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A. a.(1)(a) i) a)S ($0 ($0 0 (($0 0 0   A_ekqwDocumentDocument StyleI.1.A.a.(1)(a)i)a)jo4Tech InitInitialize Technical StyleS #  1 .1 .1 .1 .1 .1 .1 .1 S CuyTechnicalTechnical Document Style11.11.1.11.1.1.11.1.1.1.11.1.1.1.1.11.1.1.1.1.1.11.1.1.1.1.1.1.1x?t2PleadingHeader for numbered pleading paper %  &5(    qXNNXX?.''*dE*??.''*dE*?HH1HH2HH3HH4HH5HH6HH7HH8HH91011121314 .+8 Ї1516171819202122232425262728  +((~24!$ -C!  7yNNdd7  & `CG Times  CRight ParRight-Aligned Paragraph NumbersI.A.1.a.(1)(a)i)a)3|x=6X9`(CourierNNx6X@UN@& `CG TimesNNj PE3UNP(cC$  7NNdd7 dU DDPPPӀEDI#y   Z6Times New Roman Regular 6Times New Roman Regular(9 Z 6Times New Roman Regular9TABLE A -C!  79NNdd7  ݛTRX3'3'3' Letter3'T79NNdNNd7  3NNNN3?D?N3NSLU582 `     h      p   Email:bocallaghan@selu.edu  500WesternAvenue    h      p   Phone:(504)5492169  Hammond,LA70402    h      p   Fax:(504)5492099 h 3X>X?3?D   `     h      p    `     h      p    `     h      p @rrCalculators,Attitudes,andSuccess@)@@)by@ BrianR.O'Callaghan  DepartmentofMathematics@SoutheasternLouisianaUniversity  Abstract    Astudywasconductedinvolvingsixgraphingcalculatorsectionsandthreetraditionalsectionsofacollegealgebracourse.Thecalculatorstudentsshowedsignificantimprovementsintheiroverallattitudetowardmathematics,theirselfconceptrelativetomathematics,andtheirenjoymentofmathematics.Theyratedthecalculatorsandteachersveryhighly,andtheyweremoresuccessfulthanthetraditionalstudents.  ,|   Ӝ755==dNNd7Calculators,Attitudes,andSuccess T     (X>XX3X>(NNX(X>Technologyhasrevolutionizedalmostallaspectsofourinformationagesociety,andithas   nowbecomeamajorfactorineducationateverylevel.ThereisnearlyuniversalagreementintheMathematics/MathematicsEducationcommunitythattechnologywillcontinuetodevelopasaveryprominentfeatureintheeducationallandscape.AccordingtotheCurriculumandEvaluation ,   StandardsforSchoolMathematics(NCTM,1989),calculatorswithgraphingcapabilitiesshould 4  beavailabletoallstudentsatalltimesandacomputershouldbeavailableinallclassroomsfordemonstrationpurposes.TheTI82(or83)calculatortogetherwithitsoverheadprojectionunitisideallysuitedtosatisfybothoftheserecommendations.Itisanexcellentdemonstrationdeviceforteachersaswellasapowerfultoolforstudentstoexploremathematicalideasandsolveproblems.  Background  #3NNN(N #6NNN3N#6X>XN6N$ #  SoutheasternLouisianaUniversityisarapidlygrowing,openadmissionsuniversitywitha \ studentpopulationofapproximately15,000students.Mostofthestudentsarefromlowertomiddlesocioeconomicstatusfamiliesandareofaveragescholasticability.TheirmeanACTscoresare19.0(composite)and17.9(mathematics).Manyofthesestudentshavedifficultysatisfyingtheuniversitysgraduationrequirementsofsixhoursofmathematicsatthelevelofcollegealgebraorhigher.  TheDepartmentofMathematicsnormallyteachesabout4,000studentspersemester,includingapproximately50sectionsofcollegealgebra.Thecombinedwithdrawal/failurerateinthiscourseisgenerallyabout50percent,whichisacauseofgreatconcernforstudents,faculty,andadministration.Thissituationhasspawnedmanyuniversityanddepartmentalinitiativesthathavefocusedonimprovingthestudentssuccessrateinourmathematicscourses.Thispaperreportsononesuchproject.