Learning Curve: Theory, Meaning, Formula, Graphs [2022]

A learning curve is a correlation between a learner's performance on a task and the number of attempts or time required to complete the task ... LearningCurveTheDefinitiveGuideKnowledgeHubAnalyticsDescriptiveanalyticsHRanalyticsKirkpatrickModelLearninganalyticsPredictiveanalyticsPrescriptiveanalyticsWorkforceanalyticsCommunicationCommunicationstylesConstructivecriticismConstructivefeedbackHowtoimprovecommunicationskillsTypesofcommunicationTypesoffeedbackEmployeeperformanceIncentivemanagementPerformancemanagementPerformancemanagementprocessPerformancemanagementcyclePerformanceappraisalPerformanceimprovementplanTypesofmotivationWaystoimproveworkperformanceEmployeetraining&developmentCybersecuritytrainingDiversityandInclusiontrainingEmotionalintelligenceintheworkplaceEmployeedevelopmentEmployeedevelopmentmethodsEmployeedevelopmentareasEmployeedevelopmentplanEmployeetrainingCompliancetrainingJobrotationJobshadowingOn-the-jobtrainingResiliencetrainingReskillingUpskillingHumanresources306090DayPlan9/80WorkScheduleCareermobilityCodeofconductCompetencymanagementCompetencymodelEmployeeengagementEmployeeonboardingprocessEmployeeonboardingchecklistEmployerValueProposition(EVP)ExitinterviewHardSkillsvsSoftSkillsInstitutionalKnowledgeKnowledgemanagementNepotismintheworkplaceOffboardingSkillsMatrixSuccessionplanningTalentacquisitionTalentmanagementWorkcultureWorkethicWorkforceplanningLeadershipHowtobeagoodmanagerLeadershipcommunicationLeadershipdevelopmentplanManagementstylesSharedLeadershipManagingbywalkingaroundConflictManagementStylesLearning&DevelopmentCorporatetrainingCustomertrainingDigitalTransformationofLearningLearningoutcomesMicrolearningMobileLearningGamificationSteeplearningcurveLearningtheoriesADDIEmodelAdultlearningtheoryAdultlearningprinciplesBlendedlearningBloom’sTaxonomyCareerdevelopmenttheoriesCognitivelearningContinuouslearningCollaborativelearningCooperativelearningLearningcurveLifelonglearningOrganizationallearningPersonalizedlearningPhenomenon-basedlearningSociallearningtheoryTransformativeLearningVicariouslearningTechnologiesWhatisanLXP?WhatisanLMS?Whatisanauthoringtool?WhatisxAPI?WhatisSCORM?UselearningdatatoacceleratechangeTheDataofLearningWorkbookishere!Becomefamiliarwithlearningdataandobtainapracticaltooltousewhenplanninghowyouwillleveragelearningdatainyourorganization.DownloadworkbookUpdatedFebruary17,2022Discover:Whatisalearningcurve?TheLearningCurveTheoryLearningcurveformulaLearningcurvemodelsandexamplesProsandConsofthelearningcurvetheoryApplicationoftheterm“learningcurve”WheretoapplythelearningcurveRealworldexamplesofapplicationthelearningcurvetheoryWhatisasteeplearningcurve?Whatisalearningcurve?Alearningcurveisacorrelationbetweenalearner'sperformanceonataskandthenumberofattemptsortimerequiredtocompletethetask;thiscanberepresentedasadirectproportiononagraph.Thelearningcurvetheoryproposesthatalearner’sefficiencyinataskimprovesovertimethemorethelearnerperformsthetask.Graphicalcorrelationbetweenalearner'sperformanceonataskandthenumberofattemptsortimerequiredtocompletethetask.TheLearningCurveTheoryEbbinghaus'forgettingcurveWhiletheterm"learningcurve"cameintouseintheearly20thcentury,Dr.HermannEbbinghausdescribedthistheoryasearlyas1885.Hemostlywasfocusingonmemorystudiesanddevelopedaforgettingcurvetheory.Thistheoryhelpsustounderstandhowourmemoryworks,andretainsinformation,relatingtospecificthingspeopleattempttolearn.ThemodernMicrolearningtheoryisbasedonEbbinghausmemorystudies.Nowadaysithelpsusunderstandwhenandwhyweforgetcertaininformationandhowwecantacklethis.Later,ArthurBillsdescribedthelearningcurveinhiswork“Generalexperimentalpsychology”(Bills,ArthurGilbert,in1934,page192).Inhiswork,hedescribesitsaying,“thelearningcurveisagraphicaldeviceforpicturingtherateofimprovementintermsofagivencriterionofefficiency,asaresultofpractice.”Hedescribedtwosidesofthesameprocessandhadpresentedtwolearningcurvegraphs.The1stcurveofachievementrepresentsanincreaseinproductivityovereachunitoftrial.Acqusitivecurveofamount-“Generalexperimentalpsychology”(Bills,ArthurGilbert,in1934,page193)The2ndillustratesaneliminative,ordeclining,curveoftimeneededtoperformthesametask.Eliminativecurveoftime-“Generalexperimentalpsychology”(Bills,ArthurGilbert,in1934,page194)Wright’sexperiencecurveThisisthebasisforthelearningcurveformula,the“CumulativeAverageModel”(or“Wright’sModel”),whichwasdescribedbyT.P.Wrightin1936inhiswork"FactorsAffectingtheCostofAirplanes",afterrealizingthatthecostofaircraftproductiondecreasedwiththeincreaseinproductionperformance.Therearecurrentlydifferentvariationsoftheoriginalformulausedtodayinspecializedapplications,buttheidearemainsfamiliartotheoriginalformula.Theexperiencecurvetheorystatesthattheefforttocompleteataskshouldtakelesstimeandeffortthemorethetaskisdoneovertime.Ifoneweretoplottherepeatedattemptsofalearneragainstthetimetakentocompletetheattempt,apatterncanbeidentifiedindicatingthatthetasktakeslesstimeasthelearnergainsmoreexperienceviarepeatedattempts.Thetheorycanalsobeexpressedasamathematicalfunctionthatcanbeusedasapredictiontool.LearningcurveformulaTheoriginalmodelusestheformula:Y=aXbWhere:YistheaveragetimeoverthemeasureddurationarepresentsthetimetocompletethetaskthefirsttimeXrepresentsthetotalamountofattemptscompletedbrepresentstheslopeofthefunctionTheformulacanbeusedasapredictiontooltoforecastfutureperformance.Theformulastipulatesthatthemoreattemptsthatareincluded,themoretheoveralltimewilldecrease.Theformulacanbeusedtopredictalearner’srateoflearningofasimpletaskorevenhelpbusinessestopredicttheproductionrateofaproduct.Foramoredetailedlookathowtousethisformula.LearningcurvemodelsandexamplesAlthoughthetheorystatesthatmoreattempts=adecreaseintime,itdoesnotalwaysworkoutthatway.Manyfactorscanimpacttheend-results,resultinginavarietyofdifferentlearningcurveshapes.Herearefourcommontypesofalearningcurveandwhattheymean:1.Diminishing-ReturnsLearningCurveTherateofprogressionincreasesrapidlyatthebeginningandthendecreasesovertime.Thisdescribesasituationwherethetaskmaybeeasytolearnandprogressionoflearningisinitiallyfastandrapid.Progressionlevelsoffasthelearnerobtainfullproficiency.Thiscouldbedescribedasaplateau,wheretheindividualisnolongerprogressing.Itcouldsignalthatthelearnerhasreachedalimitintheirabilityorthatatransitionmaybeoccurring.Itcouldalsomeanthattheindividualhaslostmotivationorisfatigued.2.Increasing-ReturnsLearningCurveTherateofprogressionisslowatthebeginningandthenrisesovertimeuntilfullproficiencyisobtained.Thismodeldescribesasituationwhereperhapsacomplextaskisbeinglearnedandtherateoflearningisinitiallyslow.3.Increasing-DecreasingReturnLearningCurve(theS-curve)Thismodelisthemostcommonlycitedlearningcurveandisknownasthe“S-curve”model.Itmeasuresanindividualwhoisnewtoatask.Thebottomofthecurveindicatesslowlearningasthelearnerworkstomastertheskillsrequiredandtakesmoretimetodoso.Thelatterhalfofthecurveindicatesthatthelearnernowtakeslesstimetocompletethetaskastheyhavebecomeproficientintheskillsrequired.Oftentheendofthecurvebeginstoleveloff,indicatingaplateauornewchallenges.4.ComplexLearningCurveThismodelrepresentsamorecomplexpatternoflearningandreflectsmoreextensivetracking.Thebeginningofthecurveindicatesthatlearningisinitiallyslow.Thesecondstageofthecurveshowsanincrease,whichindicatesthatthelearnerisbecomingproficientintheskill.Thethirdstageofthecurveindicatesthatthelearnerisplateauinginhisproficiencyoncethelearnerfeelshehasmasteredtheskill.Thefourthstageofthecurverepresentsthatthelearnerisactuallystillimprovingtheskill.Thelaststageofthecurverepresentsthepointatwhichtheskillbecomesautomatic,musclememoryforthelearner,oftentermed