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


• Whatpercentofparentsfeelitistheirresponsibilitytoteachtheirchildrenaboutmoneyandsavings?• 81%


• WhatpercentofsurveyedadultsgavethemselvesgradesofC,D,orFontheirknowledgeofpersonalfinance?• 51%

Na'onalFounda'onforCreditCounseling2015FinancialLiteracySurvey

FinancialLiteracyQuiz• 37%ofhighschoolseniorssurveyedreceiveallowances.Whatpercentsaidthattheirparents“some'mes”talkwiththemabouthowitshouldbehandled?• 54%


• Ofhighschoolseniorssurveyed,whatpercentsaidthattheseconversa'ons“rarely”or“never”takeplace?• 30%

FinancialLiteracyQuiz• Whatpercentofparentswithchildreninhighschool&collegegiveschoolsbelow-averageorfailinggradesforteachingstudentsresponsiblespending?• 57%

AmericanExpress,2011


• Whatpercentofteensreportthebest'metolearnaboutmoneymanagementiskindergartenthroughhighschool?• 76%

JuniorAchievement/AllstateFounda'onTeensandPersonalFinanceSurvey,2013


• 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)


•  Mathema'csisuseful.•  Connec'ngmathema'cstofinance

canhelpstudentsseethepowerofmathema0cs.


•  Financialliteracy,iftaughtoutsideofamathema'cscourse,orendoesn’taddressthemathema'calaspectsoffinancialliteracy.

•  Mathema'csteacherscanhelpbridgethefieldsofmathema'csandfinance.

Americansrackedup57.1billioninnewcreditcarddebtin2014,andthisfigurewasexpectedtoincrease5%in2015.

-Picchin.d.

UnravelingtheMysteryofCreditCardPayments

Whatvariablesaffectcompoundinterest?

Whateffectdoespayingtheminimumbalanceoncreditcarddebthaveontheactualcostofapurchaseditem?


A.SSE.1:Interpretexpressionsthatrepresentaquan'tyintermsofitscontext.F.BF.1:Writeafunc'onthatdescribesarela'onshipbetweentwoquan''es.


CreditandDebt:Developstrategiestocontrolandmanagecreditanddebt.•  Standard1:Analyzethecost

andbenefitsofvarioustypesofcredit.

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?


S.MD.4:Developaprobabilitydistribu'onforarandomvariabledefinedforasamplespaceinwhichprobabili'esareassignedempirically;findtheexpectedvalue.S.MD.5:Weighthepossibleoutcomesofadecisionbyassigningprobabili'estopayoffvaluesandfindingexpectedvalues.


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?


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.


Inves0ng:Implementadiversifiedinvestmentstrategythatiscompa'blewithpersonalfinancialgoals.•  Standard2:Evaluateinvestment

alterna'ves.


Whichop'onisbeherandwhy?1. Invest$2,000ayearfor10years($20,000)toaccumulate$611,817byage64.

2. Invest$2,000ayearfor30years($60,000)toaccumulate$361,887byage64.


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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mathemacs + financial literacy investigaons · insurance and probability risk management and...

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