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Assessing the Impact of "Standards"-Based Middle Grades Mathematics Curriculum Materialson Student AchievementAuthor(s): Robert Reys, Barbara Reys, Richard Lapan, Gregory Holliday, Deanna WasmanSource: Journal for Research in Mathematics Education, Vol. 34, No. 1 (Jan., 2003), pp. 74-95Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/30034700

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Journalfor Researchin MathematicsEducation

2003, Vol. 34, No. 1, 74-95

Assessing the Impact of

Standards-Based Middle GradesMathematics Curriculum Materials onStudent Achievement

RobertReys, BarbaraReys, RichardLapan,andGregoryHolliday,Universityof Missouri,Columbia

DeannaWasman,

HickmanHigh School, ColumbiaMissouri PublicSchools

Thisstudycomparedthemathematicsachievementofeighthgradersinthefirstthreeschooldistrictsin Missourito adoptNSF-fundedStandards-basedmiddlegradesmathematicscurriculummaterials(MATHThematicsor ConnectedMathematicsProject)withstudentswhohadsimilarpriormathematicsachievementandfamilyincomelevelsfromotherdistricts.Achievementwasmeasuredusingthemathematicsportionof theMissouriAssessmentProgram(MAP)administeredto all8thgradersin the stateannuallybeginningin thespringof 1997.Significantdifferencesin

achievementwereidentifiedbetweenstudentsusingStandards-basedcurriculummaterialsfor at least2 yearsand studentsfromcomparisondistrictsusingothercurriculummaterials.Allofthesignificantdifferencesreflectedhigherachievementof studentsusingStandards-basedmaterials.Studentsin eachof thethreedistrictsusingStandards-basedmaterialsscoredhigherintwocontentareas(dataanalysisandalgebra),andthesedifferencesweresignificant.

KeyWords:Achievement;Curriculum;Middlegrades,6-8;Reforminmathematicseducation

Concernsaboutthe mathematicsachievementof U. S. youtharecommonplaceandbased on evidence from a varietyof nationalandinternationalstudies(Beatonet al., 1997; Kilpatrick,1992, 1997; National Research Council, 1989, 1998;Schmidt,McKnight,&Raizen, 1997; Wu, 1997).Generalagreementis found thatthe qualityof school mathematicsprogramsmust improveto affordall students

opportunitiesto succeedinmathematics.Strengtheningandclearlyarticulatingmath-ematicscurriculumstandardsfor theK-12 schoolyearsandproducingcurriculum

TheresearchreportedherewassupportedbytheNationalScienceFoundation(NSF)underGrantESI94-53932.Twoof theauthors(BarbaraReysandRobertReys)arecodirectorsof theShow-MeCenter,anationalcenterfordisseminatingandsupportingNSF-fundedmiddleschoolmathematicscurricula.Thenarrativedoes not necessarilyreflect the positionor opinionof the NationalScienceFoundation.The authorsgratefullyacknowledgethecooperationandsupportofschooldistrictpersonnelinprovidinginformationforthisstudy.



R.Reys,B.Reys,R.Lapan,G.Holliday,andD. Wasman 75

materialsto guide teachers and studentsare majorefforts that are underway to

improveschool mathematicsprogramsandstudentlearningoutcomes.

In thisarticle,we use the termmathematicscurriculumstandardsto referto the

set of learninggoalsarticulatedacrossgradesthatoutlinetheintendedmathematicscontentandprocess goals atparticularpointsin time (e.g., gradesorgradebands)

throughoutthe K-12 school mathematicsprogram.School leaders, textbook

authors,assessmentdevelopers,andultimatelyclassroomteachersuse curriculumstandardsasthey design productsororganizemathematicsinstructionfor students.

The NationalCouncilof Teachersof Mathematics(NCTM)hasprovideda set of

mathematicscurriculumStandards(NCTM, 1989, 2000).Curriculummaterials(e.g., textbooks)provideguidanceand structureto teachers

asthey

enact the intended school mathematicscurriculum.Researchhas docu-

menteda stronginfluence of textbooks on the mathematicscontentthat is taughtand learned(Driscoll, 1980; Porter, 1989; Robitalle & Travers,1992; Schmidt,

McKnight,& Raizen, 1997; Schmidtet al., 2001). If mathematicalcontent is not

includedin curriculummaterials,then teachersareunlikelyto presentthe content.

Likewise, the instructionalapproachsuggested by the materialsoften influences

teachers'pedagogicalstrategies.Indeed,theimplementedcurriculumoftencloselymirrorsthe contentandpedagogical approachpresentedin textbooks.

Beginningin 1990,the NationalScience Foundation(NSF)fundedseveralmath-

ematicscurriculumdevelopmentprojectstorespondto the needfor curriculummate-rialsto be moreclosely alignedwith the NCTM's Standards.Curriculumdevelop-ment teamsconsistedof mathematicseducators,mathematicians,and classroom

teachers.Thecurriculummaterialswereextensivelyfield-testedandrevisedonthe

basisof feedbackfromteachersandevidenceof studentlearning(Senk&Thompson,

2002). Final versionsof the materialswerepublishedand distributedby commer-

cialvendorsbeginninginthe mid 1990s(Reys,Robinson,Sconiers,&Mark,1999).Inthisarticle,we referto curriculummaterialsthatarealignedwiththe contentand

pedagogical expectationsarticulatedin the NCTM's Standardsdocuments and

developedwithsupportfrom the NSF as "Standards-basedcurriculummaterials."A summaryof the characteristicsof Standards-basedcurriculummaterialscan be

found elsewhere(e.g., Trafton,Reys, & Wasman,2001).Informationabouttheimpactof Standards-basedmathematicscurriculummate-

rials on studentlearningis clearly needed. This kind of researchis difficult to

conductfor manyreasons,including gainingaccess to schools, documentingthe

fidelityof implementationof curriculummaterials,gatheringdataovera substan-

tialperiodof time,identifyingappropriatecomparisongroups,andaccessingvalid

measures of student performance(Hiebert, 1999; Schoenfeld, 2000; Usiskin,

1999).Despitethesedifficulties,two recentlypublishedstudiesprovideevidenceof thepositive impactof middlegradesStandards-basedcurriculummaterialsas

well as the need to embed curriculumreformwithin a largersystemic effortthat

includes attentionto professionaldevelopmentof teachers.

