Exploratory Analysis of Students’ Mathematics Achievement ......and their associated students (14 teachers, 263 students) used Freckle in their classrooms, whereas the other half

Exploratory Analysis of Students’ Mathematics Achievement After Using Freckle

Written in partnership with WestEd

Freckle and Student Mathematics Achievement

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Table of Contents

Abstract..........................................................................................................................................................................1

Executive Summary...................................................................................................................................................2

Introduction..................................................................................................................................................................3

Method.........................................................................................................................................................................4

Participants....................................................................................................................................................4

Data Analysis................................................................................................................................................6

Results...........................................................................................................................................................................6

Baseline Equivalence..................................................................................................................................6

Post-Score Analysis………………………………………………………………………………………....……………………………………........7

Discussion.........................................................................................……………………….....................................................8

Study Limitations...................................................………………………...............................................................8

Conclusions....................................................................................……………………….........................................8

References................................................................................................……………………….............................................9

Appendix A........................................................................................……………………….................................................10

Appendix B...........................................................................………………………...............................................................13


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List of Figures

Figure 1. Sample Report Card data view available for teachers in Freckle Math..............................3

Figure 2. Means for students’ beginning and end of year MAP scores by grade and condition..........5

Figure 3. Covariate-adjusted means for each group’s end of year MAP scores.......................................7

List of Tables Table 1. School Demographic Information..........................................................................................................4

Table 2. Teacher and Student Counts by Grade Included in Final Analytic Sample..............................5

Table 3. Growth norms observed in MAP scores throughout the year.........................................................6

Table 4. Random Effects.........................................................................................................................................11

Table 5. Fixed Effects...............................................................................................................................................11


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ABSTRACTWestEd—anonpartisan,nonprofitresearch,development,andserviceagency—partneredwithFreckletoexplorewhetherstudentswhouseFreckleexhibitdifferentmathematicsachievementoutcomesthanstudentswhodonotuseFreckle.AruralschoolshareddataonFreckleadoptionandstudentscoresontheNorthwestEvaluationAssociation’s(NWEA)MeasureofAcademicProgress(MAP)inmathematicswithFreckle.WestEdusedthesedatatoconductanindependentanalysistodeterminewhetherornotFreckleusewasassociatedwithhigherNWEAMAPtestscores.ResultsareconsistentwiththehypothesisthatusingFreckleintheclassroomresultsinhigherachievementinmathematics.Limitationstothestudyandfutureresearchdirectionsarealsodiscussed.


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EXECUTIVESUMMARYFreckleisacomputerizedmathandreadingcomprehensionprogramthatprovidesadaptivefeedbackandpracticeopportunitiesforK-8students.Freckleishypothesizedtoimprovestudents’readingandmathematicsoutcomesineducation.Inthepresentstudy,WestEdexploredthepotentialofFreckletosupportstudents’mathematicsachievementinKindergarten,Grade1,andGrade2classrooms.Studyparticipantsconsistedof466Kindergarten,Grade1,andGrade2studentsand25teachersinaruralelementaryschoolduringthe2014-2015academicyear.TeacherschosetouseFreckleorchosenottouseFreckleduringthecourseoftheschoolyear.Approximatelyhalfoftheteachersandtheirassociatedstudents(14teachers,263students)usedFreckleintheirclassrooms,whereastheotherhalf(11teachers,203students)participatedinbusiness-as-usualclassroomactivities.ThisstudyexploreswhetherresultsareconsistentwiththepredictionsthatFrecklesupportsstudentlearninginmathematics.Towardsthisend,students’endofyearmathematicsscoresontheMeasureofAcademicProgress(MAP)assessmentwascollectedforeachstudent.PreliminaryanalysesindicatedthatFrecklestudentsexhibitedhigherbeginningofyearMAPscoresthanthecomparisonstudents.However,ananalysisthatattemptedtocontrolforbeginningofyearMAPscoredifferencesaswellasgradelevelindicatedthatstudentsintheFreckleconditionscoredapproximately4.6pointshigherontheirendofyearMAPscoresrelativetostudentswhodidnotuseFreckle,astatisticallysignificantdifference(p<.001).TheresultsofthisexploratorystudyareconsistentwiththehypothesisthatFrecklepositivelyimpactsstudents’mathematicsachievementinK-2Grades.However,becauseteacherswerenotrandomlyassignedtouseFreckle,theresultsshouldnotbeusedtoclaimthatFrecklecausedhigherstudentachievement.Inaddition,thestudyreliesonadatasetwithlimitedinformation:TeacherschosetouseFreckleornotforreasonsunknowntothestudyteam.Inaddition,potentiallyimportantdemographicinformationonteachersandstudentsaremissing,therebylimitingthegeneralizabilityofthefindings.FuturestudiescanbeconductedthatutilizerandomassignmenttogroupsandthatcollectinformationonfactorsthatmaypotentiallyinfluencetheeffectivenessofFreckle.SuchstudieswillincreaseconfidencethatFreckleuseleadstoimprovedmathematicsoutcomes.


