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**Tiered Math Instruction**OrRTI Project Site Visit April 22, 2010**Objectives**• Explore the latest research on Response to Intervention systems for Math • Have dialogue about what would be necessary for a system to move toward RTI for Math**Do not worry about your problems with mathematics,**I assure you mine are far greater. -Albert Einstein**The Process is Ongoing and Long-Term**CONSENSUS INFRASTRUCTURE CONSENSUS IMPLEMENTATION CONSENSUS INFRASTRUCTURE Adapted from**The Math Caveat**• A lit search for studies on reading disabilities studies and math disability studies from 1996-2005 found over 600 studies in the area of reading and less than 50 for mathematics (12:1) • Specific RTI mathematics studies for a recent annotated bibliography totaled 9 studies**Interventions**Progress Monitoring Decision Rules and protocol Core Curriculum with strong instruction Universal Screener Data based teaming Leadership Professional Development**Assessment Recommendations**• Recommendation 1: Universal Screening • Recommendation 7: Progress Monitoring**Recommendation 1**Screen all students to identify those at risk for potential mathematics difficulties and provide interventions to students identified as at risk. Evidence: Moderate**Coherent Assessment Systems**• Each type of assessment has a purpose • The design of the tool should match the purpose • What are the implications for screening tools used with all students? • Think purpose not tool • How do each of these purposes fit together? Ben Clarke, 2009**General Features**• Short duration measures (1 to 5 minute(s) fluency measures) • Note many measures that are short duration also used in progress monitoring. • Longer duration measures (untimed up to 20 minutes) often examine multiple aspects of number sense • Issue of purpose is critical to examine • Most research examines predictive validity from Fall to Spring. Ben Clarke, 2009**Universal screener**• The Math Measures: • K-1: • Missing Number • Quantity Discrimination • Number Identification • Grades 2-8: • Basic Facts • Concepts and Applications • Math Focal Points • Secondary: • Prealgebra**Early Numeracy CBM:Missing Number**• K & 1 assessment • One minute measure • Individually administered**Early Numeracy CBM:Quantity Discrimination**• K & 1 assessment • One minute measure • Individually administered**Math-CBM:Computation**• Grades 1-8 • Grows in complexity through the grades • Two to four Minute assessment (depending on grade) • Scored on digits correct • Group administered 5th grade example**Math-CBM:Concepts and Applications**• Grades 2-8 • Grows in complexity through the grades • Aligned with NCTM Focal Points • Four to eight minutes (depending on grade) • Scored on correct answers (some have multiple answers) • Group administered**easyCBM**• Items created according to NCTM Focal Points for grade level • 48 items for screening (16 per focal point) • Computer-based or pencil and paper administration • Ongoing research Ben Clarke, 2009**CBM-Algebra**• Designed by Foegen and colleagues (Iowa State University) • Assess pre-algebra and basic algebra skills. • Administered and scored similar to Math-CBM**Talk to a neighbor**What was something that you already knew? What was something new? What is your district’s next step on this recommendation? Consensus? Infrastructure? Implementation? Are there questions you still have?**Math Assessment Resources**• National Center on Student Progress Monitoring www.studentprogress.org • National Center on RTI www.rti4success.org • Intervention Central’s Math Worksheet Generator www.interventioncentral.com • AIMSwebwww.aimsweb.com • easyCBMeasyCBM.com • Monitoring Basic Skills Progress(Fuchs, Hamlet & Fuchs, 1998) • The ABC’s of CBM (Fuchs, Fuchs, & Howell, 2007)**Suggestions**• Have a district level team select measures based on critical criteria such as reliability, validity and efficiency. • Use the same screening tool across a district to enable analyzing results across schools Ben Clarke, 2009**Suggestions**• Select screening measures based on the content they cover with a emphasis on critical instructional objectives for each grade level. • Lower elementary: Whole Number • Upper elementary: Rational Number • Across grades: Computational Fluency (hallmark of MLD) • In grades 4-8, use screening measures in combination with state testing data. Ben Clarke, 2009**Recommendation 7**Monitor the progress of students receiving supplemental instruction and other students who are at risk. Evidence: Low**Suggestions**• Monitor the progress of tier 2, tier 3 and borderline tier 1 students at least once a month using grade appropriate general outcome measures. • Use curriculum-embedded assessments in intervention materials • Will provide a more accurate index of whether or not the student is obtaining instructional objectives • Combined with progress monitoring provides a proximal and distal measure of performance Ben Clarke, 2009**Growth rates for Math are much lower**• Grade 1, .3 digit per week growth • Grade 3, .4 digit per week growth • Grade 5, .7 digit per week growth**Talk to a neighbor**What was something that you already knew? What was something new? What is your district’s next step on this recommendation? Consensus? Infrastructure? Implementation? Are there questions you still have?**Instructional/Curricular Recommendations**• Recommendation 2: whole numbers/rational numbers • Recommendation 3: systematic instruction • Recommendation 4: solving word problems • Recommendation 5: visual representation • Recommendation 6: fluent retrieval of facts • Recommendation 8: motivational strategies**Recommendation 2**Instructional materials for students receiving interventions should focus intensely on in-depth treatment of whole numbers in K-3 and on rational numbers in grades 4-8. Evidence: Low**Core curriculum content**• Whole number • Rational number • Critical aspects of geometry and measurement Source: Ben Clarke & Scott Baker Pacific Institutes for Research**Suggestions**• For tier 2 and 3 students in grades K-3, interventions should focus on the properties of whole number and operations. Some older students would also benefit from this approach. • For tier 2 and 3 students in grades 4-8, interventions should focus on in depth coverage of rational number and advanced topics in whole number (e.g. long division).