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ArtsECOFellows2018

UWMLessonPlanTemplate(adaptedfromPSOAArtEducationArea)

Name: OliviaPeterson Email: oap@uwm.eduLessonTitle: 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.