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INTRODUCTIONFreckleisanadaptivemathandreadingcomprehensionprogramthatensureseverystudentreceiveshigh-quality,individualizedmathandreadingpractice.Byaddressingstudentweaknessesandbuildingoffofstrengths,Freckleisdesignedtoincreaseconfidenceandpromotegrowthinallstudents,regardlessoftheirabilitylevel.WhenstartingonFreckle,studentstakeadiagnostictodeterminewhattheyalreadyknowandareasthattheycouldusemorepracticein.Then,astheycontinuepracticing,theprogramadaptstoprovideindividualizedinstructiontailoredforeachstudent’sskilllevel.Freckleisdesignedtobeusedmultipletimesaweekintheclassroomtobuildstudents’mathfluency,andprovidesteachersdataforeachstudentsuchasthereportshownbelow:

Figure1.SampleReportCarddataviewavailableforteachersinFreckleMath.Thisstudyaddressedthequestion:DostudentswithteacherswhousedFreckleexhibithigherendofyearmathematicsscoresthanstudentsfromteacherswhodidnotuseFreckle?Towardsthisend,WestEd,anonprofitresearch,development,andserviceorganization,analyzeddatathatwasprovidedbytheparticipatingschool,whichincludedendofyearmathematicsscoresontheMeasureofAcademicProgress(MAP)assessmentforallKindergarten,Grade1,andGrade2studentsattheschool.TheMAPassessmentisadministeredbytheNorthwestEvaluationAssociation(NWEA)andisanadaptivemeasureofstudents’mathematicsachievement.ItwaspredictedthatifFrecklesupportsstudents’mathematicsachievement,studentsofteacherswhousedFrecklewouldexhibithigherendofyearscoresontheMAPassessmentrelativetostudentsofteacherswhodidnotuseFreckle.


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METHODThisstudyisnotarandomizedcontroltrialstudy(i.e.,studentswerenotrandomlyassignedtoconditions).Becauseofmanythreatstointernalvalidityunderthisdesign,thisstudydoesnotattempttomakecausalclaimsontheimpactofFreckleinstudentscores.Rather,itexploreswhethertheresultsareconsistentwiththehypothesizedpredictionsrelatedtotheimpactofFreckleonstudentachievement.

PARTICIPANTSParticipantsinthisstudywerefromarural,publicelementaryschoolintheSouthernUnitedStates(seeTable1).Participantsconsistedof25teachers(14teachersintheFrecklegroupand11teachersintheComparisongroup)and466students1(263studentsintheFrecklegroupand203studentsintheComparisongroup).The25teacherscomprisedalloftheteachersofKindergarten,Grade1,andGrade2attheparticipatingschool.SomeoftheteachersusedFrecklewiththeirstudentswhereassomeoftheteachersdidnotuseFreckle(henceforth,thesegroupsarereferredtoastheFreckleandComparisongroups,respectively).Theschooldidnotprovideinformationonteachers’reasonsforoptingtouseFreckle.StudentsinbothgroupstooktheMAPMathassessmentatthebeginningandendofthe2014-2015academicyear(i.e.,theFallandSpring,respectively).Attrition.Thirty-fivestudents(16studentsfromtheFreckleconditionand19studentsfromtheComparisoncondition)didnothavecompletepreandpost-testdataandthereforeareexcludedfromallanalyses.Thecompleteanalyticsamplethenconsistedof431students(247intheFreckleconditionand184studentsintheComparisoncondition)(seeTable2).Table1.SchoolDemographicInformation

