LETTINGGOOFASSUMPTIONSABOUTHOWSTUDENTSUNDERSTAND

STATISTICALLANGUAGE

USCOTS2009BreakoutSession

DianeFisher,UniversityofLouisianaatLafayeGeJenniferKaplan,MichiganStateUniversityNealRogness,GrandValleyStateUniversity

MoPvaPonforStudyingLanguage

• Languageplaysacrucialroleintheclassroom.(Thompson&Rubenstein,2000)

– meansofcommunicaPngnewideas

– wayinwhichstudentsbuildunderstandingandprocessideas

– methodofassessment

• Theuseofaspecializedvocabularywithanoviceinadomaincreatesa“mysPque”aboutthesubject.(Lemke,1990)

LexicalAmbiguityWordsorphrasesthatarethesameorsimilarbutcanbeusedtoexpresstwoormoredifferentmeanings.

Homonymy

Leavesofatreevs.7minus3leaves4Polysemy

Thefactorymakesaproductvs.theproductistheresultofamulPplicaPon

Homophony

Sumvs.Some,Pievs.Pi,Too/To/TwoShi.sofApplica4on

Sta$s$csvs.Sta$s$c

MoPvaPonforStudyingLexicalAmbiguiPes

• Learningthemeaningofawordisacomplexandincrementalprocess(Leung,2005).

• Peopleconnectwhattheyheartowhattheyhaveheardandexperiencedinthepast(Lemke,1990).

• WhencommonlyusedEnglishwordsareusedasdomainspecificwordsstudentsmaymakeincorrectconnecPonsbetweenwordstheyknowandwordsthatsoundsimilarbuthavespecificmeaningsinstaPsPcsthataredifferentfromthecommonusagedefiniPons

MoPvaPonforStudyingLexicalAmbiguiPesintheUndergraduate

StaPsPcsClassroom• InastudyofelementaryschoolstudentsitwasfoundthatdetecPonoflexicalambiguiPesexhibitedasteady,almostlinearimprovementacrossgrades.(Shultz&Pilon,1973.)

• Therefore,collegestudents,oncemadeawareoftheambiguiPes,shouldbeabletocorrectlyprocessthestaPsPcalmeaningsoftheambiguouswords.

ResearchQuesPonsforPilotStudy

• Whatarethemeaningsofthe5targetwordsmostcommonlyusedbystudentsenteringanundergraduatestaPsPcscourse?

• WhattypesofstaPsPcaldefiniPonsdostudentsdevelopbytheendofaonesemesterintroducPontostaPsPcscourse?

• Arecertainpre‐exisPngdefiniPonsmoreusefulfordevelopingstaPsPcalunderstanding?

• DousagepaGernschangeoverPme?

PilotStudy

PilotStudyPre‐TestResultsWord Numberof

Defini>onsMostCommonDefini>ons

AssociaPon 5•Bodyofpersonscombinedforcommonpurpose(36)•LooserelaPonship(20)

Average 10

•Normal,typical,mediocre,common(25)•Mean(15)•Medianormiddle(11)

Confidence 3 Self‐esteem,beliefin,assurance(62)

Random 7

•Anoccurrencethatisunplannedorhaphazard(29)•SelecPng:‐withoutorderorpaGern(10)‐withoutcriteria(13)

Spread 9•ScaGer,disburse,distribute(25)•Smear,coverevenly(17)

LargeScaleStudy

• Fall2008Pre‐andPostTestDesignwithdatacollectedfromthreecampuses

293(4)392(7)294(3)

associaPonaverage

confidencerandomspread

Fall2008

UniversityofLouisianaatLafayeGe

GrandValleyState

University

MichiganState

UniversityTargetWordsSemester

NumberofStudents(NumberofInstructors)

Think‐Pair‐ShareAcPvityOne

• WritesentencesanddefiniPonsforthestaPsPcalmeaningsofthewordsonthehandoutasyouthinkaGOODSTATISTICSSTUDENTwouldattheendofaonesemesterintroducPontostaPsPcscourse.

