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Smarter Balanced Mathematics Assessments

Smarter Balanced Mathematics Assessments. Agenda. U n d e rstand i ng the C o ntent of the Grade 1 1 S ummative Mathematics Ass e ssment E x p l ori n g Inno v ative W ays to U s e T ec h n o l o gy to Measure, C a pture, & Sc o re M athematical R e aso n i n g

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Smarter Balanced Mathematics Assessments

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  1. SmarterBalanced MathematicsAssessments

  2. Agenda • Understandingthe Content of theGrade 11Summative • MathematicsAssessment • ExploringInnovativeWaystoUseTechnologyto • Measure, Capture,&Score MathematicalReasoning • Updates on Mathematics PerformanceTasks • DRAFT Calculator Policy

  3. Understandingthe SmarterBalanced Grade 11 SummativeMathematicsAssessment

  4. MathematicsClaims Claim#1- Concepts & Procedures Claim#2- ProblemSolving Claim#3- Communicating Reasoning Claim#4- Modelingand Data Analysis “Studentscanexplainandapplymathematicalconceptsand interpretandcarry outmathematicalprocedureswith precisionand fluency.” “Studentscansolvearangeofcomplexwell-posedproblemsinpure andappliedmathematics,makingproductiveuseofknowledgeand problemsolvingstrategies.” “Studentscanclearlyandpreciselyconstructviableargumentsto supporttheirown reasoningandtocritiquethereasoningofothers.” “Studentscananalyzecomplex,real-worldscenariosandcan constructandusemathematicalmodelstointerpretandsolve problems.” “Studentscandemonstrateprogresstowardcollegeandcareer readinessinmathematics.” “Studentscandemonstratecollegeandcareerreadinessin mathematics.” OverallClaimfor Grades3-8 OverallClaim for Grade 11

  5. Whyshouldthegrade11assessment drawoncontentfrom earlier thangrade9? CSSM,p.84: “…someof the highestpriority contentfor collegeand career readinesscomes fromGrades6-8.This bodyof materialincludespowerfullyuseful proficienciessuchas applyingratio reasoningin real-worldandmathematical problems, computingfluently withpositiveandnegative fractionsanddecimals,andsolvingreal-worldand mathematicalproblemsinvolvinganglemeasure,area, surfacearea, andvolume.” Source: CommonCoreState Standards for Mathematics

  6. AlignmentoftheSmarter Balanced • SummativeContentSpecifications • “Tasksgeneratingevidencefor Claim#2in a given grade willdrawuponknowledgeandskillsarticulatedin theprogressionof standardsup through thatgrade, though more complexproblem-solvingtasks maydraw upon knowledgeandskillsfromlowergradelevels.” Source: ContentSpecificationsforthe summative assessmentof the Common CoreState Standards for Mathematics

  7. HowhasSmarterBalancedusedtheresearchand • the informationin thePublisher’sCriteria? • Claim1(ConceptsandProcedures)has 16 targetsin high school,whichcorrespondto 16 CCSS-Mclusters with relativelyhighimportanceforCollege& Career. • Highschoolstandards thatdo not appearasa separate targetinClaim1 or on thelistsfor Claims2,3, &4 (in thefollowingslides)willNOTbe measuredon thegrade 11summative assessment.

  8. Claim#2:Studentscansolvea rangeofcomplexwell-posed problemsinpureand appliedmathematics,makingproductive useofknowledgeandproblemsolving strategies.

  9. Claim#3:Studentscanclearlyandpreciselyconstruct viablearguments tosupporttheirownreasoningand tocritiquethereasoningofothers.

  10. Claim#4 - Studentscananalyzecomplex,real-worldscenarios and canconstructandusemathematicalmodelstointerpret andsolveproblems.

  11. Rationalefornotmeasuringevery • standardonthegrade11 summative • Contentidentifiedfortheassessment is basedon research relatedto prerequisiteskillsforcollege-and- career readiness • Allowstates tomake gooddecisionsabouthowto structurethe content across high school,including options thatspread the standards across four years instead of three • Exampleof content notmeasuredon Grade11 summative • G.C.AUnderstandand applytheoremsaboutcircles • G.C.A.1Prove thatallcircles aresimilar.

  12. Pushing the Limits on MeasuringMathematical ReasoninginAssessment

  13. Whyiscapturingstudents’reasoningso important? “OntheCMT[ConnecticutMasteryTest],Iwork and work andworkon a problem.ThenIgo to fillinmy answer andit’s not there. But this test[Smarter Balancedpilot] let me tellhowI solvedit.” --Grade3 student fromWethersfield,CT, whenasked by thedistrictmathcoordinatortogivefeedback onthe SmarterBalancedmathpilot

  14. But capturingandscoring students’mathematical reasoningvia technologyis easier saidthandone.

  15. Chloeisresponsmleformaking32centerpiecesforthetables atthisyear's:&ehoo·lprom Shev.riUplace8-inchtallcylindiica]cand es intopr-mv cs ofthe sameheight.Thenshewi11fill thespacebetweenthecandlesandthevaseshalfwarywithbiucsand. candle 4.5 in. vase 8.0in. ..··-· - ··--....-...·- •' 5.0in. Sand·isso!ldin240cubic·inchba at$4.79perbag.How·muchWillChloe spendonthesand tocreate32centerpieces?Show·yourworkorexplain'howyonfound)'Ouranswer.

