IMPROVTECHNIQUESFORTHEMATHEMATICSCLASSROOM

Althoughthegoalsofimprovisationalcomedyandmathematicseducationmayseemdiametricallyopposed—oneistoentertainandtheotheristoinstruct—infact,theideasoftheformercanhelptoachievethelatter.Inthisinteractivepresentation,Iwilldemonstratehowsomeofthemostfundamentaltenetsofimprovcanbeappliedtocreatinganopenandengagingmathematicsclassroom.Participationwillbeencouraged.

Whatisimprov?Improvisationalcomedyistheaterthatismadeuponthespot,withnoscriptorplanning,andusuallywithnoorminimalpropsandsets.Someexamplesofwell‐knownimprovshows/troupes/theatersare“Who’slineisitanyway?”,SecondCity,theGroundlings,ImprovOlympic,andtheUprightCitizensBrigadetheater.

Whyinvolveimprovinthemathclassroom?

Itismyexperiencethatmanyofthestudentsthatweseeinourlowerlevelmathclasseshaveacertainideaofwhatmathis—scary,rigid,hard,formulaicarealladjectivesIhaveheard.Evenmanystudentswhoaregoodatmathlikeitbecauseoncetheylearntheprocessofacertaintypeofproblem,theycanbesuccessfulonassignmentsandexams.Asmathematicians,weknowtheamountofcreativityandimaginationthatisrequiredtodoandunderstandhigh‐levelmathematics.Sowhydowetakethecreativityandimaginationoutofmathclasses?Ihopetodemonstratethat,byusingtechniquesfromimprovcomedy,onecancreateaclassroomenvironmentthatencouragesoriginalthoughtandstimulatingdiscussion.BesidesbeingaresearchpostdoctoralfellowinthemathematicsdepartmentattheUniversityofArizona,Ihaveperformedasanimprovisationalcomedianforthepast9years.Ihaveperformedinliterallyhundredsofimprovshows,havebeenafoundingmemberofseveralimprovtroupes(GirlsGirlsGirlsImprovisedMusicals,JunkImprov,andtheFoolishMortals,tonameafew),havetraveledalloverthecountrytoperforminimprovfestivals,andhavegenerallydevelopedagreatloveandrespectfortheartform.IhaveappliedimprovtechniquesineverymathclassIhavetaught,tovaryingdegreesofsuccess.BLOCKSTOCREATIVITYOnereasontostudyimprov(ortoapplyitinyourclassroom)isthatitcanhelploosenblocksonourcreativity.In(Timpson,2002),theauthorsdiscussten“locksthatconfineourminds”:

i. Insistenceonthe“right”answerii. Apreoccupationswithwhatisassumedtobelogicaliii. Aconformingimpulsetofollowtherules

iv. Thecallforpracticalityv. Thepressuretostayontaskvi. Theavoidanceofambiguityvii. Thefearofmakingmistakesviii. Theprohibitionsagainstplayix. Thecommandmenttobeseriousx. Theassumptionbymanythattheylackcreativity

Improvcanclearlybeappliedtoanyoneoftheselocks.Byallowingourstudentstoexplorewhichofthesestopthem,weinvitethepossibilityofincreasingtheirabilitytothinkcreatively.PhysicistsattheEuropeanOrganizationforNuclearResearch,orCERN,haverecognizedtheutilityofimprov,bothinbecomingmoreeffectivecommunicatorsandindevelopingtheabilitytothinkonone’sfeet.InpreparationforswitchingontheLargeHadronCollider(andforthecontroversythatwasboundtoensue),agroupofthescientistshiredImprovOlympicfounderCharnaHalperntoteachthemaboutimprov.BobStanek,aparticlephysicistwhoisleadingCERN'simprov‐comedyexperiment,hadthistosay:

Improvhasgottobemoredifficultthandoingphysics.Youhavetothinkinmilliseconds.Whenyou'rediscussingthingsthatgoonhereonadailybasis‐‐whyyourdetectordoesn'twork,whyyourmachineisn'tcollectingdata‐‐youhavetoknowhowtorespondinaquickmanner.

Moredetailscanbefoundathttp://online.wsj.com/article/SB122048206487796841.html?mod=most_emailed_day.

