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ŠÓ  ÓÓÓņ ņŌ‡čMŒē%&ŻlŌEffect€of€K-12€Calculator€Usage€on€College€Gradesó óŌ#†&Żl%ēčMŒ\#ŌŠ ° ŠĢĢŌ‡„Ā.„%&ŻlŌņ ņResultsó óŌ#†&Żl%„„Ā.é#ŌŠ ž N ŠĢWe€collected€various€information€from€the€students€in€the€large€multi-section€mathematics€courses€at€theŠ XØ  ŠJohns€Hopkins€University€in€the€fall€of€2002.€€We€asked€students€if€parents€ever€helped€them€withŠ P  Šmathematics€and€if€calculator€usage€was€š šemphasized€and€encouragedšš€in€K-12.€€We€put€this€together€withŠ Øų  Štheir€grades€in€these€courses€and€their€SAT€mathematics€and€verbal€scores.€€Regression€analysis€led€to€theŠ P  Šfollowing€fit€to€the€data:Š ųH ŠÓ;ÓĢą  ąņņgrade€=€constant€+€parents€š5š€.21547€-calc€š5š€.23239€+€Ō_ŌmsatŌ_Ō€š5š€.00350€+€Ō_ŌvsatŌ_Ō€š5š€.00057.óóŠ H˜ ŠĢÓ  ÓHere,€ņņparentsóó€is€1€if€parents€ever€helped€and€0€if€not;€€ņņcalcóó€is€1€if€calculators€were€encouraged€and€emphasizedŠ –ę Šand€0€if€not.€€Ō_ŌņņmsatŌ_Ōóó€and€€Ō_ŌņņvsatŌ_Ōóó€are€the€mathematics€and€verbal€SAT€I€scores€respectively.€€The€grades€are€on€theŠ >Ž Šusual€4.0€scale.€€We€did€the€usual€3.3€for€a€B+,€3.0€for€a€B,€2.7€for€a€B-,€etc.€€The€constant€isn't€relevant.Š ę6 ŠĢLet's€first€look€at€the€verbal€SAT€score.€€200€points€would€raise€the€grade€by€.1,€which€isn't€much.€€Worse,Š 6#†" Šthe€p-value€is€.32€so€even€this€isn't€significant.€€This€is€a€disappointing€result€as€anecdotal€evidence€suggestedŠ Ž$. $ Šthere€might€be€something€interesting€here.Š †&Ö!& ŠĢThe€question€about€parent's€help€was€motivated€by€the€many€reform€mathematics€programs€that€instructŠ Ö)&%* Šchildren€to€not€talk€about€mathematics€with€their€parents.€€Its€p-value€is€.01€and€the€standard€deviation€isŠ ~+Ī&, Š.08349.€€This€question€is€fraught€with€difficulties€because€of€the€Ō_ŌsocioŌ_Ō-economic€issues€that€could€underlieŠ ° Šit,€so€we€don't€want€to€push€this.Š XØ ŠĢThe€real€heart€of€the€matter€for€us€is€the€combination€of€the€mathematics€SAT€and€the€question€aboutŠ Ø ų Šcalculator€usage.€€We€are€not€that€familiar€with€the€literature€but€what€we€have€seen€suggests€that€SAT€scoresŠ P   Šare€not€that€good€at€predicting€grades€in€college.€€Although€the€SAT€score€does€have€some€input€here€(theŠ ų H  Šp-value€is€.00000€and€the€standard€deviation€is€.00066)€it€would€take€286€points€to€account€for€a€full€letterŠ  š  Šgrade€and€the€entire€spread€of€our€mathematics€SAT€scores€is€only€280.€€Š H˜  ŠĢThe€-.23239€contribution€from€calculator€usage€has€a€p-value€of€.00377€and€a€standard€deviation€of€.07992.€Š ˜č ŠIt€may€not€seem€like€much€but€with€plus€and€minus€grades€it€suggests€that€a€fair€number€of€students€are€aŠ @ Šgrade€notch€lower.€€Our€students€care€about€each€step€in€the€grades.€€This€requires€66€points€on€theŠ č8 Šmathematics€SAT€to€make€up€for€it,€another€thing€our€students€care€about.Š ą Š€€Š 8ˆ ŠWe€did€this€without€the€SAT€scores€first€and€since€we€are€unfunded€we€thought€we€would€stop€there.