Framework for Math - Western Washington University

Possible Solutions•Educators must use the most efficient problemsolvingprocesses that will lead to the most effectiveinstructional practices.•Curriculum-based evaluation (CBE), embeddedwithin response to intervention (RTI), is thatproblem-solving process.OSPI ConferenceB. Kelley, WWU

Response to Intervention (RTI)• The practice of a) effective teaching based onstudents’ needs and (b) using student data to (c)make instructional decisions.• Success of RTI depends on effectivecollaboration between general and specialeducation teachers.• RTI practices are proactive and effective at alllevels from early childhood through high school.OSPI ConferenceB. Kelley, WWU

Reviewing RTI (Problem Solving)Class-wide (School-wide) Decision MakingWho is notmeeting thestandard?EvaluateProgressIdentify andDefine theArea ofConcernImplementthe PlanDesign theInterventionand ProgressMonitoringPlanOSPI ConferenceB. Kelley, WWU

Building Level Blueprints• Component 3: Implementation• Action 2: Implement logistics of assessments• School-wide assessment plans• Assessment calendar• Schedule, Support• Consistent standards and competencies• Research (Stein et. al. 2006)• NCTM (www.nctm.org )• OSPI• Assessment data system (www.aimsweb.com )• Valid and reliable assessment toolsOSPI ConferenceB. Kelley, WWUProblemsolvingprocess

Identify and Define the Area ofConcern• Identify the specific math area• Computation• Addition, subtraction, multiplication, division• Application• Measurement, geometry, algebra• Problem solving• Determine the specific skill deficit• Conceptual, declarative, strategic knowledgeOSPI ConferenceB. Kelley, WWUProblemsolvingprocess

Screening/BenchmarkingOSPI ConferenceB. Kelley, WWU

Ji –5 th Grade StudentOSPI ConferenceWWUB. Kelley,

Computation Math Status SheetObjective CL Item S1 S2 S3MultiplicationSolve one-digit by one-digit number; CAP 100% 4 9 N N NSubtractionSolve four-digit from four-digit number w/zero in the hundredscolumn; CAP 100%Solve two-digit from two-digit number with renaming from tens toones; CAP 100%Solve one-digit from two-digit number with no renaming required;CAP 100%4 8 N N N3 6 N N N2 5 P P PSolve conceptual introduction subtraction facts; CAP 100% 1 2 P P PAdditionSolve three-digit and a two-digit number with renaming from onesto tens; CAP 100%Solve two-digit and one-digit number with renaming from ones totens; CAP 100%OSPI ConferenceB. Kelley, WWU3 7 P P P2 4 P P PSolve three-single digit addition problems; CAP 100% 2 3 P P PSolve basic addition facts; CAP 100% 1 1 P P P

Determining Specific Skill DeficitOSPI ConferenceB. Kelley, WWU

Status SheetOSPI ConferenceB. Kelley, WWU

RIOT MatrixReview Interview Observe TestInstructionWork/practice sheetswithout non-examplesTeacher: “Triedeverything” andneed to „move on‟Conceptual, limitedexplicit instruction.Independ. practice.CurriculumMultiplication facts ingeneral educationclassroom.Teacher: Subtractiona concernGeneral ed teacheruses Investigationsand manipulativesEnvironmentGood arrangement;good peerinteractionsLearnerJi 5 thgradeHealthy, good vision,hearing, good attend.Ji says that he likesmathJi counts on hisfingers, uses dashlinesSubtractionOSPI ConferenceB. Kelley, WWUProblemsolvingprocess

Additional AssessmentOSPI ConferenceB. Kelley, WWUStrategic orconceptualerrors

Who is not meeting the standard?• For each unit/area• In each classroom• At each grade level• Within each schoolOSPI ConferenceB. Kelley, WWUProblemsolvingprocess

Number of Problems Solved CorrectlyClassroom DataPre-test for Subtraction with Regrouping2018161412108skill errorcorrect6420Ce Co Cr Da Dv De Ed Es Fe He Iv Jo Ka Ko La Lr Lo Mis NoStudentsOSPI ConferenceB. Kelley, WWUProblemsolvingprocess

Building Level Blueprints• Component 3: Implementation• Action 3: Implement logistics core,supplemental, and intensive instruction• Ensure that core curriculum and instruction isresponsive to classroom/school diversity• Implement supplemental and intensive instructionthat is based on student need• Implement efficient interventions• Teach for generalizationOSPI ConferenceB. Kelley, WWU

Design Intervention/InstructionPlans• Intervention/instruction plan includes:• Measureable objective• Effective teaching components• Plan remediates skill deficit• Intervention is research basedOSPI ConferenceB. Kelley, WWUProblemsolvingprocess

Sample Teaching Objectives• Given 10 two-digit subtraction problems, 5 requiringtrading and 5 that do not require trading, S. will identify5/5 problems that need trading on two separateoccasions.• Given 10 two-digit subtraction problems, S. will correctlydemonstrate trading in ones and tens column in 10/10problems using a strategy card on two separateoccasions.• Given 10 two-digit subtraction problems, S. will correctlysolve 10/10 problems using a strategy card on twoseparate occasions.OSPI ConferenceB. Kelley, WWUDesigningInterventions

Effective Teaching Components• Preskills• Clear, measureable objective• Engaging lesson opening• Explicit instruction• Clear, consistent vocabulary• Visual supports• Active participation• Practice opportunitiesOSPI ConferenceB. Kelley, WWUDesigningInterventions