Icebreakers/Risk­takingAtthebeginningofthesemester,Inormallyfindthatmanyofmystudentsarehesitanttoaskquestionsoreventotalktoeachotherinsmallgroupsettings.Itisvitaltothesuccessofmyclassestocreateanenvironmentwhereeveryonefeelscomfortableparticipating.Formany,answeringaquestioninfrontoftheclassorevenaskingoneisperceivedtobeARISK.ThesoonerIcanconvincemystudentsthattherewillbenonegativeoutcomefromtakingsucharisk,thesoonerIgetthelevelofinteractionthatIdesire.

A. Thecircusbow:Abig,overlydramaticbowwhilesaying“Ifailed”.a. Improvapplication:I’veseenthisusedinbeginningimprov

classestoencouragestudentstotakerisksand,iftheyfail,tofailgracefullyandshamelessly.Bydoingsomethingsillylikethecircusbow,evenfailingcanbefun(andfunny).

b. Mathapplication:Minimizingtheperceivedriskofansweringoraskingaquestioninclass.OnthefirstorseconddayofclassIwilltellmystudentsthatIhaveaverydifficultlessontoteachthem—thatitsoktomakemistakesinclass.Ihavethemallstand,andIdemonstratethecircusbow.ThenIhavethemdoitasaclass(and

Imakethemrepeatituntileveryoneparticipates).ItellthemthatIdon’texpectthemtodoacircusboweverytimetheymakeamistake,buttheyarewelcometodoso(I’llusuallydooneoccasionallytokeepthetoneofclasslight).

B. Namegames:Iliketolearnmystudents’namesassoonaspossible,andjustasimportantly,Ilikethemtolearneachother’snames.Thereareaplethoraofnamegamesoutthere.Herearesomeofmyfavorites.

a. Namewithphysicalaction(highrisk):Studentsstandinacircleandeachstudentwillsaytheirnameanddoaphysicalaction.Thenwewillallrepeatthenameandthephysicalaction.Aftereveryonehasgone,Imightgoaroundthecircleagain(doingthesameactionsalltogether)tosolidifynames.Thisissometimesnotverysuccessfulatthebeginningofthesemester,becauseitrequiresawillingnesstolooksilly.Alessriskyversionwouldbehavingstudentssayanalliterativeadjectiveandtheirname(e.g.AwesomeAndrea).

b. Namewithpointing(lowerrisk):Studentsstandinacircleandsomeonewillpointatanotherstudentandsayhisorherownname.Thatpersonpointsatsomeoneelsewhilesayinghisorherownname.Thegamecontinuesuntileveryonehasbeenpointedatseveraltimes.Timepermitting,thesecondpartofthegamecontinuesasthefirst,exceptthatthepersonsaysthenameofthepersontheyarepointingat.See(Gwinn,2003)formorevariations.

C. Sillywarm‐upgames:SometimesifIknowtheday’slectureisgoingtobeabitdryorifenergydrasticallywanesduringclass,I’llplaythesequickgames.Theycanworkasicebreakersorasenergy‐raisers.

a. Screamcircle:Havethestudentsstandinacircleandputtheirheadsdown.Onthecountofthree,theyallraisetheirheadsandlookatsomeone.Ifthatpersonisalsolookingatthem,theybothscreamandleavethecircle.Ifthatpersonisnotlookingatthem,theystayinthecircle.Continueuntilthereareonlytwopeopleleft.Thisexercisecanalsobeusedtodividethestudentsintopairs.

b. Movementcircle:Havethestudentsstandinacircle.Startamotion(withorwithoutsound).Thenextpersonshouldcopythemotionandsoundascloselyaspossible.Themotionmovesaroundthecircleandprobablywillmorph.Goaroundthecircleafewtimes.

Yes,and

Thissimplephraseisreallythebasisofallimprovtheory.Theideaisthatwecancreatesomethingfromabsolutelynothingifwebothagreetoagreewiththerealitywesetupandtocontributetothat.Itslikebuildingabrickwall.Yousetabrick,Isetoneontop,yousetoneontopofthat,andbeforeweknowit,wehavethisawesomewall.Well,maybeourwallisnotverytallorstructurallysound,butwe

havebuiltitourselves,outofnothing(exceptbricks).ImagineifinsteadyouhadstartedbuildingawallandthatIhaddecidedthatIwouldbuildaboatinsteadofhelpingyouwithyourwall.Orevenworse,imagineIhaddecidedtotakebricksdownjustasyouputthemup.Eitherway,wearen’tgoingtoendupwithmuchofawall.Thismetaphorisgettingmuddy.Thepointisthatsaying“yes,and”isthebest(mostefficient?Easiest?)waytomakesomethinghappenonstage.

