Brian Bottge, Principal Investigator University of Kentucky

Transcription

1 EnhancedAnchoredInstructionUnits (FractionsatWork,FractionoftheCost,Hovercraft,Kim skomet,grandpentathlon) Mappedto CommonCoreStateStandards Mathematics:Grade7 Evaluating the Efficacy of Enhanced Anchored Instruction for Middle School Students with Learning Disabilities in Math U.S. Department of Education, Institute of Education Sciences Cognition and Student Learning in Special Education Goal 3 - Research 4 years, 7/01/2009 6/30/2013 Developing Enhanced Assessment Tools for Capturing Students Procedural Skills and Conceptual understanding in Math U.S. Department of Education, Institute of Education Sciences Cognition and Student Learning in Special Education Goal 5 - Measurement 4 years, 7/01/2015 6/30/2019 Brian Bottge, Principal Investigator University of Kentucky bbott2@uky.edu 1

2 TableofContents MathematicsGrade7Introduction 3:4 EAIUnitSummaries 5:7 EAIUnitsmappedtoCommonCoreStateStandardsforMathematics 8:11 EAIUnitsmappedtoStandardsforMathematicalPractice 12:13 ApplicationtoStudentswithDisabilities 14:15 2

3 Mathematics» Grade 7» Introduction In Grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples. 1. Students extend their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems. Students use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes, tips, and percent increase or decrease. Students solve problems about scale drawings by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish proportional relationships from other relationships. 2. Students develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percents as different representations of rational numbers. Students extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, and multiplication and division. By applying these properties, and by viewing negative numbers in terms of everyday contexts (e.g., amounts owed or temperatures below zero), students explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers. They use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems. 3. Students continue their work with area from Grade 6, solving problems involving the area and circumference of a circle and surface area of threedimensional objects. In preparation for work on congruence and similarity in Grade 8 they reason about relationships among two-dimensional figures using scale drawings and informal geometric constructions, and they gain familiarity with the relationships between angles formed by intersecting lines. Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections. They solve real-world and mathematical problems involving area, surface area, and volume of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms. 4. Students build on their previous work with single data distributions to compare two data distributions and address questions about differences between populations. They begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences. Grade 7 Overview Ratios'and'Proportional'Relationships' o Analyzeproportionalrelationshipsandusethemtosolvereal:worldandmathematicalproblems. The'Number'System' o Applyandextendpreviousunderstandingsofoperationswithfractionstoadd,subtract,multiply,anddividerationalnumbers. Expressions'and'Equations' o Usepropertiesofoperationstogenerateequivalentexpressions. o Solvereal:lifeandmathematicalproblemsusingnumericalandalgebraicexpressionsandequations. Geometry' o Draw,constructanddescribegeometricalfiguresanddescribetherelationshipsbetweenthem. o Solvereal:lifeandmathematicalproblemsinvolvinganglemeasure,area,surfacearea,andvolume. 3

4 Statistics'and'Probability' o Userandomsamplingtodrawinferencesaboutapopulation. o Drawinformalcomparativeinferencesabouttwopopulations. o Investigatechanceprocessesanddevelop,use,andevaluateprobabilitymodels. Mathematical'Practices' 1.Makesenseofproblemsandpersevereinsolvingthem. 2.Reasonabstractlyandquantitatively. 3.Constructviableargumentsandcritiquethereasoningofothers. 4.Modelwithmathematics. 5.Useappropriatetoolsstrategically. 6.Attendtoprecision. 7.Lookforandmakeuseofstructure. 8.Lookforandexpressregularityinrepeatedreasoning. 4