• Discussyourresponseswithyourneighbor

• Wewillaskyoutoshareyourresponses

RubricCreaPonandCoding• ForbotheverydayandstaPsPcal

meanings,codingrubricswerecreatedbasedonthepilottestdata.

• Oneresearchercreatedtherubricandtheothertwousedtherubrictocodetheinstruments

• Disagreementswerediscussedandtherubricsweremodified

• Arandomsampleofthelargescalestudydatawereselected(validaPonsample)

• Eachwordwascodedbytworesearchers

• Disagreementswerediscussedandtherubricsweremodified

81%81%82%98%60%55%Spread

85%85%82%96%88%78%Average

75%75%80%96%59%87%AssociaPon

Post‐StaPsPcal

Post‐Everyday

Pre‐Test

Post‐StaPsPcal

Post‐Everyday

Pre‐Test

LargeScaleStudyPilotStudyIni>alInter‐raterReliability

ReportoutDefiniPonsfor

AssociaPon

InordertoplantransportaPonandparkingneedsataprivatehighschool,administratorsaskedarandomsampleof200studentshowtheygettoschool.Somerodethebus,somerodewithparentsorfriendsandothersused“personal”transportaPon–bikes,skateboards,orwalking.Thetableandbarchartsummarizetheresponsesfromboysandgirls.

Transporta>onType

Bus Ride Personal Total

Male 30 42 25 97

Female 41 45 17 103

Total 71 87 42 200

QUESTION:WriteafewsentencessummarizingwhatthetableandchartshowabouttheassociaPonbetweengenderandtransportaPontypeforthestudentsinthesample.

STUDENTRESPONSE:ThetableandchartrevealliGleassociaPonbetweenthegenders.ThehighestassociaPonbetweengendersisinthecategoryof“ride.”

QUESTIONFORAUDIENCE:Whatdoesthestudentmean?

StaPsPcalDefiniPonsofAssociaPon

Defini>on NumberofSubjects

PilotStudy ValidaPonSample

Incorrectstatements:notaboutrelaPonshipsorcomparing 10(21%) 3(5%)

Havingsomethingincommon 3(6%) 10(16%)

Numericalcomparisons 10(21%) 9(14%)IndeterminaterelaPonshipsorlinkages 15(31%) 23(37%)

RelaPonshipsbetweenvariables 9(19%) 16(25%)

Notclassified 1(2%) 2(3%)

ReportoutDefiniPonsfor

Average

From CBS News, May 12, 2009: President Obama's call lastyear for "shared sacrifice" doesn't extend to federalemployees, at least based on the details of hisadministration's 2010 budget released this week. There'slittle belt-tightening in evidence in Washington, D.C.:Counting benefits, the average pay per federal worker willleap from $72,800 in 2008 to $75,419 next year.

From MSNBC, June 14, 2009: The Sierra Club hasendorsed Feinstein's version (of the Clunker Car Bill). Thedirector of the environmental group's Green Transportationcampaign says the House and similar Senate bill arestructured to sell cars more than to get gas guzzlers off theroad. She thinks it's not too much to ask that the finallegislation does both. "Automakers already produce a fleetof cars that exceed the current 27.5 mpg average so weshould ensure our tax dollars go to help sell cars that areabove that average."

Sta>s>calDefini>onsofAverage

NumberofSubjects

PilotStudy ValidaPonSample

MeasuresofCenter

Mean

Wordonly 11(22%) 26(35%)

StaPsPcal:incompleteorinaccurate 5(10%) 11(15%)

StaPsPcal:completeandaccurate 9(18%) 17(23%)

Median

Wordonly 1(2%) 1(1%)

Colloquial:inthemiddle,normal,standard 3(6%) 6(8%)

StaPsPcallycorrect 0 0

Mode

Wordonly 0 0

Colloquial:majority,mostcommon 5(10%) 5(7%)

