&odifferentiatemeansmakingfinerandfinerdisations。Thisdifferentiationamoutuinguishiicaldifferebeusedfdistins。Thesedistiuresaresimplydimensionsinwhigsvary，andtheybeusedfapartinstannohus，perceptuallearningamountstdis-tiuresorcritisionsofvariation。IfInolytheterminologyoftraoperceptuallearinSituationAthelearodiffereweeninstaninstauatioerssomethingthatiseitheraninstanoheextentthatthelearcorrectlydifferentiatianouationBasaresultofhavingpartiSituatiohereositiveimpaSituationAonSituationB。IfweagreewiththeGibsonianviewofperceptuallearning，thenperformauationBisafunofthedifferehinSituatiohediffereionsAandB。Eleanibson（1969）citedatraudycarriedoutbyVurpillotetal。（1966）inwhichitwasdemoperceptuallearninginvandtransferringdistihatseparateinstannoninstances（asopposedtandtransferriheinstanceshaveinon）。
Thisistrue，oflyifthelearnersaregivenopportunitiesfsuchdisatioionfromPavlovisrelevahatreflexesthatwereedtoastimulusweregehersimilarstimuli（duetosameness）。
&questionwas，then，howdifferentiationbelearned?Pavlovbelievedthatthereweretwooptions。Oherrepeatedlyreiioimulus，oronetrodureirastalongwiththereiioimulus。Hefoumethoddidnotwork。Therewasiohoughthestimuluseatedwithreihan1000times。Oherhand，evenasingleappli-ofurastcouldleadtorapiddifferentiation（Pavlov，1927，ascitedbyE。J。Gibson，1969）。
&erinE。J。Gibson's（1969）bookoiinswithaquotefromthe19th-turyBritishphilosopherandtheologiaiexplaihedifferentiatirasts。
Whenaredivoryball，seeime，hasbeenillleaveameionofitself，inwhichallthatsimultaneouslygaveuswillindistinguishablycoexist。Letawhiteballsucceedtoit;now，andnotbefore，willanattributedetachitself，andthecolor，byfortrast，beshakenoutintroueballbereplaegg，andthisnewdifferencewillbriosslumber，andthusthatwhibybeingsimplyaoutfrsesforusfirstaredobjearedrou，andsoon（Martineau，EssaysPhilosophidTheological，asquotedbyE。J。Gibson，1969）。
Thisisaingquoteiha。First，itdescribeswhatwemightcallretrospesfer:howtheimageofaisaffectedbyexperiencesfollowihoftheimage。Sed，welookattheeffethereversedireelyhowtheperofobjectsisaffectedbypreviousexperieheobservermayedoutaheformofthewhiteeggwithouthavihewhiteballjustbefore，normayshehaveseparatedoutahecolorofthewhiteballwithouthaviheredballjustbefore。
M
In1975，Schmidtpublishedhisarticle“ASchemaTheoryofDiscreteMotorSkillLearning”，whichhasbeehighlyiiali。Oknownimplisofthetheoryisthevariabilityofpracticehypothesis，whichstatesthatvariedpractice（“SituationA”ierminology）islikelytoenhananewsituation（SituationB）。Whatisiingisthattherelationshipisnotsideredasafunewosituations，butasafunofdifferencesacrosssituatiohesisreceivedagreatdealofsupportfromempiricaltestsduringtheyearsfollowingitspubli（Shapiro＆Schmidt，1982;Shea＆Wulf，2005;Sherwood＆Lee，2003）。
&uslookatatypicalstudyoxley（1979）。Eighty，aged6to8yearsold，partitheexperimeributedacrosstwos。Thetaskwastotrytohitatarget（acarpet）withashuttleeofthesthethrew20timesfromfivedifferentangles，eaedistaingonthefloorwiththeirfeetpointingtopositewall。Iionthehadtothrowshuttleesfromthesameposition。Afterwardsbothgroupstriedtohitthetargetwithshuttleaion。Thegroupsubjectedtothevariedsucceededbestwiththetask。
KerrandBooth（1978）ilarstudy，inwhichthetaskwasagaintohitahecriticaldiffereswasthedistahetaskwastohitatargetwithmihirty-sixwithanaverageageof8。3yearsand28withanaverageageof12。5yearspartitheexperiment。Bothagegroupswererandomlyassigyandschemagroups。Allweretestedinthebeginningaheexperiment，theyrfrom3ftandtheolderfrom4ft。Thedeviatiowasmeasuredaftereachthrowandthediffereheaverageerroratthebeginningaheexperimentwasthemeasureoftheeffectofthepractithetwotests。
&iceforthespecificitygroupsistedofagreathrows，allfromthedistafortheyoungerand4ftfortheolder。intheschemagrouppracticedatavarietyofdistaneofwhichwasthedistaisioheintheschemagroupoutperformedtheiygroup。Therefsomethihanwhatwastestedwasmoreeffepragexactlywhatwastested。