  16. cl' ' % o...Y't\oflthuit <-C....VV'J '"' e<A.(... ?'e-fun1:M' G.f.;c -Q)S' ot>i'- +o v-oW\W ho'vCalculation l.P• Y'A'lS,Jo."'o \00- lD"'?,. CD(ld..<:, - VOL \\c..4_.}.'-\ ::7 '-\..'15s\ ')...'-\()

  17. Smarter Balanced AssessmentConsortium

  18. Attemptsto“Capture”StudentWorkoftenEliminatetheAutonomousReasoningCalled forintheContentSpecifications • Imaginethe same problemwas posedas a seriesofquestionsin anattemptto “capture” reasoning: • Whatis the volumeof ½ the candle? • Whatisthevolumeof ½the vase? • Howmuchsandin eachvase? • Howmanysandforallvases? • Howmanybagsofsand? • Howmuchwouldthatcost?

  19. OtherSystemLimitations • F.IF.C.7Graphfunctionsexpressedsymbolicallyandshowkeyfeatures of thegraph,byhandinsimplecasesandusingtechnologyformore complicated cases. • Graphlinearandquadraticfunctionsandshowintercepts,maxima,and minima. • Graphsquareroot,cube root, andpiecewise-definedfunctions, includingstepfunctionsandabsolutevaluefunctions. • Graphpolynomialfunctions,identifyingzeros whensuitable factorizations are available,andshowingend behavior. • (+)Graph rationalfunctions,identifyingzeros andasymptoteswhen suitablefactorizationsareavailable,and showingendbehavior. • Graphexponentialandlogarithmicfunctions,showingintercepts and end behavior,and trigonometricfunctions,showingperiod,midline,and amplitude.

  20. 0 u and Teller had at nt that is 8 t-by-I0 fee . 3-fe t by 6-feet. ch adult h s sl p1ng bag hat 1s h t fau a.0ru s id dults wout fit et of floor spac an he nt. ach a ult . 8 r is I 8 8 18- n eds 18 squ re t n is 80 squ r f t, so th 72. h oom to sp re. T ller said that it in ent C. h tried and coul no get four adults to b. ...1.Smarter s! l!£ Slide 34 Gavin,M.K.,CasMeasuring withthe opley,J.II.,& Sheffield,L.J.{2008}.ProjectM2:UsingEverydayMeasures:e-IIMIIfiJI'!o!:mProjectM2: Mentoring YoungMathematicians series.

  21. KnownGaps • Sometypesofgraphsandothermathematicalmodelsare difficulttoconstructin awaythatmirrorsthe kindofstudent understanding gainedthroughhand-drawn • Claim2ProblemSolving • Knowngapofcapturingstudentsresponsesviatechnology (graphicimagesaswellasa seamlessintegrationoftypewritten explanationswith equations/mathsymbols) • Claim3CommunicatingReasoning • Inparticular,targetBthatasksforstudentstopresentchainsof autonomousreasoning • Presentationofcontentrelatedtoreasoning(writtentextonthe assessmentvs.audio/visualin classroominstruction)

  22. PurposesoftheMathReasoningProject • Enhancetheknowledgebaseregardingauthenticevidenceof mathematicalreasoning. • Increasethevalidityoftestscoresbyincreasingthebreadthofthe • CommonCorestandardsthataremeasurableviacomputers. • Strengtheneducatorengagementandownershipofthe • assessments. • Enablestudentstoincorporategraphicalrepresentationsusing • naturaluserinterfacesin theirresponsetomathematicsitems. • Improvetheefficiencyofthescoringof mathematicalreasoningby • useofautomatedprocesses.

  23. ImmediateNextSteps • Expertcombinedmathematicscontentandtechnologypanelwill meetin earlyOctobertodefinetheevidencegapbetweenwhatwe wanttobe abletomeasureandwhatwearecurrentlyable to measure • Twophasedevelopmentplan • Phase1developmentfocusedon itemsthatwecanalready capture,butwanttobe abletoscoreusingtechnology • Phase2will focusonnewertechnologiesasdefinedand • prioritizedafterthepanelmeeting

  24. PerformanceTasksin Mathematics

  25. PerformanceTasks:Whatdidwelearn duringpilot? • Morehandscoringis neededtomeasurecomplexreasoning, application,andresearchskills,andrubricsmusttakeintoaccount theentiretasknotjustindividualparts • Earlygradesperformancetaskstaketoolong • ClassroomInteractionwill beavailableforallperformancetasksin • fieldtest

  26. Sample SBAC Math PerformanceTasks SBAC Practice Test Portal: http://sbac.portal.airast.org/practice-test/ Scoring Guides: http://sbac.portal.airast.org/practice-test/resources/

  27. DRAFT Calculator Policy

  28. CalculatorsontheSmarter Balanced MathAssessments • Grades3–5CalculatorPolicy • SmarterBalancedsummativemathematicsassessmentsforgrades3–5donot • allowforcalculatorusage. • Grades6–8CalculatorPolicy • In grades6–8,theSmarterBalancedsummativemathematicsassessmentsare • dividedinto twosections: CalculatorAvailableandCalculatorNotAvailable. • TheSmarterBalancedsummativemathematicsassessmentforgrade6allows an • onlinefour-functioncalculatorduring theCalculatorAvailablesection. • TheSmarterBalancedsummativemathematicsassessmentsforgrades7and8 • allowanonlinescientificcalculatorduringtheCalculatorAvailablesection. • HighSchoolCalculatorPolicy • Inhighschool, theSmarterBalancedsummativemathematicsassessmentsare • dividedinto twosections: CalculatorAvailableandCalculatorNotAvailable. • TheSmarterBalancedsummativemathematicsassessmentsforhigh school allow • onlinecalculators withscientific,regression,andgraphing capabilitiesduringthe • CalculatorAvailablesection.

  29. FindOutMore SmarterBalancedcanbefound onlineat: SmarterBalanced.org

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