Keynotepresentation

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Becomingun-DisciplinedwithScienceandMathematics JulianWilliams

The University of Manchester, UK

Abstract STEM, if it is to be more than a political arrangement of convenience aiming to coral industry-government funding and marginalize the others’, seems to imply inter-disciplinarity in the service of problem-solving that speaks to ‘real’ concerns of humanity. Exploring the historical and cultural roots of disciplines and inter-, trans-, and un-disciplinary activity dialectically, I propose a theoretical perspective that draws (pace Foucault) on power-knowledge in discourses, and (pace Bourdieu and Activity Theory from Vygotsky and Bakhtin) on theories of field, activity/practice, and identity/subjectivity. The main substantive conclusion is that in the disciplinary landscape of academe, the problem-solving Subject is not only ‘disciplined’ but can also better be ‘un-disciplined’, and self-consciously so. Thus not only the disciplines of STEM¹, but also STEM itself is negated by its practice ‘outside school’, addressing interests that might challenge the STEM-elites.

IntroductionI aim in this talk to think with you about where STEM is or should be going in education, and I hope we will take seriously the idea that educating for STEM is not just about feeding industry and the economy with the workforce it—or the government—thinks it needs. Rather, I want us to be concerned for the wider problems and needs of humanity, of our communities, and of the learners or students we work with. I will suggest this involves interdisciplinarity, but goes beyond that, to a certain kind of lack of discipline that is aware of the disciplines but not ultimately limited or disciplined by them. I realize there is a contradiction here: how to be disciplined and undisciplined at the same time—we will get to that soon. Along the way I will visit some of the practical work we in Manchester have been engaged in with schools and colleges, but also some of the theoretical work that has informed us, and that is relevant to this discussion. I know many, perhaps most teachers do not like talk of theory in education. But don’t you think it is strange that we spend most of our teaching day teaching children theoretical concepts in mathematics and science, but then scorn theory in education? I suspect the horror of theory in social science is one that comes less from the poverty of such theory than of its radical nature, mostly threatening to the powers that be in industry and government. However, my main reason for having to talk about theory is because without it we are rudderless: or worse we are steered by an ‘everyday just plain folk’ theory that is un- or ill-considered. We all have folk theories – I ask you to try to point to the direction of Sydney, say (to anchor you in your local geography), and eventually to point to Manchester… did any one of you point down through the ground? We are all flat-earthers in our daily lives, and Galileo’s universe only occurs to us in scientific situations that call for it.

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But things are worse in the social sciences. You can see the kind of thing I mean even in the language of education—on a daily basis I am asked to ‘deliver’ a lecture or seminar, implying that teaching is a process involving the packaging, postage, and unpacking of knowledge. The learner here is only active as a receiver at the last stage, and if it is junk mail it perhaps goes straight in the bin. The idea that learners should be engaged in what they learn, even decide what they are interested in, does not really enter this model, and of course this uncritical attitude is quite helpful to our industrial and political masters…Galileo had to deal with the pope, but we have to deal with the ruling classes and their ideologies, and even with their language; we must expect many defeats in our effort to shrug this off. But let me go to my own professional history in STEM and you will see what I mean.

My teaching history, modeling and problem solving in mechanics

ThestoryofmyinvolvementwithDeakingoesallthewaybacktotheearlyyearsoftheMechanicsinActionProject,whichwasanattempttore-designtheteachingandlearningofpre-university—whatwecalledASorA-level—courses(andlaterallthewaydownthroughschool)inappliedmathematics.Atypicalactivityinvolvedthe‘rulerproblem’,whichinvolvesmodelingofasituationwherefrictionisthekeytheoreticalconcept(forsolutions,etc.seeSavage&Williams,1990).

Figure1‘Placeahorizontalrulerasymmetricallyonyourtwoindexfingers.Whathappenswhenyouslowlymoveyourtwofingerstogetherunderneaththeruler…’(Savage&Williams,1990).

ManyteachersevenwhoknowPhysicsfinditdifficulttopredictinadvance,andaresurprisedbytheirexperiencethatresults.Iurgeyoutotryitnowandexperiencethisforyourself.

ButotherexampletasksstartedwithrealworldengineeringproblemssuchastheTacomaNarrowsbridgecollapse.https://www.google.co.uk/?gws_rd=ssl#q=tacoma+narrows+bridge+collapse+video&*Themainideaherewastomotivateandengagestudents’curiosity,andtoencouragethemtomodelwithmathematics,preferablywithexperimentalworkandmeasurementofsomekindnotfaraway.Themodelingcyclesomehowneedsdatatopushitalong,oritstopsafterone‘round’ofmodeling.Anexample,in‘Smashingwindscreens’,modelingthedistanceyouneedtokeepbetweencarsonanewly

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gravelledroadisnottoodifficultforstudentsstudyingtheparabolainvolvedinprojectilemechanics.Themostcommonsolutionhasasimpleformulathatgivesthesafetydistanceasafunctionofspeed(assumethegravelfliesoffatthespeedofthewheelrotationatsomesensibleangle…However,thereisnowayforthestudenttochecktheformula,sothemodelingstopshere.

