Tiered Math Instruction OrRTI Project January 9, 2008

Do not worry about your problems with mathematics, I assure you mine are far greater. -Albert Einstein

Objectives Look at Universal Screening and Progress Monitoring in Mathematics Understand the major findings of the National Math Advisory Panel report and it’s implications to core curriculum Look at possible interventions to support struggling mathematicians

Expectations Turn off cell phones Limit side conversations Ask clarifying questions

The Math Caveat A lit search for studies on reading disabilities studies and math disability studies from 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

Math Protocol

Universal Screening Decision Rules –K: Students receiving only “o” and/or “/” in the “Progression of Mathematics Stages” on the Progress Report are screened using CBM. –1-2: Students receiving only “1” and/or “/” in “math” on the Progress Report are screened using CBM. –3-5: Students receiving only “1,” “2,” and/or “/” in “math” on the Progress Report AND scoring below the 30 th percentile on the OAKS, are screened using CBM. –Students who meet the above criteria are assessed using Curriculum Based Measurements (CBM: Missing Number for K/1 and Basic Facts for 2-5). Students scoring below the 25 th percentile on CBMs are placed in Second Tier Interventions.

Universal Screening The Math Measures: –K-1: Missing Number (CBM) –Grades 2-5: Basic Facts (CBM) The Decision Rule: –Students scoring at or below the 30%tile on CBMs are placed in Second Tier interventions

Missing Number - 1 One Minute assessment Individually administered

Number Identification - K One Minute assessment Individually administered

Computation – 5 Two to four Minute assessment (depending on grade) Group administered

Progress Monitoring Decision Rules CBMs are given every other week –Trained instructional assistants will complete progress monitoring Review trend lines every 12 weeks –We need a longer intervention period because: Growth on math CBMs happens in small increments

Growth trajectories for responders/non responders can be based on local and class or grade performance Or use projected rate of growth from national norms—eg AIMSweb 50 th %tile –Grade 1,.03 digit per week growth –Grade 3,.04 digit per week growth –Grade 5,.07 digit per week growth

Math Screening & Monitoring National Center on Student Progress Monitoring ( Intervention Central’s Math Worksheet Generator ( AIMSweb ( Monitoring Basic Skills Progress (Fuchs, Hamlet & Fuchs, 1998) The ABC’s of CBM (Hosp, Hosp,& Howell, 2007) DIBELS Math (2 nd year Beta) Easy CBM

Point of Discussion “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, p. 145 as quoted in Journal of Learning Disabilities, “Early Identification of Students with Math Disabilities,” July/August 2005 p 294

Core Program National Mathematics Advisory Panel Final Report, 2008 Curricular Content moving toward algebra Fluency and Automaticity Conceptual Understanding Teacher Proficiency Problem Solving

Curricular Content Depth Breadth Focus + Coherence =

Linear proficiency vs. Spiraling (Closure after Exposure)

Learning Processes Conceptual understanding, computational fluency and problem-solving skills are each essential and mutually reinforcing. Effort-based learning has greater impact than the notion of inherent ability The notion of “developmentally appropriate practices” based on age or grade level has consistently been proven to be wrong. Instead, learning is contingent on prior opportunities to learn.

Core curriculum content Whole number: understand place value, compose/decompose numbers, leaning of operations, algorithms and automaticity with facts, apply to problem solving, use/knowledge of commutative, associative, and distributive properties, Rational number: locate +/- fractions on number line, represent/compare fractions, decimals percents, sums, differences products and quotients of fractions are fractions, understand relationship between fractions, decimals, and percents, understand fractions as rates, proportionality, and probability, computational facility Critical aspects of geometry and measurement: similar triangles, slope of straight line/linear functions, analyze properties of two and three dimensional shapes and determine perimeter, area, volume, and surface area Lack of number sense is a serious problem because it interferes with algorithms and facts and prevents use of strategies to verify if solutions are reasonable. Computational fluency is critical; dependent on automatic recall and requires fluency with standard algorithms and properties. Difficulty with fractions is pervasive and impedes further progress in mathematics Source: Ben Clarke & Scott Baker Pacific Institutes for Research

Professional Development Teacher induction programs have positive effects on all teachers. Professional development is important- continue to build content knowledge as well as learning strategies. Teachers who know the math content they are teaching, including the content before and beyond, have the most impact on student achievement.