€Š ą0 ŠHowever,€it€turned€out€to€be€much€easier€than€expected€to€get€the€scores.Š ˆŲ ŠĢCalculators€clearly€have€a€place€in€the€classroom€but€we€suspect€that€they€are€sometimes€misused.€€OurŠ Ų (" Šstudents€get€quite€upset€when€we€show€them€these€statistics.Š €"Š$ ŠĢŌ‡„Ā.„%&ŻlŌņ ņBackgroundó óŌ#†&Żl%„„Ā.>#ŌŠ Š% !( ŠĢIn€the€fall€of€2002€a€questionnaire€was€handed€out€with€the€final€exams€in€most€of€the€large€multi-sectionŠ **z%, Šservice€courses€in€the€mathematics€department€at€the€Johns€Hopkins€University.Š Ņ+"'. ЇThe€courses€surveyed€were€as€follows:€€110.105,€Introduction€to€Calculus,€our€pre-calculus€course.€€ThisŠ ° Šcourse€is€actually€quite€small€but€since€it€has€two€sections€it€was€included.€€110.106-7,€Calculus€I€and€II€forŠ XØ ŠBiological€and€Social€Sciences.€€110.108€Calculus€I€for€Physical€Sciences€and€Engineering.€€Regrettably,€theŠ P ŠCalculus€II€course€in€this€sequence€did€not€get€surveyed€because€of€a€breakdown€in€communication.€€110.201,Š Ø ų ŠLinear€Algebra.€€110.202,€Calculus€III€-€Calculus€of€Several€Variables.€€We€overlooked€the€higher€levelŠ P   Šmulti-section€differential€equations€course.Š ų H  ŠĢThere€were€a€total€of€776€students€who€finished€the€surveyed€courses€with€a€grade.€€Of€these,€we€had€signed,Š H˜  Šcomplete,€surveys€from€663€of€these€students.€€A€number€of€students€handed€in€the€survey€but€didn't€put€theirŠ š@  Šnames€on€it€so€we€couldn't€check€their€grades.€€And,€of€course,€some€students€just€didn't€do€the€survey.€€OtherŠ ˜č Šstudents€gave€ambiguous€answers.€€Of€these€663€students€we€had€SAT€scores€for€607€of€them.€€Johns€HopkinsŠ @ ŠUniversity€doesn't€require€the€SAT€for€admission€(but€most€students€take€it).Š č8 ŠĢCalculators€were€allowed€on€exams€for€only€one€of€the€surveyed€courses€(107).€€Most€faculty€at€JohnsŠ 8ˆ ŠHopkins€University€don't€feel€the€need€for€calculators€in€basic€mathematics€courses.Š ą0 ŠĢThe€department€has€a€grading€policy€that€tries€to€keep€grades€in€all€of€these€courses€within€a€certain€range.€Š 0€  ŠThus€the€percentage€of€A€grades,€B€grades,€etc,€doesn't€vary€dramatically€from€one€course€to€the€next.Š Ų (" ŠĢŌ‡„Ā.„%&ŻlŌņ ņThe€surveyó óŌ#†&Żl%„„Ā.“#ŌŠ ($x& ŠĢThe€first€question€on€the€survey€asked€the€student€to€circle€one:€š šIn€K-12,€your€parents€(or€tutors)€helped€youŠ ‚(Ņ#* Šwith€mathematicsšš€(1)€regularly,€(2)€a€little,€or€(3)€not€at€all.€€We€combined€the€first€two€answers€together€forŠ **z%, Šour€analysis.Š Ņ+"'. ЇThe€second€question€was:€š šIn€K-12,€calculator€usage€wasšš€(1)€emphasized€and€encouraged,€(2)€was€taughtŠ ° Šbut€not€pushed,€or€(3)€not€much€at€all.€€Here€we€combined€the€last€two€answers.Š XØ ŠĢIn€addition€we€asked€a€couple€more€questions€that€weren't€very€good.€€Things€we€would€like€to€know€but€findŠ Ø ų Šit€difficult€to€find€out€are€what€kind€of€geometry€course€a€student€has€had€in€high€school€and€what€texts€theyŠ P   Šused€for€algebra.