Figure2:Howhighuptherampmusttheballstartfromtolooptheloop?(Savage&Williams,1990,figure9.28).

Ontheotherhandwhenmodelingtheheightuptheramprequiredforarollingballto‘looptheloop’(orradiusr)(seeFigure2)thefirstroundofmodelingmightgiveyoutheanswerh=2r(conservationofenergysuggeststheball‘just’makesittothetopoftheloop…);thiscanbecheckedandfoundwanting,drivingasecondroundofmodeling(togeth=2.5r),andsometimesevenathird(h=2.7r).

AllthiswasgreatfunformeandthestudentsIworkedwith.IrecalltakingatranscripttoaresearchdayofBSRLM(seewww.bsrlm.org.uk)andinvitingfellowteacher-researcherstohelpmeanalysethediscussion.Anoldguy(myagenowperhaps?)madeastrikingcomment,‘It’sthefactthatthisdiscussionhappenedatallthatweshouldnote.’AndthatledmeeventuallytoworkwithSusieGrovesBrianDoig,andJohnCripps-ClarkeonaPrimarymechanicsprojecthereinMelbourne/Australiathatsoughtsimilarlytodevelopconceptualdiscussionsinmodelingcontexts(wearenowre-inventingthewheelinanewprojecttoreintroducetheseideasintomiddleschoolyearsinmathematicsagain).

Butsuchinnovationsalwaysmeetwithproblems.SomestudentscomplainedthattheexcitingsessionIranthatattractedthemtomechanicswasneverrepeatedwhentheyactuallystudiedtheA-level(Iwasn’tteachingitthatyear,andtheteacherinvolveddidn’tseeitashelpfultopassingtheexams).Ingeneral,wehadahugetasktodevelopequipmenttosupplyschools(alldisappearedfromthemarketnow)andtraintheteachers(bestpartoftenyearsofthis)andfinallytochangetheassessmentsystemtoallow‘modellingprojects’andtraintheteacherstoassesstheseinhouse(alsoabouttenyearswork).

Thepinnacleofthiseffortinmyexperiencecameinthe90swhenIvisitedamechanicsclasstosupportastudentteacheronmyPostGraduateITEcourse(bythenI’dbecomeauniversitylecturertrainingteachersaswellasdevelopingallthesecurriculum,assessmentandtrainingtasksandmaterials).Theschoolmentorcamewithmetotheclass,ashewaskeen‘toseeifthisworks’.Thestudentbegantheclassandwasobviouslynervous,andtheconversationwasstilted.Butthen‘Nowwehavetodothis

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practical,sohere’sthestufflet’sseewhatyoucando…’Thepracticalinvolvestwosmallsnookertypeballsbeingreleasedfromlaunchersandrunninginparallelalongatabletopatthesamevelocity;thensomeonehitsoneoftheballswithabookatarightangletotheball’smotion,inanattempttogettheballtomisstheotherball…Well,thelawofmomentumdidactuallywork,thankgoodness,butthat’snotthepoint.Themainpointwastheimmediatechangeintherelationshipofteacherandstudentsinthisactivity,fromstiltedto‘easy’,toajointengagementinthetask,withlaughterandcuriosity.Andthementorwaspleasedalso!

ButasinVictoria,theministryeventuallydecidedthatcourseworkwasnotsuitableforhighstakesassessmentsandkilledthewholeactivityoff.Thematerialsandassessmenttoolsstillexistsomewhere,buttheequipmentmanufacturerappearstohavegoneoutofbusiness,andthewonderfultextbooksnolongermatchtheconstantlychangingcurriculumverywell.

ThiswaswhenIrealizedthatIneedtothinkabitaboutwhatisgoingonhere:whyinfactcanthishappentosuchinnovation?Whydowehavetorepeatedlypushwateruphill?Thisisthesortofquestionasocialtheoryofeducationmightaddress:mywritinginthisareaisprobablybestdescribedassocio-culturaltheory,itdrawsonMarx,Vygotsky,cocalledCultural-historicalActivityTheory,andsociologistssuchasBourdieuandFoucault.