Type %Free/ReducedLunch Enrollment %White %Black %Hispanic %Asian/PI

Public,TitleI 69% 572 72% 21% 2.6% 0.3%

1Onestudentidappearedintwoclassroomsinthedatasetsprovidedandisnotconsideredintheseanalyses.


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Table2.TeacherandStudentCountsbyGradeIncludedinFinalAnalyticSample Kindergarten FirstGrade SecondGrade Total

Students Teachers Students Teachers Students Teachers Students Teachers

Freckle 66 4 86 5 95 5 247 14

Comparison 63 4 82 5 39 2 184 11

Total 129 8 168 10 134 7 431 25

TheaveragebeginningandendofyearMAPscoresbygradeandconditionareprovidedinFigure2.

Figure2.Meansforstudents’beginningandendofyearMAPscoresbygradeandcondition.


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Table3showstheobservedandexpectedgrowthforstudentsforeachparticipatinggradelevelandcondition.MAPgrowthnormsarebasedonthebeginningtoendofyeargrowthontheMAPmathematicsassessment(NorthwestEvaluationAssociation,2015).Table3.Growth(andstandarddeviations)observedinthestudyrelativetothegrowthnormsfromthebeginningtoendoftheacademicschoolyearontheMAPmathematicsassessmentforeachgradelevel.

Kindergarten Grade1 Grade2

FreckleGrowth 25.71(7.51)

25.52(7.73)

20.68(8.19)

ComparisonGrowth 23.08(7.17)

22.56(7.16)

12.79(5.11)

MAPGrowthNorms 19.1(7.59)

18.4(7.45)

15.2(7.11)

DATAANALYSISStudentachievementdatafromtheMAPassessmentwereanalyzedbyWestEd.TheprimaryanalyticstrategyforassessingstudentachievementscoresinvolvedfittingHierarchicalLinearModels(HLM).Thisanalysiswaschosenbecauseitaccountsforthenestedstructureofthedata(i.e.,studentsnestedwithinteachers;Raudenbush&Bryk,2002)(seeAppendixA).FrecklealsoconductedinterviewswithasubsetofFreckleteacherstogaininsightintotheperceivedvalueofFreckle(asummaryoftheteacherinterviewsisincludedinAppendixB).

RESULTSBASELINEEQUIVALENCEAnanalysiswasfirstconductedtodeterminewhetherstudentswerestatisticallyequivalentontheirbeginningofyearMAPscores.ThisanalysisindicatedthatstudentsintheFreckleconditionscoredhigher(MFR=161.44,SEFR=4.22),butnotstatisticallyhigher,onthepre-MAPassessmentthanstudentsintheComparisoncondition(MComp=156.05,SEComp=4.77;p=.41).Tomeasuretherelativesizeofthebaselinedifferencesbetweenthegroups,aneffectsizestatistic(i.e.,hedgesg)wascalculated.Theeffectsizestatisticisameasureofthesizeofthedifferencesbetweenthegroupsinstandarddeviations.TheeffectsizedifferencebetweentheFreckleandComparisongroups’baselinescoreswas.31,whichisconsideredsubstantive(WhatWorksClearinghouse,2014).Thedifferenceinbeginning-of-yearperformanceislargeenoughthatthetwogroupsshouldbeconsiderednon-equivalent(WhatWorksClearinghouse,2014).


