Framework for Math - Western Washington University
Framework for Math - Western Washington University Framework for Math - Western Washington University
- Page 4: Possible Solutions•Educators must
- Page 7 and 8: Reviewing RTI (Problem Solving)Clas
- Page 9 and 10: Identify and Define the Area ofConc
- Page 11 and 12: Ji -5 th Grade StudentOSPI Conferen
- Page 13 and 14: Determining Specific Skill DeficitO
- Page 15 and 16: RIOT MatrixReview Interview Observe
- Page 17 and 18: Who is not meeting the standard?•
- Page 19 and 20: Building Level Blueprints• Compon
- Page 21 and 22: Sample Teaching Objectives• Given
- Page 23 and 24: • Math skillsList of Preskills•
- Page 25 and 26: Sample Visual SupportSLIP STRIP2-di
- Page 27 and 28: Smartboard• Technology that provi
- Page 29 and 30: Other Considerations• Time delay/
- Page 31 and 32: Progress Monitoring Plans• Progre
- Page 33 and 34: Progress Monitoring Tools• CBM•
- Page 35 and 36: Number of itemsOSPI ConferenceB. Ke
- Page 37 and 38: Number of Problems Solved Correctly
- Page 39 and 40: Reviewing RTI (Problem Solving)Clas
- Page 41: Resources• Aimsweb -http://www.ai
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 <strong>Math</strong> 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 <strong>for</strong> 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 <strong>for</strong> 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
• <strong>Math</strong> skillsList of Preskills• <strong>Math</strong> 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 <strong>for</strong> 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 <strong>for</strong> all students• Varied• More than “thumbs up if…”• Appropriate• Student• LessonOSPI ConferenceB. Kelley, WWU
Smartboard• Technology that provides opportunities <strong>for</strong>students 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 <strong>for</strong> gatheringin<strong>for</strong>mation about student per<strong>for</strong>mance…”(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 <strong>for</strong> 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 <strong>for</strong> 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 <strong>for</strong> 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 <strong>for</strong> 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