problem-solving facilitator guide
TRANSCRIPT
Problem-SolvingFacilitatorGuide
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Overview&PreparationPre-WorkshopChecklist• Reviewallresourcesrelatedtotheworkshop,including:
o Facilitatorguideo Handouto Workshopevaluation
• Haveallmaterials(seenextpage)preparedtouse.OverviewInmathandsciencecourses,studentsareusuallyassessedontheirabilitytosolveproblems.Typesofproblemsvarybetweencourses,butmanyofthestrategiesandtechniquesnecessaryforsolvingthemareuniversal.Inthisworkshop,studentswilllearnhowtodevelopgoodhabitsforsucceedinginproblem-solvingcourses.LearningOutcomesAfterparticipatinginthisworkshop,studentswillbeableto: • Developaproblem-solvingstrategy• Monitorthestrategy• Evaluatethestrategy• Maintaingoodhabitsforsuccessinproblem-solvingcoursesElementsoftheWorkshop1. Introduction2. Agenda3. Learningobjectives4. Conversationwithatriangle5. Anoddproblem6. Possiblestrategies7. Atougherproblem8. Goodhabits9. Q/A10. Learningportfolioreflection11. Feedback
Materials ● PowerPointPresentation● Problem-solvinghandouts● Blankpiecesofpaperforeachparticipant● FeedbackformsSpeakingNotesandInstructions
Introduction 2Min.
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Takeamomenttointroducetheworkshopandyourself.● Yourself
o Nameo RolewithintheStudentSuccessCentre
● Workshopo Thisworkshopisdesignedtohelpyoutackledifficultproblemsmoreeffectively.o Itshouldlastaboutanhour.o Questionsarewelcomeatanytimeduringtheworkshop.
Agenda&WorkshopObjectives 3Min.Brieflyoutlinetheworkshopagenda,asshownonthepowerpointpresentation• Learningobjectives• Conversationwithatriangle• Anoddproblem• Possiblestrategies• Atougherproblem• Goodhabits• Q/A• Learningportfolioreflection• Feedback
Explainthattheobjectivesofthisworkshoparetohelpstudentsto…• Developaproblem-solvingstrategy• Monitorthestrategy• Evaluatethestrategy• Maintaingoodhabitsforsuccessinproblem-solvingcoursesExplainthatthisworkshopinvolvesactivelearningandsharinginordertodrawupontheskillsandknowledgethateachparticipanthasbroughttotheroom.Conversationwithatriangle 15Min.Thisactivitywillgivethestudentsachancetowarmuptheirbrains,asitwere.Thequestionisthis:ifyouputatriangleinabox,howmuchoftheboxdoesittakeup?
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Givethestudentsfiveminutestoworkontheproblem.Tellthemtofeelfreetodrawallovertheboxordowhatevertheywant.Tellthemthatiftheyfigureitoutbeforethetimeisup,theyshouldtrytocomeupwithanalternatesolution,ortomaketheirsolutionsimplerandmoreelegant.Oncethefiveminutesisup,you’llwalkthroughapotentialthoughtprocessforsolvingthisproblem.Thefirstthoughtyoumighthaveistotrytomeasurethelines.Butthatwillonlygiveanansweraspreciseasourmeasurementdevice,andwe’reinterestedintheabsoluteanswer.Besides,we’reinterestedinageneraltriangleinabox,notnecessarilythistriangleinthisbox.Someasuringisnogood.Sothenmaybeyouhavethethoughtthatyoucouldcutthetriangleinhalfalongthehorizontal.
Maybeyouseethebeginningofapatternoftriangleshere,butthepathtothesolutionisn’tentirelyclear.Soperhapsyouhavethethoughttocutitdownthecentreoftheboxtoo.
But that’s no good. That helps even less. Now you have a bunch of extra quadrilaterals that are evenmoredifficulttokeeptrackof.Whataboutcuttingitdownthediagonals?
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Nope,thisdoesn’tworkeither.Soperhapsitoccurstoyouthatyoucouldtrysolvingasimplerproblem.Whatifthetrianglewereisosceles?
Nowtheproblemlooksmucheasier.Whatifwegobacktoourveryfirststrategy?(asidefrommeasuring)
Itworks!Whenwesplititlikethis,it’sveryeasytoseethatthetriangletakesuphalfofeachhalf,sothetriangletakesuphalf itsbox.Whathappens ifwegoback to theoriginal case, splitting the triangledown the centreinsteadofthebox?
Itworks!Doesitworkforalltrianglesinboxes?
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Well,itseemstoworkinallcases.Sothat’saprettysatisfyingsolution.Askthegrouptosharewhattheytried,especiallyiftheydidn’treachthesolution.Theimportantthingisthestrategies.Anotherproblem 10Min.Question:Ifwe’regiventhesumandthedifferenceoftwonumbers,howcanweknowwhatthenumbersare?Givethestudents5-10minutestoworkonthisproblem,thenaskthemtosharewhatthey’vecomeupwith.Therearenofollow-upslidesforthefacilitatoronthisproblem,becausethegoalistogetthestudentstosharetheirstrategiesandsolutions.Ontheoff-chancethatnobodyfiguresitout,here’swhatyoudo:First,divide thesumby two; thisgivesyou theaverageof the twonumbers.Then,addandsubtracthalf thedifferencefromthisaveragetogetthetwonumbers.
Sum/2±Difference/2Possiblestrategies 10Min.• Thesearestrategiesthatmaybeusedwhentryingtosolveallsortsofproblems.
o Guessandchecko Solveasimplerproblemo Try proving that the problem cannot be solved;where the proof breaks down, that’swhere you
attacktheproblemo Retrogradeanalysis(workbackwardsfromthesolution)o Lookforapatterno Drawapicture/diagram
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Extraproblems 2Min.• Whatistheprobabilitythatann-digitnumberwillhavea5init?• Whyistheproductoftwooddnumbersalwaysodd?• Whataretheanglesinsidearegularn-sidedpolygon?Goodhabits 2Min.• Prepareforclass/labbeforehandbyreadingyourtextbookorlabmanual.• GOTOCLASS.• Reviewyourclassnotesattheendoftheday.• Useshortbutfrequentstudysessions.• Onceyouunderstandtheconcepts,doasmanypracticeproblemsasyoucan!• Writeneatly,evenwhenpractising–thecleareryourwriting,thecleareryourthinking.• Startbywritingoutalltherelevantinformationthatyoualreadyknow.Q/A 2Min.Reviewtheobjectivesoftheworkshop,andforeachobjective,askifthereareanylingeringquestions.LearningPortfolioReflection 5Min.Ask theparticipants tocreateaReflection in theirLearningPortfoliosandanswera fewquestionsabout theworkshop’ssubjectmaterial.Questions:• Whatstrategiesdidyouusetosolveproblemsinthisworkshop?Weretheyeffective?• Doyouplantochangeanythingaboutthewayyousolveproblemsorstudyforproblem-solvingcourses?If
so,what?Conclusion 2Min.● RemindstudentsabouttheotherservicesofferedbytheStudentSuccessCentre–allfree!
FeedbackForm 3Min.● Asktheparticipantstoanonymouslyfillouttheworkshopfeedbackform.