5 EAIUnitSummaries FractionsatWork(FAW):Multimedia,Hands6OnApplication Aseriesofcomputer:basedmodulesandconcretizedmanipulativescalledFractionsatWork(FAW)developsstudents understandingandproceduralcompetencewithrationalnumbers.fawcontainssevenchaptersdividedintoself:containedunitsto helpstudentsunderstandconcepts(e.g.,fractionequivalence)anddeveloptheircomputationalskills(e.g.,addingandsubtracting fractions).thefirstchapterdescribespropertiesoffractions,includingtheirpurposeandfunction.thegoalofthesecondchapteris tohelpstudentsunderstandtheconceptofequivalence.usingfractionsindicatedonaninteractivetapemeasure,thecomputer screensshowhowthevalueoffractionsdependsonthenumberofpartsintowhichaninchisdivided(i.e.,denominator)andthe numberofthesepartsavailable(i.e.,numerator).inthethirdchapter,studentsareshownhowtoaddsimplefractionsthathavethe samedenominator.multipleexamplesareusedtoemphasizewhyitisnotappropriatetoadddenominators.chapters4and5 describehowtoaddsimplefractionswithunlikedenominators.studentsarefirsttaughttocheckwhethertheycanmultiplythe smallerdenominatorbysomenumbertomakeitequaltothelargerdenominator.inchapter6,studentsareledthroughaseriesof stepsonhowtoaddandsubtractmixednumbers,includingproceduresforrenamingandsimplifyingfractions.thelastchapter summarizesthecontentinthepreviouschaptersandincludesanassessmenttocheckforunderstanding. AsstudentsworkonFractionsatWork,teachersuseconcretematerialssuchasfractionstripstohelpstudentsunderstanddifficult conceptssuchasequivalence.forexample,teachersgivenarrowstripsoftagboardtostudentsandaskthemtoimaginethatone ofthestripsisalongcandybarthatneedstobesharedbytwopeople.studentsrepresenthowtosharethecandybarbyfoldingthe stripinhalf.theteacherthenasksthemtolabelthefold1/2.thestudentsrepeattheprocesswiththeotherthreestrips candy barsthatneededtobesharedamongfour,eight,andsixteenpeople usingrepeatedfoldingtoshoweachsegment,whichthey thenlabel.whenstudentshavelabeledallfourofthefractionstrips,theteacherposesquestionsaboutequivalence,relativesize, andthefunctionofandrelationshipbetweennumeratoranddenominator.studentsusetheirstripstoshowhowtoaddandsubtract fractions. FractionoftheCost(FOC):Multimedia Theproblemsolvinganchor,FractionoftheCost(FOC),includesan8:minutevideoonCDthattellsthestoryofthreefriendswho wishtobuildaskateboardramp.availableinenglishandspanish,thevideostarsthreestudentsfromalocalmiddleschool.the videowasfilmedatalocalskateboardingstoreandinacomputerroom,garage,andbackyardofalocalhome.theteensstudya schematicplanofaskateboardrampandthendiscusshowtheycanaffordtobuildarampwiththematerialsandmoneytheyhave available.studentsaretodeterminewhethertherampcanbebuiltand,ifso,whatcombinationofavailableboardsandnewboards areneededandhowtheseboardsshouldbecut.thesolutionpathisnotastraightforwardone,thusrequiringstudentstopersevere whiletryingdifferentcombinationsuntilfindingonethatkeepsthemunderbudget.studentsneedtorefertothevideoanchor throughouttheprocesstofindtheinformationtheyneed(e.g.,lengthofavailableboards,costofnewboards).tosolvetheproblem, 5