Althoughthevariabilityofpracticehypothesisreceivedmuchempiriidt's（1975）theoryhasbeenseriouslyquestioned（seeShea＆Wulf，2005;Sherwood＆Lee，2003）。IwouldalsoliketoihevariabilityofpracticehypothesisinawaythatdiffersfromSchmidt&#inalformulatiovariedprahaureperformahhaributioiorerobustschemagbehavior。Myiionisthatvariationisnecessaryfordist，andthattheleardiscriticaldiffereioobeabletoadjusttoions。
MakiicUseofVariationtoEnhang
&aioweenwhatstudeheandeningintheairalquestioiohisquestionhastypiaddressedbyrelatinglearnihewaysinwhigisanized（individualizedinstrus，whole-classteag，pr，peerlearning，reciprocalteadsodifferenhisanecessarilysayanythingaboutdifferehetoraboutdifferelearo。Ioideer，wehavetoparedifferentsinwhichthesametisaddressed。emightwhenspeteh，someofitsaspectsarevaried，whereasothersremaininvariant。Whenlookingatthegraphicalrepresentatioionsoftheformy=ax+b，forieachermightkeepbinvariant（e。g。，b=0）andsubstitutedifferentvaluesf。，a=1，12，2，3，…），thusfogattentionontheslopeoftheline。Inasimilarmaeachermightkeeptheslopeinvariantandvarythebvalue，thusfogattentiononparallellinesandvaryis。Ifonlytheslopeisvaried，thestudentsmightlearhing。Ifoerceptisvaried，thestudentsmightlearhing。Ifbothparametersarevaried，thestudentsmightlearnathirdthing。Ifbothsourcesofvariationaremixedinarandomfashiolearlyagain。Ifthereisonelineinaatesystemohestudentsgebypluggivaluesiiony=ax+b，theoutayagai。
Differevariesandwhatisinvariantmakedifferentthingspossibletolearhepatternofvariationandinvariandealingwithsomepartitentishighlycorrelatedwithwhatthestudethatple，MartonandPang（2006）foundthatinfiveparablehigh-agsedaryschoolclasses，taughtbyfivehighlyexperieheproportioswhomasteredadiffiiceptvariedbetween6%and97%dependingonthedifferentpatternsofvariationandinvarianhowsystematicallythosepatternswereusedinthes。IwosesIexploretheeffectofthesystematicuseofvariationinsbygseveralexamples。
Learningesewords。
IntwoparablesedgradeHongKosweresupposedtolearnsevenesewordsiofashortstory（Chik＆Lo，2004）。Theirsuccesswasmeasuredbymeansofa“cloze-test”，ashorthanumberofwordsdeleted，leavihewords。Thestudeofillihtheappropriatewords。Itossibletofillthegapsbyusingthesevenwordsthathadbeenstudied。InClassA，all30studeaskcorrectly，whereasinly9of31studentsdidso。Whenparinghowthesametwashahetwoclasses，itwasfoundthatinClassAdifferesofea，meaning，pronun）weredealtwithinwithoheseaspectswerekepttogetherforeachword）。Bywayoftrast，inClassBeachaspectwasdealtwithseparately（i。e。，wroupedagtoeachaspect）。ThismeantthatinClassAtheiyoftheaiheirrelatedaspectswerekepttogether），whereasinClassBtheaspectswerekeptseparateandtheearedonceforeachaspect。
Thesametwasthusdealtwithinbothclasses，butdifferently。InClassA，foreachectsvaried。Intrast，inClassB，foreachaspectthewordsvaried。Thus，thediffereodowithhowthetwasstructured，rimarilyandwhatvariedsedarily，alearionwasattractedto。
Inmanyofthepreviousexamplespresehisarticle，Ihavearguedfortheimportarastandofvariationincriticalaspethestudyofeseasimportantthataicalaspe，meaning，andpronun）variedtogether（fromwordtoword）。Asthewordswerebasiookenwordstothestudentsalready，iolinkthespokenwordstothewrittenforms（charadtotheelaboratedmeanings，itwasadvahediffereether。ThisshowsthattherearenopatternsofvariationoriaresuperiorfortransferihepointIwapatternsofvariationandiicallyimpahespecifidepeicularobjectandonthegroupofleariginthelearningexperience。
Learniones。
Ihedistosideraninstrualapproawhichthepatternofvariationandiheoreticallybased。[3]KiandMarton（2003）ihedifficultprocessesetonesbyadultfoneseisaplexdialeese，andspokenesewuishedbybothsoundahismeansthattwoormorewordsprohesamesoundhave（andusuallydohave）twoormoredifferentmeaintoch。Therearesixdiffereonese:highlevel，highrising，midlevel，lowlevel，lowfalling，andl。ObelievethatesespeakersaremoreseonaldifferehisisagrayandDowns（1993）parednativespeakersofEnglishandeseandcludedthattheformeractuallymadefinerdisationsinpair—wiseparisonsofsingulartoheremustbeainers'difficultieswithese。
