentsacceptauthor‐itariandecisionsofadults,theresultantpotentialforconflictisinevitablyhuge.Against this backdrop, teachers are facing chal‐lengesonaprofessionalandhumanscalewhichare novel in many aspects. KeyCoMath aims atchanges of pupils' learning. In particular, moreactive, exploratory, self‐regulated, autonomous,communicativeandcollaborative learning is in‐tended.Researchonthiskindoflearningusuallyfocuses on the students’ level. Questions liketheseareraised:Howcanstudents‘ learningbewelldefined?Howcanwedescribeandexplainstudents’ progress and difficulties? However,these changes of pupils' learning are based onchangesofteaching.Teachersdevelopexpertisetoarrangelearningenvironmentsinorderforpu‐pilstoworkintheintendedwayandtodevelopkeycompetences.Researchontheteachers’level

includesquestionslike:Howcanteachersbesup‐ported in activities dealing with this kind oflearning?Whatdowelearnfromresearchwhensupportingteachersinimplementingtheselearn‐ingactivities?Teachersareconsideredtoplayacentral role in planning, implementing, and re‐searching professional development pro‐grammes.This section provides some insights and exam‐ples,howvariouscountriesdeal(t)withtheseis‐sues. In particular, examples fromAustria, Bul‐garia,GermanyandSouthTyrolareprovided.

2 Austria: The IMST Project2

Whereasinthelastdecadesofthetwentiethcen‐turymanycountrieslaunchedreforminitiativesinmathematics and science instruction, or con‐cerning teaching and teacher education in gen‐eral,similarsystemicstepsinAustriadidnothap‐pen.Thisledtoabiggapbetweenintendedandimplementedinstruction,bothinschoolsandatteachereducationinstitutions.Althoughthepro‐motionofstudents’understanding,problemsolv‐ing, independent learning, etc. and the use ofmanifold forms of instruction and didactic ap‐proachesinmathematicsandscienceinstructionwereregardedasimportant,teacher‐centredin‐structionandapplicationofroutinesdominated.Retrospectively, it seems clear that the educa‐tional system needed an external impulse, andthis appeared in the late 1990s in the form ofTIMSS1995andlaterPISA.TheinitialimpulsefortheIMSTproject3inAus‐triacamefromtheTIMSSachievementstudy in1995. Whereas the results concerning the pri‐maryandthemiddleschoolwereratherpromis‐ing, the results of theAustrianhigh school stu‐dents(grades9to12or13),inparticularwithre‐gard to the TIMSS advanced mathematics andphysicsachievementtest,turnedouttobedisap‐pointing(andevokeddiscussionsoneducationalpractice,researchandpolicy,influencedbycriti‐cal reports in the media). The ranking listsshowedAustriaasthelast(advancedmathemat‐ics)andthelastbutone(advancedphysics)of16nations(seee.g.Mullisetal.1998,pp.129,189).Thisandotherindicatorsshowedthattheteach‐ingofmathematicsandscienceinAustrianeededashiftfrom“transmission”to“inquiry”.

2 ThisexampleisbasedonKrainer&Zehetmeier(2013)andZehetmeier&Krainer(2013).3IMST=originally,InnovationsinMathematicsandScienceTeaching(1998‐1999);later,Innovationsin

Asinmanyothercountries(seee.g.PrenzelandOstermeier 2006), the responsible ministry re‐actedtothesituation.InAustria,anationaliniti‐ativewiththeaimtofostermathematicsandsci‐enceeducationwaslaunchedin1998:theIMSTproject.Sincethen,thisinitiativehasundergoneseveraladaptionsandisstillrunning.IMSTwasimplementedinthreesteps:

1. The taskof the IMST research project (1998–1999)wastoanalysethesituationofuppersec‐ondarymathematicsandscienceteachinginAus‐tria and towork out suggestions for its furtherdevelopment.Thisresearchidentifiedacomplexpictureofdiverseproblematicinfluencesonthestatus and quality of mathematics and scienceteaching: For example, mathematics educationand related research was seen as poorly an‐choredatAustrianteachereducationinstitutions.Subjectexpertsdominateduniversityteachered‐ucation, while other teacher education institu‐tionsshoweda lackof research inmathematicseducation. Also, the overall structure showed afragmentededucationalsystemconsistingoflonefighterswith a high level of (individual) auton‐omyandaction,but little evidenceof reflectionandnetworking(Krainer,2003;seesummarizedinPegg&Krainer,2008).

