affects and emergent learning - mathematics education · children can teach others, or that this...
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Affects and Emergent Learning
RicardoNemirovskyManchesterMetropolitanUniversity,UK
DonDuprezUniversityofEdinburgh,UK
MollyKeltonWashingtonStateUniversity,USA
MichiganStateUniversity,November16,2016
Teleological and Emergent Learning
Erlwanger,S.H.(1973).Benny'sConceptionofRulesandAnswersinIPIMathematics.JournalofChildren'sMathematicalBehavior,1,7-26.
• InsixthgradeBennywasregardedasoneofthebeststudentsinhismathematicsclass.Sincesecond-gradeBennyhadbeenusing“IndividuallyPrescribedInstruction”(IPI):astructuredsequenceofexercisespunctuatedbymultiple-choicetests,suchthat80%oftheanswerswererequiredtobecorrectinordertoadvanceinthesequence.Benny“wasmakingmuchbetterthanaverageprogressthroughtheIPIprogram”(p.7),
The “Case of Benny"
• Bennywascomputinganswerstoproblemsbyapplyingamultitudeofself-generatedrulesmanyofwhichwereincorrect,eventhoughinparticularcasestheywouldleadtoanswersconsistentwiththekey(e.g.theresultof.7x.5is.35because,ontheleftside,“there’stwopointsinfrontofeachnumber”(p.8)thenBennyusedthesameruletoevaluate:.3+.4=.07)
• Therules,Bennythought,wereinvented“byamanorsomeonewhowasverysmart.”Thiswasanenormoustaskbecause,“itmusthavetookthisguyalongtime...about50years...becausetogettheruleshehadtoworkalloftheproblemsout”(p.12)
• ApplyingdiverserulesBennywasabletoobtaindifferentanswerstothesameproblem,allofwhichhedeemedtobetrueones,althoughtheIPIkeyacceptedonlyoneofthem.ErlangweraskedBennywhytheteacherswouldmarkaswrongalltheseothertrueanswers:“Theymarkitwrongbecausetheyjustgobythekey.Theydon’tgobyiftheansweristrueornot”(p.12).
• TeleologicalLearningmaysucceedorfail;intheCaseofBennyitwasachievedtoacertaindegree,ashemademorethanaverageprogressthroughtheIPIprogram.Ontheotherhand,emergentlearningisalwaysgoingoninwaysthatareunderdeterminedandopentotheunanticipated,suchasthedifferencebetweentruthandkeyselection.
Affects
Farrington,C.A.,Roderick,M.,Allensworth,E.,Nagaoka,J.,Keyes,T.S.,Johnson,D.W.,&Beechum,N.O.(2012).Teachingadolescentstobecomelearners.Theroleofnoncognitivefactorsinshapingschoolperformance:Acriticalliteraturereview.Chicago:UniversityofChicagoConsortiumonChicagoSchoolResearch.
Khine,M.S.,&Areepattamannil,S.(Eds.).(2016).Non-CognitiveSkillsandFactorsinEducationalAttainmentRotterdam:SensePublishers.
LaCaze,M.,&Lloyd,H.M.(2011).Philosophyandthe'affectiveturn'Parrhesia,13,1-13
Theongoingburstofliteratureon“non-cognitivefactors”ineducation(Farringtonetal.,2012;Khine&Areepattamannil,2016)suggeststheneedfortheoreticalworkonaffects,suchthattheycanbethoughtofwithoutthemisleadingshadowoftheirnot-being-cognitive.
Affects vs. Cognition
“Theturntoaffectcannotbetakenwithoutatthesametimebeingaturnawayfromsomethingelse.Importantlyitisaturnawayfromtherationalisttraditionsofphilosophywhichareoftencharacterizedsimplyas“Cartesian”tosignifycognitiveorreason-basedapproaches.Sothe“turn”isconstructedasaturnawayfromminds,towardsbodies.”(LaCaze&Lloyd,2011p.6)
Ongoing “Affective Turn”
Affects
1. Affectsdonotoriginatefromindividuals;rather,theycirculatethroughindividualsandpervadetheworldstheyinhabit.Individualsundergocirculatingaffectsinwaysthatsometimesdejlectandrejlectthem.
2. Affectspropagatenotonlyacrosspresentsurroundingsbutalsothroughacomplexpast,ormemory,broughtforthbythepeople,things,andsoundsinhabitingthem.Memoryisnotjustamatterofindividualrecollectionsbutofbringingtobeartraditionsandperformanceswhoseoriginsare,forthemostpart,unbeknowntotheparticipants.
3. Affectsasqualitativemultiplicities
4. Asaffectscirculate,theyanimatebodilyandmaterialexpressionsoffeelingsandinterpretations.
5. Thingsanddiscreteentitiesbecomeinthemidstofjlowingaffects
Affects
1. Affectsdonotoriginatefromindividuals;rather,theycirculatethroughindividualsandpervadetheworldstheyinhabit.Individualsundergocirculatingaffectssometimesdejlectingorrejlectingthem.