6 students(a)calculatepercentofmoneyinasavingsaccountandsalestaxonapurchase,(b)readatapemeasure,(c)convertfeet toinches,(d)decipherbuildingplans,(e)constructatableofmaterials,(f)computemixedfractions,(g)estimateandcompute combinations,and(h)calculatetotalcost. Inadditiontotheproblemsolvingvideo,theCDcontainsseveralinteractivetoolstohelpstudentssolvetheproblem.Forexample, studentsareabletoviewthecompletedramp(withcolor:codedindividualboards)fromanyanglebydraggingthediagram.theyare alsoabletoconstructtherampinmultimediaspacebydraggingindividualboardsontoatemplate,thushelpingthemkeeptrackof whichboardstheyhavealreadyaccountedforandwhichstillneedtobecut.studentscanalsomeasurelengthsofeachboardwith avirtualrulerandthenmarktheircutswiththevirtualpencil. Hovercraft(HOV):Hands6OnApplication TheHovercraftunitconsistsofahands:onproblemthatengagesstudentsinusingtheskillstheylearnedinFractionsatWorkand FractionoftheCost.InsolvingtheHovercraftproblemstudentsapplywhattheyhavelearnedfromthevideotoplan,draw,and constructa rollovercage forahovercraftoutofpvcpipe.eachstudentdrawsaschematicplanshowingseveralviewsofthecage andbuildsascalemodeloutofplasticstraws.thenstudentsvotetoselectthethreedesignstheywanttomake.theteacherdivides theclassintothreegroups,andeachgroupplanshowtheycanmakethecageinthemosteconomicalway,whichinvolvescutting the10:footlengthsofpipeinsuchawayastowasteaslittlepipeaspossible.oncetheteacherapprovestheplans,studentswork onmeasuring,cutting,andassembling.whenthecagesarecomplete,studentsliftthemontoa4 4:footplywoodplatform(i.e., hovercraft).aleafblowerpowersthehovercraftbyelevatingthehovercraftslightlyabovethefloor.studentstaketurnsridingonthe hovercraftsinrelayracesthelastdayoftheproject. Kim skomet(kk):multimedia Kim skomet(kk)isoneepisodeinaseriesofvideo:basedanchorscalledthethenewadventuresofjasperwoodbury(the LearningTechnologyCenteratVanderbiltUniversity,1997).Originallyonvideodisc,theupdatedversionisavailableonastudent andateachercd.accordingtotheinstructormanual,thepurposeofkim skometistohelpstudentsdeveloptheirinformal understandingofpre:algebraicconceptssuchaslinearfunction,lineofbestfit,variables,rateofchange(slope),andreliabilityand measurementerror.foundationskillsneededtosolvethisproblemincludecomputationwithwholenumbersandrationalnumbers (i.e.,decimals). Thevideoanchorinvolvestwogirlswhocompeteinpentathlonevents.Thefirstchallengeasksstudentstoidentifythethreefastest qualifiersinthreeregionalraceswheretimesanddistancesareknownbutthedistancesvary.forexample,studentsexplain whetheracarthattravels15feetin0.9secondsisfasterorslowerthanacarthattravels20feetin1.3seconds.thesecond challengerequiresstudentstoconstructagraphandlineofbestfittopredictthespeedofcarsattheendofastraightawaywhen releasedfromanyheightontheramp. 6

7 GrandPentathlon(GP):Hands6OnApplication AfterstudentssolvetheproblemsinKim skomet,theycompeteintheirownpentathloncompetitionwithafull:sizedrampand eventsliketheonesshowninthevideo.studentsmaketheirowncarsoutofblocksofwoodandtimethemfromseveralrelease pointsontheramp.aninfrareddetectormeasuresthetimeofthecarsfromthebeginningtoendofthestraightaway.afterstudents maketheirgraphsandplottheirtimes,theteacherrevealstostudentstherangeofspeedswithinwhichtheircarsshouldbetraveling tonegotiateeachevent.studentshavetoconstructtheirowngraphsandlinesofbestfittopredictthespeedoftheircarsattheend ofthestraightawayforeveryreleasepointontheramp. 7

8 8 EAIUnitsmappedtoCommonCoreStateStandardsforMathematics FractionsatWork(FAW),FractionoftheCost(FOC), Hovercraft(HOV),Kim skomet(kk),grand Pentathlon(GP) Standard ScopeofCoverage ThisstandardisaddressedinFOC,HOV,KK,andGP. Forexample,inHOVstudentsdrawmodelsofa hovercrafttoscaleandthenusetheirdrawingstobuild thefull:sizehovercraft.studentssolveproblemsabout scaledrawingsbyrelatingcorrespondinglengths betweentheobjects. Ratiosandproportionsarealso centraltokkandgpasstudentsidentifyandconvert rates,suchasfeetpersecondandcostperounce. Studentsmodelspeedandreleaseheightsoftheircars ontherampbasedontheircalculationsandlinegraphs. Theyalsolearnhowslopeofthelinerepresentsthe relationshipbetweenspeedandthereleasepointsofthe cars. RatiosProportional Relationships Analyzeproportional relationshipsandusethemto solvereal:worldand mathematicalproblems. 7.RP.1. 7.RP.2. 7.RP.3. FullyAddressed Thesestandardsare addressedacrossfourofthe fiveinstructionalunits. Oneofthemainobjectivesandfoundational underpinningsoftheseunitsistohelpstudentslearn howtosolvereal:worldandmathematicalproblems involvingthefouroperationswithrationalnumbers.to solvefoc,hov,andkkproblems,studentsmustadd, subtract,multiply,anddividewholenumbers,fractions, anddecimals.forexample,infractionofthecost, studentscalculatethepercentoftheirsavingstheycan usefortheskateboardrampproject.theyalsocompute withwholeandmixednumberstofigureoutthemost economicaluseof2 x4 dimensionlumberforbuilding theramp.inkkandgp,studentsidentify fractional/decimalequivalenceandcomputewith decimalstoproblemsolveandcalculatespeed. TheNumberSystem Applyandextendprevious understandingsofoperations withfractionstoadd,subtract, multiply,anddividerational numbers. 7.NS.1. 7.NS.2. 7.NS.3. MostlyAddressed Studentsdonotlearnto explainandinterprettherules foradding,subtracting, multiplying,anddividingwith negativenumbers.theyalso donotlearnspecificrulesthat integerscanbedivided, providedthatthedivisorisnot zero,andeveryquotientof integers(withnon:zero divisor)isarationalnumber.