RiordanandNoyce (2001) comparedthe mathematicsachievementof students

from two groupsof schools on the Massachusettsstate-mandatedassessment of



76 Standards-BasedMiddleGradesCurriculumMaterials

mathematics.OnegroupincludedstudentsfromeveryschoolinMassachusettsthathadadopteda Standards-basedtextbookin the fourthoreighthgradefor at least

2 years.The othergroupincluded studentsfrom Massachusettsschools carefullyselectedto matchthe firstgroupon twoimportantpredictorsof achievement-priorachievementand socioeconomic status. The resultsindicatedthatstudentsusingStandards-basedcurriculummaterialsas theirprimarytextbookperformedsignif-icantlybetteron the state-mandatedmathematicsassessmentthandid studentsin

schoolsusingtraditionaltextbooks.Thedifferenceswereconsistentacrossvarious

content strands, assessment problem types, and student subpopulations.

Additionally,in schools thathad used the materialsforlongerperiodsof time(i.e.,at least4 years), performancegainswere more dramatic.Theirresearchis consis-tent with other studies

showingthe benefits of Standards-based curricula to

studentsof varyingabilities,includingthose at thehigherandlowerachievinglevels

(Briars,2001; Griffin,Evans,Timms,& Trowell,2000).The Third InternationalMathematics and Science Study-Repeat(TIMSS-R)

study conductedin 1999 offers additionalevidence of the impactof Standards-based middle gradesmathematicscurriculummaterials.Two groupsof studentsfrom Michigan participatedin TIMSS-R. The first group, the Michigan state

sample, included studentsfrom a set of schools randomlyselected by TIMSSresearchers.The secondgroupincluded studentsfroman "invitational"groupof

schools thatmetthefollowingcriteria:useof Standards-basedinstructionalmate-rials, a well-articulateddistrictcurriculum,the use of assessment data to informinstructionaldecisions, professional developmentto supportteachers,and goodcommunicationwiththecommunity.Theinvitationalgroupconsistedof 21 schools

representingrural,suburban,andurbanenvironments.AlthoughtheMichiganstate

samplewas the highestperformingstategroupamongthe 12 statesparticipatingin TIMSS-R(averagescore of 517), the Michiganinvitationalgroup performedsignificantlyhigherthan the Michiganstatesample(averagescore of 532) indi-

cating the positive effect of Standards-basedreformefforts withinthese schools

(Mulliset al., 2001).Studies investigatingthe impactof elementaryor secondaryStandards-basedcurriculummaterialsreportsimilarfindings. For example, Fuson, Carroll,andDrueck(2000) foundthatstudentslearningfromEverydayMathematics(EM),an

elementaryStandards-basedcurriculum,scoredas well as orbetterthan students

studyingfromtraditionalmaterialson standardtopics including place value and

computation.Inaddition,theStandards-basedgrouphadopportunitiesto studyawiderrangeof curriculumtopics (e.g., geometry,fractions,algebra)typicallynot

given much attentionin traditionalmaterials,and evidence was found thatthis

opportunityled to increasedlearning.For example, the EM group significantlyoutperformedstudentsin theNationalAssessment of EducationalProgresssampleon geometryitems.

Huntley, Rasmussen, Villarubi, Sangtong, and Fey (2000) investigated the

impactof the Core-PlusMathematicsProject(CPMP)curriculummaterialson the

growthof studentunderstanding,skills,andproblemsolvinginalgebra.Theirfind-




ings underscorethe need to clearlyarticulatedesiredlearningoutcomesbecause

differenttypesof curriculummaterialstend to focus on differentpriorities.On the

one hand,researchersfound thatStandards-basedcurriculummaterialssupportedthedevelopmentof theabilityto solve algebraicproblemswithinappliedcontextswhen studentsusedgraphingcalculators.On the otherhand,studentsusingconven-

tionalalgebracurriculawere more successfulinmanipulatingsymbolicexpressionswhen those expressions were presentedfree of context and without the aid of

graphingcalculators.

Thestudyreportedhere examinedthemathematicsachievementof eighth-gradestudentsin the first three school districtsin Missouri to adopta Standards-based

middlegradestextbook series.Eighthgraderswere the focus of this investigationbecause

theywere the

only groupof middle

gradesstudentswho

participatedin

the state-mandatedMissouri Assessment Program(MAP) mathematicsexam.

Thus,a commonmeasureof mathematicsachievementwas availableforalleighth

gradersin Missouri.The researchwasorganizedtoexplorethefollowing question:How doesthe achievementof eighth-gradestudentswho have used Standards-based

mathematicscurriculummaterialsfor at least2 years(in Grades6 and7) comparewith that of studentsusing other curriculummaterialsas measuredby the state-

mandatedmathematicsMAP test?

METHODOLOGY

The studywas designedto comparethe mathematicsachievementof students

who had studiedmathematicsusing Standards-basedcurriculummaterialsfor at

least 2 years(Grades6 and7) withthe achievementof studentswho had not used

Standards-basedcurriculummaterials.Mathematicsachievementat the district

level priorto implementationof Standards-basedcurriculummaterials and the

percentof studentseligible for free/reducedlunch were the primaryfactors used

to matchdistricts.The measureof mathematicsachievementused was the state-

mandatedMAP mathematicsexam.

ParticipatingSchoolDistricts

The threedistrictsusingStandards-basedcurriculummaterialsadoptedthese text-

books and began using them in Grade 6 and 7 in fall 1996. Two districts(onesuburbanand one small city) implementedMATHThematics(MT)(Billstein &

Williamson,1998)andone district(suburban)implementedthe ConnectedMathe-

maticsproject(CMP)(Lappan,Fey, Fitzgerald,Friel,& Phillips,1997).In the 1st

yearof implementation,theMTdistrictsusedprepublicationmaterials,thenpurchasedthepublishedversionswhentheybecameavailablethefollowingschoolyear.

