the math process: kansas mtss · strategic competence–ability to formulate ... mathematics...

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TheMathProcess:KansasMTSS

PaulaHough,KansasMTSSStateTrainer

KansasMTSSisfundedthroughPartBfundsadministeredbytheKansasStateDepartmentofEducation’sEarlyChildhood,SpecialEducationandTitleServices.KansasMTSSdoesnotdiscriminateonthebasisofrace,color,nationalorigin,sex,disability,orageinitsprogramsandactivities.Thefollowingpersonhasbeendesignatedtohandleinquiriesregardingthenon-discriminationpolicies:DeputyDirector,KeystoneLearningServices,500E.Sunflower,Ozawkie,KS66070,785-876-2214.

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ObjectivesofSessionAttheendofthissession,participantswillhaveanunderstandingofthe:• Criticalconceptsandproficienciesinteachingmathematics

• Needforastrongcoreandevidencebasedinstructionalstrategies

• Purposeanduseofamathscreener,otherassessments,andinterventioncurricula

• KSMTSSgroupingprocess

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KansasMTSS

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MythsaboutMathematics• Noteveryoneiscapableoflearningmath.

• Mathissomethingyoudoalone.

• Mathisforboys.

• Mathisaboutmemorizationandspeed.

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“Mathematicsisoneofhumanity’sgreatachievements. Byenhancingthecapabilitiesofthehumanmind,mathematicshasfacilitatedthedevelopmentofscience,technology,engineering,business,andgovernment. Mathematicsisalsoanintellectualachievementofgreatsophisticationandbeautythatepitomizesthepowerofdeductivereasoning. Forpeopletoparticipatefullyinsociety,theymustknowbasicmathematics. Citizenswhocannotreasonmathematicallyarecutofffromwholerealmsofhumanendeavor. Innumeracydeprivesthemnotonlyofopportunitybutalsoofcompetenceineverydaytasks.”

- NationalResearchCouncil(2001)

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DemandforMath•80%ofUnitedStates’fastestgrowingcompaniesrequireproficiencyinmathematicsand/orscience.(Murray,2009)

•Lessthanhalfofboth4th gradeand8th gradestudentsachievedhighstandardsonthe2011TIMSS.(TIMMS,2011)

•STEMoccupations3xthegrowthofnon-STEMjobsfrom2002– 2012.(Murray,2013)

• U.S.ranked26/38inthe2012PISA.(OECD,2015)

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CoreBeliefsofMathematics•AllStudentsCanbeMathematicallyProficient.

•AllStudentsNeedaHigh-QualityMathematicsProgram.

•EffectiveMathematicsProgramsMustTeachConceptualUnderstanding,ProceduralFluency,FactualKnowledge,andProblem-SolvingSkills.

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CoreBeliefsofMathematics• EffectiveInstructionMattersandSignificantlyImpactsStudentLearning.

• TeachersuseaBalanceof“Student-Centered”and“Teacher-Directed”InstructionWithintheCore.

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MathematicsCore

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NumberandOperationsProgressionOperationsandAlgebraicThinking

ExpressionsandEquations

Algebra

→ →

NumberandOperations—BaseTen

→

TheNumberSystem

→

NumberandOperations—Fractions

→

K 1 2 3 4 5 6 7 8 HighSchoolhttp://achievethecore.org/page/399/introduction-to-the-math-shifts

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MathematicalProficiencyStrands

AdaptiveReasoning

Strategic Competence

Conceptual Understanding

Productive Disposition

Procedural Fluency

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StrandsofMathematicalProficiency❖ConceptualUnderstanding – comprehensionof

mathematicalconcepts,operations,andrelations

❖ProceduralFluency – skillincarryingoutproceduresflexibly,accurately,efficiently,andappropriately

❖StrategicCompetence – abilitytoformulate,represent,andsolvemathematicalproblems

❖AdaptiveReasoning – capacityforlogicalthought,reflection,explanation,andjustification

❖ProductiveDisposition – habitualinclinationtoseemathematicsassensible,useful,andworthwhile,coupledwithabeliefindiligenceandone’sownefficacy.

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AdaptiveReasoningA BA

C D

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ProductiveDisposition

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TheCORE• 50– 60mineachday• Research/Evidencebasedcurriculum• Research/Evidencebasedinstructionalpractices• 10minofdifferentiatedcomputationalfluency• Ensurefidelitytotheprogram• ProfessionalDevelopment

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InstructionalStrategies• ExplicitInstruction• CRA--Concrete/Representational/Abstract• OpportunitiestoRespond•Scaffolding•ImmediateFeedback•SchemeBasedInstruction

PrinciplesofExplicitInstruction

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AssessmentsType Who/Frequency Purpose

Universal Screener All students 3X a year - Health of students- Students making adequate

progress- Identification of students

for intervention

Progress Monitor Students not at benchmarkEvery 3-4 weeks

- Short, frequent skills based assessments

- Determine if instruction/interventions are improving student learning

Diagnostic Non-responding Students - More in depth and specific information/problem solving

Adapted from Response to Intervention (2010), Witzel and Ricommini

Data-based decision making should be ongoing. It provides information to improve instruction effectiveness and determine students’ need for more instruction.

