Problem-SolvingFacilitatorGuide

1

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.

Problem-SolvingFacilitatorGuide

2

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?

Problem-SolvingFacilitatorGuide

3

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?

Problem-SolvingFacilitatorGuide

4

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?

Problem-SolvingFacilitatorGuide

5

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

Problem-SolvingFacilitatorGuide

6

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.