For thepurposesof this study,three districtswere selected to serve as compar-ison districts. Because prior student achievementand socioeconomic level are

recognized as strong predictorsof student achievement in mathematics(e.g.,Riodan & Noyce, 2001), these two variableswere taken into accountin selecting




thecomparisondistricts.Inaddition,because eachof the Standards-basedschool

districtsused a Grade6-8 buildingconfiguration,this conditionwas included as

a criterionfor identifyingcomparisondistricts.We did so primarilyto insurethe

integrityof the sixth-gradecohort.In districtswhere sixthgradersarepartof an

elementarybuildingconfiguration(i.e., K-6 orK-8) morevariationtendsto occurin curriculummaterialsused formathematics,given multiple"feeder"elementaryschoolbuildings.Finally,we restrictedthecomparisondistrictsto thesamegeneral

geographicregion,in partas anothermeansof drawingfromcommonpopulationclusters. Therefore,the comparisondistricts were selected on the basis of the

following variables:Grade6-8 middleschoolorganizationalstructure;geograph-ical location (i.e., close proximityto theirStandards-basedcomparisondistrict);

percentof students

eligiblefor free/reducedlunch;and a

historyof

comparablemathematicsachievementin Grade8.

The MAP mathematicsassessmentwas used as thebaselinemeasureof studentachievement for identifying comparison districts. We examined eighth-gradeachievementdatainspring1997,thelastyearbeforestudentsused Standards-based

curriculummaterials.Althoughthe Standards-basedschool districtsbeganusingthe curriculumin 1996, none of the eighthgradersin spring1997 hadused thesenew materials.

The Missouridistrictprofiledatabasewas used to locatedistrictscomparableon

the identified variablesto the Standards-baseddistricts.In all cases, only one ortwo districtsmatchedcloselyeach of theStandards-baseddistricts.Whenmorethanone close matchexisted,we chosethedistrictthatwas biasedin favorof thecompar-ison district (lower free/reduced lunch percentageand/orhigher district MAP

scores)to ensurethatno advantagewould be givento the Standards-baseddistrict.The comparisondistrictsused a varietyof mathematicstextbooksin Grades6

through8, but throughspring 1999 none used a Standards-basedmiddlegradesmathematics textbook series. Appendix A provides a summaryof the demo-

graphics of each district, including the mathematicscourse organizationand

curriculummaterialsused in Grades6, 7, and8.Comparison1. One of the MT (MATHThematics)districts(denotedas SB1)

includestwo middleschoolsenrollinga total of approximately2,000 studentswithabout30%of thesestudentseligible forfree/reducedlunch. The districtis locatedin a city with a populationof about36,000. All sixth and seventhgraderswereenrolledina courseusingMT.In thisdistrict,75%of eighth-gradestudentsaretypi-cally enrolled in a prealgebracourse. The remainingstudentsareenrolled in an

algebraI course. Thecomparisondistrict(denotedas Cl) enrolledapproximately800 studentsin one middleschool with 24%eligible for free/reducedlunch. The

district is located in a city with a populationof about 20,000. In sixth grade,studentswereenrolledin one of two courses withapproximately20%inthe accel-eratedcourse.Inbothseventh andeighthgrade,studentsaretypicallyenrolledin

one of three courses designed for varying ability levels. These courses useddifferenttexts.




Comparison2. The seconddistrictusingMT(SB2) includedtwo middle schools

enrolling approximately1,000 studentswith about 25%eligible for free/reduced

lunch. The districtis locatedin a suburbof a metropolitanareawith a populationof about2 millionpeople. All sixthandseventhgraderswere enrolledin a course

usingMT.Ineighth grade,50%of the studentswere ina courseusingMT,whereas

theothers were enrolledin analgebraI course. Thecomparisondistrict(C2) is an

adjacentsuburbandistrict.The studentpopulationfor C2 was approximately1,000with about20%of the studentseligiblefor free/reducedlunch.At eachgradelevel,two mathematicscourses were offered. About 20% of the studentsin each class

wereplacedin an acceleratedcoursesequence.Theremaining80%were enrolled

in a regularmathematicscourse.

Comparison 3. The district using CMP (Connected Mathematics Project)(denotedSB3) enrolledapproximately600 middlegradesstudentsin onebuildingwith about13%eligible for free/reducedlunch. The districtis locatedin a suburb

of the same metropolitanarea as SB2 and C2. In sixth grade,all studentsin the

districtwere enrolledina courseusingCMP.In seventhandeighthgrades,approx-

imately75%of the studentscontinuedusingCMP as theirprimarytext. The other

25% of the studentswere enrolledin an acceleratedprogramand used CMP as a

supplementto analgebraI text. Locatedina suburbancommunityinthe samelargemidwesterncity, thecomparisondistrict(C3) had a middle school studentenroll-

mentin one buildingof approximately800 studentswith about 11%eligible forfree/reducedlunch.InGrades6 and7, everystudentwas enrolledinthe samemath-

ematicscourse.In Grade8, studentswereplacedineitheraprealgebracourse(40%)or analgebraI course(60%).

As notedin AppendixA, none of the school districtsused a single curriculum

seriesfor all studentsthroughoutthe middlegrades.Thus,themiddle school math-

ematicscurriculummaterialsusedby these districtscan be characterizedasahybridcurriculum.However,inthe Standards-baseddistricts,all sixth andseventhgradersin two districtsand 75%in thethirdand at least 50%of theeighth gradersin two

districtsused NSF Standards-basedcurriculummaterials.Consequently,Standards-based curricularepresenta significant learningtool for middle grades students

within the three Standards-basedschool districts.