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POST-SCOREANALYSISToexaminestudentachievementforstudentswhoseteachersusedFrecklerelativetostudentswhodidnot,weusedanHLMmodelthatattemptedtocontrolforstudents’gradelevelandtheirbeginningofyearscores(seeAppendixA).ThisanalysisindicatedthatstudentsintheFrecklegroupexhibitanendofyearMAPscorethatisanestimated4.64pointshigherthanstudentsintheComparisongroup.Thisdifferenceisconsideredsignificant.Theeffectsizeforthisdifferenceis.29(seeFigure2formeansofeachgroups’endofyearMAPscores)2.

Figure3.Covariate-adjustedmeansforeachGroup’sendofyearMAPscores.Errorbarsrepresentstandarderrorsofthemeans.

Tointerprettheeffectsizeestimateof.29inamoremeaningfulway,weconvertedthisstatisticusingpropertiesofthenormaldistribution.ThisanalysissuggestedthatifstudentsintheComparisongroupwereatthe50thpercentileofanormedsample,theFrecklegroupstudentswouldbeplacedatthe59th--60thpercentileofanormedsample(i.e.,approximately9.86percentagepointshigherthanthecomparisonstudents).WealsocomputedaneffectsizeforeachgradelevelandcomparedthiseffectsizetothetypicalexpectedMAPgrowthinmathematics(NorthwestEvaluationAssociation,2015).ThisanalysissuggestedthattheFrecklegroupstudentsareapproximatelytwomonthsaheadofComparisongroupstudentsinmathematicsachievement(seeAppendixA).

2ResultsweresimilarwhenexcludingtheGrade2students.


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DISCUSSIONStudentsintheFrecklegroupexhibitedhigherendofyearachievementscoresthanstudentsintheComparisongroup.Thiseffectheldwhencontrollingforbeginningofyearscoresandgradelevel.Thus,findingsfromthisstudyareatleastconsistentwiththehypothesisthatusingFreckleintheclassroomimprovesstudentachievementoutcomes.STUDYLIMITATIONSBecausethisstudyreliedondatacollectedpost-hocfromanaturalisticimplementation,therearemanyissuesthatmaylimittheconfidenceinconclusions.First,thedatasetprovidedbytheschoolwaslimitedinthatitcontainedlittlebackgroundinformationaboutparticipatingstudentsandteachers,includingreasonswhyteacherschosetouseFreckleattheschool.Thisinformationwouldhavebeenusefulforinferringthegeneralizabilityoffindings,aswellasforexploringfactorsthatmaymoderatetheeffectivenessofFreckle.Second,becausethisstudydidnotutilizerandomassignment,itispossiblethatvariablesotherthanFreckleuse-suchasmoreeffectiveteachersoptingtouseFreckle-contributedtheincreaseinstudentscores.Third,studentsintheFrecklegrouphadbaselineMAPscoresthatweresubstantivelyhigherthantheComparisongroupandthereforecannotbeconsideredequivalentpriortotheintervention.Finally,sincethestudywasconductedonarelativelyhomogeneousandnarrowpopulation(participantswithinasingleschool),theeffectsmaybelargerthanwouldbeobservedifthestudywereconductedonadiversepopulation(e.g.,multipleschoolsindifferentgeographicregions)(Lipseyetal.2012).CONCLUSIONSThisstudyisexploratoryinnatureandrepresentsaninitialstepinunderstandingtheeffectivenessofFreckleonstudentachievementoutcomes.ThesefindingssupportthehypothesisthatFreckleimprovesstudents’mathematicsoutcomes.However,futurestudiescanutilizerandomassignmenttogroupsandcollectbaselineandimplementationinformationtomoreconclusivelydetermineFreckle’simpactonstudentoutcomes.