2. The IMST² development project (2000–2004)focusedontheuppersecondarylevelinresponsetotheproblemsandfindingsdescribed.Inaddi‐tion,itelaboratedaproposalforastrategyplanfortheministry,aimingatimprovingtheinquiry‐based learning (IBL) of STEM in secondaryschools.Thetwomajor tasksof IMST²were(a)the initiation, promotion, dissemination, net‐working and analysis of innovations in schools(andtosomeextentalsointeachereducationatuniversity);and(b)recommendationsforasup‐portsystemforthequalitydevelopmentofmath‐ematics,scienceandtechnologyteaching. Inor‐dertotakesystemicstepstoovercomethe“frag‐mentededucationalsystem”,a“learningsystem”(Krainer,2005)approachwastaken. Itadoptedenhancedreflectionandnetworkingasthebasicinterventionstrategytoinitiateandpromotein‐novations at schools. Besides stressing the di‐mensionsofreflectionandnetworking,“innova‐tion”and “workingwith teams”were twoaddi‐tional features. Teachers and schools defined

Mathematics,Science,andTechnologyTeaching(2000‐2009);since2010‐motivatedbyaddingGer‐manstudiesasonemoresubject‐InnovationsMakeSchoolsTop.

theirownstartingpointforinnovationsandwereindividually supported by researchers and pro‐jectfacilitators.TheIMST²interventionbuiltonteachers’strengthsandaimedtomaketheirworkvisible (e.g., by publishing teachers’ reports onthewebsite).Thus,teachersandschoolsretainedownership of their innovations. Another im‐portant feature of IMST² was the emphasis onsupportingteamsofteachersfromaschool.

3.TheIMST3 support system(infourstages2004–2006, 2007–2009, 2010–2012, 2013–2015, afifthstage2016–2019isinpreparation)startedto implementparts of the strategyplan, amongotherwaysbycontinuouslybroadeningthefocustoallschool levelsandtothekindergarten,andalsotothesubjectGermanlanguage(duetothepoorresultsinPISA).TheoverallgoalofIMSTisto establish a culture of innovation and thus tostrengthen the teaching of mathematics, infor‐mationtechnology,naturalsciences,technology,andrelatedsubjectsinAustrianschools(seee.g.Kraineretal.2009).Here,cultureof innovationmeansstarting fromteachers’ strengths,under‐standingteachersandschoolsasownersoftheirinnovations, and regarding innovations as con‐tinuousprocesses that lead to anatural furtherdevelopmentofpractice,asopposedtosingularevents that replace an ineffective practice (formoredetailsseee.g.AltrichterandPosch1996;Krainer2003).

Forthe future, theministryexpressed its inten‐tiontocontinueIMST.Theoverallgoalissettingupandstrengtheningacultureofinnovationsinschoolsandclassrooms,andanchoring thiscul‐turewithintheAustrianeducationalsystem.

3 Bulgaria: How can Teachers be Supported in Inquiry-Based Mathematics Education with Focus on Key Competences

3.1 Background

To create a class culture inwhich the teachersandthestudentscouldworkasaresearchteamusing the ICT in support of the inquiry‐basedlearning has been the goal of a long‐term re‐searchinBulgariadatingfromtheearly80’s.Thefirst attempts are related with the ResearchGrouponEducation (RGE)–havingcarriedoutaneducationalexperimentlaunchedbytheBul‐garianAcademyofSciencesand theMinistryof