Differech（ofwhiakeupaspecialcase）arealsoimportantinnontonallaiheyareusedtomakedistinsatthesentencelevel（e。g。，betweeiveaivemodes），nottoindicatedifferethewordlevel。tly，eakerofanatonallaonallanguageinwhicheverywordhasbothasoundandato，sheautomaticallytriestodistiweenmeaningsintermsofdifferensoundalone。Bydoingsosheremainsinakiialdistinperorinprodubetweenwordsthathavethesamesoundbutdifferenttos。Whenvariationinsoundissuppressedandvariationintoneandmeaningisafforded，thelear，however，usetonalvariatidisti>
KiandMarton（2003）foundthatbyinvitingnoolearsofesewordsthathavethesamesoundbutdifferenttoheylearendtotonaldifferenakedistiweenmeaningsonthewordlevel。Thisrepresentedafulearners'attentioonlydidtheleareratdistinguishiweenmeaniardsthewordsitheyalsogotbetteratlearningtodistiweenmeanioioweensoundspressed。Inafollow-upstudy，KiandMarton（2005）demobyfirstseparatingvariationintoneandmeaningandkeepingsoundinvariaingvariationinsoundandmeanioneinvariant，andfiingallthreedimensionsvarysimultaneously，learnersmakegreatprogresstowardhandlingtheplexitiesofeverydayuseofese。
&ospellthetj（dinSwedish。
Audyshowedthatwhatdistinsthelearnersmake—aomake—ishighlyimp。AgroupofSwedishteachers，wwitharesearcher，desigtheythoughtwouldtributetstudents'spellingofwordswithatjsound（Holmqvist，Gustavss，2005;iherearedifferentellthissoundthattoverembasedont-vowelbinatioaiioeacherscarriedoutthelessohegroup。Afterwardsthegrhelesson，anditwascarriedoutbyasedteacherwithanroupofstudents。Thegrouprevisedthelessonagain，anditwascarriedoutbyathirdteacherwithathirdgroupofstudespartigihreelessonsdiffereheywerekepttogetherforonelessonoheyreturheirowhreegroupstookthesamespelliimmediatelyafterthelesson，againafter4weeks，andonafteranother8weeks。Ohegroupslaggedbehiwogroupsinitiallybutsurpassedbothgroupssometimeaftertheexperiment。Thisgroupimprovedo，whereastheroupsremaihesamelevelhtlyweaker。Theresearvestigatedhowtheinstrualtreatmentstributedtothedifferencesacrossgroups。
Toexplainwhyonegroupimprovedmorethahergroupsafterthelearningo，theresearjecturedthatthestudentsinthemoresuccessfulgrouplearopayattentiontothedifferejsoundandthesjsound（andothersouodifferentspellijsoundasparedtodifferentspellingsofthesjsousbesitizedteofdifferehestudehergroups。HeheyhadmoreopportunitiesfwhattheyhadlearheyreadorwrotesomethinginSwedishsubsequeiihisplyabetterpreparationforfuturelearning，inthesenseusedbyBransfordandSchwartz（1999）。
Providingforindividualdifferences。
&udydestheprevioussewasablendofJapaudy”anddesign-basedresearqvistetal。，inpress）。Insudedapproach，calledlearningstudy，aisbyagroupofteachersassistedbyaresearcher。Thestudents'prioftheobjectisrevealedbymeansofapretest。Oneormorelessudentsdevelopaandingoftheobjectbybuildingupos'pris。Thelesson（orsequenceoflessons）iscarriedoutbyoeachers。Studentsareassessedafterthelessosaredisrelationtolathe。Asaresult，thelessonisrevisedandtaughtbyaeaestudymightpriseoofoursuchiterativecycles。
&y-seveiaresearddevelopmeaimedatprovidingforindividualdifferehrstudiesinHongKoentionaidtolow-agstudeicuseofvariationtedasthemainapproachtotheei（Lo，Pong＆Chik，2005）。Seventeenlesshanumberbeingrevisedowice，foratotalof27lessons。Inallofthelessons，variatioemati25ofthe27cases，studentsperfnifitlybetterafterthelessonthantheyhadbefore。Furthermore，thisimprovementwassignifitlyhigheramonginitiallylow-agstudentsthanamonghigh-agstudents，eveionwasmadefeffesfertotheannualattaiwasfound，especiallyforthelow-agstudents。Finally，researchersobservedthathigh-agstudentsdevelopedinsightsthatweheobjectameasuredbytheassessmenttools。