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ArtsECOFellows2018
UWMLessonPlanTemplate(adaptedfromPSOAArtEducationArea)
Name: OliviaPeterson Email: [email protected]: ArtisticResponsetoPolarFunctionsLevel/Grade/Age: PreCalculus/Calculusage16-18+
BIGIDEA(Describehowthebigideaisimportanttothisagegroupinrelationtostudentassetsandthecontentarea):Inthisartisticresponsetopolarfunctions,studentswillcreateworksofartbymanipulatinggraphsinpolarcoordinates.Throughthecompletionofthisprojectstudentswillbeabletoidentifytransformationfactorsandpredictgraphsoffunctionsinpolarcoordinatesaswellasunderstandtheuseofartformsinrelayingandinternalizinginformation.Studentswillbepresentedwithvariousexamplesofhowmathisincorporatedintoartandalsothesimilaritiesbetweendifferentprocessesinmathandart.Experimenting,investigating,andrefiningwillbeprocessesthatthestudentswilluseinboththemathematicalandartisticaspectsofthisproject.Uponcompletionstudentswillhavecreatedaworkofart,awrittendescriptionoftheirartworkincludingwhichfunctionstheyusedtocreateit,andawrittenreflectiondescribingwhattheylearnedaboutgraphingtransformationsinpolarcoordinatesandhowitrelatedtotheirartisticandmathematicalprocess.OBJECTIVESANDNATIONALSTANDARDS:http://www.nationalartsstandards.org/ArtCreating#VA:Cr1.2 Artistsanddesignersshapeartisticinvestigations,followingorbreakingwithtraditionsinpursuitofcreativeartmakinggoals.Whydoartistsfolloworbreakfromestablishedtraditions?
- VA:Cr1.2.HSIIIChoosefromarangeofmaterialsandmethodsoftraditionalandcontemporaryartisticpractices,followingorbreakingestablishedconventions,toplanthemakingofmultipleworksofartanddesignbasedonatheme,idea,orconcept.
#VA:Cr2.3 Artistanddesignersdevelopexcellencethroughpracticeandconstructivecritique,reflectingon,revising,andrefiningworkovertime.Whatroledoespersistenceplayinrevising,refining,anddevelopingwork?
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- VA:Cr3.1.HSIIIReflecton,re-engage,revise,andrefineworksofartordesignconsideringrelevanttraditionalandcontemporarycriteriaaswellaspersonalartisticvision.
Presenting#VA:Pr6.1 Objects,artifacts,andartworkscollected,preserved,orpresentedeitherbyartists,museums,orothervenuescommunicatemeaningandarecordofsocial,cultural,andpoliticalexperiencesresultinginthecultivatingofappreciationandunderstanding.Howdoesthepresenting&sharingofobjects,artifacts,&artworksinfluence&shapeideas,beliefs,&experiences?
- VA:Pr6.1.HSIIICurateacollectionofobjects,artifacts,orartworktoimpacttheviewer’sunderstandingofsocial,cultural,and/orpoliticalexperiences.
Responding #VA:Re7.1Individualaestheticandempatheticawarenessdevelopedthroughengagementwithartcanleadtounderstandingandappreciationofself,others,thenaturalworld,andconstructedenvironments.Howdoeslearningaboutartimpacthowweperceivetheworld?Whatcanwelearnfromourresponsestoart?
- VA:Re7.1.HSIHypothesizewaysinwhichartinfluencesperceptionandunderstandingofhumanexperiences.
Connecting #VA:Cn10.1Throughart-making,peoplemakemeaningbyinvestigatinganddevelopingawarenessofperceptions,knowledge,andexperiences.Howdoesmakingartattunepeopletotheirsurroundings?
- VA:Cn10.1.HSIDocumenttheprocessofdevelopingideasfromearlystagestofullyelaboratedideas.- VA:Cn10.1.HSIIUtilizeinquirymethodsofobservation,research,andexperimentationtoexploreunfamiliarsubjectsthroughart-making.