Education in 1979 (Sendov 1987, Sendov, Fili‐monov, Dicheva 1987; Sendova 2011). It com‐prised29pilotschools(2%oftheBulgarianK‐12schools)anditsmaingoalwastodevelopanewcurriculumdesignedtomaketheuseofcomput‐ers one of its natural components. The guidingprinciplesofRGEwerelearningbydoing,guideddiscovery, and integrated school subjects. TheRGEexperimentranfor12years.SpreadingthepositiveexperienceofRGEonabroaderscaleatthetimeturnedouttobeverydifficultforvariousreasons–botheconomicandpolitical.However,evenwiththeseisolatedexperimentsthelessonslearnedwerevaluable–the learners’ and teach-ers’ creativity alike can be enhanced when pro-vided with appropriate environments.At a university level new courses were intro‐duced, reflecting the need to prepare teachersworkinginthestyleofprojectbasedlearningandguideddiscovery learningpromoted in theRGEschools,e.g.attheFacultyofMathematicsandIn‐formatics at SofiaUniversity the curriculum forfuturemathematicsteacherswasenrichedbythecourseTeaching Mathematics in Laboratory Type Environment (Nikolova, Sendova, 1995). Afteryearsofstudyingandreproducingverysophisti‐catedmathematicalfactstheseteachers‐to‐beex‐perienced situations in which they could say:“Look atmy construction!”, “Can you provemytheorem?” (Denchev, Kovatcheva, Sendova2012).Suchaspiritofdiscoverywasexpectedtobe transferred lateron to their students.Still, anegative tendency (noticednotonly inBulgariabutalsointhemostofEasternEurope)wastheslowdeclineoftheeducationalsysteminthe90’sand the early 2000’s (Denchev, Kovatcheva,Sendova2012).

3.2 New Life for Inquiry-Based Learning

WiththeadventofpowerfulICTandspeciallyde‐signededucationalsoftwareformathematicsex‐plorations awaywas opened for inquiry‐basedlearning (IBL) in a number of European coun‐tries. Mathematics was an especially importantdomainofIBLthankstothedevelopmentandthedisseminationofdynamiclearningenvironmentsinwhichvariousexperimentswithmathematicalobjectscouldbeperformedleadingtotheformu‐lationandverificationofhypothesesofthelearn‐ersthemselves.Activitiesofthiskindwerethefo‐calpointoftheinvolvementoftheBulgarianKey-CoMath team members in previous European

projects,includingInnoMathEd, Fibonacci, Dyna-Math, Math2Earth, Mascil and Scientix(Kenderov2010;Kenderov,Sendova,Chehlarova,2012).Ourworkwithin‐serviceteachersisbasedontheunderstanding that for the teachers tobemoti‐vated theyshouldexperience thesame intellec‐tual pleasure we expect their students to un‐dergo.Theinquiry‐basedmathematicseducation(IBME)ispromotedbyourteamattwolevels–nationallyandlocally,inmajorregionalcentres.On a national level the promotion instrumentsareworkshops,seminarsandspecialsectionsofthenationalconferencesorganisedbytheUnionof Bulgarian Mathematicians. On a local levelIBME is promoted and supported by multipletraining andpresentation sessionsorganised infifteen Bulgarian regions with the help of localboards (Chehlarova, Sendova 2012; Sendova,Chehlarova2012).

3.3 Activities and Resources in Support of Inquiry Based Mathematics Education

The activities of the Bulgarian KeyCoMath re‐searchteamintermsoforganisingeventsandde‐velopingeducationalresourcesembracethefourlevelsoftheIBL:Level1‐ConfirmationInquiry,inwhichstudentsconfirmaprinciplethroughanactivitywherebytheresultsareknowninadvance;Level2‐Structuredinquiry,inwhichstudentsin‐vestigateateacher‐presentedquestionthroughaprescribedprocedure;Level3‐Guidedinquiry,inwhichstudentsinves‐tigate a teacher‐presented question through aproceduretheydesigned/selectedthemselves;Level4‐Openinquiry,inwhichstudentsinvesti‐gateaquestiontheyhaveformulatedthemselvesthrough a procedure they designed themselves(Banchi,Bell2008;Sendova2014).Hereisashortdescriptionofsuchactivitiesandresources:

PD courses (from 2 to 128 hours) Thesecoursesarebeingorganizedby the Insti‐tuteofMathematicsand Informaticsof theBul‐garian Academy of Sciences (IMI‐BAS) in theframework of European projects (InnoMathEd,Fibonacci, Mascil, KeyCoMath and Scientix), aswell as by sections of the Union of BulgarianMathematicians(UBM),bytheMinistryofEduca‐tionandScience,bypublishinghousesforeduca‐tional literature, and by PD centers. The maingoalofthecoursesisinharmonywiththemostrecent educational strategies for updating the

mathandscienceeducationintheECcountries:the development of key competences by imple‐mentingtheinquirybasedlearninginintegrationwith the world of work. These PD courses arebasedona teamwork(of the lecturersand theparticipants alike) and implement educationalmodelsadaptabletovariousschoolsettings.Thecrucialpartofthecoursesisfortheparticipantsto experience different stages and levels of IBLwithemphasisonkeycompetences.Each summer in the years 2014 and 2015 theKeyCoMathteamhasofferedtrainingcoursesforIBLforteachersinBulgariawhoarenotinvolveddirectlyintheprojectbutwanttolearnandusethemethodsofIBL.Theteachersworkonpeda‐gogicalproblemsrelatedwith: reformulatingmathproblemsinIBLstyleso

as to enhance the development of specifickeycompetences;

formulating their own math problems re‐flectingreal‐lifesituations,notsolvablewiththecurrentmathknowledgeofthestudentsbut allowing for explorations by means ofdynamicgeometrymodelsleadingtoagoodenoughapproximationofthesolution;

studyingandproposingmethodsfortacklingproblemswhichareunstructured,orwhosesolutionsareinsufficientorredundant;

solving “traditional problems” with “non‐traditional”data,forwhichtheuseofacom‐putingdeviceisnecessary;

applying game‐design thinking soas to en‐gagebetterthestudentsintheproblemsolv‐ing;

formulatingmorerelevantevaluationcrite‐riaforthestudents’achievements;

project‐basedworkwithpresentationoftheresults;

assessmentoflearningresourcesintermsofformationanddevelopmentofIBLskillsandkeycompetences(Kenderov,Sendova,Cheh‐larova2014;Chehlarova,Sendova2014).

Thecourseshavetwophases.Inthefirstphase(3daysinthebeginningofthesummer)theteach‐ersbecomeacquaintedwiththedynamicgeome‐trysoftwareGeoGebraaswellaswithplentyofexamplesofhowtousedynamicscenariosintheIBLstyle.Theparticipantsofthecoursesareas‐signedprojectsasa“home‐work”.Inthesecond“follow‐up” phase (with duration 1‐2 days andconductedattheendofthesummer)thepartici‐pants present the advancement in thework ontheirprojectinfrontoftheotherparticipantsinthecourse.

PD events (seminars and workshops) in the frames of conferences Thekeyfeatureofthese eventsisthattheteach‐ersplayanactiveroleandactaspartnersinare‐searchteam–theysharetheirgoodpracticesinoral or poster presentations (sometimes jointlywiththeirstudents),work ingroupsonspecifictasks and present their ideas to the rest of theparticipants.TypicalexamplesincludetheScien-tix National ConferencewithintheNationalsemi‐narInquiry Based Mathematics Education,theDy-namic Mathematics in Educationconference(Fig.1),theseminarswithintheSpringconferencesofUBM, theregionalconferencesorganizedbyUBMsections, the International UNESCO workshopQED(Chehlarova2012;Sendova2015).

Fig 1. The Scientix National Conference demon-strated good practices of teachers implementing IBL with emphasis on specific key competences

The inquiry based learning, its connectionwiththeworldofwork,goodpracticesandproblemsdirectedatthedevelopmentofspecifickeycom‐petences,havebeen the focusofourworkwithin‐serviceteachers:

