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UsingTechnologytoEngageStudentswithData

RickHudsonJune14,2019

USIQuantitativeReasoningConference

1.  Discussdifferencesbetweenmathematicsandstatisticsandwhythesedifferencesareimportant.

2.  LearntouseCODAP,atoolforinvestigatingdata.3.  Investigatethreedatasets–focusingonboth

quantitativevariablesandcategoricalvariables.4.  DiscussteachingconsiderationsofusingCODAP.

Goalsofthissession

*  Ifyouhadtoexplainthephrase“statisticalthinking”toapersonwhohadneverusedstatistics,howwouldyouexplainit?

*  Howisstatisticalthinkingdifferentfrommathematicalthinking?

Whatisstatisticalthinking?

*  CrucialRoleofContext

Statisticsv.Mathematics(Rossman,Chance,&Medina,2006)

*  IssuesofMeasurement

*  TheLackofDefinitiveConclusions

Focus:TwoOutcomes

Discuss:ThinkaboutthestatisticstasksyouuseinyourteachingofQR.

Howdoyouchoosedatasetsforyourstudentstoanalyze?

Howwouldyoudescribethecharacteristicsofthatdataset?

ReflectingonDataSets

TextbookExample

*  It’sokaytobe‘big’---multiplevariables,multiplecases.

*  It’sokaytobe‘messy’---somedataneedtobecleaned.

*  It’sokaytobefun!---studentsshouldhaveaninterest.(Dotheycareaboutcellphonesubscriptionsovertime?)

Datasets

IntroducingCODAP

http://codap.concord.org/

*  Gotohttps://tinyurl.com/GSWCODAPandfollowthedirections.

GettingStartedwithCODAP

Rollercoasters

* Whataresomeofthefeaturesthatmakesrollercoastersfun?* Whataresomeofthedifferencesbetweenrollercoasters?

ComparingRollercoasters

VisitthewebsitebelowtoinvestigateCODAP:http://tinyurl.com/157uscoastersWhatattributesdowehaveinformationaboutinthedataset?

RollercoasterDataSetinCODAP

*  Whatdoyounoticeaboutthetopspeedofthesecoasters?Whatfactorsmayberelatedtothespeedofacoaster?

*  Dowoodencoasterstendtohavethesameheightascoastersmadefromsteel?Howdothewoodenandsteelcoastersdifferwithothervariables?Doesanythingsurpriseyou?

*  Doyouagreethatrollercoastersthathaveinversionsaretallerthanrollercoasterswithoutinversions?Whyorwhynot?

Investigatethesequestions

*  Considerhowthelength(x)ofarollercoasterisrelatedtoitsduration(y).*  Addamoveablelinethatyouthinkestimatestheassociationwell.Shareoutyourresults.*  Who’sestimationisbest?*  Addtheleast-squaresline.*  Whatdoesthislinetellus?*  Howdoweinterprettheslope?Y-intercept?R2?

Least-SquaresRegression

FocusonCategoricalData

Whatiscategoricaldata?

Categoricaldataconsistsofnameorlabels.Forexample,ifweweretalkingaboutattributesofthestudentsinclass,somecategoricalattributeswouldinclude:*  Gender*  HairColor*  HighSchool

Althoughnumbersaretypicallyassociatedwithquantitativeattributes,numberscanbetreatedascategoricalwhentheydescribelabelsthatdonotrepresentcountsormeasurements.Forexample,ZipCodesaredescribedintheUnitedStatesasafive-digitnumber.Sincetheysignifyyourlocationofanaddress,asopposedtoacountormeasurement,ZipCodesareanexampleofanumberbeingusedasacategoricalattribute.

*  Navigatetowww.tinyurl.com/codaptitanic.

*  EachcaserepresentsoneTitanicpassengerwithdataaboutfourcategoricalvariables.

*  Poseaquestionthatyouwouldliketoinvestigatewiththisdataset.