9 9 FractionsatWork(FAW),FractionoftheCost(FOC), Hovercraft(HOV),Kim skomet(kk),grand Pentathlon(GP) Standard ScopeofCoverage ThisstandardisaddressedinFAW,FOC,HOV,KK,and GP.ForexampleinFractionsatWork,studentsare askedtore:representmixedfractionsasoneimproper fractionandviceversa. ExpressionsEquations Usepropertiesofoperations togenerateequivalent expressions. 7.EE.1. 7.EE.2. PartiallyAddressed Studentslearninformallyhow torepresenttheseconcepts. Themainemphasisineachoftheunitsissolvingreal: worldproblemsincontext.theproblemsrequire studentstorecognizethequantitiesandtheir relationships.theyusethisinformationtoconstruct simpleequationsandinequalitiestosolveeachproblem. Studentsuseestimationandmentalcomputationto checkthereasonablenessoftheirstrategies.for example,infocstudentsneedtofigureouthowtocut2 x4 lengthsofwoodincombinationstowasteaslittle woodaspossible.theyneedtointerpretthelengthsof woodfromaschematicplan. Solvereal:lifeand mathematicalproblemsusing numericalandalgebraic expressionsandequations. 7.EE.3. 7.EE.4. MostlyAddressed Theunitsdonotemphasize formallearningofalgebraic expressionsandequations. Studentsdonotlearncontent of7.ee.4.

10 10 FractionsatWork(FAW),FractionoftheCost(FOC), Hovercraft(HOV),Kim skomet(kk),grand Pentathlon(GP) Standard ScopeofCoverage AcentralobjectiveofFOCandHOVistointerpret schematicplans,makescaledrawings,buildscale modelsfromtheirdrawings,andconstructprojectsthat arefullsize.forexample,inthehovunitstudents designtheirrollovercagesforahovercraftongraph paperandthenusetheirknowledgeofratiosto determinethelengthsofthepipeneeded.studentslearn informallyanglesbecausethepvcconnectorsare availablein45degreeand90degreeangles. Students alsointerpretdrawingsofaskateboardramp,whichfrom thesideview,formsarighttriangle.studentslearn, informally,therelationshipbetweenthesidesandangles. Geometry Drawconstruct,anddescribe geometricalfiguresand describetherelationships betweenthem. 7.G.1. 7.G.2. 7.G.3. PartiallyAddressed Studentsareafforded opportunitiestonotice propertiesofgeometric shapes(sidesandanglesof righttriangle)andconstruct models,buttheydonotlearn standard7.g.3.inaformal way. IntheFOCandHOVunitsstudentslearnconceptsand applicationsrelatedto7.g.6.solvingreal:lifeproblems involvingtwo:andthree:dimensionalobjects. Solvereal:lifeand mathematicalproblems involvinganglemeasure, area,surfacearea,and volume. 7.G.4. 7.G.5. 7.G.6. PartiallyAddressed Studentsdonotlearn formulassuchas circumferenceandareaof circle7.g.4.orterminology relatedto7.g.5.