Wecanapplytheconceptof“yes,and‐ing”tomathinatleasttwoways.First,studentscan“yes,and”theirownideas.Often,astudentwillcometoofficehourshavingstartedaproblem(correctly)butwillhavestopped,assumingtheywerewrong.Usually,alltheywillneedisabitofencouragementfromme,andtheywillfinishtheproblemontheirown.Iftheycouldlearntoagreewithandsupporttheirownideas,theycandevelopconfidenceintheirownthoughtprocesses.Secondly,“yes,and‐ing”othermembersofagrouphelpsfosterdialogueandhelpstosupporteachother’ideas.

A. JumpTogether:Thisexerciseemphasizestheideaofsurrenderingone’sindividualdesiretothatofthegroup.Havethestudentswalkinacircle.Thegoalistoalljumpatthesametime,withoutanyoneclearlyleading.Theideaisthattheyshouldbeabletobeintunewiththeirclassmatesandshouldfeelthemomenttojump.Youmightstartcallingoutwhentojump,togeteveryoneusedtothefeelingofjumpingtogether.Eyecontactcanhelp.

B. OnePersonWalking:Thepurposeofthisgameistoseamlesslytakeleadershipandgiveitaway.Thisskillisquiteapplicabletogroupwork.Sometimesonepersonmakesagoodleaderforagroup,butthenthetopicofthegroupworkchanges,andallofasudden,anothermemberwouldbemorefittolead.Beingcomfortablegivingandtakingleadershipisanimportant(andsometimesdifficultskill).Havethestudentsstandanywhereintheroom.ThegoalistohaveEXACTLYonepersonwalkingatanytime.Ifonepersonstartswalking,whoeverwaswalkingpreviouslymuststop.Similarly,ifthepersonwhowaswalkingstops,someoneelsemustimmediatelystart.Thisgamecanbeexpandedtohaveexactlytwo,three,ornstudentswalkingatanytime.

C. Thatmeans:Thisgamereallyemphasizessayingyes.Pairupyourstudentsandplayallatonce.StudentAshouldmakesomedeclarativestatement.(It’sraining,Ihavenomoremoney,Ithinkmathisawesome.)StudentBthenrepeatsthestatementandadds,“Thatmeans___”.Continuethispattern.Forexample:“Ithinkmathisawesome.”“Youthinkmathisawesome.Thatmeansyouhavegoodtaste.”“Ihavegoodtaste.ThatmeansIshouldstartmyownfashionline.”Andsoon.

Thisexercisecanalsobeusedtoreviewconceptsandcreateconnectionsbetweenideas.Forexample,thefollowingexchangecouldbeusedtoreviewbasicEuclideangeometry.“Anisoscelestrianglehastwoequalsides.”“Anisoscelestrianglehastwoequalsides.Thatmeansthatithastwoequalangles.”Andsoon.

Supportingfellowplayers

Afundamentalprincipleofimprovisthattherearenowrongchoices.However,thisisclearlynotentirelytrue.Thebeautyofimprovisthatwecreateanentireworldrightbeforetheaudience’seyes.Thedifficultyofimprovisthattheaudienceseeseverythingthatwedoandtruststhatwemeantodoit,eventhoughmostofthetime,wearenotsocertain.Werelyonourteammatestomakeour“mistakes”lookpremeditatedoratleasttonotletthemderailasceneorshow.

Forexample,supposethatShanaandIareinashow,andhercharacter’snameisSandra.Webothenterthestageforanewscene,andImistakenlycallherSylvia.Shehasseveralchoices:1)shecanpanic,lookaround,andrunoffstage,therebyhighlightingthefactthatImadeamistake;2)shecancorrectmeinanynumberofways(“mynickname/middlenameisSylvia”,“I’msureyoumeantSandra”,“Sylviaismytwin”,etc),whichisbetterthanthefirstchoicebutitstillacknowledgesmymistake;3)shecanchoosetoplayathrowawaycharacternamedSylvia.Withoption3,Shanahasturnedmymistakeintoadeliberatechoice.