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REFERENCES Bates,D.,Maechler,M.,Bolker,B.,&Walker,S.(2015).FittingLinearMixed-EffectsModelsUsing

lme4.JournalofStatisticalSoftware,67(1),1-48. Lipsey,M.W.,Puzio,K.,Yun,C.,Hebert,M.A.,Steinka-Fry,K.,Cole,M.W.,Roberts,M.,Anthony,K.S.,

Busick,M.D.(2012).TranslatingtheStatisticalRepresentationoftheEffectsofEducationInterventionsintoMoreReadilyInterpretableForms.(NCSER2013-3000).Washington,DC:NationalCenterforSpecialEducationResearch,InstituteofEducationSciences,U.S.DepartmentofEducation.ThisreportisavailableontheIESwebsiteathttp://ies.ed.gov/ncser/

NorthwestEvaluationAssociation(2015).2015NWEAMeasuresofAcademicProgressNormative

Data.https://www.nwea.org/content/uploads/2015/08/2015-MAP-Normative-Data-NOV15.pdf

RCoreTeam(2015).R:Alanguageandenvironmentforstatisticalcomputing.RFoundationfor

StatisticalComputing,Vienna,Austria.ISBN3-900051-07-0,URLhttp://www.R-project.org/Raudenbush,S.W.,&Bryk,A.S.(2002).Hierarchicallinearmodels:Applicationsanddataanalysis

methods(2nded.).ThousandOaks,CA:SagePublications.U.S.DepartmentofEducation,InstituteofEducationSciences,WhatWorksClearinghouse.(2014,

March).WhatWorksClearinghouse:ProceduresandStandardsHandbook(Version3.0).Retrievedfromhttp://whatworks.ed.gov


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AppendixA.Statisticalandmethodologicaldetailsofthemethodsandanalysesconducted.

DATAANALYSISStudentachievementdatafromtheMAPassessmentwereanalyzedbyWestEd.TheprimaryanalyticstrategyforassessingstudentachievementscoresinvolvedfittingHierarchicalLinearModels(HLM)witharandomeffecttermforteachers(Raudenbush&Bryk2002).Thisanalysiswaschosenasitaccountsforthenestedstructureofthedata(i.e.,studentsnestedwithinteachers).ModelswerefitusingRestrictedMaximumLikelihoodEstimation(REML).Fixedeffectsinthemodelincludetreatmentgroup,students’baselineachievement,andgradelevel.WeusedRstatisticalsoftware(RCoreTeam,2015)version3.1.2andthelme4package(Batesetal.2015)version1.1-7toconducttheHLManalysesonstudentachievement.

QUANTITATIVEANALYSESWestEdanalyzedstudentMAPscoresusingHierarchicalLinearModeling(Raudenbush&Bryk2002).PreliminarymodeltestingindicatedthatHLMisasuitablechoice,astheteacherintraclasscorrelationwassizeable(ICC=.69)intheunconditionalmodel.BaselineEquivalence.AnanalysiswasfirstconductedtodeterminewhetherstudentswerestatisticallyequivalentatbaselineonthepreMAPscore.ToexaminewhetherstudentsexhibitedsimilarpreMAPscores,studentpreMAPScoreswereregressedontothegroupingvariable(FreckleorComparison)whileincludingarandomeffecttermforteachers.ThisanalysisindicatedthatstudentsintheFreckleconditionscoredhigher(MFR=161.44,SEFR=4.22),butnotstatisticallysignificantlyhigher,onthepre-MAPassessmentthanstudentsintheComparisoncondition(MComp=156.05,SEComp=4.77;p=.41).Theeffectsizeforthisdifferencewashedgesg=.31,whichisconsideredsubstantive.TheWhatWorksClearinghouse(2013)standardsconsidersthislevelofbaselinedifferencetobenon-equivalent.Post-ScoreAnalysis.ToexaminestudentachievementforstudentswhoseteachersusedFrecklerelativetostudentswhodidnot,weusedanHLMmodelwhichincludedfixedeffectstermsforgradeandbeginningofyearscores,aswellasarandomaeffecttermtoaccountforthenestingofstudentswithinteachers.TheHLMmodelthatwasusedispresentedbelow:

𝑃𝑜𝑠𝑡𝑆𝑐𝑜𝑟𝑒)* = 𝛽.. + 𝛽.0𝐹𝑟𝑒𝑐𝑘𝑙𝑒 + 𝛽0.𝑃𝑟𝑒𝑆𝑐𝑜𝑟𝑒)* + 𝛽.4𝐹𝑖𝑟𝑠𝑡𝐺𝑟𝑎𝑑𝑒* + 𝛽.9𝑆𝑒𝑐𝑜𝑛𝑑𝐺𝑟𝑎𝑑𝑒* +𝜉.*

+ 𝜖)*where𝑃𝑜𝑠𝑡𝑆𝑐𝑜𝑟𝑒)*istheendofyearmathematicsscoreontheMAPassessmentforthei-thstudentofthej-thteacher,𝛽..isthegrandmeanofscores,𝛽0.𝑃𝑟𝑒𝑆𝑐𝑜𝑟𝑒)*representsstudents’beginningofyearMAPscore,and𝛽.4𝐹𝑖𝑟𝑠𝑡𝐺𝑟𝑎𝑑𝑒*and𝛽.9𝑆𝑒𝑐𝑜𝑛𝑑𝐺𝑟𝑎𝑑𝑒*representdummyvariablesfor1stand2ndgradeclassrooms,respectively(withKindergartenservingasthebaseline).𝜉.* isarandom


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effecttermforteachersandand𝜖)*isarandomerrorterm.ThedifferencebetweenscoresofstudentsofteachersusingFrecklevs.studentsofteachersintheComparisongroupiscapturedby𝛽.0𝐹𝑟𝑒𝑐𝑘𝑙𝑒.AsummaryoftherandomandfixedeffectsofthismodelarepresentedinTables4and5,respectively.

Table4.RandomEffectsTable.

Variance St.Dev.

Teacher 5.62 2.37

Residual 46.08 6.79Table5.FixedEffectsTable.

Coefficient St.Error p-value

Intercept 54.62 4.89 <.001***

PreScore 0.77 0.03 <.001***

FirstGrade 5.05 1.57 .003**

SecondGrade 0.66 1.86 0.72

Freckle 4.64 1.19 <.001***Note.**p<.01,***p<.001IfthehypothesisaboutFreckleimprovingstudents’mathematicsscoresiscorrect,theoutputinTable4suggeststhatthestudentsintheFrecklegroupwouldhavegrownanestimated4.64pointshigherthanstudentsintheComparisongrouphadthegroupsbeenfullyequivalentpriortotreatment.Thisdifferenceissignificantatthe⍺<.001significancelevel.Theeffectsizeforthisdifferenceishedge’sg=.29.Thecovariate-adjustedmeansfortheFreckleandComparisongroupsare184.52and179.88,respectively,andtheunadjustedstandarddeviationsforthesegroupsare16.12and16.45,respectively.BecauseGrade2hadsubstantiallydifferentsamplesizesintheFrecklegrouprelativetotheControlgroup,wererantheabovemodelexcludingGrade2students.ThemodelcoefficientforFreckletermusingthissubsetteddatawasstillpositive,andsignificant(B=3.93,p=.007).


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Tointerprettheeffectsizeestimateof.29inamoremeaningfulway,weconvertedthisstatisticusingpropertiesofthenormaldistribution.Inthenormaldistribution,a1standarddeviationincreasecorrespondstoa34pointpercentileincrease.Thus,inanormedsample,aneffectsizeof.29correspondstoa9.86pointpercentileincrease(i.e.,34x.29=9.86).Therefore,theresultssuggestthatifstudentsintheComparisongroupwereatthe50thpercentileofthenormedsample,theFrecklegroupstudentswouldbeplacedatthe59th-60thpercentileofthenormedsample(i.e.,50+9.86=59.86).WealsocomputedaneffectsizeforeachgradelevelandcomparedthiseffectsizetothetypicalexpectedMAPgrowthinmathematics.Tothisend,wereranthemodelpresentedaboveseparatelyforeachgradelevel(i.e.,weexcludedthegrade-leveltermsfromeachmodel).TheeffectsizesfortheFrecklevariablefromthesemodelsare.29,.38,and.34forKindergarten,Grade1,andGrade2,respectively.BasedonthebeginningandendofyearstudentstatusnormsontheMAPmathematicsassessment(NorthwestEvaluationAssociation,2015),theestimatedbeginningtoendofyeareffectsizesforMAPmathematicsare1.33,1.39,1.14foreachofthesegrades.ComparingtheeffectsizesobservedinthepresentstudytotheeffectsizesoftheaveragegrowthfortheMAPassessmentsuggeststhattheobservedeffectsizesarenoteworthy,correspondingto22%,27%,and30%oftheexpectedgainoverthecourseofaschool-yearinKindergarten,Grade1,andGrade2,respectively(e.g.,forKindergarten,.29/1.33=.22,etc.).Multiplyingtheaverageschool-yeargainforallgrade-levels(.26)by9months(thetypicalnumberofmonthsinaschoolyear),weestimatethattheFrecklegroupstudentsareapproximatelytwomonthsaheadofComparisongroupstudentsinmathematicsachievement.