StaPsPcallycorrect 1(2%) 0

OtherDefiniPons

Sum 4(8%) 2(3%)

Frequency 1(2%) 0

ApproximaPon 2(4%) 0

RepresentaPvenumber 2(4%) 1(1%)

Numberusedininference 1(2%) 0

Notclassified 4(8%) 6(8%)

ReportoutDefiniPonsfor

Spread

SaidthestaPsPcianfromwestTexas…

Howdy!Welcometomyspreadandmakeyourselfathome.Goaheadandspreadoutyourpapersandhelpyourselftoallthefood–it’squiteaspread,huh?BesuretotrysomeofthatbuGerspread;justspreadaliGleonacracker.Yum!Andtakealookatthatfancytablecloth;mygrandmamadethatspreadforme.Onceyou’reallseGledinwe’llopenupthatspreadsheetandseeifwecan’tfigureoutthespreadofthosedata.

Sta>s>calDefini>onsSpread

NumberofSubjects

PilotStudy ValidaPonSample

Aspreadsheet(withdata) 14(30%) 8(11%)

Range 5(11%) 20(27%)

Data(inaspreadsheetorlist) 14(30%) 1(1%)

Tospacenumbersapart 1(2%) 2(3%)

ScaGerednumbers 2(4%) 2(3%)

Anon‐specificmeasureorcalculaPon 2(4%) 0

EqualdistribuPon 1(2%) 4(5%)

DistribuPonofnumbers 1(2%) 12(16%)

Measureofvariability 0 11(15%)

Non‐specificinformaPonfromfigureorgraph

2(4%) 5(7%)

Notclassified 5(11%) 9(12%)

Think‐Pair‐ShareAcPvityTwo

• Nowthatyouhaveseentheresults,selectoneofthethreewords:associaPon,averageorspreadandthinkabouthowyoumightintroducethatworddifferentlyfromwhatyouhavedonebefore.

• Discussyourresponsesingroupsoffour

• Wewillaskyoutoshareyourresponses

Think‐Pair‐ShareAcPvityThree

• Brainstormalistofwordsthatyouwouldbeinterestedinhavingusresearch.

• Discussyourresponseswithyourgroup

• Wewillaskyoutoshareyourresponsesincludingasummaryofwhyyouthinkthewordisworthyofstudy.

FutureDirecPons

• CreateRubricsfor5newwordsonwhichdatawerecollectedinSpring2009:Bias,Error,Independence,Normal,Significant.

• AnalyzetheDatacollectedinthe2008‐2009largescalestudy

• CreateTeachingModules,basedonthedata,fortargetwords

• AssessTeachingModules,linkingtostudentlearningoutcomes

Acknowledgements

ThisworkwascompletedundertheCAUSEmosresearchclustergrantfundedbyNSFDUE‐0618790.Theauthorswouldliketothanktheirresearchmentors,SterlingHilton,JohnHolcomb,andMarshaLoveGfortheirinvaluablehelp.

References

Durkin,K.&Shire,B.(1991a).LexicalambiguityinmathemaPcalcontexts.InK.Durkin&B.Shire(Eds.)LanguageinMathema4calEduca4on:ResearchandPrac4ce.Philadelphia,PA:OpenUniversityPress,71–84.

Lemke,J.(1990).TalkingScience:Language,LearningandValues.Norwood,NJ:AblexPublishingCorporaPon.

Leung,C.(2005).MathemaPcalvocabulary:FixersofknowledgeorpointsofexploraPon.LanguageandEduca4on,19(2),pp.127–135.

Shultz,T.&Pilon,R.(1973).DevelopmentoftheAbilitytoDetectLinguisPcAmbiguity.ChildDevelopment,44,pp.728–733.

Thompson,D.&Rubenstein,R.(2000).LearningmathemaPcsvocabulary:PotenPalpirallsandinstrucPonalstrategies.MathemaPcsTeacher.pp.568–574.