Practices That Work Using formative assessments Low achievers need explicit instruction in addition to daily core instruction Technology supports drill practice and automaticity Gifted students should accelerate and receive enrichment

Instructional Materials  Reduce breadth  Increase depth  Reduce errors  Increased agreements on topic and content taught at specific grade levels

So What? Now What? What information coincided with your understanding of effective math instruction, or practices in your district? What surprised you? What implications does the report have for this school year? Future years?

Tier I minutes core instruction K-12 curriculum alignment Systematic instruction and feedback Teach content to mastery Focus on fractions!

Mindset Incorporate social and intellectual support from peers and teachers Teach students that effort has a huge impact on math achievement

Math Instruction: Research Foundation Focused, coherent progression of curriculum leading to proficiency in algebraic skills Proficiency: –Automaticity: Recall of Facts –Fluency with +, -, x, -/- –Properties: Commutative, Distributive, Associative Content: –Whole #s –FRACTIONS –Geometry –Measurement Skills: –Conceptual –Fluency –Problem Solving

What about interventions? Emphasis on research-based instructional strategies (not “programs”) Increase opportunities to practice a skill correctly –Guided practice (“I do, We do, You do”) –Correction routine

Tier II Interventions for Math (Within the Core) Kindergarten –Increased teacher attention during math Grades 1-5 –10 minutes of additional guided practice per day OR –10 minutes of Computer Assisted Instruction (CAI) per day

Tier II & III: Research on Best Practices Baker, Gersten, and Lee, 2002 Demonstrated, significant effects for: –Progress monitoring feedback, especially when accompanied by instructional recommendations –Peer Assisted Learning –Explicit teacher led and contextualized teacher facilitated approaches –Concrete feedback to Parents

Math Interventions Formative Assessment + Problem Solving Tutoring Increase Guided Practice Up to 20 minutes Tier II 30 minutes Tier III

Strong Evidence of Effectiveness Slavin, 2007 Classwide Peer Tutoring Missouri Mathematics Program Peer Assisted Learning Strategies Student Teams-Achievement Divisions Team-Accelerated Instruction

Strong Evidence of Effectiveness Slavin, 2007 Classwide Peer Tutoring (IP) –Program: Paired learning approach, students take turns as teacher and learner –Grade levels: K-12 –Content focus: any –Logistics: model expected behaviors, pair students –Appropriate for: Tier II –Contact: Charles Greenwood at

Strong Evidence of Effectiveness Slavin, 2007 Missouri Mathematics Program (IP) –Program: Focused on active teaching, classroom management, motivation –Grade levels: Elementary and Middle School –Content focus: All –Appropriate for: Tier II –Contact: Thomas Good at

Strong Evidence of Effectiveness Slavin, 2007 Peer Assisted Learning Strategies (PALS; IP) –Students work in pairs with teacher guidance –Grade levels: K-6 –Content focus: Basic skills –Logistics: Teachers trains students in strategy; provides folders and worksheets; supplemental, 30 min. 2-3X/week –Appropriate for: Tier II –Contact:

Strong Evidence of Effectiveness Slavin, 2007 Student Teams-Achievement Divisions (STAD; IP) –Structured cooperative learning approach –Grade levels: 2-12 –Content focus: All –Logistics: Teacher presentation  Students study in heterogeneous teams  Students take quiz  individual quiz scores are summed  teams are rewarded. One cycle takes 3 to 5 classes Appropriate for: Tier II –Contact: Nancy Madden at

Strong Evidence of Effectiveness Slavin, 2007 Team-Accelerated Instruction (TAI) (IP, CAI) –Combines cooperative learning and individualized instruction; allows children to progress on an individual basis; teaches cooperation. –Grade levels: 3 to 6; older students not ready for algebra –Content focus: All –Logistics: Heterogeneous groups of students, individually assigned content, assess each other’s work, provide feedback. Group rewards on their mutual efforts. –Appropriate for: Tier II –Contact: Brent Farmer, Charlesbridge Publishing

Moderate Evidence of Effectiveness Slavin, 2007 Classworks (CAI): advantage.com Cognitively Guided Instruction (S): dg.org Connecting Math Concepts (S/C): Consistency Management-Cooperative Discipline (S): Jerome Freiberg, Project SEED (S): Small-Group Tutoring (S): Lynn Fuchs,

Point of Discussion “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