11 11 FractionsatWork(FAW),FractionoftheCost(FOC), Hovercraft(HOV),Kim skomet(kk),grand Pentathlon(GP) Standard ScopeofCoverage StudentsgatherdatainKKabouttheircars.Theylookat therelationshipbetweenthereleaseheightontheramp andthefinalspeedofthecarattheendoftheramp. StudentscomputeaverageratesoftheircarsinKK basedontimetrials.studentslearnalternatewaysof computingandrepresentingcentraltendency.theyalso drawinferencesfromtheirdata,exploresourcesoferror, andrefinetheirconclusionsbasedonsimulatedsamples oftheirdata. StatisticsandProbability Userandomsamplingtodraw inferencesabouta population. 7.SP.1. 7.SP.2. PartiallyAddressed Studentsdonotlearnformal waysofsamplingorof knowingifthesampleis representativeofthe populationfromwhichiswas drawn. CentralobjectivesofKKarecalculatingaveragespeed, usingfunctiontables,graphingfunctions(linegraph), drawinglineofbestfit,interpretingslopeofagraphed function,andmakinginferencesbasedonthesedata. Studentstesttheirinferencesandrevisetheirpredictions basedonobserveddatasources. Drawinformalcomparative inferencesabouttwo populations. 7.SP.3. 7.SP.4. PartiallyAddressed Studentsdonotlearnformal waysofgeneratingmultiple samplesfromthepopulation tomakepredictions. Investigatechanceprocesses anddevelop,use,and evaluateprobabilitymodels. 7.SP.5. 7.SP.6. 7.SP.7. 7.SP.8. NotAddressed EAIUnitsmappedtoStandardsforMathematicalPractice

12 TheCoreStandardsdocumentprovidesStandards'for'Mathematical'Practice,whichdescribesvarietiesof expertisethatmathematicseducatorsdevelopintheirstudents.thesepracticesaredrawnfromthenational CouncilofTeachersofMathematicsprocessstandardsandtheNationalResearchCouncil sreportaddingitup. HowAddressed TheinstructionalapproachtoFOC,HOV,KK,andGPdependsonthestudentsfiguringout forthemselveshowtoapproachaproblemandthenperseveretosolveit.forexample,in FOC,studentsarerequiredtoworkwithagroupinordertocomeupwithamaterialslistand costfortheskateboardrampbygatheringinformationfromtheinstructionalvideowithout step:by:stepteacherdirections. Thisstandardisaddressedthroughoutallofinstructionalunits:FAW,FOC,HOV,KK,and GP.Forexample,inFAWstudentsusefractionstripstodevelopadeeperunderstanding aboutequivalence,relativesize,andthefunctionofandrelationshipbetweennumeratorand denominator. InFOCandHOVstudentsareaskedtolookateachgroupmember splansforthesolutionto theproblemanddeterminewhichplanusesthematerialsefficientlyandisthusmostcost effective. ThisisoneofthemaingoalsofFOC,HOV,KK,andGP.Eachoftheseinstructionalunits aimstousemodelingtodemonstratetheimportanceandusefulnessofmathematics. MathematicalPractices Makesenseofproblems andpersevereinsolving them. Reasonabstractlyand quantitatively. Constructviable argumentsandcritique thereasoningofothers. Modelwithmathematics. 12

13 13 HowAddressed MathematicalPractices InFOC,theuseofarulerforameasurementtoolisapracticedskill.Calculatorsandgraphs arealsousedthroughouttheunits. Useappropriatetools strategically. InFOC,HOV,andKK,attentiontodetailsandprecisioninmeasurementsandrecordingdata isimportant.infocandhov,studentsmustbesuretohaveaccuratelength measurements.inkk,studentswillrealizethedifferenceatenthofasecondwillmaketo theirdatacollection. Attendtoprecision. Notformallyaddressed. Lookforandmakesure ofstructure. Thisstandardisaddressedineachunitofinstruction:FAW,FOC,HOV,andKK.For example,inthefocandhovunitsstudentsusetheirskillstoorganizethematerialsand costlistforseveralbuildingprojects. Lookforandexpress regularityinrepeated reasoning.