#3X>XX6X>> #ԛ  GraphingCalculatorInitiative H' 0   Asapartofoureffortstoaddressthisproblem,theDepartmentofMathematicsdecidedtoinitiatetheuseofgraphingcalculatorsinthecollegealgebracourse.6X>XX3X>Ourgoalwasto  *#4 implementthisaspectofmathematicseducationreformwiththehopethatitwouldhaveapositiveeffectonourstudents𛀜performance#3X>XX6X>#.Thisdecisionraisedseveralissuesatvariouslevels ,|&8 withintheuniversitythathavetoberesolved.Administratorswereconcernedabouttheimpactofthecalculatorsonourstudentsandabouttheaddedcostincurredbythestudents.Somefacultymemberswerereluctanttochangetheirpedagogicalapproaches;andothersvoicedepistemologicalobjections,suchastheargumentthatourstudentswouldbecomebuttonpushersratherthanproblemsolvers.Aftermonthsofdiscussions,meetings,planningsessions,andletterwriting,ourplanwasfinallyapproved.Sixsectionsofcollegealgebraweredesignatedasgraphingcalculatorsections,andTI82'swereprovidedtothestudents.  DesignoftheStudy    Inadditiontothesixcalculatorsections,threetraditionalsectionsofthecoursetaughtbythesameinstructorswereincludedascontrolgroups.Thesectionsvariedinsizefrom25to44withthetotalnumberofstudentparticipantsequaling328.Weattemptedtoevaluatetheimpactofthetechnologyonthesestudentsfromseveraldifferentperspectivesandwithmultipleinstruments.  Weadministeredtwoattitudemeasurestothecalculatorclassesandcontrolgroupsatthebeginningandendofthesemester.ThefirstwasTheRevisedMathAttitudeScale(Dutton, \ 1962),whichrateseachstudentsoverallattitudetowardmathematics.ComplementingthiswasTheMathematicsAttitudeInventory(MAI)(Sandman,1980).TheMAIgivessixscoresper t   studentmeasuringthefollowingconstructs:perceptionofthemathematicsteacher,anxietytowardmathematics,valueofmathematicsinsociety,selfconceptinmathematics,enjoymentofmathematics,andmotivationinmathematics.WealsoaskedthestudentstofilloutquestionnaireswhichIdevelopedspecificallyforthisstudy(seeAppendix).Thequestionsaskedthestudentstogivetheiropinionsaboutvariousaspectsofthecourse,suchastheinstructor,thetextbook,andthecalculators.  Results    Thestatisticalanalyses(repeatedmeasures)ofthedatafromtheattitudescalesrevealedthatthecalculatorsectionsshowedsignificantimprovementsin(a)theiroverallattitudetowardmathematics,(b)theiropinionoftheteacher,(c)theirselfconceptrelativetomathematics,and(d)theirenjoymentofmathematics(seeTable1).Incontrast,thetraditionalsectionsshowednochangesintheirattitudes.   -&8 Table1MeansforCalculatorSections b *w9.:ddd Xdd Xdd X(#(#w,` dd ,dd ,dd +       Measure '| ( 'Pre '| (" 'Post '| (" '  Dutton @6  {Gz-.04{Gz@ӄ.04 @64    {Gz-.04 {Gz @  .26* '    '] MAI | (    | (    | (  ЀTeacher @6   :@26.0:@@26.0 I?4 " :@26.0 :@ I28.3*  " ЀAnxiety @6 |(  (@12.4(@@12.4 ka4|( " (@12.4 (@ 333333(@12.1333333(@k12.1 @64|( " 333333(@12.1 333333(@ @ЀValue @6   333336@22.7333336@@22.7 ka4 " 333336@22.7 333336@ 6@22.66@k22.6 @64 " 6@22.6 6@ @ЀSelfconcept @6 |(  -@14.8-@@14.8 I?4|( " -@14.8 -@ I16.0* |( " ЀEnjoyment @6   1@17.51@@17.5 I?4 " 1@17.5 1@ I18.4*  " ЀMotivation ?5 |( !@8.8!@?8.8 i_3|(" !@8.8 !@ !@8.8!@i8.8C97|(" !@8.8  !@ C*significantatp<.05  Wealsoanalyzedthestudents'responsestothecoursequestionnaire.BelowisasummaryofstudentresponsestoQuestions15andsomestatisticsfromQuestion6.*,XX4 XX*0  1.04(#(#Thestudentslistedthecalculators,theinstructors,andtheteachingmethods(hands B' on,groupwork)asthemostbeneficialtotheirlearning. 4(#4(#   2.0 4 Mostfoundnothingtobeleastbeneficial,butsomementionedlogarithms,lackof Z+ time,andhomework. 4(#4(#   3.0 4 Thestudentslikedtheoverheadcalculatorexamples,thegroupwork,theproblem "/ solving,andtheinstructors'thoroughexplanations,patience,andcaring. 4(#4(#   4.0 4 Moststudentsfoundnothingleastbeneficialabouttheteachers'style.$34(#4(#   5.0 4 Suggestionsforimprovementincludedslowingthepaceandmorecalculator D&5 workshops. 