Using specific learning scenarios in support of IBL Agood repositoryofsuchresourcesistheVirtual School Mathematics Laboratory (Fig. 2,http://www.math.bas.bg/omi/cabinet/) beingdevelopedbyIMI‐BAS(Chehlarova,Gachev,Ken‐derov,Sendova,2014),whichcontainsover800scenarioswithdynamicfilestransparentfortheusers. Theway teachers are encouraged to usetheseresourcesistostimulatestudentstobehavelike working mathematicians: to make experi‐ments,tolookforpatterns,tomakeconjectures,toverifythemexperimentally,toapply“what‐if”strategies so as tomodify/generalize the prob‐lem,andeventousethemasapreparationforarigorousproof.Todo thiswithout leaving theircomfortzone,theteachersentertheroleoftheir

studentsandexperiencethesametypeofactivi‐ties during our courses, and when working ontheirown.They firstuse thedynamic files sup‐porting the scenarios as a ground for explora‐tions.Thenextstepforthemistoproposeappro‐priatemodificationof the files forsimilarprob‐lems,ortousethemasamodelforcreatingoneoftheirownfromscratch.Thus,itwouldbequitenatural for them to tell the students: “I don’tknowtheanswer,but Ihope to find it togetherwithyou,thankstoYOURefforts,toourjointef‐forts…”

Fig. 2. Virtual School Mathematics Laboratory: dy-namic files for the open problem on finding the lo-cus of a regular m-gon inscribed in a regular n-gon

Building and developing competences necessary for the students to participate in new types of mathematics contests Examples are “Mathematics with a computer”and“Themeofthemonth”(Fig.3,seeKenderov,Chehlarova2014;Chehlarova,Kenderov2015).

Fig 3. “Theme of the month”: an invitation for a long-term activity on a chain of math problems modeling real-life situations

Mathematics performances Eventsraisetheawarenessofthegeneralpublicabouttheroleofmathematicsforenhancingchil‐dren’sscientificcuriosityandendeavortolearn.The examples include: Performance at the His‐toryMuseum in Stara Zagora, organizedby theUBM section in the town, performances duringthe Researchers’ Nights (2011‐2015), Sciencefestivals (in Italy, Romania, Greece). It is im‐portanttonotethattheteachersactasmultipli‐ersoftheIBLideasduringtheseeventsaswell–they participate with their students, and occa‐sionallyleadtheperformance.

Fig. 4. Posters for math performances within Sci-ence Fairs and Researchers’ nights

Individual work with teachers Itincludessupportforthedevelopmentofales‐son, educational materials, mathematical festi‐vals,courseprojects,peerreviews,andprepara‐tionofapedagogicalexperiment.

Activities in support of the Open Inquiry The fourth level of IBL (the Open Inquiry) hasbeen promoted to reach teachers and studentsfromalloverthecountrywithpotentialtodore‐searchinmathematicsandinformatics.ThishasbeendoneintheframesoftheHigh‐SchoolStu‐dents’ Institute ofMathematics and Informatics(HSSI) where secondary school students work

(underthesupervisionofamentor)ontheirownprojects,focusedonthestudyofagivenproblemfromMathematics, Informatics and/or IT (Ken‐derov, Mushkarov, Parakozova 2015). The stu‐dentsdelivertheirresultsandfindings,inwrittenandoralform,infrontofajuryandpeersattwosessions – in January and April. A three weekSummer School is organized for the involvedteachersandthebestachievingstudents.Duringthe SummerResearch Schools special seminarsfor teachers are organized. During these semi‐narsexperiencedteacherssharetheirgoodprac‐ticesinmentoringstudentswithhighpotentialindoing research, andprofessional researchers inmathematicsandinformaticstogetherwithPhDstudents (HSSI alumni)deliver lectureson con‐temporarytopicsinthesefieldssuggestingpossi‐bletopicsforfutureresearchprojects.

3.4 The Main Achievements

A community of teachers who implement andspreadtheinquirybasedlearningofmathematicsand informatics has been created. Theypartici‐pateinpedagogicalexperimentsnotonlyasare‐ality‐proofofresearchersbutasmembersofare‐search team.These teachers implement,modifyanddevelopfromscratcheducationalresourcesin support of IBL, share their good practices atseminars,nationalandinternationalconferencesandinprofessionaljournals.Someofthemorgan‐izepubliceventsataschoolandregionallevelforpopularizingtheinquirybasedmathematicsedu‐cation.TeachersarealsokeyfiguresinorganizingthenewmathematicscontestsMathematics with a computer andTheme of the month, inmakingthemknowntoabroaderaudience.