StudentSample

The studentsampleforthisstudyconsistedof eighth-gradestudentsfromthe six

schooldistrictscompletingtheMissouriAssessmentof Performance(MAP)math-

ematics exam in 1997 and 1999. In the two suburbandistrictsthat used NSF

Standards-basedcurricula(SB2, SB3), the researcherswereable to examineindi-vidual student records.From these records, the researchersidentified students

who hadcompletedat least 2 yearsof the NSF Standards-basedcurriculum.Data

from students who had recently moved into the districtand had, therefore,not

studiedfrom Standards-basedcurriculawere deletedfrom thesample.Inthesmall

city district(SB1) and the threecomparisondistricts(C1, C2, C3), datafromindi-




vidual studentrecordswere not available.Instead,dataon the entireeighth-gradeclass for each of these four districtswere used in the analysis.

TeacherProfessionalDevelopmentand Program Implementation

A growing research base is documenting the challenges of implementingStandards-basedmathematicscurricula(Ball, 1996; Clark, 1995; Clarke, 1993;

Henningsen& Stein, 1997;Lambdin& Preston, 1995;Tetley, 1998). The chal-

lenges include teaching unfamiliarcontent, higher cognitive expectations for

students,differentroles for teachersandstudents,andnew assessmenttools. These

factorsindividuallyandcollectively influence the mannerin which mathematics

curricula are implemented(Bay, Reys, & Reys, 1999). New content and new

instructionalandassessmenttechniquesrequireincreasedprofessionaldevelopmentfor teachersimplementingStandards-basedmathematicscurricula.

Teachersusing a Standards-basedcurriculumin this studyhadparticipatedin

professionaldevelopmentdesignedto help themunderstandthe rationalefor the

changes in curriculummaterialsandprepareto use the materials.These teachers

were among nearly200 teachersfrom23 school districtswho participatedin the

Missouri Middle Mathematics(M3) Project,a 3-yearNSF teacher-enhancement

project(1995-1998) thatused the examinationof Standards-basedmiddlegradesmathematicscurriculaas a vehicle for

professionaldevelopment (Reys&

Reys,1997). Althoughdistrictsinvolved in the M3Projectwere not obliged to adopta

Standards-basedcurriculum,the three Standards-baseddistricts in this studychose to adoptandimplementeitherCMPorMT.

None of the teachersin the comparisonschools participatedin theM3Project.However, teachersin these districts were involved in professionaldevelopmentactivities sponsoredby theirdistrict andby the statedepartment.These profes-sional development activities were guided by the state Show-Me Standards,whichwereinfluencedby, andalignedwith,the NCTM'sStandards.Forexample,

the Missouri Departmentof Elementaryand Secondary Education sponsoredworkshopsthroughoutthe statefocusingon themandatedstateassessment(MAP).Because mathematics was the first discipline addressedin the state-mandated

assessment, the MAP mathematicstest, including its content and expectations

regardingstudentresponseformats,was the focus of these workshops.In addi-

tion, summer institutes for middle school mathematicsteachers were offered

eachyear througha state-sponsoredgrant.Theseworkshopsfocused onimprovingopportunitiesfor middle gradesstudents to develop as problemsolvers. Middle

school teachersfromeach of thecomparisondistrictsparticipatedin thesesummer

workshops, although the extent of the influence of these workshops on theirteachingis unknown.

No visits weremade to comparisonschools to determinetheextentand manner

inwhich theirdistrict-adoptedmathematicscurriculumwas used.However,conver-sations with school districtpersonnel(curriculumcoordinatorand/ormathematics

departmentchair) confirm that the middle school teachers in the comparison




districtsused thedistrict-adoptedtextbookas theirprimaryinstructionalguidewith

regardto the contentemphasizedand instructionalapproachused. Observations

were made in some, althoughnot all, of the middle grades classrooms in the

Standards-basedschoolsintwo differentstudies(Bay, 1999;Wasman,2000).Theseobservationssupportthatteacherswereusingthedistrict-adoptedStandards-based

curriculaas theirprimarytext.

MissouriAssessmentof Performance(MAP)MathematicsExam

Missouristudentsin Grades4, 8, and 10 arerequiredto take the mathematics

portionof the MissouriAssessment of Performance(MAP)exam at the end of the

schoolyear.The MAP was developed by theMissouriDepartmentof Elementary

andSecondaryEducationandCTB/McGraw-HillPublishingCompanyto reflectMissouri's Frameworkfor CurriculumDevelopment in Mathematics, K-12

(MissouriDepartmentof ElementaryandSecondaryEducation,1996).The frame-

work is designed aroundsix content strands:numbersense (including computa-tion);geometricandspatialsense;dataanalysis,probability,andstatistics;algebra;mathematicalsystems;and discretemathematics.

The eighth-gradeMAP exam in mathematicsincludes three sections, each

administeredandcompletedon separatedays.Each of the first two sections of the

exam include 8-10 open-ended items requiringstudent-constructedresponses,

and calculatorsareallowed. The thirdsectionconsists of 31 multiple-choiceitemsdrawnfrom the Terra Nova assessments preparedby CTB McGraw-Hill.The

recommendedtime frame for each of the three sections is 55 minutes.However,MAP is not intended to be a timed test, and teachers are encouragedto allow

studentsadequatetime (up to 90 minutes)to complete each of the constructed-

responsesections of the test.AppendixB containsadescriptionof the contentand

sampleitems from each section of theMAP mathematicsexam. Table 1 includes

Table1TypeandNumberof Itemsfor Each ContentStrandon the 1999Eighth-GradeMAPMathematicsExam

Itemtype Total Percent

Constructed Multiple points of total

response choice points

NumberSense 6 11 25 33GeometricandSpatialSense 2 8 12 16DataAnalysis,Probability,and

Statistics 5 6 16 21Algebra 3 2 10 13MathematicalSystems 2 4 8 11DiscreteMathematics 2 0 4 6

Total 20 31 75 100

Note. Constructedresponseitems are worth either2 or4 points,andmultiple-choiceitems are worth1 point.




informationabouttheeighth-gradeMAPmathematicsexamby contentstrandand

itemtype.Additionalreleasedandsampleitems,aswell asscoringguides,areavail-

ableatthe MissouriDepartmentof ElementaryandSecondaryEducationWeb site

at www.dese.state.mo.us/divimprove/assess.