“overlearning”.ProsandconsofthelearningcurvetheoryProofthelearningcurvetheoryUsingalearningcurvecanhelpabusinesstoimprovetheperformanceandproductivityoftheirworkforceandreducecosts.Whenusedtotrackorpredictperformance,itcanprovidepsychologicalmotivationandstrategicplanning:Performanceimprovementcannothappenonitsownandisconnectedwithlearning.Byincorporatingalearningculturewithintheorganizationwhereemployeesareencouragedandsupportedtokeeplearning,performancelevelscanbeexpectedtoincreaseonthecurve.Therateoflearningisalsoconsideredtobeconsistentenoughthattrendscanbeestablishedusingthelearningcurve,enablingbetterforecastingandbusinessdecisions.ConsofthelearningcurvetheoryAsacon,alearningcurveisverydependentonassumptionsmadeaboutperformance.Asmentionedearlier,manyvariablescanimpactlearningandfutureperformance:Usingalearningcurvetopredictoverallperformanceoflargergroupsorprocessesmeansthatmanyassumptionsaremadeonvariableslikemotivation,sociologicalfactors,workplacedynamics,trainingresources,andpreviousknowledgeorexperience.Alearningcurvethatmaynotshowexpectedresultswouldneedfurtheranalysistodeterminetheunderlyingvariablesimpactingitsshape,asthecurvedoesnottellthewholestory.Applicationoftheterm“learningcurve”Twoapplicationsoftheterm“learningcurve”canbefound:GeneralizedThelearningcurveisoftenusedincolloquialspeechtodescribethetimeandeffortrequiredwhenlearningsomethingchallenging.Theapplicationcanbebroadandgeneralized,suchasdescribingthelearningcurveinvolvedinlearningtoread.Inthesescenarios,agraphicalrepresentationusingmathematicsisnotbeingappliedtoexplainlearningprogression.Thetermisthereforeusedasaqualitativedescriptionoflearningprogressionovertime.MeasuredTheotherapplicationoflearningcurveisquantitative,wheremathematicalmodelsarecreatedtorepresenttherateofproficiencyormasteryofatask.Thislearningcurvemodelisonlyapplicablewhenusedtomeasuretherealrateofprogressforcompletingaspecifictaskagainsttime.Thetaskneedstoberepeatable,measurable,andconsistofonlyonevariablewithinaprocedure;itcannotmeasureanentireprocedureonitsown.WheretoapplythelearningcurveTherearemanyvariablesinlearningthatimpacttherateofprogressionandcannotbeaccuratelyreflectedinthelearningcurvemodel.Intheexampleoflearningtoread,thevariablescouldincludephonetics,vocabulary,typeofreadingmaterial,teachingmethods,motivation,previousknowledgeorexperience,qualityofpractice,andmuchmore.Thelearningcurvemodelrequiresthatonevariableistrackedovertime,isrepeatableandmeasurable.Individualmotivation,forexample,wouldbedifficulttomeasure.Asawhole,learningtoreadisacomplexprocedureinvolvingmanyvariablesandisnotidealforalearningcurve.Anexampleofwherealearningcurvecanbeappliedcouldbeameasurabletasklikeafactoryworkerlearningtooperateanewmachinethatrequiresspecific,repeatablesteps.Astheworkerlearnstooperatethemachinefollowingtheproceduralsteps,hebecomesfasterandmoreproficientatusingit.Alearningcurvewouldmeasurethisrateofprogressionandmastery.Thelearningcurvemodelisusedmostcommonlyinorganizationalorindustrialmanagementtoimproveoutputbywayofimprovingtheperformanceofthehumanworkforce.ThemodelwaswidelyappliedduringWorldWarII(WWII)whenitwasrealizedthatthecostofaircraftdecreasedwiththeincreaseinproductionperformance.Itwaslatertakenupbytheindustrialandbusinesssectorforavarietyofperformanceimprovementapplications.RealworldexamplesofapplicationthelearningcurvetheoryThelearningcurveisknownbydifferentnamespartlyduetoitswidevarietyofapplication.Termsusedtodescribethelearningcurveinclude:experiencecurve,costcurves,efficiencycurves,productivitycurves.Themodelcanbeusedtodeterminehowlongittakesforasinglepersontomasteraskillorhowlongittakesagroupofpeopletomanufactureaproduct.Inmostapplications,the“learning”inthecurveisactuallyreferredtoasprocessimprovement.Let’stakealookatsomedifferentexamplesofwherethelearningcurveisbeingappliedtoday