• Math skillsList of Preskills• Math facts, number sense• Study skills• Organization, memorization• Language skills• Ask questions, vocabulary, pragmatics,“explain your thinking”(one may need to teach these preskills prior to teaching the targetedmath skill)OSPI ConferenceB. Kelley, WWUEffectiveTeachingComponents

Vocabulary• Vocabulary pre-teaching (if needed)• Consistent• Long term applicability• Visual supportsOSPI ConferenceB. Kelley, WWU

Sample Visual SupportSLIP STRIP2-digit numbers Look at ONES column Read the problem Repeat ruleWrite rule here Do I need to trade?Yes – tradeTrade 1 ten for 10 onesCross out 1 ten in tenscolumnAdd 10 ones in ones columnORNo Subtract ones Write/record answer Subtract tens Write/record answer Check workOSPI ConferenceB. Kelley, WWU

• FrequentActive Participation• Throughout lesson (not just at beginning)• Many opportunities for all students• Varied• More than “thumbs up if…”• Appropriate• Student• LessonOSPI ConferenceB. Kelley, WWU

Smartboard• Technology that provides opportunities forstudents with diverse learning needsOSPI ConferenceB. Kelley, WWUEffectiveTeachingComponents

Practice Opportunities• Multiple practice opportunities• Guided practice• Practice specific to skill taught• Practice of reviewed skillsOSPI ConferenceB. Kelley, WWU

Other Considerations• Time delay/pacing• Self monitoring• Manipulatives (Miller, S. P. et. al., 1998).• Diversity Responsive Teaching• GLAD training (http://www.projectglad.com/)• SIOP model (http://www.siopinstitute.net/)• Price & Nelson text (2007)OSPI ConferenceB. Kelley, WWU

Possible Instructional PlanOSPI ConferenceB. Kelley, WWUProblemsolvingprocess

Progress Monitoring Plans• Progress monitoring includes:• Easy administration• Sensitive and frequent measures• Valid and reliable measures• Matches instructional objective• Correlates to standardsOSPI ConferenceB. Kelley, WWU

Monitor Progress• Progress is monitored frequently• Student data are analyzed• Instructional decisions are based on studentdataOSPI ConferenceB. Kelley, WWUProblemsolvingprocess

Progress Monitoring Tools• CBM• “…a quick and reliable method for gatheringinformation about student performance…”(Kelley, Hosp, Howell, 2008)• Resources• Aimsweb• www.interventioncentral.org• ExamplesOSPI ConferenceB. Kelley, WWU

Progress Monitoring Examples56-3943-1783-4692-2874-6561-3531-1452-4728-1963-4895-27OSPI ConferenceB. Kelley, WWU81-492 digit subtraction with trading

Number of itemsOSPI ConferenceB. Kelley, WWUProgress MonitoringRegrouping Progress Chart1211109876543210Oct. 20 Oct. 27 Nov. 3 Nov. 10 Nov. 17 Nov. 22DateNumber of regroupingstrategy errorsNumber of fact errorsNumber correctInstructionalchange

Problems Solved CorrectlyStudent Progress121086Student Progress42020-Oct 27-Oct 3-Nov 10-Nov 17-NovOSPI ConferenceB. Kelley, WWU

Number of Problems Solved CorrectlyClassroom DataPre-test for Subtraction with Regrouping2018161412108skill errorcorrect6420Ce Co Cr Da Dv De Ed Es Fe He Iv Jo Ka Ko La Lr Lo Mis NoStudentsOSPI ConferenceB. Kelley, WWUProblemsolvingprocess

Number of Problem Solved CorrectlySample Class Data20Post-test for Subtraction with Regrouping181614121086skill errorfact errorcorrect420Ce Co Cr Da Dv De Ed Es Fe He Jo Ka Lo Mi NoStudentsOSPI ConferenceB. Kelley, WWU

Reviewing RTI (Problem Solving)Class-wide (School-wide) Decision MakingWho is notmeeting thestandard?EvaluateProgressIdentify andDefine theArea ofConcernImplementthe PlanDesign theInterventionand ProgressMonitoringPlanOSPI ConferenceB. Kelley, WWU

Resources• Howell, K. (2000). Resources for implementing Howell and Nolet’scurriculum-based evaluation: Teaching and decision making (3 rd ).• Howell, K.W. & Nolet, V. (2000). Curriculum-based evaluation:Teaching and decision making (3 rd ). Belmont, CA:Wadsworth/Thomson Learning.• Belmont, CA: Wadsworth/Thomson Learning.• Miller, S. P. (1998). Validated practices for teaching mathematics tostudents with learning disabilities: A review of literature. Focus onExceptional Children, 31, 1, 24 pgs.• Price, K.M., & Nelson, K.L. (2007). Planning effective instruction:Diversity responsive methods and management. Belmont, CA:Wadsworth/Thomson Learning.• Stein, M., Kinder, D., Silbert, J., & Carnine, D. (2006). Designingeffective mathematics instruction: A direct instruction approach (4thed.). Columbus, OH: Merrill/Prentice Hall.OSPI ConferenceB. Kelley, WWU

Resources• Aimsweb -http://www.aimsweb.com/measures/math/• Worksheet generatorhttp://www.interventioncentral.org/• Otter Creek Institute - http://www.ocisems.com/Products/ProductLine.aspx?cat=501• Flashcard creatorhttp://www.aplusmath.com/Flashcards/Flashcard_Creator.htmlOSPI ConferenceB. Kelley, WWU