Mathemacs + Financial Literacy INVESTigaons · Insurance and Probability Risk Management and...
Transcript of Mathemacs + Financial Literacy INVESTigaons · Insurance and Probability Risk Management and...
Mathema'cs+FinancialLiteracyINVESTiga'ons
NCTM2016AnnualMee0ngSanFrancisco,CA
SusanA.PetersUniversityofLouisville
SherriMar'nieKansasStateUniversity
JenniferM.Bay-WilliamsUniversityofLouisville
WhyIsFinancialLiteracyImportant?
Children'sspendinghasroughlydoubledeverytenyearsforthepastthreedecades,andtripledinthe1990s.
-MakingtheCaseforFinancialLiteracy
WhyIsFinancialLiteracyImportant?
Morethan1in5youthsaged12to19havetheirowncreditcardsorhaveaccesstoparents'creditcards,and14%havedebitcards.
–MakingtheCaseforFinancialLiteracy
FinancialLiteracyQuiz
• WhatpercentofteensgavethemselvesgradesofAorBfortheircurrentknowledgeoffinancialresponsibility?• 76%CapitalOne’s2012AnnualBack-to-SchoolShoppingSurvey
FinancialLiteracyQuiz
• Whatpercentofparentsfeelitistheirresponsibilitytoteachtheirchildrenaboutmoneyandsavings?• 81%
FinancialLiteracyQuiz
• WhatpercentofsurveyedadultsgavethemselvesgradesofC,D,orFontheirknowledgeofpersonalfinance?• 51%
Na'onalFounda'onforCreditCounseling2015FinancialLiteracySurvey
FinancialLiteracyQuiz• 37%ofhighschoolseniorssurveyedreceiveallowances.Whatpercentsaidthattheirparents“some'mes”talkwiththemabouthowitshouldbehandled?• 54%
FinancialLiteracyQuiz
• Ofhighschoolseniorssurveyed,whatpercentsaidthattheseconversa'ons“rarely”or“never”takeplace?• 30%
FinancialLiteracyQuiz• Whatpercentofparentswithchildreninhighschool&collegegiveschoolsbelow-averageorfailinggradesforteachingstudentsresponsiblespending?• 57%
AmericanExpress,2011
FinancialLiteracyQuiz
• Whatpercentofteensreportthebest'metolearnaboutmoneymanagementiskindergartenthroughhighschool?• 76%
JuniorAchievement/AllstateFounda'onTeensandPersonalFinanceSurvey,2013
FinancialLiteracyQuiz
• Whatpercentofteensreportfinancialliteracyprogramscurrentlyareinplace?• 29%
JuniorAchievement/AllstateFounda'onTeensandPersonalFinanceSurvey,2013
WhatDoWeMeanByFinancialLiteracyMathema'csLessons?
Mathema'csContent
FinancialLiteracyContentFL
M
Jump$tartStandards
1. Spending&Saving2. Credit&Debt3. Employment&
Income4. Inves'ng5. RiskManagement&
Insurance6. FinancialDecision
Making
hhp://www.jumpstart.org/assets/files/2014_Na'onalStandardsBook-WEB.pdf
WhyDoWeNeedFinancialLiteracyMathema'csLessons?
Studentswholearnaboutfinancialliteracy…• makebeherfinancialdecisions;• aremorelikelytosave;• arelesslikelytomaxoutcreditcards;• aremorelikelytopaycreditcardsoffinfull;• arelesslikelytobuythingscompulsively.
(Guher,Copur,andGarrison2010)
WhyDoWeNeedFinancialLiteracyMathema'csLessons?
• Mathema'csisuseful.• Connec'ngmathema'cstofinance
canhelpstudentsseethepowerofmathema0cs.
WhyDoWeNeedFinancialLiteracyMathema'csLessons?
• Financialliteracy,iftaughtoutsideofamathema'cscourse,orendoesn’taddressthemathema'calaspectsoffinancialliteracy.
• Mathema'csteacherscanhelpbridgethefieldsofmathema'csandfinance.
Americansrackedup57.1billioninnewcreditcarddebtin2014,andthisfigurewasexpectedtoincrease5%in2015.
-Picchin.d.
UnravelingtheMysteryofCreditCardPayments
Whatvariablesaffectcompoundinterest?
Whateffectdoespayingtheminimumbalanceoncreditcarddebthaveontheactualcostofapurchaseditem?
UnravelingtheMysteryofCreditCardPayments
A.SSE.1:Interpretexpressionsthatrepresentaquan'tyintermsofitscontext.F.BF.1:Writeafunc'onthatdescribesarela'onshipbetweentwoquan''es.