4(#4(# 0  6.04(#(#Thestudentswereaskedtorateseveralaspectsofthecourseonascalefrom0 )"9 (Failing)to4(Excellent).Themeansareasfollows: 4(#4(# 6,XX4` X,XX4 X6   4  ` Teacher3.54 h      p Text2.61 +x%=    4  ` Calculator3.55 h      p Expectedgrade2.55 .-&? & &   Thegradedistributionsfromthecalculatorsectionsarelistedbelow:   4  ` Grade:   A h B  C  D p F  W   b    4  ` Percent:  8.6 h 11.1  20.0  15.6 p 14.7  30.2  '&T,     Thecombinedwithdrawalandfailurerateof44.9%representsasmallbutencouragingimprovementoverthedepartment'straditionalresults.Thecorrespondingrateforthecontrolsectionswas46.6%.  Conclusion    Ingeneral,researchontheincorporationoftechnologyintothemathematicscurriculumhasshownmanypositiveresults.Whenusedinconjunctionwithothermathematicseducationreformideas,technologicalcurriculahaveenrichedstudents'understandingofmathematicalconcepts,increasedtheirproblemsolvingabilities,andimprovedtheirattitudestowardmathematics.Webelievethatoureffortsinthisdomainhaveproducedsimilarresults.Inparticular,(X>XX3X>(NNX(X>we#3NNN(N1#6NNN3N#6X>XN6N1#wereabletodocumentsomepositiveeffectsofgraphingcalculatorsonour  studentsattitudesandtheirsuccessinthecourse.Theseresults,coupled#3X>XX6X>2#3NNX3X>(NNN3NԀ#3NNN(N73##3X>XN3N3#withotherbenefitsof N graphingcalculators,ledtotheiradoptioninallofourmathematicscourses.  Inadditiontothesepromisingresults,therearemanyotheradvantageswhicharisefromtheuseofthesecalculators.Theyallowthestudentstoexploreandsolvemorerealisticproblemsituations.Thecalculatorscanbeusedtohandlesomeofthelowerleveltasks,thusallowingformoretimetobedevotedtothedevelopmentofhigherordercognitiveabilities,suchasproblemsolvingandconceptualunderstanding.Theyalsohehelpourstudentstobecomemorefamiliarwithandproficientintheuseoftechnology,whichisavitalskillintoday'sworld.  Manyofourfacultyhavebecomeveryexcitedaboutthisinitiative,whichnowhasthefullsupportofbothfacultyandadministration.Itisnolongeraquestionastowhethertechnology,andinparticulargraphingcalculators,shouldbeincorporatedintothemathematicscurriculum.Thequestionnowishowtobestcapitalizeonthispowerandpotentialforimprovingourstudents'mathematicalexperiences.  ("2   References    Dutton,W.(1962).Attitudechangeofprospectiveelementaryschoolteacherstowardarithmetic.TheArithmeticTeacher,9,421. N   NationalCouncilofTeachersofMathematics.(1989).Curriculumandevaluation z & standardsforschoolmathematics.Reston,VA:Author. f    Sandman,R.(1980).Themathematicsattitudeinventory:Instrumentanduser'smanual. >  JournalforResearchinMathematicsEducation,11,148149.  *    AppendixCourseQuestionnaire    Nowthatyouhavejustaboutfinishedthesemester,pleaseprovidefeedbackandsuggestionsaboutyourlearningandexperiencesinthisclass.Youdonothavetosignyournameasallresponsesaretobeanonymous.9,X4` X,XX4` X9:1.  Whataspectsofthisclassweremostbeneficialtoyourlearning? *  2.  Whataspectsofthisclasswereleastbeneficialtoyourlearning?   3.0  Whatteachingtechniqueoraspectoftheteacher'sstylewerethemostbeneficialtoyour ^  learning? (#(# 4.0  Whatteachingtechniqueoraspectoftheteacher'sstyleweretheleastbeneficialtoyour  learning? (#(# 5.  Whatsuggestionsdoyouhaveforimprovementinthefollowing:    Coursecontent?  Courseactivities?6.0  Ratethefollowingaspectsofthecourseintermsofitshelpfulnesstoyourlearning:"((#(# 0  (0=Failing,1=Poor,2=Average,3=Good,4=Excellent) (#(# ?,X4,X,X4` X?  Teacher: `  01234 %X,   Textbook: `  01234 ' .   Calculator: 01234 p("0 7.  Whatgradedoyouexpecttomakeinthisclass?ABCDF )~#2   Pleaseusethebackofthisformforanyadditionalcommentsyoumayhave.