Reports of MAP performanceinclude (a) achievement level, (b) a national

percentilescore fortheTerraNova portionof theexam,and(c) percentcorrectbycontent strand.Responseson all threesections of theexam are used to categorizeeach student'sperformanceinto one of five achievementlevels. Fromthe lowest

possiblecategoryto thehighest,theseachievementlevels areStep 1,Progressing,

NearingProficiency,Proficient,andAdvanced.A descriptionof each of theselevels

is providedin Table 2. The MissouriDepartmentof Elementaryand SecondaryEducation uses the

percentagesof students

scoringin the

toptwo

categories(ProficientandAdvanced)and the bottomtwo categories(Step1andProgressing)as importantindicatorsof success in themandatorystate school accreditationand

improvementprocess.

Table2Descriptorsof theLevelsofAchievementon the Eighth-GradeMAPExam

Level DescriptorStep1 Studentsperformbasicoperationswithwholenumbers;solvesimpleword

problemswith whole numbers;identify,describe,compare,andclassifygeometricfigures;readinformationfromtables,graphs,andcharts;recog-nize and extendsimplenumericpatterns;and orderintegers.

Progressing Studentsperformbasic operationsof rationalnumbers;solve simplewordproblems using rationalnumbers;use protractorand ruler to measure;identifylines of symmetry;interpretinformationfromtables,graphs,andcharts;find measuresof centraltendency;extendpictorialpatterns;solveequationsusing a replacementset; orderrationalnumbers;and interpretsimple Venndiagrams.

Nearing Students solve problems with decimals, percents; identify congruent,Proficiency similar figures; find elapsed time; convert measurements; find area,

perimeter,volume;findprobability;use samplingprocedure;findmeasureof centraltendency;solve equations;use order of operations;find, orderequivalentfractions,decimals,createtreediagrams;generalizepatterns;usedeductive,inductivereasoning.

Proficient Studentsshowprocesses;applyratios,proportions,percents;useconceptsof congruent, similar shapes; show rotations,reflections, translations;apply perimeter,area,volume;predictfromdatadisplays;applymeasuresof centraltendency;describepatterns,relationshipsusing algebraicequa-tions;applypropertiesof realnumbers;identify primes,multiples,factors,

exponents.Advanced Studentsjustifyanswers;use scaledrawings;applytransformationincoor-

dinategrid;comparetheoreticalandexperimentalprobability;defenddatapredictions;recognizedependent,independentvariables;describepatterns,relationshipsusingalgebraicinequalities;usediagrams,patterns,functionsin problem solving; apply primes, factors, multiples, exponents; solveproblemsusing strategies.




Data Analyses

For this study,MAP scores were analyzedin the following ways. Comparable

priormathematicsachievementbetween each of the threepairsof districts wasestablishedusing eighth-gradeMAPdataarchivedin 1997,the 1styearof requireduse of theMAP math exam in thatgrade.Studentstakingthe 1997 Grade8 MAP

mathematics exam were the last set of eighth gradersin the Standards-based

districtswho hadnot used the new curriculummaterials.A chi-squarestatisticwas

calculated for each Standards-based/comparisondistrictpairto test for possibledifferencesin thepercentagesof studentsscoringin threeMAPachievementlevel

categories.Inaddition,t tests were usedto comparethe six content standardsand

TerraNova scores between the threeStandards-baseddistrictsand theircompar-

ison districts.The t tests between Standards-basedandcomparisondistrictswereusedonthe basisof the meanstandardizedscore foreighth gradersin eachdistrict.

Eachstandardizedscorerepresentsthemeanpercentcorrectachievedby students

in each districtfor each subtestof the MAP.MAP scores in spring1999provideda basis to compare the mathematics achievementof students who had used a

Standards-basedcurriculumfor at least2 yearswith thatof eighth graderswho had

not used such a curriculum.Using 1999 data, three chi-squarestatistics were

computedto test for differencesin studentMAP achievementlevels. Again using1999 data,t tests were used to comparethe six content standardsand TerraNova

scoresbetween the threeStandards-baseddistrictsandtheircomparisondistricts.The t tests used the standardizedscores reportedby the MAP for individual

studentson the six content standardsand TerraNova.

RESULTS

Table 3 containsthe chi-squareanalysesthatcomparethe numberof students

scoringin the threeMAP achievementlevels priorto theuse of Standards-based

curriculummaterials(in 1997). A separatechi-squarewas calculatedfor each of

the threecomparisons(i.e., SB1 andC1, SB2 andC2, and SB3 andC3). No statis-

Table3NumberandPercentageof EighthGradersScoringin EachAchievementLevel(byDistrict)on the 1997 MAP MathematicsExam

Comparison Step1and Nearing Proficientand Chi-squaredistricts Progressing Proficiency Advanced

SB1 307 (48%) 211 (33%) 121 (19%)Cl 124 (50%) 76 (31%) 47 (19%) 4.21 ns

SB2 189(49%) 123(32%) 73 (19%)C2 219(55%) 111(28%) 68(17%) 2.97ns

SB3 51(34%) 53(36%) 42 (29%)C3 92 (35%) 73 (28%) 97 (37%) .46 ns

Note. SB1, SB2, and SB3 are the districtsthatimplementedStandards-basedcurricula.C1, C2, andC3 are the districtsbeing used as the comparisonsfor the Standards-baseddistricts.ns representsa

nonsignificantchi-squarevalue (p > .05).




than its comparisondistrict.Further,SB2 scoredsignificantlyhigheron Content

Standard6 (discrete mathematics)(p < .005). However, the comparisondistrict

outscoredSB3 on Content Standard1 (numbersense) (p < .05). No other differ-

ences werenoted between Standards-basedandtheircomparisondistricts.These

data,inconjunctionwith theMAPachievementleveldatareportedinTable3, arguefor comparablemathematics achievement between Standards-basedand their

comparisondistrictsat the time thatnew curriculummaterialswere introducedin

the Standards-basedschool districts.