UnravelingtheMysteryofCreditCardPayments
CreditandDebt:Developstrategiestocontrolandmanagecreditanddebt.• Standard1:Analyzethecost
andbenefitsofvarioustypesofcredit.
UnravelingtheMysteryofCreditCardPayments
① Whatarevariousformsofcredit?
② Whenisagood'metouseacreditcard?Whenisitnotagood'me?
③ Whydopeopleusecreditcards?Whydobanksoffercreditcards?
④ Howisacreditcarddifferentfromaloan?
Inagroupof4:Eachpersonwriteadifferentlabelonanotecard:“What,”“When,”“Why,”or“How.”
MinimumPayments:What’stheCost?
Thelatestandgreatesttabletwasjustreleasedbyyourfavoritetechnologycompany.YouwanttopurchasethetabletASAPandwithasmanybellsandwhistlesaspossible!Yourunouttothestore.Areryouaddaccessoriesandtaxes,yourtabletcosts$1067.Nothavingthecash,youpaywithacreditcardandmakepaymentsover'me.
TurnandTalkabouthowyoupredictyourstudentswouldanswerques'ons1and2
MinimumPayments:What’stheCost?
Creditcardcompanieschargehighinterestratesforcredit,andtheycompounditdaily.Whenacreditcardstatementreportsaannualpercentagerateof12%,itmeansthatyoutakeayeartopayofftheitem,youwillpayanaddi'onal12%pluscompoundingforthatitem.
Usingthisinforma'onanswer
ques'ons3-7
Usingthetable,turnandtalktoyourneighboraboutques'ons9&10…
• Compareyoures'mates(#1and#2)totheactual'metopayoffthetabletwhenpayingtheminimumbalanceonacreditcardthatcharges12%interest.Whatdoyouno'ce?
• Whatsugges'onswouldyougivetosomeonewhotellsyouthatheorshepaystheminimumbalancedueeachmonthonhis/hercreditcard?
TimeforReflec'on• Inwhatwaysdidyouseeopportuni'estomakesenseofthemathema'cs?• Inwhatwaysdidyouseeopportuni'esforstudentstogaininsightsintothefinancialliteracy?• Whatadapta'onscouldyouseemakingtothelesson?• Howorwhencouldyouseeusingsuchalesson?
ThemanwhowroteStateFarm’s“LikeaGoodNeighbor”jinglein1971isalsothemanwhosings,“Iwritethesongs”—BarryManilow.Anar'cleatBankrate.comcontainsthisandotherfuntriviaaboutfiveofthebiggestinsurancecompanies.
-MacDonald,n.d.
RiskyBusiness:InsuranceandProbability
Howcanyouemployprobabilitytomanagetherisksassociatedwithautomobileinsurance?
RiskyBusiness:InsuranceandProbability
S.MD.4:Developaprobabilitydistribu'onforarandomvariabledefinedforasamplespaceinwhichprobabili'esareassignedempirically;findtheexpectedvalue.S.MD.5:Weighthepossibleoutcomesofadecisionbyassigningprobabili'estopayoffvaluesandfindingexpectedvalues.
RiskyBusiness:InsuranceandProbability
RiskManagementandInsurance:Applyappropriateandcost-effec'veriskmanagementstrategies.• Standard1:Iden'fycommontypesofrisks
andbasicriskmanagementmethods.• Standard2:Jus'fyreasonstouseproperty
andliabilityinsurance.
• Haveyouevercomplainedaboutthehighratesyoupayforcarinsurance?
• Forcarinsurancetocoverteenagedrivers?
• Whydowebuycarinsurance?
• Whyareinsurancerateshigherforteenagersthanforolderadults?
Event Prob-ability
DegreeofImpact
Youwillbeinjuredafterbungeejumpingfroma200-ftbridgeunderthesupervisionofagovernment-certifiedcompanyinoperationsince1989.
Youwillbecomeillwiththecommoncoldatleastonceduringthenextyear. Youwillbefacedwithfloodwaterswhenhikingthroughaslotcanyon(ahighlyflash-floodpronearea)duringwidespreadseverethunderstormwarnings.
YouwillsustainaninjuryafterplayingFrisbeegolfwithagroupoffriends.
Levelofriskbasedonprobabilityofoccurrenceanddegreeofimpact.
Howmightyoumanageriskforeachtypeofevent?
Event Prob-ability
DegreeofImpact
Youwillbeinjuredafterbungeejumpingfroma200-ftbridgeunderthesupervisionofagovernment-certifiedcompanyinoperationsince1989.