Figure3:theself-similarityofthefractalsetonthecoverisintendedtoevoketheaimofavisionary,outward-lookingcurriculumhttps://royalsociety.org/~/media/education/policy/vision/reports/ev-2-vision-research-report-20140624.pdf

KeyliteraturereviewsforpolicyandpracticeinSTEMHereIreportthetwoliteraturereviewsIhaverecentlybeenengagedinthatrelatetoSTEM,particularlyasregardsinterdisciplinaryactivity(Howesetal.,2014;Williamsetal.,2016).Theywerebothdesignedtoaddressthestateoftheartforpolicyandpractice,withthefutureofcurriculum,assessmentandprofessionaldevelopmentinmind.Seefigure3foroneoftheseavailableontheRoyalSociety.

Bothreportsemphasisethatinterdisciplinaryprojectworkhasbeenshowntohaveitsstrongesteffects(i)onaffectandmotivationoflearnersand(evenmoresoof)teachers;(ii)onsomeaspectsofproblem

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solvingcapability;but(iii)tohavelesseffectontraditionalmeasuresofknowledge/skill,(iv)tohavelesseffectoftenonmathematicsthanscienceandtechnology;and(v)tosuffer,asmanyinnovationsdo,fromregressiontothetraditionalnormsofseparatedisciplinesovertime(i.e.wearepushingwateruphill!).Still,motivationoflearnersisakeyconcernformanyteachersandothers,andbeliefininnovationscontinuestobestrong,internationally.

Unfortunately,empiricalresearchintheareaof‘interdisciplinarity’suffersfromafailuretodefinewhatinter-disciplinarityisandwhatinterdisciplinarypracticemightbe.AusefulclarificationisdrawnoninWilliamsetal(2016)betweenproblemsolvingwhichis:mono-disciplinary;multidisciplinarity;inter-disciplinary;transdisciplinary,andperhapsalsometa-disciplinary.

Mono-disciplinaryproblemsolvingtypicallyisaboutusinga‘discipline’likePhysicsorMathematicstomodeltheworldinordertotacklesomerealproblem.Sincemanyproblemsdonotmakemajordemandsonmorethanoneacademicdiscipline(andofcoursemanymakedemandsonnodisciplineatall)thisisanimportantelementinproblemsolving,andindevelopingunderstandingofanyacademicdiscipline.Vygotskyspecificallyreferredtothisideaastheinterweavingof‘scientificconcepts’(hemeansacademic,disciplinaryknowledgeingeneral,includinggrammarandsocialsciences,forinstance)withthe‘everyday’practicesand‘spontaneousconcepts’associatedwiththem.Anypurelyacademicunderstandingisinclinedto‘pureverbalism’otherwise(andthereisstillalotofthisabout,isn’tthere?).

Multi-disciplinarityinvolvesmorethanonedisciplinebutitmaybethecasethatthedisciplinesdonotsignificantlyworktogether.IntegratedtopicworkinPrimaryschoolisoftenabitlikethis:someexcuseismadefordoingsomemathematicsintheprojecton‘TheEgyptians’butitisnottrulyintegratedinthesenseofcontributingtosolvingorinformingasignificanthistoricalproblem.

Inter-disciplinaryworkontheotherhandmighttrulyinvolveaninterweavingoftwodisciplinessuchasisnormalinMathematical-Physics,orBio-chemistry.OnecansaythatastudentwhowritesareportfortheclassofascienceexperimentorprojectisusingthedisciplineofcommunicatingwithEnglishlanguageaswellas‘problemsolvinginscienceandmathematics’–andmaybetheygetcreditfortheworkinboth‘disciplines’.Howfartheworkisinterdisciplinaryismoot,butonemightsaythetwodisciplinescometogetherinreflectingonthegenreofscientificreportage,anddiscussionofwhoistheaudienceforexperimentalwrite-ups.Theinteractionbetweendisciplinesreachesahighpointwiththeformationofhybrid,newspecialismslikebio-mechanicsornanotechnology.

Thecategoryoftrans-disciplinarityrefersusuallytothedisappearanceofthedisciplinesandtheirdifferencesinsidethetaskofsolvingaparticularproblem.Ifthetaskreallyisto‘buildabridge’thentherealityofthecontextwins,andmaybenoadvancedmechanicsisinvolvedbecausewedothisbyassemblingakitpurchasedforthepurpose.Ofcoursethedangertothecurriculuminsuchprojectactivityisthattheacademicdisciplineswewanttomotivatedisappear,butIargue(orwearguedinHowesetal.,2014)thatsuchprojectsreflectingtheinterestsofthestudentareimportantenoughinthemselves,andthatthedisciplineswouldservethemasexpertconsultanciesshowing—overtime—howthedisciplinesmightenhancethestudentsunderstandingandtheirdevelopingportfolioofprojects.