TitanicData

Tocreateatwo-waybinnedplotinCODAP

1.  ClickonGraphinthetoolbar.2.  Dragonecategoricalvariableto

thehorizontalaxis.3.  Dragasecondcategorical

variabletotheverticalaxis.4.  Clickonthegraph.Fromthe

Rulermenuatheright,choosecountsandpercents.SelectRowPercent,ColumnPercent,orCellPercentdependingonthequestionunderinvestigation.

TocreateabargraphinCODAP

1.  Clickongraphfromthetoolbar.2.  Dragonecategoricalvariabletoeitherthehorizontal

ORverticalaxis.3.  Clickonthegraph.FromtheConfigurationmenuatthe

right,choose“FuseDotsintoBars.”

TocreateasegmentedbargraphinCODAP

1.  Aftercreatingabargraph,dragasecondcategoricalvariableintothecenterofthegraphtocreatealegendattribute.Thebarswillbereorganizedandcolor-codedbythenewattribute.

2.  Tocompareproportions,clickonthegraph.Fromtheconfigurationmenu,choosetheScaletobedisplayedasapercent.

AssociationforCategoricalVariables

Twocategoricalvariablesaresaidtobeindependentiftheirdistributionofconditionalrelativefrequenciesofonevariablearethesameforeverycategoryoftheothervariable.Otherwise,thevariableshaveanassociation,orarelationship.WhataretwovariablesyouthinkareassociatedintheTitanicdataset?Investigateit!

EmergenceofDataScience

*  OldViewofStats:Poseaquestionandcollectthedatatofindout.

*  NewViewofStats: Ihavethedata,whatquestionscanIanswer?

OldStatsv.NewStats

*  OurnextdatasetincludesthenumberofbirthsintheUnitedStatesforeverydayintheyears2000to2014.Everycaserepresentsoneday.

*  DISCUSS:Whatdoyouthinkthedistributionwouldlooklike?Why?

*  Navigatetohttps://tinyurl.com/codapbirthdatestoinvestigatethedata.Whatdoyounotice?Whattrendsdoyoufind?Whydoyouthinkthesetrendsexist?

Births

InferentialReasoning:ModelingaCarnivalGame

AcarnivalDuckPondgamehasacollectionofrubberducksinapondwhere20%ofducksaremarkedontheirbellyforaprize.Ifaplayerpicksamarkedduck,theywinaprize!•  Onceaduckispickeditisreturnedto

thepondandtheboothoperatorswirlsthemaroundinthepondtomixthemup.

•  Eachplayerpays$1.00topick3ducks•  Theboothownersexpectabout50

studentstoplaythegameatthecarnival.

ModelingaDuckPondGame

*  Howmanyprizesshouldtheybepreparedtogiveawayafter50studentsplaythegame?Whatvariationmightweexpectinthetotalnumberofprizesthatwouldbewonafter50studentsplay?

*  Afterchoosing3ducks,howmanyprizeswillmoststudentswin?0,1,2,or3?

*  Iftheownersoftheboothexpecttomake$50fromstudentspayingtoplay,howmuchshouldtheyspendonbuyingtheprizesfortheirboothtomakeagoodprofit?

*  Ifattheendofthedayonly10prizeswerewon,wouldyouthinktheownersweretellingthetruthabout20%ofducksbeingmarked?

PossibleInvestigations

*  Gotowww.tinyurl.com/codapduckstoinvestigatethesimulationofthegame.

Investigate

TeachingwithCODAP

HowdoStudentsInteractwithCODAP?

*  Whatarethepros/consofusingthistoolwithQuantitativeReasoningstudents?

*  Whatsuccessesandstrugglesmightfacultyencounterwhenengagingwiththisrollercoasterdataandtool?

Discuss:ConsiderationsforTeaching

UsingCODAP

*  https://codap.concord.org/

*  Hurricanes(greatexampleofhierarchicaldata!)

ResourcesAvailable

*  Createanewfile

*  Createtwovariablesandaddsomedata.

*  Addathirdvariableusingaformula.

*  Inwebmenu,choose“Share”then“Getlinktosharedview”

Enteringandsharingdata

ThankYou!Questions?

RickHudsonrhudson@usi.edu

Students with Data - faculty.usi.edufaculty.usi.edu/media/1527/usi-qr-conference-codap-2019.pdf ·...

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