Thefurthergoalistoreachfasterandmoreeffec‐tivelylargergroupsofotherteachersandschoolstudentsinacquiringtheIBLapproachwithfocusonthedevelopmentofkeycompetences.TheactivitiesoftheHighSchoolInstituteofMath‐ematicsandInformaticsandtheteachersresultsareencouraging.For its15yearsofexistence ithasprovedthatresearchpotentialofthestudentsshouldbesupportedanddevelopedstartingataveryearlyagetogetherwiththedevelopmentofother important competences including teamworkandpresenting(orallyandinwrittenform)tovariousaudiences.Someofthestudents’find‐ingswereonsuchahighlevelthattheywerepub‐lished(andinsomecasesquotedbyspecialists)in mathematics research journals. The HighSchoolStudent’sInstituteplaysanimportantrole

withrespecttothedisseminationofIBLbecausethe participating students (and their mentors)arecomingfromdifferenttownsinthecountry.AnotherpositiveeffectisthatanumberofHSSIalumni act as mentors (virtually and face‐to‐face),thuspassingthetorchontothenextgener‐ationofyoungresearchers.

4 Germany: Multipliers Concept for the Urban Network of Primary Schools

TheUniversityofBayreuth,Germany,developedapractice‐basedmultipliersconceptforanurbannetworkofprimaryschoolswith theaimtode‐velopmathematicseducationandtosupportpu‐pils’keycompetences.The idea is implementedon a local scale and addresses primary schoolteachersofthecityAugsburg.Theconceptisre‐alisedwithintheframeworkoftheEuropeanpro‐ject KeyCoMath. 28 primary schools are takingpartinaface‐to‐faceprofessionaldevelopment.

4.1 Involved Parties

Ontheurbanscale,theUniversityofBayreuthco‐ordinates,organisesandsupervisesactivitiesfortheprofessionaltrainingofprimaryschoolteach‐ers. It works directly with a group of qualifiedmaths teachers as coaches for teachers' profes‐sional development. These teachers with theiradvisoryfunctionformalinkbetweenuniversityandschoolandbetweenscienceandpractice,be‐causetheyareresponsibleforappointedmathe‐maticaltutorsfromprimaryschoolsintheentirecity.

4.2 Organisation

TheChairofMathematicsandDidacticofMathe‐maticsisregularlyincontactwiththelocaledu‐cationauthorityandwithninededicated teach‐erswhowereassignedtobecomeadvisorsduetotheirhighprofessionalexpertiseandtheirinno‐vationcapacity.Groupsoftwoorthreeteacher‐advisorsguide28primaryschools in theentirecity. Therefore, a classification into four schoolgroupsaccording to location (north, south, eastand west) has been assigned. Every primaryschoolappointsatleasttwomathematicaltutors– oneresponsible forthefirstandsecondform,the other for the third and fourth form. Hence,oneschoolgroupconsistsofaminimumoftwelve

mathematical tutors who will further intro‐duce/present newly gained acquaintances totheirlocalcolleagues.

4.3 Functions

TheteamattheUniversityofBayreuthhassev‐eralduties: theykeep in touchandmakeallar‐rangements with the local education authority.Teacher‐advisors are appointed and meetingsare summoned.Theyprovide an academic sup‐portforschoolsandmakefundsaswellaslearn‐ing and teachingmaterials available. Above all,they operate a hosting platform for the infor‐mationandmaterialexchange.Theninemathe‐matical teacher‐advisors meet the universityteam regularly and they organise and guideschool group meetings. There, they assist themathematical tutors in planning teaching units.Thetutorstakeanactivepartinthemeetingsintheirassignedschoolgroup.Theyprepareandre‐alise planned mathematical lessons and docu‐mentteachingapproaches.