Table5 presentschi-squareanalysesthatcomparethe numberof studentsscoringinthe threeMAPachievementlevels in spring1999when theeighth-gradestudents

in threedistrictshad beenusingStandards-basedcurriculummaterialsfor at least

2years.Separatechi-squares

were calculatedfor eachof the threecomparisons(i.e.,the Standards-baseddistrict and theircomparisondistrict).No differenceswere

found between the SB2 and C2 districts,as well as the SB3 and C3 districts.

However, a statistically significantdifference(p < .02) was found between SB1andC1.Resultsindicatedthatagreaternumberof studentsin theStandards-based

(SB 1)districtscoredin thehighestachievementlevels of theMAP(i.e., Proficient

andAdvanced),whereas a greaternumberof studentsin the comparisondistrict

Cl scoredinthe lowest two MAPachievementlevels (i.e., Step1andProgressing).It is importantto note that between 1997 and 1999 the statedepartmentchanged

the cut scoresfor assigningstudentsto one of the five MAP achievementlevels.Unfortunately,this change makes a directcomparisonof school- districtmathe-

matics-achievement-levelscores in 1997 and 1999 impossible.

Table5NumberandPercentageof EighthGradersScoringin Each AchievementLevelbyDistricton the 1999 MAP MathematicsExam

Comparison Step1and Nearing Proficient Chi-squaredistricts Progressing Proficiency andAdvanced

SB1 335 (49%) 240(35%) 112(16%)C1 153 (58%) 83 (32%) 27 (10%) 8.65*

SB2 189(46%) 148(36%) 74 (18%)C2 219(51%) 140(32%) 72(17%) 1.98ns

SB3 59 (35%) 61(36%) 51(30%)C3 96(32%) 100(34%) 102(34%) .96ns

Note. SB1, SB2, and SB3 are the districtsimplementingStandards-basedcurricula.Cl, C2, andC3are the districtsbeing used as the controlcomparisonsfor the Standards-baseddistricts.

*p<.02

Table 6 reportst-testresults for the six ContentStandardsand TerraNova for

SB1 and its comparisondistrictCl and shows that studentsusing Standards-

based curriculum(SB 1)hadstatisticallysignificanthigherscores thanstudentsin

C1 in thefollowing contentareas:numbersense;geometricandspatialsense;data

analysis, probability, and statistics; algebra; and discrete mathematics.Also,




Table6T-TestComparisonsof 1999 MAPContentStandardand TerraNova Scoresfor SB1 andCl Districts

SB1 (n = 708) Cl (n = 274)M SD M SD

NumberSense 64.55*** 23.03 57.27 22.99GeometricandSpatialSense 49.17** 24.16 43.22 24.30DataAnalysis,Probability,andStatistics 59.27** 22.95 53.79 23.80Algebra 69.98*** 28.54 59.06 29.76MathematicalSystems 61.52 27.45 63.54 28.44DiscreteMathematics 45.44* 28.13 40.71 27.98TerraNova 63.21*** 27.66 56.26 27.84

*p<.05. **p<.01. ***p<.005.

Standards-basedstudentshadsignificantlyhigherTerraNova scoresthannonusersin the comparisongroup.

Table 7 presentsMAP ContentStandardandTerraNova scores for SB2 andC2 schooldistricts.Resultswere similarto thosereportedinTable6. Forexample,studentsusingaStandards-basedcurriculum(SB2) outperformednonuserson thesame five contentstandards.To be more specific, SB2 studentshad statistically

highertest scoresthanC2 studentsonNumberSense;GeometricandSpatialSense;Data Analysis, Probability,and Statistics;Algebra;and Discrete Mathematics.

Similarly,SB2 studentshadsignificantlyhigherTerraNova scores than theirC2

counterparts.

Table7T-TestComparisonsof 1999 MAPContentStandardand TerraNova Scoresfor SB2 andC2 Districts

SB2 (n = 411) C2 (n = 440)

M SD M SD

NumberSense 66.07** 21.13 62.40 25.21GeometricandSpatialSense 53.18* 23.38 47.91 25.55DataAnalysis,Probability,andStatistics 63.63** 20.43 56.35 23.96Algebra 73.53** 23.62 66.46 30.19MathematicalSystems 70.52 24.68 69.34 28.07DiscreteMathematics 55.33** 25.43 47.88 29.65TerraNova 67.55** 26.46 60.30 29.84

*p<.05. **p< .01.

Table 8 shows thatstudentsusing the NSF Standards-basedcurriculum(SB3)had significantly higher scores than nonusers (C3) on two of the six ContentStandardscales: dataanalysis,probability,andstatistics;andalgebra.The MAP




scoresforboth of thesedistrictswerehigherthanfor theotherdistrictsinthestudy.Their exceptionally strong performanceis consistent with the strongacademic

orientationthathas traditionallycharacterizedeach district.

Table8T-TestComparisonsof 1999MAPContentStandardandTerraNovaScoresfor SB3andC3Districts

SB3(n= 171) C2(n= 298)M SD M SD

NumberSense 69.54 21.22 70.52 23.65

GeometricandSpatialSense 60.94 25.51 57.27 25.91DataAnalysis,Probability,andStatistics 69.94* 21.52 64.44 24.92Algebra 79.80* 23.29 74.25 26.67MathematicalSystems 70.00 26.12 70.29 27.73DiscreteMathematics 58.65 24.79 56.04 28.58TerraNova 74.96 27.57 72.16 26.93

*p< .05

Summary

This researchprovides empiricalevidence that studentsusing the Connected

MathematicsProjectorMATHThematicscurriculummaterialsfor at least2 yearsin the middle grades equaled or exceeded the achievement of students from

matchedcomparisondistrictson the mandatedstatemathematicsachievementtest.