Thento‘meta-disciplinarity’.Thisreferstothepossibilitythatthroughinterdisciplinaryworkthedifferentnaturesofthedisciplinesshouldbecomeclarified.Anexamplemightbethenaturesof‘usingevidence’inhistoryandscience.Becomingawareofwhatadisciplinedoes,andwhatitcandoforaprojectwouldseemtobecrucial‘meta-knowledge’,ifanacademicdisciplineistobreakoutofits‘pureverbalism’andbecomeaccessibletostudentsinproblemsolving.Itisasadfactthatthiskindofknowledgeandmetacognition(asopposedtootherkindssuchas‘learningtolearn,orselfregulationgenerally)ingeneralreceivesasyetlittleattentioninschools.

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Withallthisinmindwemadearecommendationthatspaceshouldbefoundinthecurriculumateverylevelforstudent-ledprojectsthatwouldhavenosubstantivedisciplinaryknowledgeassuch,butprovideexpertfacilitationfromteachersincludingthosewithSTEMknow-how.Theintendedoutcomewouldbeportfoliosofevidenceoftheseprojectsthatshowwhatastudentisinterestedinandwhattheycando.Quitealotofthereportwasabouthowschoolsmightmanageassessmentofthese,butwewerealsoconcernedabouttheprofessionaldevelopmentimplicationsofpreviousexperiencesofthiskindofcurriculuminnovation(e.g.theYutoriinJapan).

NowIwanttogotosomeoftheunderlyingprinciplesthatdrivethisargument,andtoeducationaltheory.

KeysocioculturaltheoriesandSTEM:beforeandafterVygotskyIwillstartwiththesocioculturaltheoristVygotskyandhisrootsinHegel-Marx,becauseheprovidesanoptimisticviewofwhatteachingandacademecandoatits‘scientific’bestforeducation,andlearners’development.Vygotsky(andneo-Vygotskyanworksince)raisesformetwokey,relatedideas:‘obuchenie’andtheZPD.Iwillcometoakeythirdidea,‘perezhivanie’,later.ButfirstIwanttoslightlycorrectwhatIseeasoverlymechanisticandunhelpful—actuallyundialectical—interpretationsofVygotsky’sworkintheWestwheretheZoneofProximalDevelopment(ZPD)haslargelybeenreducedtoateachingapproachthrough‘scaffolding’.

VygotskywantedtobuildaHegelianandMarxist,thatisadialecticalandmaterialisttheoryofpsychology:asocialpsychologythatstudiesthemindinpracticalactivity.Themodelofthisthinkingrelatesto‘humanlabour’whichisessentiallycollectiveandsocial,andachievesmorethantheindividualcanontheirownthroughthedivisionoflabour.Inalabouractivity(Vygotsky’soldstudentLeontievanalysedtheprimalhuntasthearchetype)weengagewithothers(inthetribe)andacttogether(hunting)totransformnature(theanimal)toproduceoutcomes(food/clothing)thatcansatisfyourneeds(hunger,warmth).[NBregardingtheapparentharmonyofthe‘primalhunt’:whentheactivitybecomescomplexinadivisivesociety,andwhenmoneyintervenes,the‘activity’oflabourbecomeswagelabour,andtheentrepreneurputstheproductsoflabourtogetherandsellscommoditiesonthemarket,thenonebeginstoseealienationoflabourfromitsproductandproducer,etc.SeeWilliams,2011,2012,andJones’response,2012.)

Soitis,ormightbe,ineducationalso,byworkingtogetherwithothers(andcometothatwithtoolsandresourcesthatexpandtheirpossibilitiesforaction)thestudentcanachievemorethanontheirown.Soitiscollectiveactivitythatcanbe‘expansive’,andcanprovideadevelopmentalzoneforlearning(theZPD).IthinkthisisanappropriatedevelopmentofVygotsky’sthinkinginmodernActivityTheory,orCultural-historicalActivityTheory(ChAT).(SeeanexamplefromscienceeducationinRoth&Lee,2007.)

Thenitisimportanttoalsounderstandthatin‘educationallabour’inwhich‘solvingaproblem’and‘actingtogetheronanobject’isprimaryandlearningoutcomesandpersonaldevelopmentaresecondarythoughimportanteffectsoftheactivity.MymodelhereisVygotsky’sanalysisofthebaby‘learningtopoint’(seeWilliams2016fordetails.)Thebabyreachesouttograspsomeobject(maybeashinytoy)andfails….Perhapsshedrawstheattentionofthecarerinsomeway,butanywaythecarerrecognizesthebaby’sneedforthetoy,andhelpsbypushingthetoywithinreach.Overtime,thebaby’s‘reachingtograsp’becomesasigntothecarerforhelp(pointing)andthebabyhas‘learnttopoint’.Sothedevelopmentofalearnerarisesfroma‘contradiction’betweentheneedsofthecommunity(or

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dyad)andtheindividual’sresources;thisis‘overcome’throughcollectiveactivity,fromwhichindividualactors/studentsgetaccesstonewactivityandimplicitlearning.

