Tiered Math Instruction

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Tiered Math Instruction

• OrRTI Project
• January 9, 2008

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

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Objectives

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

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Expectations

• Turn off cell phones
• Limit side conversations
• Ask clarifying questions

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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 (121)
• Specific RTI mathematics studies for a recent
  annotated bibliography totaled 9 studies

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Math Protocol
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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 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.

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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 30tile on CBMs
  are placed in Second Tier interventions

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Missing Number - 1

• One Minute assessment
• Individually administered

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Number Identification - K

• One Minute assessment
• Individually administered

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Computation 5

• Two to four Minute assessment (depending on
  grade)
• Group administered

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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

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

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Math Screening Monitoring

• National Center on Student Progress Monitoring
  (www.studentprogress.org)
• Intervention Centrals Math Worksheet Generator
• (www.interventioncentral.com)
• AIMSweb
• (www.aimsweb.com)
• Monitoring Basic Skills Progress
• (Fuchs, Hamlet Fuchs, 1998)
• The ABCs of CBM (Hosp, Hosp, Howell, 2007)
• DIBELS Math (2nd year Beta)
• Easy CBM

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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

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Core Program

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

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Curricular Content

• Depth Breadth

Focus Coherence
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Linear proficiencyvs. Spiraling(Closure after
Exposure)
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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.

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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
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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.

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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

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Instructional Materials

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

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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?

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Tier I

• 45-90 minutes core instruction
• K-12 curriculum alignment
• Systematic instruction and feedback
• Teach content to mastery
• Focus on fractions!

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Mindset

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

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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

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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

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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

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Tier II IIIResearch 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

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Math Interventions

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

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Strong Evidence of Effectiveness Slavin, 2007

• Classwide Peer Tutoring
• Missouri Mathematics Program
• Peer Assisted Learning Strategies
• Student Teams-Achievement Divisions
• Team-Accelerated Instruction

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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 greenwood_at_ku.edu

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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 good_at_u.arizona.edu

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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 www.kc.vanderbilt.edu/pals

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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 nmadden_at_jhu.edu

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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
  others work, provide feedback. Group rewards on
  their mutual efforts.
• Appropriate for Tier II
• Contact Brent Farmer, Charlesbridge Publishing

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Moderate Evidence of Effectiveness Slavin, 2007

• Classworks (CAI) www.curriculum advantage.com
• Cognitively Guided Instruction (S)
  lindalevi_at_teachers dg.org
• Connecting Math Concepts (S/C)
  www.sraonline.com/math
• Consistency Management-Cooperative Discipline
  (S) Jerome Freiberg, cmcd_at_uh.edu
• Project SEED (S) www.projectseed.org
• Small-Group Tutoring (S) Lynn Fuchs,
  lynn.fuchs_at_vanderbilt.edu

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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