Affects2. Affectspropagatenotonlyacrosspresentsurroundingsbutalsothroughacomplexpast,ormemory,broughtforthbythepeople,things,andsoundsinhabitingthem.Memoryisnotjustamatterofindividualrecollectionsbutofbringingtobeartraditionsandperformanceswhoseoriginsare,forthemostpart,unbeknowntotheparticipants.
Affects
3. Affectsasqualitativemultiplicities
Affects
4. Asaffectscirculate,theyanimatebodilyandmaterialexpressionsoffeelingsandinterpretations.
Affects5. Thingsanddiscreteentitiesbecomeinthemidstofjlowingaffects
Affects
1. Affectsdonotoriginatefromindividuals;rather,theycirculatethroughindividualsandpervadetheworldstheyinhabit.Individualsundergocirculatingaffectsinwaysthatsometimesdejlectandrejlectthem.
2. Affectspropagatenotonlyacrosspresentsurroundingsbutalsothroughacomplexpast,ormemory,broughtforthbythepeople,things,andsoundsinhabitingthem.Memoryisnotjustamatterofindividualrecollectionsbutofbringingtobeartraditionsandperformanceswhoseoriginsare,forthemostpart,unbeknowntotheparticipants.
3. Affectsasqualitativemultiplicities
4. Asaffectscirculate,theyanimatebodilyandmaterialexpressionsoffeelingsandinterpretations.
5. Thingsanddiscreteentitiesbecomeinthemidstofjlowingaffects
Part II: The Field Trip to the Science Museum
Becoming Ruth, Evelyn, and Sylvia
Affectsdonotoriginatefromindividuals;rather,theycirculatethroughindividualsandpervadetheworldstheyinhabit.Individualsundergocirculatingaffectsinwaysthatsometimesdejlectandrejlectthem.
Forthemostpart,people,things,andeventsundergoaffectsAffectsasqualitativemultiplicities
The Affective Continuum Thingsanddiscreteentitiesbecomeinthemidstofjlowingaffects
Becoming Hmong PeopleAsaffectscirculate,theyanimatebodilyandmaterialexpressionsoffeelingsandinterpretations.Forthemostpart,people,things,andeventsundergoaffects
A Shelving Unit Becoming Shamanic AltarAffectspropagatenotonlyacrosspresentsurroundingsbutalsothroughacomplexpast,ormemory,broughtforthbythepeople,things,andsoundsinhabitingthem.Memoryisnotjustamatterofindividualrecollectionsbutofbringingtobeartraditionsandperformanceswhoseoriginsare,forthemostpart,unbeknowntotheparticipants.
Asaffectscirculate,theyanimatebodilyandmaterialexpressionsoffeelingsandinterpretations.
Place Becoming
• Emergentlearninginvolvesgettingengagedineventsandplacesandparticipatinginthecirculationofaffectsimbuingthem.Aswedoso,affectsintermingle,pervadingnotonlythecircumstancesofthepresentbutalsothepastthatweall(livingbeings,things,weather,symbolicexpressions,luminosity,andsoforth)bringtotheeventorplace.Whatemergesfromeachoftheseengagementsisaqualitativelydistinctaffectivecontinuum,interminglingthepastandpresentofthesurroundings.
• Emergentlearningisgraduallyshapedbythegrowthofaffectivecontinua
• Theunpredictabilityofemergentlearningisaresultofthevastscopeanddiversityoftheaffectscirculatingthroughthepastandpresentofthesurroundings-anyofwhichmay,inprinciple,beembracedorletgobyacertainaffectivecontinuum
• Istartedthistalkbydistinguishingbetweenteleologicalandemergentlearning.
• Inacoupleofoccasionsinwhichweshowedthevideotodiversemuseumstaff,thespecterofteleologicallearningsurfacedinsomeofthesubsequentremarks,likepointingoutthattheactivity“hadfailed”becausethechildrenwere“off-task,”orthatnosuccessorfailurecouldbeascertainedunlessthechildrenweretestedfortheirunderstandingoftessellation.
• Thetheoryofemergentlearningweoutlinehereinspiresustoarguethatthegenesisofanaffectivecontinuumblendingtessellationandshamanismhadapotentialmuchmoresignijicantthanwhataspecializedpost-testcouldreveal,suchasundergoingthesensethatHmongaltarsincorporatemathematicalpatterns,thathavinggrandparentsshamanscanbesomethingtobeproudoff,thatHmongchildrencanteachothers,orthatthissciencemuseumcaresaboutmathematicsandHmongculture.
Affects and Emergent Learning
RicardoNemirovskyManchesterMetropolitanUniversity,UK
DonDuprezUniversityofEdinburgh,UK
MollyKeltonWashingtonStateUniversity,USA
MichiganStateUniversity,November16,2016