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 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

Math Protocol

Universal ScreeningDecision 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 30th 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 25th 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 50th %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

(www.studentprogress.org)• Intervention Central’s Math Worksheet Generator

(www.interventioncentral.com)• AIMSweb

(www.aimsweb.com) • Monitoring Basic Skills Progress

(Fuchs, Hamlet & Fuchs, 1998) • The ABC’s of CBM (Hosp, Hosp,& Howell, 2007)• DIBELS Math (2nd 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 BreadthFocus + Coherence =

Linear proficiencyvs.

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

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 breadthIncrease depthReduce errorsIncreased 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

• 45-90 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

Moderate Evidence of Effectiveness Slavin, 2007

• Classworks (CAI): www.curriculum advantage.com• Cognitively Guided Instruction (S):

lindalevi@teachers dg.org• Connecting Math Concepts (S/C):

www.sraonline.com/math• Consistency Management-Cooperative Discipline

(S): Jerome Freiberg, cmcd@uh.edu• Project SEED (S): www.projectseed.org• Small-Group Tutoring (S): Lynn Fuchs,

lynn.fuchs@vanderbilt.edu

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