**Difficulty with fractions is pervasive and impedes further**progress in mathematics**Talk to a neighbor**What was something that you already knew? What was something new? What is your district’s next step on this recommendation? Consensus? Infrastructure? Implementation? Are there questions you still have?**Recommendation 3**Instruction provided in math interventions should be explicit and systematic, incorporating modeling of proficient problem-solving, verbalization of thought processes, guided practice, corrective feedback and frequent cumulative review. Evidence: Strong**Suggestions**• Districts should appoint committees with experts in mathematics instruction and mathematicians to ensure specific criteria are covered in-depth in adopted curriculums. • Integrate computation with problem solving and pictorial representations • Stress reasoning underlying calculation methods • Build algorithmic proficiency • Contain frequent review of mathematical principles • Contain assessments to appropriately place students in the program**Suggestions**• Ensure that intervention materials are systematic and explicit and include numerous models of easy and difficult problems with accompanying teacher think-alouds. • Provide students with opportunities to solve problems in a group and communicate problem- solving strategies. • Ensure that instructional materials include cumulative review in each session. • May need to supplement curriculum with more modeling, think-alouds, practice and cumulative review.**Can you support this?**“Explicit instruction with students who have mathematical difficulties has shown consistently positive effects on performance with word problems and computations. Results are consistent for students with learning disabilities, as well as other student who perform in the lowest third of a typical class.” National Mathematics Advisory Panel Final Report p. xxiii**Talk to a neighbor**What was something that you already knew? What was something new? What is your district’s next step on this recommendation? Consensus? Infrastructure? Implementation? Are there questions you still have?**Recommendation 4**Interventions should include instruction on solving word problems that is based on common underlying structures. Evidence: Strong**Suggestions**• Teach students about the structure of various problem types, how to categorize problems, and how to determine appropriate solutions. • Math curriculum material might not classify the problems in the lessons into problem types, so in-district math experts may need to do this • Teach students to recognize the common underlying structure between familiar and unfamiliar problems and to transfer known solution methods from familiar to unfamiliar problems.**Schema-based Strategy Instruction (Jitendra, 2004)**• Teach students to represent quantitative relationships graphically to solve problems. • Use explicit strategies: • Problem Identification • Problem Representation • Problem Solution • Be systematic: Teach one type of problem at a time until students are proficient. • Provide models of proficient problem solving Kathy Jungjohann**Talk to a neighbor**What was something that you already knew? What was something new? What is your district’s next step on this recommendation? Consensus? Infrastructure? Implementation? Are there questions you still have?**Recommendation 5**Intervention materials should include opportunities for students to work with visual representations of mathematical ideas, and interventionists should be proficient in the use of visual representations of mathematical ideas. Evidence: Moderate**Suggestions**• Use visual representations such as number lines, arrays, and strip diagrams. • If necessary consider expeditious use of concrete manipulatives before visual representations. The goal should be to move toward abstract understanding. • Because many curricular materials do not include sufficient examples of visual representations, the interventionist may need the help of the mathematics coach or other teachers in developing the visuals.**Recommendation 6**Interventions at all grade levels should devote about 10 minutes in each session to building fluent retrieval of basic arithmetic facts. Evidence: Moderate**Suggestions**• Provide 10 minutes per session of instructionto build quick retrieval of basic facts. Consider the use of technology, flash cards, and other materials to support extensive practice to facilitate automatic retrieval. • For student in K-2 grade explicitly teach strategies for efficient counting to improve the retrieval of math facts. • Teach students in grades 2-8 how to use their knowledge of math properties to derive facts in their heads.**“Basic” math facts are important!**• Basic math facts knowledge • Difficulty in automatic retrieval of basic math facts impedes more advanced math operations • Fluency in math operations • Distinguishes between students with poor math skills to those with good skills (Landerl, Bevan, & Butterworth, 2004; Passolunghi & Siegel, 2004)**Can you support this?**“the general concept of automaticity. . . is that, with extended practice, specific skills can read a level of proficiency where skill execution is rapid and accurate with little or no conscious monitoring … attentional resources can be allocated to other tasks or processes, including higher-level executive or control function” (Goldman & Pellegrino, 1987)

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