4.4 Activities

Once a year, amajor event for all involvedpri‐mary school teachers takesplaceat theuniver‐sity.Suchameetingconsistsofalecturetoasu‐perordinate topic like developing key compe‐tencesbymathematicseducation.Theattendingteachersreceivetheoreticalinputandadoptitaf‐terwards inworkshops.The inclusionofpupils’utterancesandsolutionprocessesconditionedbythestudyofpupils’writtenexercises,calllogsorvideoshotsdemonstrateshowchildrenoperateinaspecificlesson’ssequence.In addition, every local primary school has thepossibility to book in‐house advanced trainingcoursesforitsteachingstaffaccordingtothere‐quirements. Normally, four school groupmeet‐ingsperschoolyearareorganisedbytheteacher‐advisors. For thesemeetings, themathematicaltutorshavetopreparethefollowing:Theyprevi‐ously realise a teaching unit in their own classand collect pupils' approaches. Above all, themembersofaschoolgrouporganisejointvisitstoclasses, compare their varying approaches ofteachingonthesamespecificmathematicaltopic,togetherreflectonone’sownworkandexchangetheir ready‐made experiences, wherebymathe‐maticseducationcanberefined.

Thefocusisnotsolelysetonspreadingteachingmaterialsandongivingrecommendationsforles‐sons.Theobjectiveof theproject lies toagreatdegree on developing the level of inner convic‐tionsandbeliefsteachershaveoftheirsubject,onteachingandlearningprocesses,andtheirroleinthelessons.Theseplayamajorrolefortheplan‐ningandimplementationoflessons(Blömekeetal.2010;Kunteretal.2011).

4.5 Experience

Thismultipliersconceptfortheurbannetworkofprimaryschoolshasprovenitselfoveryearsandwillbecontinuedinfuture. Acoordinatorsays:“It is encouraging to witness how mathematics education progresses at many primary schools in Augsburg, how teachers set out together to develop good mathematical assign-ments and how they bring teaching concepts of the common retrospect into question and thus improve them. By observing the children, I recognized their growing interest for mathematical issues, their creative dealing with numbers, patterns and struc-tures, a greater openness for mathematical obser-vations of everyday life and an increasingly safer handling with basic mathematical skills and abili-ties. The cooperation with school administration (education authority, administration) is successful because of good personal contacts.”

Theinvolvedprimaryteachersworkasmultipli‐ersduring their leisure time, includinganaddi‐tionaleffortintheirdailyworkload,whichisun‐fortunately neither compensated nor squaredwith class hour reduction, but which demon‐strates the commitment of the participatingteachers–since"Staying still means taking a step back"(ateacheradvisor).

Concerningtheobservationoflessons,itisnotal‐wayseasytofindavolunteerwillingtopresenttheown teaching approach to colleagues.How‐ever,thisriskiseffectivelypreventedbytheofferof a joint preparation of classes. "I can work through exciting new ideas and discuss problems with motivated colleagues. Instead of sitting alone in my room I have many like-minded people around me."(aparticipatingteacher)and"At the moment it's the only opportunity to get a direct look at the work of my colleagues. I can challenge myself with the implementation of the curriculum and at the same time receive inspiration through the teachers and their contact with students. Eve-

ryone learns from each other in a relaxed atmos-phere without the pressure of being judged." (ateacherwhoisonparentalleave)

5 South Tyrol: Cooperative Design of Learning Environments

IntheframeworkofKeyCoMaththeGermanDe‐partmentofEducationinSouthTyrolorganisedateacher training for thedevelopmentof compe‐tence‐focusedtasksformathematicseducationatsecondary schools. In a series of meetings theteachersweremadeacquaintedwithpedagogicalanddidacticaltheoriesconcerning openquestions, networking, individuallearning, dialogiclearningand assessment.

The participants, working in teams, developedtasksfortheirownlessons.Theseweretestedintheclassesandthen,afteracommonreflection,optimised.Thetasksfocusedontheacquisitionofmathematicalcompetences,butalsooncommu‐nicative,socialanddigitalcompetences.Thebestpracticeexamplesofthetaskswerepublishedina printed book „Tasks for competence‐focusedteachingofmathematics“(Höller,Ulm2015)andonthewebsitewww.KeyCoMath.eu.