Andwheredoestheteacherfitin?TheteachershaveakeyroleforVygotskyanthinking,becausetheycanhelpprovidethekindsoftoolsandconceptsthatmightbeneededfortheclassoflearnerstosolvetheproblem(s)theyaremotivatedtotackle.Butnotethatthisdoesnotmeanthattheymustpresentthecommunitywithready-madesolutionstoteacherorcurriculummadeproblems;therewasnocurriculum‘tolearntopoint’,indeedthecarerhadnointendedlearningoutcomeatall.Ifweadmitit,maybethisisalsotrueofalmostallreallysignificantdevelopment(e.g.theacquiringthedesiretobeascientist?)

Alienationenterstheclassroom,inthisview,whenthelearningoutcomeisdeterminedbythecurriculum,‘delivered’tolearnersbythe‘teacher’,andabsorbedbythelearner,mainlyforthepurposesofregurgitationinlaterassessment.Thecredentialsandgradesawardedtothelearnerserveratherlikethemoneyforwagelabourinthemarket(andperhapsservicetherequisiteideologyinturn).Thisdegradeslearning,butalsoteaching.Theteacherteacheswhattheyknow,andthisactivityisalwaysseparatedfromtheactionsoflearning,andbecomesalientothelearninginvolved.

Figure4:Nico’saquariumandthe‘maths’offishesledmetoquestion,whatistheshapeofafish?

Butletsbepractical:whatelsecanastudentandateacherdo?Vygotksy’sanswerwas‘obuchenie’,asinglewordforlearning-and-teachingwhichIinterpretasa‘jointactivity’ofworkingonatask/projectorexplorationofaproblemoranissue.Theteachermaybringsuperiorresourcestothisjointendeavour,butisstillapartnerintheproject.Insucharole,theirteachinginvolveslearningabouttheprojectalso,andlearningtoworkwiththestudents,understandtheirmotivations,understandingsandwhattheyknowabouttheproject.Inthismodetheteacherdoesnotconstructlearneroutcomesasateaching-and-assessmentobject,buthelpsthelearnerandtruststhemtodeveloptheirownunderstandingsaccordingly.This,anyway,ismyChATinterpretationofobuchenieinaneo-Vygotkyanactivitytheoreticsense.

IgaveanexampleortwoofmomentsthatmighthavefitthisbillfromsomerecentempiricalworkofcolleaguesinManchesterwherewearetryingtodevelopacriticalpedagogy,particularlyacriticalmathematics.Thefirstwasofa5yearoldinterviewedaspartofapilotresearchusinga‘fundsof

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knowledge’approach(Molletal.,1992).Thesefirstyearchildrenseemalreadytobebecoming‘schoolified’,andtheiralienationwasexpressedquitesuccinctlybyNico.Themathscurriculumisendlesscounting,and‘boring’.Aspartofhisproject,thechildandfamilywereinvitedtotakephotographsofmathsintheirhomeorstreet,andNicohadcomebackwithaphotographofhisaquarium.Hetalksaboutshapesofthecolumnsandsooninthewater,andofthefish…Iwonderifyoueverthoughtabouttheshapeofafishasamathematical,orSTEMproblem?

Agoogle“whatistheshapeofafish?”producesafascinatingvarietyofshapes.”Whatdotheyallhaveincommon,andwhydotheyvarysomuch?Dothesefinsremindyouoffinsinotherplaces,e.g.oncars?Clearlythismakesshapeinterdisciplinaryandraisesquestionsforscienceandtechnology,aswellasmathematics.

Oneclearpropertythegoogledshapes,and‘shape’generallyinthemathscurriculumhasistwo-dimensionality.Buttheverynatureofthefishshapeisclearlythree-dimensional.Furthermoretherealshapeofafishisdynamic,andisshaped(unlikethecar,withfinsornot)byitsmotion,i.e.itsdynamicpropertyisessentialtounderstandingitsgeometry.Shapesthatmove(andevengrowintime)caninfactreadilyenterthemathscurriculum,andIdon’tthinkitwasacoincidencethatothers’(egLehrer’sandTytler’smodelingofgrowthandmovement)workreportedinthisconferenceinvitedchildrentomodelgeometryandmotiondynamicallyaswell.

Thisexampleinvitesconsiderationofthe‘gameoflife’.Thereisnowsoftwarethatinvitesuserstotryoutdifferentshapesthatmoveaccordingtosomesimplerules,andsomequiteinspiringsimulationsof‘gliders’,‘gliderguns’andsoon.Ithinkthismightofferopportunitiesthatwouldstretchbothteachersandstudentsinjointinquiry,andwhereteachingdoesnotreducetodeliveringpre-specifiedandschoolifiedknowledgeandskillfromteachertostudent,followedbyregurgitationforassessment.(SeeFigure5withcaptionlinkingtogameoflifesites.)