MathCommonCoreStateStandards:MathematicsCCSS.MATH.CONTENT.HSF.IF.B.4Forafunctionthatmodelsarelationshipbetweentwoquantities,interpretkeyfeaturesofgraphsandtablesintermsofthequantities,andsketchgraphsshowingkeyfeaturesgivenaverbaldescriptionoftherelationship.Keyfeaturesinclude:intercepts;intervalswherethefunctionisincreasing,decreasing,positive,ornegative;relativemaximumsandminimums;symmetries;endbehavior;andperiodicity.CCSS.MATH.CONTENT.HSF.IF.C.7Graphfunctionsexpressedsymbolicallyandshowkeyfeaturesofthegraph,byhandinsimplecasesandusingtechnologyformorecomplicatedcases
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CCSS.MATH.CONTENT.HSF.IF.C.8Writeafunctiondefinedbyanexpressionindifferentbutequivalentformstorevealandexplaindifferentpropertiesofthefunction.CCSS.MATH.CONTENT.HSF.IF.C.9Comparepropertiesoftwofunctionseachrepresentedinadifferentway(algebraically,graphically,numericallyintables,orbyverbaldescriptions).Forexample,givenagraphofonequadraticfunctionandanalgebraicexpressionforanother,saywhichhasthelargermaximum.LANGUAGEFUNCTIONUSEDTHROUGHOUTLESSON:Typeoflanguagefunction:http://www.eldstrategies.com/languagefunctions.html
Comparingandcontrasting,askingquestions,indicatingcauseandeffect,predicting
Emphasisoflanguagefunction(describethemainpurposeofusingthislanguagefunctionforyourlesson):
BycomparingandcontrastinggraphsinpolarcoordinatestographsinCartesiancoordinatesitwillgivestudentsabetterunderstandingoftherelationshipbetweenthetwoandhowtheycanbetranslated.Comparingdifferentpolarfunctionsandtheirgraphswillalsohelpstudentsrecognizethetranslationalcomponentsofthefunctionandhowitrelatestothegraph.Studentswillbeencouragedtoaskquestionstodispelmisconceptionsandtofurthertheirknowledgeandcuriosity.Indicatingcauseandeffecthelpsthestudentsfurthertheirunderstandingoffunctions,whichinitssimplestsenseisthemathematicalmodelofinputandoutputorcauseandeffect.Studentswillbeaskedtoindicatethecauseofthespecificshapesbeinggeneratedintheirgraphs.Predictingisthemainlanguagefunctionbeingaskedofstudentsinthislesson.Bytheendofthisprojectstudentsshouldbeabletopredictthegraphisshownthefunction.Throughtheirexperimentationstudentswilllearntopredictthepatternsbeinggenerated.
Wherelanguagefunctionwillbepracticed(i.e.,throughwriting,speaking,artmaking):
Comparing,indicatingcauseandeffect,andpredicting,willbeapparentinthestudent’swrittenreflectionandalsointheirexperimentationofmanipulatinggraphs.
UNITorLESSONDETAIL(provideforeachlessonsession):Motivation/introduction:
Aslideshowwillbeshowntointroducethisproject.Imagescaninclude:
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Toshowthedifferentshapesandpatternsthatarepossiblefrompolargraphsandalsoaslightindicationofhowtheycanbetransformed.Demonstrationsofgraphingcanbedoneusinghttps://www.desmos.com/calculatorontheboardsostudentsseehowtheycanutilizethiswebsite.Intheslideshow,anemphasisonthePolarCoordinatesseries(1980)byFrankStella,willbeshownasthecrossoverbetweenthemathandtheartworkstudentswillbedoing.Theycanalsoseehowaprojectusingtraditionalmediumscanbedone.