Thenotionofsupportingone’sfellowplayersgoesmuchdeeperthanjustcoveringothersmistakes.Itencompassestheimmediateacceptanceofothers’ideasandthewillingnesstoheighten,orcontribute,tothoseideas.Itinvolvesputtingtheneedsofthetroupeortheperformancebeforetheindividualneedsofbeingthestaroftheshow.

Howdoessupportofteammatescomeintoplayinthemathclassroom?Inmath,therearerightandwronganswers,andsomeideastosolveaproblemjustaren’tasgoodasothers.Icanthinkofatleasttwoapplicationsofteammatesupport.

Firstofall,supportingone’sfellowperformersorclassmatescanbequiteusefulingroupwork.Idoalotofgroupworkinmyclasses,andIsometimeshavestudentsthatdonotmaximizethepotentialofthisexercise,whetheritbebyworkingaloneorbyrushingthroughanassignmentwithoutmakingsureallmembersunderstandthegroup’ssolution.Byencouragingthespiritofhelpfulness,thesetypesofcounter‐productivebehaviorareminimized.

Secondly,ashyortimidstudentismorelikelytosharehisorherideasiftheyknowthattheideawillatleastbeexplored.Ratherthanshootingdownideas,group

memberscandiscussanddebatevariousapproachesbeforedeterminingthebestone.

A. Whoosh,Bang,Pow:Haveallthestudentsstandinacircle.Thereare3

movesinthisgame.“Whoosh”goesaroundthecirclewithabigarmswing,“Bang”hastheplayercrosstheirarmsinanXanditreversesthedirectionofthewhoosh,and“Pow”goesalongwithapointingmotiontoaplayeracrossthecircle.Youcannotbangapow.Ifanerroroccurs,youcaneitherjustcontinuewithplayorhaveallthestudentsjoinhandsandcometothecenterofthecircleandmakeasillynoiselike“ah‐oo‐gaa.”

B. Enemy‐defender:Thisgameisgoodforincreasingawarenessand

connectionbetweenstudents.Havethestudentswalkaroundtheroom(youshouldmovechairs/desks).Tellthemtosilentlypickanotherstudentwhoistheirenemyandonewhoistheirdefender.Whenyousay“go”,theyshouldcontinuewalking,allthewhilekeepingtheirdefenderbetweenthemandtheirenemy.Theyshouldtrytonotmakeitobviouswhotheir“chosen”peopleare.Thingswillprobablynotsettleintoastaticsituation;ratheritwillprobablygetmorechaotic.Asecondleveltothisgameistohavethestudentschoosetwodifferentpeopleandtrytomakeanequilateraltrianglewiththetwo.Yourclasswillprobablyeventuallyfindanequilibrium.

C. Three‐headedexpert:Thisgamereliesonsupportandcouldalsobeafun

waytoreviewdefinitionsforanexam.Havethreestudentscometothefrontoftheclassandintroducethemasamathematicalexpert.Thestudentsshouldrespondtoyourquestionsonewordatatime(i.e.asthoughtheyarethreeheadsonthesamebody).Theyreallyhavetolistentowhattheother“heads”saysothattheymakesense.Youcanhavefuntryingtogetthemtocomeupwithanameortellyouwheretheyarefrom.Ithinkthiscouldbeanenjoyable,creativeadditiontoareviewday.

D. Speakinonevoiceexpert:Thisissimilartothethree‐headedexpert,butit

tendstobemorechallenging(andoftenmorefun).Havethreestudentscometothefrontoftheroom.Theymustanswerquestionsspeakingallinonevoice.Goingslowlyandmakingeyecontactcanhelpensuresuccess.

WorksCitedGwinn,P.(2003).GroupImprovisation:themanualofensembleimprovgames.ColoradoCity,CO:MeriwetherPublishing,Ltd.Timpson,W.a.(2002).TeachingandPerforming:Ideasforenergizingyourclasses.Madison,WI:AtwoodPublishing.