Figure5:snapshotoftheglidergunfromConway’sgameoflife(https://bitstorm.org/gameoflife/

I’dliketomentionalsoanexampleattheotherendoftheschoollife-courseforalienatedmathematicseducation.Weengagedinanevaluationofa‘CriticalMathsEducation’courseforpost-16studentswho,notwishingtostudyatypicalacademicAlevelpre-universitycourseinmathematics,areneverthelesswillingtoengagewithsomemathematicsto‘stayinthegame’.Oneunitcalled‘Medicalscreening’isdesignedtodevelopunderstandingsofriskandprobabilityinthecontextoffalsepositivesinmedicalandothercontexts(suchasspam,forensicidentificationetc.)Theideaisthatissuesofjeopardy

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motivateinterest.IsitOKtoexposewomentoinvasivediagnosticsinpregnancy,forexample,orpainfulinterventionstopreventpossiblecancersdeveloping,ifthepercentageriskisquitesmall?

Inourresearchhowever,anobservationofaclassledtoaninterestingmoment.Thestudentswerediscussingfalsepositives‘intheirreallives’andonegroupofyoungwomenstartedtodiscusspregnancytests—apparentlyafriendhadanegativetestresultbutwasinfactactuallypregnant—afalsenegative.Theemotionalmotivetounderstandtheworldthroughmathematicsseemedsuddenlysalienthere.Itseemstomethiswasateachablemomentwhereateachermighthaveenergizedadiscussionthatwasofrealconsequenceforthestudents.Iseesuchamomentasapotentialfor‘reachingout’toimportantmathematics,ifanobservantteachercanonlybesufficientlyawareandpreparedtohelpsuchalearnergraspitinthemoment.

ThisbringsmetoafinalconceptthatVygotskystartedtodevelopandthatneo-Vygotskyansthesedaysareconcernedwith:‘perezhivanie’.ThistermhasalonghistoryinRussiancultureand,inprobablyover-simplisticterms,involvesadramaticeventorcrisiswithemotionalcharge,onethatmayrequireasignificantdegreeofpersonalworkanddevelopmentforanindividualto‘overcome’.VygotskyusesthisideatodevelopascientificconceptthatconnectspersonaldevelopmentwithemotionsANDlearningexperiences(Vygotsky,1994).

InSwansonandWilliams(2014)wegaveanexamplewhichwenowseeassuchanevent,thoughoriginallywedidnotanalyseitasaperezhivanie.ItwaspartofSwanson’sstudyofmathematicsindartsplaying,andthediscussionofafamousdartsplayer’sautobiography–thatofBobbyGeorge(seeyoutubeonBobby’smasterclass:https://www.youtube.com/watch?v=eMjBGmdQAKQ).BobbywasaworkingclassLondonerwholeftschoolbarelyabletoreadorwrite,actuallyemployedasabounceronce,whenacareerindarts‘madehim’.Earlyinhisprofessionalcareer,therecameamomentwhen,muchtohisembarrassment,hewasexposedasunabletodealwiththearithmeticofdarts.

“There'snowayyoucanloseplayinglikethat”…Whathedidn'tknow,ofcourse,wasthatIstillcouldn'tcounttosavemylife.Iwasfacedwitha90out-shottobeatRogerandwinthetitlebutIdidn'thaveacluehowtogoaboutit.“Treble18,Bob”,heshoutedfromthefloor.Well,Ihittreble18butmymindwasstillacompleteblankaboutwhatIshoulddonext.NervessometimesmakemomentslikethatevenworseandIjuststoodattheochebewildered,lookingforhelp...Itisnowondersomeoftheolderplayersdespairedofme.Iadmititwasabloodyridiculousstateofaffairs.

DeepdownIknewIhadtorelyonmyselftoprogress.AnotherEssexplayer,GlenLazero,andIworkedouteachandeverypossiblepermutation...Mygameimprovedalmostovernight.Isawhowtreblesandsinglesthatsitnexttoeachotherontheboardcanworkinyourfavour…IwasneveranygoodatmathematicsatschoolbutIfoundthatdartsismoreaboutrememberingnumbersandcombinations.Ihadtocrackthisandittooksometime...Tothisday,Idon'tdoanyformofarithmeticwhenIplaydarts.Ijustknowhowallthenumberswork...Workingoutallthosecombinationsgavemeconfidence.