Low High
Youwillbecomeillwiththecommoncoldatleastonceduringthenextyear. High LowYouwillbefacedwithfloodwaterswhenhikingthroughaslotcanyon(ahighlyflash-floodpronearea)duringwidespreadseverethunderstormwarnings.
High High
YouwillsustainaninjuryafterplayingFrisbeegolfwithagroupoffriends. Low Low
AcceptAvoid
MinimizeTransferorShare
Therewere28,319teenagedriversinNorthDakota.UsethedataaboutteenagedrivercrashesinNDto
completeAc'vity10.1.
TypeofCrash NumberAverageCost($)
Crashwithfatalities 16 1,500,000perfatality
Crashwithinjuries 684 80,700perinjury
Crashwithpropertydamageonly 2162 9,300
• Useexpectedvalueofcrashlosses(bothwithandwithoutinsurance)andthelarge-lossprincipletoarguefortheimportanceofpurchasingautomobileinsurance.
• Comparethelevelsofriskforteenagerswithinsurancetoteenagerswithoutinsurance.
Complete1-4forAc'vity10.2.
• Considertossingadie60,000'mes.Howwouldtheexperimentalprobabili'esfor60,000tossescomparewiththeexperimentalprobabili'esforsixtosses?
• Withthetheore'calprobabili'es?
Howdotheresultsofthesimula'oncomparewithyourpredic'ons?
Wecannotpredictwhetherapar'cularteenagerwillcrash.Predic'onsaboutgroupsofteenagers,however,becomeincreasinglymoreaccurateasthenumberofteenagersincreases.Actuariesusethelawoflargenumbersandexpectedvaluestodetermineproperinsurancepremiumstochargeindividuals.
Howdoesinsurancebenefitbothindividualsandinsurancecompanies?Refertoprobability,degreeofimpact,levelorrisk,andriskmanagementinyourresponse.
TimeforReflec'on• Inwhatwaysdidyouseeopportuni'estomakesenseofthemathema'cs?• Inwhatwaysdidyouseeopportuni'esforstudentstogaininsightsintothefinancialliteracy?• Whatadapta'onscouldyouseemakingtothelesson?• Howorwhencouldyouseeusingsuchalesson?
WallStreetwasactuallynamedarerawall.Duringtheseventeenthcentury,WallStreetwasthenorthernboundaryofaDutchSehlementonManhahanisland.ThewallwasbuilttodefendDutchcolonistsfromtheBri'sh,Na'veAmericans,andNewEnglandcolonists.-Sco'abank,n.d.
Inves'ga'ngInvestments:WhichisBeher?
Howcanyouusegraphicalrepresenta'ons,sta's'calmeasures,andsimula'onstohelpdecidewhichinvestmentisabeherchoice?
Inves'ga'ngInvestments:WhichisBeher?
S.ID.1:Representdatawithplotsontherealnumberline(dotplots,histograms,andboxplots).S.ID.2:Usesta's'csappropriatetotheshapeofthedatadistribu'ontocomparecenter(median,mean)andspread(interquar'lerange,standarddevia'on)oftwoormoredifferentdatasets.S.ID.3:Interpretdifferencesinshape,center,andspreadinthecontextofthedatasets,accoun'ngforpossibleeffectsofextremedatapoints(outliers).S.IC.1:Understandsta's'csasaprocessformakinginferencesaboutpopula'onparametersbasedonarandomsamplefromthatpopula'on.S.IC.5:Usedatafromarandomizedexperimenttocomparetwotreatments;usesimula'onstodecideifdifferencesbetweenparametersaresignificant.
Inves'ga'ngInvestments:WhichisBeher?
Inves0ng:Implementadiversifiedinvestmentstrategythatiscompa'blewithpersonalfinancialgoals.• Standard2:Evaluateinvestment
alterna'ves.
Inves'ga'ngInvestments:WhichisBeher?
Whichop'onisbeherandwhy?1. Invest$2,000ayearfor10years($20,000)toaccumulate$611,817byage64.
2. Invest$2,000ayearfor30years($60,000)toaccumulate$361,887byage64.
Inves'ga'ngInvestments:WhichisBeher?
1. Compareandcontrastdistribu'onsofsamplefive-yearaverageratesofreturnfordifferenttypesofinvestments.
2. Comparesamplefive-yearaverageratesofreturnwithpopula'onsoffive-yearaverageratesofreturn.
3. Usesimula'onstodeterminethesignificanceinaverageratesofreturnfordifferentinvestmenttypes.
WhatIsYour“TakeAway”FromthisWorkshoponFinancialLiteracyMathema'csLessons?
Mathema'csContent
FinancialLiteracyContent
FLM
ForNEWmembers:• $20offfullmembershipOR• $10offe-membershipOR• $5offstudentmembership
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