Strategies for Teachers’ Professional Development Particularly valuablewas the commonwork ontasksintheteamofteachers–fromtheconcep‐tiontothereflectionandoptimisation.Therefore,theplanningoffurthertrainingsessionswillnotonlyincludecontentsandmethods,butalsowaysof cooperative learning. The cooperation of theparticipantswilltakeplaceas: teachingdevelopmentinpeergroups, commonlearningwithmutualobservation, exchanging views through e‐learning plat‐

forms.Thefocusliesonthedevelopmentofteachingbythecommondesignoflearningenvironmentsforstudents.Moreover,theissueofevaluationisin‐cluded.

Thesebasicstrategiesforteachers’professionaldevelopment are shown by the following dia‐gram:

Fig. 5. Teachers’ professional development by working with learning environments

6 Conclusion

IntheprojectKeyCoMathpartnersfromeightEu‐ropean countries developed concepts for inno‐vatingmathematicseducation.The focus layonsupportingstudents’keycompetences.Althoughtheapproachesinthedifferentcountrieshadtoconsidernationalframeworks,acommonpatternofthestrategiescanbeidentified.

Aiming at Teachers Thekeypeopleforinnovationsinschoolaretheteachers. Their beliefs, motivation and profes‐sionalexpertisearecrucialforeverydayteachingand learning. Thus, KeyCoMath focused on theteachers’professionaldevelopment.

Networks of Schools Since learning is a social process, regional net‐worksofschoolswereestablished.Theyofferedframeworksforteachers’exchangeofexperienceandfortheircooperativelearning.

Coaches for Teachers’ Professional Development Theregionalschoolnetworkswereledbyacoachorateamofcoacheswhocouldbee.g.veryexpe‐riencedteachers,teachereducatorsorscientists.Theteachersweremadefamiliarwithgeneraldi‐dactical andpedagogical concepts.They relatedtheseideastotheirdailyworkatschool;theyde‐signedlearningenvironmentsfortheirstudents,andusedthemintheirclasses.Theteacherspre‐sented,discussedandreflectedtheirexperiences

cooperativelyintheirnetworkofschoolsguidedbytheircoach.

Aiming at the Meta-Level Initiativesforsubstantialinnovationsoftheedu‐cational systemshouldaimat themeta‐level ofteachers’attitudesandbeliefs.Thisconcernse.g.theroleof the teacher, theroleof thestudents,thenatureofthesubjectsandgeneralaimsofed‐ucation.

Development of Learning Environments Tobridge thegapbetween theoryandpractice,teachers individually and cooperatively devel‐oped learning environments for their students,workedwiththeminclass,optimizedthemonthebasisofallexperiences,andexchangedanddis‐cussedthemintheirschoolnetwork.Thus,byde‐signingandworkingwithspecificlearningenvi‐ronmentsteachersbecameacquaintedwithgen‐eral pedagogical ideas. Learning environmentsfunction as tools for systemic teachers’ profes‐sionaldevelopment.

Areas of Activity Participating schools and teachers should con‐centrateononeorafewareasofactivity,e.g.ex‐ploratorylearning,promotingstudents’coopera‐tion,cumulativelearningorfosteringkeycompe‐tences. Such bounded fields of activity enableteacherstobeginwithsubstantialchangeswith‐out the risk of losing their professional compe‐tenceinclass.

Universities as Innovation Centres Intheseprocessesteachersandcoachesreceivedguidance and advice from universities. Theyservedas innovationcentres for teachereduca‐tion. They provided regular and systematic in‐serviceteachereducationoffersandcoachedthecoaches.

(Inter-)National Teacher Education Teachers and teacher educatorsweregiven theopportunity to exchange experiences with col‐leaguesandtoparticipateinprofessionaldevel‐opment offers on a regional or anational level.Theyunderstood thatproblems andnecessitiesofinnovationshavesystemiccharacterandcon‐cern the fundaments of education far beyondtheirownprofessionalsphere.Moreover,theyre‐ceivedideasforinnovationactivitiesfromalargecommunity.

Input

Cooperation

DevelopmentofLearningEnvironments

TeachinginClass

Reflection

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