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AppendixB.DescriptionofteacherinterviewsconductedbyFreckle.

TEACHERINTERVIEWSTeachers’perceivedvalueoftheprogramwasdefinedastheextenttowhichFrecklecouldbeusedeffectivelyandefficientlybyclassroomteachers.TogainanunderstandingoftheperceivedvalueofFreckle,FreckleconductedinterviewswiththreeteacherswhousedFreckleabouttheirexperiencewiththeprogram.Theinterviewswereconductedoverthephoneinthefallof2015,andconsistedofquestionsabouthowFreckleusageimpactedstudentengagementandoutcomesinmath.TheteachersinterviewedhadusedFreckleinthe2014-2015schoolyearandwerewillingtodiscusstheirexperienceswiththeprogram.QuestionsincludedhowtheyfeltFreckleimpactedgrowthintheirclassroom,students’engagementinmath,andtheireffectivenessasteachers.Interviewslastedapproximately30minuteseach.Ingeneral,Frecklewasusedinmathcenterswithsmallgroupsofstudentsforabout30minutesaday,afewtimesaweek.AlltheteachersinterviewedsaidtheywouldrecommendFreckle,citingitsindividualizedpracticeasthemainbenefitoftheprogram.TheinterviewedteachersreportedthattheysawtremendousgrowthfromusingFreckle.Forinstance,oneteachersaid,“atthebeginningoftheyearlastyear,Ihadkidswhoweresignificantlybelowgradelevel.Bytheendoftheyear,outofthekidsIhad,only1or2werenotongradelevelorabove”.TeachersalsoappreciatedthewayFreckledeepenedstudents’understandingofmathconcepts.Oneteacherremarkedthat“itbuilttheirconfidence,becausetheproblemswerehuge,andoncetheycouldbreakitdownintoitsparts,theygotit.Theyusedstrategiestosolvetheproblem.Ibelieveitexposedthemtothinkingoutsidethebox”.AnotherteacherreportedthatstudentsenjoyeditsomuchthattheywantedtouseFreckleathome.TeachersreportedthatFreckleallowedthemtobettermeettheneedsofeverychildintheirclassroom,givingthemtheabilitytofocusonsmallgroupsofstudentsatatime.OneteacherstatedthatFreckle“allowsmetoseewhatIdon’tneedtowastetimeon.I’mabletobettermanagestudents’instructionandmanagemytimebetter”.Overall,theinterviewedteachersviewedFreckleasaneffectivetool,withonesaying“onceIfoundoutaboutit,Ibasicallyuseditallthetime”.InterviewresponsessuggestthatFrecklecanbeavaluableclassroomtool.ThoughonlyasmallsubsetofteachersthatusedFreckleparticipatedininterviews,theseteacherssuggestedthatFrecklewasfluidlyintegratedintotheirclassroominstruction,andthattheywereabletouseclasstimemoreeffectivelytosupportstudentmathematicslearning.

Documents

Exploratory Analysis of Students’ Mathematics Achievement ......and their associated students (14 teachers, 263 students) used Freckle in their classrooms, whereas the other half