“PolarCo-ordinatesVariantIIIa”1980“PolarCo-ordinatesII”1980
“PolarCo-ordinatesIV”1980“PolarCo-ordinatesV”1980
ArtMaking: Supplies:StudentswillusetheircomputerstoexperimentwithgraphingontheDesmoswebsiteandeitherusetheircomputertomakeadigitalworkofartorbringintheirownmaterialsiftheywishtocreateapieceofvisualartusingtraditionalmediums.Teacherinstruction:“Usingrecoursessuchastheinternet,yourtextbook,andhttps://www.desmos.com/calculator(forgraphing),aswellaswhatyoualreadyknowaboutgraphsofpolarfunctions,createaworkofartincorporatingatleastthreeoverlayinggraphs.”Objective:Createanimageusingdigitalortraditionmediumsthatincorporatesthegraphsofatleastthreedifferentpolarfunctions.Studentsatwork:Studentswillfirstworkonmanipulatingpolarfunctionstocreatedifferentpatternsandshapes.Studentswillbeaskedtotrackwhataspectsofthefunctioncreatedifferentshapesandhowtheirgraphmanipulationandexperimentationcontributedtotheir
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creativeprocess.Studentswillthenchose3ormoreshapestheycreatedtomakeapieceofartworkusingeitherdigitalortraditionalmediums.Theirworkcanbeabstractor,ifthey’refeelingparticularlyambitious,representational.Closure:Uponcompletion:turninyourimage,acopyofyourimagewiththegraphsyouusedoverlaidontop,awrittenexplanationofyourartworkincludingthefunctionsyougraphed,andawrittenreflectiononwhatyoulearnedabouttransformationsofpolarfunctionsandhowthisrelatestoyourartworkandyourartistic/mathematicalprocess.
ComponentsEmbeddedintheLessonProcedureOpening/Stimulus:Aslideshowwillbeshownofthedifferentpossibleshapesandpatternsthatcanbecreatedusingpolarfunctionsandalsovisualartworkbyacontemporaryartistthatincorporatesthesegraphs.Students'Misconceptions:Whataresomepossiblemisconceptionsordifficultiesthatstudentswillhavewith/aboutthematerial.
- Studentsmaylookatthisassignmentastwodifferentparts,onebeingthemathematicalpartandonebeingtheartisticpart–andtreatthemseparately–wheninrealityeachaspectshouldbehelpingthestudentcompletetheother
- Consideringpolarcoordinatesisanadvancedmathtopic,manystudentsmayhavedifficultiesconceptualizinggraphsfromthefunctions,andwhattheymeanonthecoordinateplane,butthehopeisthroughthisexperimentationgeneralizationsandpredictionscanstarttobemade
Questionstoask:Providekeythoughtprovokingquestionsthatmightrelatetostudent’smisconceptionsorkeyquestionstogetstudentstofocusoncriticalaspectsoftheactivity. (FromNationalArtStandardsAbove)
- Whatroledoespersistenceplayinrevising,refining,anddevelopingwork(artisticandmathematical)?
- Howdoesthepresenting&sharingofyourartworkinfluence&shapeideas,beliefs,&experiences?Oryourunderstandingofthistopic?
- Howdoeslearningaboutartimpacthowweperceivetheworld?Whatcanwelearnfromourresponsestoart?Areyoulearningmoreaboutthistopicbyhearingotherpeopletalkaboutandpresenttheirexperiencesofthisproject?
Objectives/Assessment:Whatevidencewillyoubelookingforthatwilltellyouhowthestudentshavemettheobjectivesofthelesson?Themajorityoftheassessmentwillcomefromthestudent’swrittenreflection.Astudentwhorecordstheirentireprocessofexperimentationwhilemanipulatinggraphsandthenreflectsonwhichaspectsofthefunctionproducedwhatkindsofpatternsdemonstratesmeetingthemathematicalobjectives.Astudentwhocommentsonhowthisprocessoftrialanderror,experimentation,refining,andinvestigatingparallelstoworkingthroughthecreativeprocessdemonstratesanunderstandingofhowthesetwosubjectscanbeconnected.Astudentthatdemonstratesthroughtheirwritinghowartworkcanbeawayofproblemsolvingandexpressingyourfindingsdemonstratesmeetingtheseobjectives.