Significant differences on the MAP were identified between students usingStandards-basedcurriculummaterials and studentsfrom comparisondistricts

using other curriculummaterials.All the significantdifferences reflectedhigher

performancefor studentsusing NSF Standards-basedmaterials.A significantlygreaterproportionof studentsin the SB1 Standards-baseddistrict scoredin the

highest two MAP achievement-levelcategories,whereas a greaterproportionof

studentsinthecomparisondistrictscoredin the bottomtwo achievement-levelcate-

gories.Studentsin each of the threedistrictsusingStandards-basedmaterialsscored

higherintwo ContentStandardareas(dataanalysis,probability,andstatistics;and

algebra),and these differenceswere statisticallysignificant.Furthermore,in two

districts(SB1 andSB2) studentsscoredsignificantlybetterthantheircomparisondistrictcounterparts(Cl andC2) on threeothercontentstrands(number;geometric

andspatialsense;anddiscretemathematics)aswell ason thenationallynormrefer-enced TerraNova assessment.Althoughcritics have chastisedNSF Standards-

basedcurriculafor ignoringbasic skills, this researchdoes not supportthatclaim.




DISCUSSION

For thepurposesof this study,it would have been idealto haveall studentsuse

the same textbook series throughoutthe middle grades.However, this model israrelyfoundin the real world and did not exist in the school districtsinvolved in

this study.Schools often adoptdifferentcurriculummaterialsat differentgrades

(andsometimes withingrades,as occurredin theeighth gradeof every school in

thisstudy).Each districtin thisstudyfollowed a similarpatternof trackingstudents

at either seventh or eighth grade and used different curriculummaterials for

differentcourses at thesamegrade.Althoughthis schoolphenomenonis common,it is not clearhow usingsuch a hybridcurriculumeitherstrengthensor weakens a

school program.Textbook authorsmake decisions aboutspiralingmathematics

concepts across grades.Therefore,the use of a combinationof textbooks fromdifferent series may, in fact, interruptor have otherconsequencesfor curriculum

coherence and studentlearning.

Eighthgradersin all six districtswere enrolledincoursesdenotedasprealgebraor algebraand most usedanalgebratextbook.This factreflects a nationaltrendto

enrollmost, if notall, eighth gradersin analgebracourse andis fueled, in part,bya call to make the middle school mathematicscurriculummorerigorousandless

repetitive.AlthoughStandards-basedinstructionalmaterialswere developed to

respondto this

concern,one

frequentcomplaintaboutthese middleschoolcurricula

is thattheydo notgive enoughattentionto algebra(Wu,2001). It is worthnotingthatsignificantdifferencesoccurredacrossall threegroupson thealgebraportionof the MAP. Ineverycase, studentsfrom districtsusinga Standards-basedmath-ematics curriculumscoredsignificantly higher(at leastp < .05) on the clusterof

algebraitemsthantheircomparisongroup.This evidence contradictstheargumentthat studentsusing theStandards-basedmiddle school mathematicscurriculaarenot learningalgebra.

No significantdifferenceswere foundon all the MAP scores. However,when

significantdifferences were found, they were always in favor of schools usingStandards-basedmathematicscurricula.Thisquestionis raised:Whataccountsfor

thepatternof significantdifferences on the MAP mathematicsassessment?

As indicatedearlier,the directimpactof textbooks on studentachievement is

difficult to establish. Clearly, other variables, including quality of teaching,contributesto mathematicslearning.We haveno directinformationon thequalityof teachinginanyof thesedistrictsandhave madenoeffortto linkqualityof instruc-

tion to studentperformance.Our assumptionis that considerablevariabilityin

teachingexisted across all schools.

The contentand formatof assessmentinstrumentscan also influenceestimatesof student achievement. The MAP mathematicsexam was not developed to be

advantageousto studentsusingany particularset of curriculummaterials.Instead,

the assessment reflects the Framework for Curriculum Development in

Mathematics,K-12 (MissouriDepartmentof ElementaryandSecondaryEducation,

1996),which articulatesthe mathematicsall Missouristudentsareexpectedto learn




by theend of Grade8. TheMAPfocuses on skills, concepts,andproblemsolvingand includes open-endedand multiple-choiceresponse formats.Thus, the onlyknown factor thatwas differentacross the matchedpairsof school districts was

the mathematicscurriculummaterialsused to guide teachingandlearning.Onemightaskwhy thepatternsof differencesin the thirdcomparison(SB3 and

C3) were not similar to the othertwo comparisons.Recall thatsignificantdiffer-

ences were found(atleastp < .05) on 5 of 6 subtestsand the TerraNova withtwo

pairsof districts(SB1andC1, SB2 andC2), butsignificantdifferenceswere seen

on only two of the subtestsin SB3 andC3. We have at least two explanations,the

first of which centerson curriculum.SB3 used CMPfor all sixthgradersand CMP

for aboutthree-fourthsof the seventhandeighth graders,with theremainingone-

fourthof the studentsusing

two differentmathematicstextbooks.Anotherexpla-nationrelatesto the natureof thedistrictsthemselves.SB3 and C3 arebothwealthy

districts,havingthe two highestaverage-per-pupilexpendituresin the state. The

districtspridethemselvesin beingoutstandingdistrictsand have a long historyof

sendinga high percentof theirstudentsto postsecondaryeducation(over 90%).An examinationof Tables 3 and 5 documentsthatthese two districtshave a much

higherpercentageof eighth-gradestudentsin theproficientandexemplarylevels

thanthe otherdistricts.They also have the highest scores on the TerraNova and

contentsubscores.Indeed,theywereamongthehighestinthe entirestate.TheMAP

likely provideda low ceiling for studentsin bothdistricts,therebycurtailingvari-abilityandlikely accountingfor the lack of significantdifferences.