€€The€impact€of€these€on€college€performance€would€be€very€interesting€but€this€is€notŠ ų H  Šinformation€that€can€be€extracted€from€students€unless€you€are€willing€to€take€š šit€was€a€blue€bookšš€as€anŠ  š  Šanswer.Š H˜  ŠĢŌ‡„Ā.„%&ŻlŌņ ņMore€numbersó óŌ#†&Żl%„„Ā.4 #ŌŠ ˜č ŠĢDoing€the€numbers€on€individual€courses€(without€the€verbal€SAT)€doesn't€always€work€out€because€of€theŠ ņB Šsmaller€numbers€of€students.€€In€only€one€case€does€the€calculator€coefficient€turn€up€positive.€€That€is€in€theŠ šź Šsmallest€(15€survey€respondents)€course€(105),€and€the€p-value€is€a€whopping€.80.€€The€largest€(184Š B’ Šrespondents)€course€(106)€had€a€p-value€of€.50.€€For€the€next€two€courses€(in€size)€not€only€is€the€resultŠ ź: Šsignificant€but€the€coefficient€is€quite€large.€€For€202€(with€136€respondents)€the€coefficient€is€-0.49447€withŠ ’ā Šp-value€.02172.€€In€108€(130€respondents)€the€coefficient€is€-0.43561€with€p-value€.00485.€€For€these€twoŠ : Š  Šcourses€this€is€nearly€half€a€letter€grade.€€For€the€other€two€courses,€201€(77€respondents)€and€107€(65Š ā!2" Šrespondents),€the€coefficient€is€negative€but€the€p-value€is€high.€€In€all€cases€the€p-value€for€the€parentŠ Š#Ś$ Šcoefficient€is€high.€€The€only€close€case€is€202€where€the€coefficient€is€.35088€and€the€p-value€is€0.08269.€€Š 2%‚ & ŠĢThe€numbers€for€the€parents-calculator€scores€are:€{0,0},€133;€{0,1},€73;€{1,0},€206;€and€{1,1},€195.Š ‚(Ņ#* ŠĢWe€have€various€correlations€coefficients:€Calc-grade,€-0.13;€Calc-Ō_ŌMSATŌ_Ō,€-0.11;€Grade-Ō_ŌMSATŌ_Ō,€0.24;Š Ņ+"'. ŠParent-Calc,€0.13;€Parent-grade,€0.08;€Parent-Ō_ŌMSATŌ_Ō,€-0.06.Š ° ŠĢThe€standard€deviation€for€the€Ō_ŌMSATŌ_Ō€is€64€points.€€The€standard€deviation€for€the€grades€was€1.00,€exactlyŠ P Šone€letter€grade.Š Ø ų ŠĢŌ‡„Ā.„%&ŻlŌņ ņSuggestionsó óŌ#†&Żl%„„Ā.'#ŌŠ ų H  ŠĢIt€would€be€nice€to€refine€the€questions€somewhat€and€do€this€again,€but€it€isn't€likely€that€we€will.€€InŠ R¢  Šparticular,€this€phrasing€of€the€calculator€question€allows€the€student€to€decide€what€happened€in€K-12.€€WeŠ śJ Šdoubt€if€any€of€these€students€had€calculators€emphasized€and€encouraged€all€the€way€through.€€Likewise,Š ¢ņ Šthey€clearly€took€it€to€mean€more€than€just€a€year€to€get€them€ready€for€the€SAT€exams.€€If€we€informally€askŠ Jš Ša€class€if€calculator€usage€was€emphasized€and€encouraged€for€1€or€more€years€in€K-12€then€the€Ō_ŌtheŌ_ŌŠ ņB Špercentage€nearly€doubles€from€the€44%€we€got€for€our€question.€€Thus,€it€would€be€nice€to€refine€thisŠ šź Šquestion€significantly€asking€for€a€variety€of€details€about€lower€and€middle€school,€etc.Š B’ ŠĢThe€majority€of€high€school€graduates€now€go€on€to€college.€€Thus€most€K-12€programs€are€collegeŠ ’ā Špreparatory€by€default.€€The€success€of€mathematics€programs€in€K-12€should€be€judged€by€how€well€studentsŠ : Š  Šdo€in€college.€€If€this€were€our€line€of€business,€and€we€had€significant€funding,€then€we€could€think€of€lotsŠ ā!2" Šof€studies€to€do€to€try€to€answer€the€question:€€What€should€K-12€do€to€make€a€successful€college€student?Š Š#Ś$ ŠĢ