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