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TypicalScreenerTopicsforEarlyChildhood

• Timedassessmentsin:– Oralcounting– 1to1correspondencecounting– Numbernaming– Quantitycomparison

*ENskillsareapredictorforbothreadingandmath

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TypicalScreenerTopicsforGradesK-1

• Timedassessmentsin:– Numberidentification– Quantitydiscrimination– Strategiccounting

•Missingnumber•Matchquantity•Decomposing•Numbersequence

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TypicalScreenerTopicsforGrades2-8+

• Computation(process)• Conceptsandapplications• Automaticity• Focalpoints/domains• Doesnotrequireindividualadministration

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GroupingProcess

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Tier 1

Tier 2

Tier 3

K-12MathGroupingProcess

MathGroupingProcess

MathGroupingProcess

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EnrichmentBrief

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IdentifyingaPlacementTest

•Shouldbeininterventioncurriculum

Ifnot…•Lookforincorecurriculum•Ifnoplacementtestexists,lookatuniversalscreenerinstructionalplanningreport

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MathGroupingProcess

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StepsforDeterminingInstructionalLevelforTier3Support

1. Administerprobesfrompreviousgrade2. ContinuepreviousprobesuntilallSpring

targetscoresareachieved3. Instructionallevelisonegradeabove

thatlevel

BackwardsTestingWorksheet

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Practice

4th graderMasonscoresreflectneedforTier3Support…Whatnow?

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Practice

4th graderMasonscoresreflectneedforTier3Support…

3rdGradeProbes...MCAP=12MCOMP=50

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BackwardsTestingWorksheet

M-Comp 50 M-CAP 12

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Practice

4th graderMasonscoresreflectneedforTier3Support…

2ndGradeProbes...MCAP=22MCOMP=40

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BackwardsTestingWorksheet

M-Comp 40 M-CAP 22

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K-12MathGroupingProcess

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Dibels- BackwardsTesting

Withapartner…Completethe3rdGradeMiddleofYearDataAnalysis

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WhatisIntervention?• Processofprovidingearly,systematic,researchbasedandappropriatelyintensiveassistancetochildrenwhoareatriskfororarealreadyunderperformingascomparedtoappropriategrade- orage-levelstandards.

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MathematicsInterventionis:• SmallgroupinstructioninadditiontotheCore

–Recommended30-45min4+days/week• More opportunitiesforresponseandfeedback• Evidencebasedprogramsandcurriculum• DataDriven• Comprehensive&focusedoncriticalconcepts•Proceduralandconceptual

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•Studentsaregroupedbyinstructionalneednot,chronologicalageorgrade

•Evidencebasedprogramsandcurriculum

Interventions

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WhatInterventionisNOT

• Re-teaching• Stand-alonetricks• SlowerandLouder• BasedonwhatisbeingcurrentlytaughtintheCore

• Onlyprocedures• Intendedtofillthegapquicklyandmoveforward

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8AspectsofEffectiveIntervention

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KeyStructuresofInterventionCurriculum

•Meetallinstructionallevelsofthestudents•Placementtesttoestablishtheentrypointforthestudentathand

•Frequentpre/posttestingtoensurethestudentisprogressingthroughthecurriculumadequately

•Explicitlystructuredlessons

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InterventionGoal:AccelerateLearning

•Ifaccelerationisnothappening,theinterventionneedsadjusted.

•Collaborativeteamsneedtobetaughtto:– Analyzestudents’progress–Makeadjustmentstoinstruction–UtilizetheSelf-CorrectingFeedbackLoopforcommunication.

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ComprehensiveIntervention

•Comprehensivecoverageofcrucialdomainsorprogressionsofmathematics

•Addressandbuildproficiencyofproceduralandconceptualaspects

–Adequatelybalancethetwofacetsofmathematicaldevelopment

–Beginatmostremedialneedstoavoidrogueproceduralknowledge

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School: Wayside ElementaryGrade: Third GradeYear: 2016-2017Class: Mrs. Gorf

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School: Wayside ElementaryGrade: Third GradeYear: 2016-2017Class: Mrs. Gorf

*FollowCurriculumRecommendationsfirst!

*

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Examplewaystoaccommodateinterventiongroups

Elementary• Allstudentswalktointerventionmodel

• Classroominterventionmodel

• Co-teachingmodel

Secondary• Additionalcourse/skinnies

• Advisoryorseminartime• Additional20min.flashclass– i.e.afterlunchinMiddle

schools2xaweek

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StaffMemberAStudentswhoareBenchmarkandBeyond

StaffMemberBStudentswhoareBenchmarkandBeyond

StaffMemberCStudentsreceivingInterventionatgradelevel.

StaffMemberCStudentsreceivingInterventionoffgradelevel

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4

6

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SampleWalk-ToMath

Intervention

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InstituteofEducationScienceInterventionRecommendations

forMath1. Screenall2. Materialincludewholenumbersandrationalnumbers3. Explicit&Systematicinstruction4. Wordproblems5. Visualrepresentation6. Spend10min.buildingfluencyofbasicfacts7. Progressmonitoring8. Motivationalstrategies

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Pre/PostTesting&ProgressMonitoringPre/PostTestsMeasure(unit/chapterbased):

• Studentgrowthwithinaspecificprogram,or• Whetherastudenthasmasteredspecificskills

Progressmonitoringmeasures(monthly):• Whethergrowthisoccurringoncriticalskills• Whethersufficientgrowthisoccurringforstudentstoclosethegap

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BenefitsofProgressMonitoring:• Acceleratedlearningbecausestudentsarereceivingamoreappropriateinstruction;

• moreinformedinstructionaldecisions;• Documentationofstudentprogressforaccountabilitypurposes;

• Moreefficientcommunicationwithfamiliesandcolleaguesaboutstudentprogress;

• And,higherexpectationsforstudentsbyteachers

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@ksmtss@DrHough_KS

paula@kansasmtss.org