This examinationof mathematicsachievement of eighth-gradestudents who

studiedfromNSF Standards-basedmiddle schoolmathematicsmaterialsprovidesinformationto those contemplatingcurriculumreform. More specifically, this

research,basedon datafrom six differentschooldistrictsandinvolvingmorethan

2,000 students,documents that middle school studentsusing Standards-based

mathematicscurriculafor at least2 yearsequaledor exceededtheachievementof

studentsfrommatchedcomparisongroupson the statemandatedeighth-grademath-

ematics test. Justas an artist'spicturetakes shapewith each strokeof the brush,the critical development of a strong research base to investigate the effect of

Standards-basedcurriculummaterialson studentlearningwill not be established

by any single study. The complexity of curriculumimplementationdemands

multipleinvestigationsto uncoverkey issues for considerationbyteachers,district

administrators,andpolicymakers.Thisanalysisrequiresthe contributionsof manydifferentresearchinvestigationsprovidinga varietyof perspectivesof the impactof Standards-basedinstructionalmaterials.We offer this studyas anotherstroke

for thepicturethateventuallywill emerge.

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Authors

RobertReys,303TownsendHall,UniversityofMissouri,Columbia,MO65211;

[email protected],303TownsendHall,Universityof Missouri,Columbia,MO65211;[email protected]

RichardLapan,303 TownsendHall,UniversityofMissouri,Columbia,MO65211;[email protected]

GregoryHolliday,222 LewisHall,UniversityofMissouri,Columbia,MO65211;[email protected]

DeannaWasman,1104NorthProvidenceRoad,Columbia,MO65201;[email protected]

APPENDIX A

NSF Curriculumand ComparisonDistrictProfiles

District No. of No. of School Courses Percent Textmiddle middle percent by grade ofschool school free/ studentsbuild- stu- reduced in gradeings dents lunch in

courseSB1 2 2000 30 Gr.6 Math 100 MATHThematicsBk. 1

Gr.7 Math 100 MATHThematicsBk.2

Gr.8 Math 75 GatewaystoAlgebraand Geometry

Gr.6 Alg 25 AlgebraI: ExplorationsandApplications

C1 1 800 24 Gr.6 Math 80 Mathematics:Applica-tionsandConnections1

Gr.6 Math 20 Mathematics:StructureandMethod1

Gr.7 Math1 65 Mathematics:Applica-tionsandConnections2

Gr.7 Math2 15 Mathematics:StructureandMethod1

Gr.7 Math 3 20 Mathematics:StructureandMethod2

Gr.8 Math1 65 Mathematics:Applica-

tionsandConnections3Gr.8 Math2 15 Mathematics:Structure

andMethod2

Gr.8 Math3 20 Algebra:StructureandMethod



R.Reys,B. Reys,R. Lapan,G. Holliday,andD. Wasman 93

District No. of No. of School Courses Percent Textmiddle middle percent by grade ofschool school free/ studentsbuild- stu- reduced in gradeings dents lunch in

course

SB2 2 1000 25 Gr. 6 Math 100 MATHThematicsBk.1

Gr. 7 Math 100 MATHThematicsBk.2

Gr.8 Math 50 MATHThematicsBk. 3

Gr.6 Alg 50 AlgebraI: Expressions,EquationsandAppli-

cationsC2 1000 20 Gr.6 Math1 80 Mathematics:Applica-tionsand Connections1

Gr.6 Math2 20 PassporttoMathe-matics2

Gr.7 Math1 80 Mathematics:Applica-tionsandConnections2

Gr.7 Math2 20 WindowstoAlgebraand Geometry

Gr.8 Math1 80 WindowstoAlgebraand Geometry

Gr.8 Math2 20 Algebra:StructureandMethod

SB3 1 600 13 Gr. 6 Math 100 ConnectedMathematics

ProjectGr.7 Math1 75 ConnectedMathematics

ProjectGr.7 Prealg 25 Gateways+ Connected

MathematicsProject

Gr. 8 Math 70 ConnectedMathematicsProject

Gr. 8 Alg 1 30 Algebra:Explore,Com-munication,Apply+ConnectedMathematics

ProjectC3 1 800 11 Gr. 6 Math 100 Mathematics:The Path

to Success

Gr. 7 Math 100 Middle SchoolMathematics

Gr. 8 Prealg 40 UCSMPTransitionsMathematics

Gr. 8 Alg 60 AlgebraI: Expressions,EquationsandApplications

Note: Completecitationsfor all textbooksappearin thereferencelist.



R. Reys,B. Reys,R. Lapan,G. Holliday,and D. Wasman 95

Contentstrand Description Sampleitem (Grade8)

Mathe- Mathematicalsystems Your local high school marchingbandmatical (includingrealnumbers, is marchingin today's statefairparade.Systems whole numbers,integers, Theband,composedof 126 students,

fractions),geometryand usuallymarchesin 21 rows of 6 studentsnumbertheory (primes, each. Due to illness, several bandfactors,andmultiples). membersareunableto marchin today's

parade.As drummajor,you mustassistthe band directorin rearrangingthestudentsinto rows of equalnumbersofstudents.Whenyou tried4 studentsineach row, the last row was 1 student

short.The results were the same whenrows of 5 and 6 studentswerearranged.Whenyou arrangedthe band into rowsof 7 students,all rows werecomplete.Use the informationto determinehow

manystudentsshowedupto marchinthe parade.Show yourworkand ex-

plaintheprocessthatyou used.

Discrete Discretemathematicsis A groupof campersis askedto plantheMathe- the studyof points, ideas, dinnermenus for 15 for anupcoming

matics andobjectthatareseparate campingtrip.They found that-fromeach otheror distinct. *6 people likedonly freeze-driedchili,Graphtheory,counting *4 people likedonly backpackertechniques,matrices,and spaghetti,the mathematicsof deci- *5 people liked both the chili and thesion makingareincluded spaghetti.as partof discrete How many peopledid NOT like eithermathematics. the freeze-driedchili or thebackpacker

spaghetti?Draw a Venn diagramto

help you solve theproblem.

the impact of standards based middle grades curriculum on student achievement

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