(George,2007,p.55)

Hispublicshamedrovehimtoworkatthearithmeticwithafriend,aquiteacademicexerciseofsystematicallyworkingthroughthe‘outs’thatwouldsuithimintheend-gameoffinishingonadouble(dartsplayerslikesomedoubleslike16s,butnot7s..).Thiswasanalysedasamomentwhenmathematicsbecamesignificantandacrisisinpracticewassufficienttobringanalienatedlearnerbacktoacademicmathematicsforaproject,ifonlyjustforamoment(ashesays,oncetheprojectwasdone,hedidn’tneedtothinkaboutmathematicsagain).SonowIthinkinthelightoftheperezhivanie

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literaturewecanseefurther,theemotionalcrisiswasindeedovercomethroughhardworkandascientificstudy,becausethisstudywasimportanttoBobby’sdevelopment,andhewasright.Nowhesaysinhismasterclass‘mathsis25%ofyourgame’.

LookingbackatNico’sfishtank,andtheteenagers’understandingoffalsenegativesinpregnancytests,Iseepotentialsforperezhivanie,andthesignificanceofsuchmomentsaspersonaldevelopmentofamathematicalidentity.Wearen’tlookinghereforanemotionalcrisiseverydayandineverylesson,butjusttounderstandthatthesemomentsmightbecritical,andbuildingtheseintoourunderstandingsofpersonaldevelopment.

Oneoftheparticularlyawkwardaspectsofperezhivanieforeducationisitscontextualizationinthemomentofemotionalcrisis,usuallyadramaticdisasterwhereabreakdownofsomesortoccurs,andsubsequentdevelopmentinvolves‘overcoming’it,acatharsis;thissometimesextendseventotraumathatrequirestherapy.Ineducationwedonotwishparticularlytoencouragesuchmoments,eveniftheymightbedevelopmental,thoughwhentheyarepresentinourstudents’liveswemighthopeteacherscanhelpstudentsworkwiththem.ButIthinkwegetroundthisobjectiontoperezhivaniebyconsideringitin,abroaderframework,asbeinginitiatedbyashockingbutevenperhapspleasurableeventthat‘doesnotcompute’intermsofthenormsofadullanduninterestingstudentexperience.PerhapsexperiencingmathematicsorSTEMasimportant,meaningful,dialogicalandevenanexcitinglydifferent‘awakeningtoscience’mightbethoughtofintermsofperezhivanie,then.

Whatwoulditmeanforteacherstobecomesensitivetosuchmoments?Whatsortofcurriculummightalloworencouragesuchmoments?Anotherwaytolookatthismightbe:Whydon’tthesemomentsoccurmoreoften,whyisitsodifficultforteacherstoencourage,andpickuponsuchmoments?Thisiswhereourtheoreticalexplorationgoesnext.

CriticalsocioculturaltheoriesandSTEM:beforeandafterBourdieu/FoucaultThisVygotskyanbrushpaintsapositivepictureofwhatteachersandteachingmightdoforlearningandhasinspiredmanyprojects.InspiredinpartbyLuisMoll’snotionof‘fundsofknowledge’wemightseektohavetheschoolengagewiththeneedsofitscommunities,engagingwiththestudents’realneeds,thatcaninspireprojectsinwhichSTEMmakessense.Yetwehadbetternotgettoocarriedawayandforgetthe‘discipline’ofthecurriculumandschool,theexaminationandassessmentthatservessooftentocrushthespiritoutofreforms.Weneedoureyeswideopentotherealities.Howarewetounderstandthisaspectoftheschoolandacademeinsociety?

InthisIfollowBourdieu’sworks(asperWilliams&Choudry,2016).Bourdieuexplainsthatschoolhasthesocialfunctionofreproducingthesocialstructurewithallitsoppressionandinequality.Briefly,itachievestwothings.First,throughtheprocessesofexaminationandselection,itstratifiesstudentsforthelabourmarketintofinelylayeredstrataofthemoreandthelesssuccessfullyqualified,anditensuresthat,onthewhole,itisthechildrenofthepreviousgenerations’leastsuccessful,andmostoppressed,whocomeoutatthebottomofthepile(andviceversa).Yesofcoursethereareexceptions,buttheruleisprovedstatistically,eveninBourdieu’sownempiricalresearch.

Second,itachievesthisreproductionofclassandpowerwhileatthesametimestrengtheningtheideologythat,infact,itisafairandjustprocess.Thepoorerandleastwellqualifiedemergefromschoolingonthewholebelievingtheirlackofsuccessisbecauseschoolwas‘notforthelikesofus’;whileonthecontrarythosewhoemergesuccessfully‘know’thatitisbecauseoftheircleverness,diligenceandcommitment.Onecanargue,furtherthanthis,thatthewholeschoolificationprocessisa

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preparationforalifeofsuchtreatment,wherethesuccessfulgetmoreopportunities,whilethosemostinneedofeducation(orwhatever)getleast.

Ifwetakeallthisasacriticalstartingpoint,thenwewillnotbesurprisedthatforthepoliticiansandpowersthatbe,radicalreformofschoolingintheinterestsofalllearnersisnotlikelytobeapriority!Forsure,challengestothetrialbyexaminationandselectiveaccesstoprivilegethatfavoursthewinnersisnotlikelytoappealtoconservativepoliticians.Infactonemaybesurprisedeventhatsomeoftheindustrialrulingclassarewillingtocountenancesomeproblemsolvingreforms.Anexplanationofthisisdue,perhapssectorsofindustryrecognisethatproblemsolving,andSTEMinparticular,mightbeimportanttraininggroundsforthekindoflabourtheywanttoinnovateandtostaycompetitive.Theyasklabourtobeabletothinkcriticallytoadegree,butperhapsnottoocritically,beyondtheirstation.Isuggestthatthisleadsthemtolargelyarguetomaintainthedisciplinarysystemwhichpreventsatrulyradicalcriticalapproach.

WeareledtoasknowhowSTEMinparticularfitsintothisstory,howdisciplinesdoinfactdisciplinethemindanddisciplinethethinker-worker.HereIfindFoucault’snotionofdiscoursesofdisciplineshelpful.InWilliamsetal.(2016)wedescribehowdisciplinesemergehistoricallyfromtheincreasingdivisionoflabourandspecializationofpracticesandknowledges.Akeymomentseemstobetheseparationofknowledgefromproductionintheriseofschoolsanduniversities.IntheWestatanyrate,theemergenceofacademicdisciplinesisaccompaniedbytheiralienationfromproductivelabour,andthestratificationofskilledworkintheguilds,andofthemiddleclasses’workinadministrationandthechurch.

Alongwiththedivisionofdisciplinesfromeachothercomesalsoideologiesofthesedisciplines.Thebackgroundofmonasticdisciplineandevenasceticismbringsaparticularformtothesciences.Notonlydotheacademicmiddleclasses‘speakadifferentlanguage’fromthewiderpopulation,buttheystarttospeakdifferentlanguagesfromeachother.Initsextremeformtodayinterdisciplinaryworkevenwithinafieldlikepuremathematicsresearchhasbecomealmostimpossible(thoughIrecommendyoulookatanAustralianexceptiononthispoint,Taoonpolymathprojectsseeyoutubehttps://www.youtube.com/watch?v=elWIDVI6b18).

ForFoucault,disciplinaryknowledgeispower;itisapowerthatcomesataprice.Youhavetospeakthediscoursetoexerciseit,andthisinvolvesgivingoneselfuptotheideologyandpowerofthatdiscourse.Becauseourdisciplinesimprisonus,itservesasalimitonwhatcanbedonetoresistthepowersinsocietyatlarge.ButasPaoloFreireargues:these‘limits’areclearsignalsforradicaleducatorswhoseektoempowertheoppressed.Findtheselimitsandexposethem.Ifindpreciselytheselimitsindisciplinarity.

WhenFoucaultsuggeststhatdisciplinesbothempowerandimprisonus,i.e.itisthediscoursethatspeaksthroughus…Imustadd,well,‘almost’:onemightrecognizethesourcesofthisdiscursivepowerinthedisciplineandchoosetoresistorsubvertit.ThisiswhatImeanbybecomingundisciplinedwiththedisciplines.ItisherethatIthinkinterdisciplinary,student-ledactivitycanhelpustoescapefromourdisciplinarydiscoursesandbecome,toadegree,freeminds:undisciplinedbythedisciplineslimits.Wedothisbyhavingthediscipline,butalsobybecomingawareofthedisciplineandwhatitdoes.

AndnowIamalmostoutoftime,ifnotwords.

SummaryandconclusionIhavearguedforstudentledproblemsolvingactivity,thekindofthingsweseeatthisconferencethatengagestudentsandteachersinexcitingprojectsusingSTEM,providingexperiencesthatshatternormativeexpectationsofboredom,andopenthedoorforlearnerstocometoengageagaininSTEM.

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Thisinvolvesbreakingdownthealienationoflearnerfromteachercausedbythe‘delivery’modelofteachingforpre-ordainedlearningoutcomes.Iclaimthatthesewouldsometimesnaturally,orevenusuallyleadtointerdisciplinarity,andthatthisprovidesopportunitiesforbecomingundisciplined,goingbeyondthelimitsofthedisciplines.Iwarnedalsothatthisisdangeroustotheextentthatitiscritical,andtofindcriticalitybyidentifyingandchallengingdisciplinarylimits.Inturn,beingawareofthelimitsmayhelpustofindsomespaceforcriticalactivity,ifwewanttotaketherisk.Iidentifiedacontradictioninindustrialcapitalism’sdependenceoneducationtobeideologicallyconservativeyetdynamicallycompetitiveproblemsolversandthinkers.Thisrootcontradictionmightallowustobuildinsomerhetoricalspacesforbeingundisciplinedandyetstillbesafe.Well,almostsafe…perhaps.

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