.IndustryManufacturingcostsasrelatedtoworkforceperformancecanbetrackedbyusingthelearningcurve.Insteadofperformanceandnumberofattempts,thevaluescouldbeunitcostorunitlaborhoursandcumulativeproductioninunits.Asworkersproducemoreproduct,theper-unitcostwilloftendecrease.Thelearningcurvecanbeusedtopredictpotentialcostswhenproductiontaskschange.Forexample,whenthepricingofanewproductisbeingdetermined,laborcostsarefactoredin.Ifaproducttakestwohourstoproduce,theproductisreleasedtothemarketforsaleatacostthatreflectsthetwo-hourproductionperiodplusotherassociatedcostsandmarkups.Butwhatiftheproductiontimewasbasedonthefirstfewattempts?Whatifbythe100thtimetheproductwasproduced,productiontimeisreducedtoonehour?Theproductwouldbeonthemarketatapricethatismuchtoohigh,resultinginpotentiallylowersales.Usingthelearningcurvecanprovideadditionalinsightforplanningpurposes.BusinessLearningcurvescanalsobeappliedtoorganizationalperformanceusingeitherthegeneralizedapproachorbyconductingameasuredanalysis.Determiningwhichapproachtotakedependsonwhetherthedesiredperformancecanbedirectlymeasured.Forexample,employeeslearningadifficulttask,suchaslearningtouseacomplexsoftwareprogram,mayhavepoorperformanceatthebeginningduetotheinherentdifficultyofthetask.Ifthegoalisthatemployeesneedtoknowhowtousethesoftwareintheirdaytodaytasks,thismaybedifficulttomeasureasitinvolvesmanyvariables.Byapplyingthelearningcurvetheoryasaframework,organizationscanstillbenefit.Thelearningcurveasaframeworkcanhelporganizationstounderstandinthisscenariowhatisrequiredtobecomeproficientinthesoftware.Iftrainingsupportandtimetopracticeareidentifiedasimportantfactors,thenitcanbeseenthatemployeeswhoaregivensupportandtimetopracticewiththesoftwarewillovertimehavebetterperformancethanemployeeswhoarenotgivensupportortimetopractice.Ifthesoftwareisimportantforproductivity,thenemployeeperformancecoulddecreaseovertimeifemployeescannoteffectivelyusethesoftware.Organizationscanthenprovideadditionalsupportorresourcesneeded.Toutilizeameasuredlearningcurve,organizationswouldneedtoidentifyaspecificvariabletoanalyze.Forexample,anorganizationseekingtoimprovetheperformanceofcustomerservicecoulddecidethattheimplementationofanewinitiative(#ofattempts)wouldresultinadecreaseincustomercomplaints(performance).Theorganizationcouldtrackandanalyzetherepetitivepracticeofthisinitiativeovertimetodetermineifindeedcustomercomplaintsdecreasedovertime.MedicineForsurgeonsintheoperatingroom,manyprocedureswillinvolvethesamerepetitivetasks.Becauseasurgeonisessentiallypracticingthesameskilloverandoverwheneverthatprocedureisdone,thelearningcurvecanbeappliedtoshowindividuallearningandperformanceovertime.Thisenablesnotonlyinsightintotheimprovementthatthesurgeonisachieving,butaidesinstructorswithidentifyingwheremoreresourcesandassistancecanbedirectedtoimproveperformance.UselearningdatatoacceleratechangeTheDataofLearningWorkbookishere!Becomefamiliarwithlearningdataandobtainapracticaltooltousewhenplanninghowyouwillleveragelearningdatainyourorganization.DownloadworkbookHello,weneedyourpermissiontousecookiesonourwebsite.Weusecookiesforhistoricalresearch,websiteoptimization,analytics,socialmediafeatures,andmarketingads.ReadourCookiePolicyformoredetails.PreferencesAcceptallCookiePreferencesValamisvaluesyourprivacy.Pleasechoosethecookietypesyouwanttoallow.YoucanreadourCookiePolicyformoredetails.NecessarycookiesThesecookiesareessentialforthewebsiteandcan’tbedisabledwithoutharmingthesiteperformanceanduserexperience.Wecollectanonymizedstatisticsonlyforhistoricalresearch.Thesecookiesdon’tstoreanypersonalinformation.valamis_cookie_essentialsTargetingCookiesThesecookiesusedformarketingpurposes.Theyareusedtomeasuretheeffectivenessofadvertisingcampaignsandremarketing.Thesecookiesdon’tstoreanypersonalinformation,atthesame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