Affects and Emergent Learning - Mathematics Education · children can teach others, or that this...
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Affects and Emergent Learning Ricardo Nemirovsky Manchester Metropolitan University, UK Don Duprez University of Edinburgh, UK Molly Kelton Washington State University, USA Michigan State University, November 16, 2016
Transcript of Affects and Emergent Learning - Mathematics Education · children can teach others, or that this...
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