14 Application'to'Students'with'Disabilities' TheCommonCoreStateStandardsarticulaterigorousgradeClevelexpectationsintheareasofmathematics andenglishlanguagearts.thesestandardsidentifytheknowledgeandskillsstudentsneedinordertobe successfulincollegeandcareers Studentswithdisabilities studentseligibleundertheindividualswithdisabilitieseducationact (IDEA) mustbechallengedtoexcelwithinthegeneralcurriculumandbepreparedforsuccessintheir postcschoollives,includingcollegeand/orcareers.thesecommonstandardsprovideanhistoric opportunitytoimproveaccesstorigorousacademiccontentstandardsforstudentswithdisabilities.the continueddevelopmentofunderstandingaboutresearchcbasedinstructionalpracticesandafocusontheir effectiveimplementationwillhelpimproveaccesstomathematicsandenglishlanguagearts(ela) standardsforallstudents,includingthosewithdisabilities. Studentswithdisabilitiesareaheterogeneousgroupwithonecommoncharacteristic:thepresenceof disablingconditionsthatsignificantlyhindertheirabilitiestobenefitfromgeneraleducation(idea34cfr ,2004).Therefore,howthesehighstandardsaretaughtandassessedisoftheutmostimportancein reachingthisdiversegroupofstudents. Inorderforstudentswithdisabilitiestomeethighacademicstandardsandtofullydemonstratetheir conceptualandproceduralknowledgeandskillsinmathematics,reading,writing,speakingandlistening (Englishlanguagearts),theirinstructionmustincorporatesupportsandaccommodations,including: supportsandrelatedservicesdesignedtomeettheuniqueneedsofthesestudentsandtoenable theiraccesstothegeneraleducationcurriculum(idea34cfr ,2004). AnIndividualizedEducationProgram(IEP)1whichincludesannualgoalsalignedwithandchosento facilitatetheirattainmentofgradeclevelacademicstandards. Teachersandspecializedinstructionalsupportpersonnelwhoarepreparedandqualifiedtodeliver highcquality,evidencecbased,individualizedinstructionandsupportservices. PromotingacultureofhighexpectationsforallstudentsisafundamentalgoaloftheCommonCoreState Standards.Inordertoparticipatewithsuccessinthegeneralcurriculum,studentswithdisabilities,as appropriate,maybeprovidedadditionalsupportsandservices,suchas: 14

15 Instructionalsupportsforlearning basedontheprinciplesofuniversaldesignforlearning (UDL)2 whichfosterstudentengagementbypresentinginformationinmultiplewaysand allowingfordiverseavenuesofactionandexpression. Instructionalaccommodations(Thompson,Morse,SharpeHall,2005) changesinmaterialsor procedures whichdonotchangethestandardsbutallowstudentstolearnwithintheframework ofthecommoncore. Assistivetechnologydevicesandservicestoensureaccesstothegeneraleducationcurriculumand thecommoncorestatestandards. Somestudentswiththemostsignificantcognitivedisabilitieswillrequiresubstantialsupportsand accommodationstohavemeaningfulaccesstocertainstandardsinbothinstructionandassessment,basedon theircommunicationandacademicneeds.thesesupportsandaccommodationsshouldensurethatstudents receiveaccesstomultiplemeansoflearningandopportunitiestodemonstrateknowledge,butretainthe rigorandhighexpectationsofthecommoncorestatestandards. 1 AccordingtoIDEA,anIEPincludesappropriateaccommodationsthatarenecessarytomeasuretheindividualachievementand functionalperformanceofachild 2UDLisdefinedas ascientificallyvalidframeworkforguidingeducationalpracticethat(a)providesflexibilityintheways informationispresented,inthewaysstudentsrespondordemonstrateknowledgeandskills,andinthewaysstudentsare engaged;and(b)reducesbarriersininstruction,providesappropriateaccommodations,supports,andchallenges,andmaintains ' References' IndividualswithDisabilitiesEducationAct(IDEA),34CFR (a).(2004). IndividualswithDisabilitiesEducationAct(IDEA),34CFR (b)(3).(2004). Thompson,SandraJ.,AmandaB.Morse,MichaelSharpe,andSharonHall. AccommodationsManual:Howto Select,AdministerandEvaluateUseofAccommodationsandAssessmentforStudentswithDisabilities, 2ndEdition.CouncilforChiefStateSchoolOfficers, highachievementexpectationsforallstudents,includingstudentswithdisabilitiesandstudentswhoarelimitedenglish proficient. byhighereducationopportunityact(pl110c135) 15