Scientifically Based Math Interventions

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Welcome
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Scientifically Based Math Interventions June 16,
2009 Alabama SPDG Ms. Abbie Felder,
Director Curtis Gage, Education
Specialist Alabama Department of Education
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Georgia SPDG Dr. Julia Causey, Director Georgia
Department of Education Dr. Paul Riccomini
National Dropout Prevention Center for Students
with Disabilities Clemson University
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Drs. Judy and Howard Schrag
Third Party Evaluators Alabama
and Georgia
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Our Agenda
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• What does the research say?
• Overview - Alabama SBR Math Interventions
• Evaluation of Alabama SBR Math Interventions
• Overview Georgia SBR Math Interventions
• Evaluation of Georgia SBR Math Interventions
• Summary
• Open Discussion

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Ok - Let's begin
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Lets examine the evidence
SBR Math Interventions
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Foundations for SuccessNational Mathematics
Advisory Panel

• Final Report, March 2008

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Presidential Executive OrderApril 2006

• The Panel will advise the President and the
  Secretary of Education on the best use of
  scientifically based research to advance the
  teaching and learning of mathematics, with a
  specific focus on preparation for and success in
  algebra.

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Basis of the Panels work

• Review of 16,000 research studies and related
  documents.
• Public testimony gathered from 110 individuals.
• Review of written commentary from 160
  organizations and individuals
• 12 public meetings held around the country
• Analysis of survey results from 743 Algebra I
  teachers

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Two Major Themes

• First Things First
• - Positive results can be achieved in a
  reasonable time at accessible cost by addressing
  clearly important things now.
• - A consistent, wise, community-wide effort
  will be required.

Learning as We Go Along - In some areas,
adequate research does not exist. - The
community will learn more later on the
basis of carefully evaluated practice and
research. - We should follow a disciplined model
of continuous improvement.
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Curricular Content

• Streamline the Mathematics Curriculum in Grades
  PreK-8

• Follow a Coherent Progression, with Emphasis on
  Mastery of Key Topics
• Focus on the Critical Foundations for Algebra
• - Proficiency with Whole Numbers
• - Proficiency with Fractions
• Particular Aspects of Geometry and Measurement
• Avoid Any Approach that Continually Revisits
  Topics without Closure

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Curricular Content

• An Authentic Algebra Course
• All school districts
• Should ensure that all prepared students have
  access to an authentic algebra course, and
• Should prepare more students than at present to
  enroll in such a course by Grade 8.

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Curricular Content

• What Mathematics Do Teachers Need to Know?
• For early childhood teachers
• Topics on whole numbers, fractions, and the
  appropriate geometry and measurement topics in
  the Critical Foundations of Algebra
• For elementary teachers
• All topics in the Critical Foundations of Algebra
  and those topics typically covered in an
  introductory Algebra course
• For middle school teachers
• - The Critical Foundations of Algebra
• - All of the Major Topics of School Algebra

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Learning Processes

• Scientific Knowledge on Learning and Cognition
  Needs to be Applied to the Classroom to Improve
  Student Achievement
• Most children develop considerable knowledge of
  mathematics before they begin kindergarten.
• Children from families with low incomes, low
  levels of parental education, and single parents
  often have less mathematical knowledge when they
  begin school than do children from more
  advantaged backgrounds. This tends to hinder
  their learning for years to come.
• There are promising interventions to improve the
  mathematical knowledge of these young children
  before they enter kindergarten.

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Learning Processes

• To prepare students for Algebra, the curriculum
  must simultaneously develop conceptual
  understanding, computational fluency, factual
  knowledge and problem solving skills.

• Limitations in the ability to keep many things in
  mind (working-memory) can hinder mathematics
  performance.
• Practice can offset this through automatic
  recall, which results in less information to keep
  in mind and frees attention for new aspects of
  material at hand.
• Learning is most effective when practice is
  combined with instruction on related concepts.
• Conceptual understanding promotes transfer of
  learning to new problems and better long-term
  retention.

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Learning Processes

• Childrens goals and beliefs about learning are
  related to their mathematics performance.
• Childrens beliefs about the relative importance
  of effort and ability can be changed.
• Experiential studies have demonstrated that
  changing childrens beliefs from a focus on
  ability to a focus on effort increases their
  engagement in mathematics learning, which in turn
  improves mathematics outcomes.

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Instructional Practices
Instructional practice should be informed by high
quality research, when available, and by the best
professional judgment and experience of
accomplished classroom teachers.

• All-encompassing recommendations that instruction
  should be student-centered or teacher-directed
  are not supported by research.

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Instructional Practices

• Research on students who are low achievers, have
  difficulties in mathematics, or have learning
  disabilities related to mathematics tells us that
  the effective practice includes
• Explicit methods of instruction available on a
  regular basis
• Clear problem solving models
• Carefully orchestrated examples/ sequences of
  examples.
• Concrete objects to understand abstract
  representations and notation.
• Participatory thinking aloud by students and
  teachers.

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For More Information

• Please visit us online at
• http//www.ed.gov/MathPanel

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Mathematical Proficiency Defined

• National Research Council (2002) defines
  proficiency as
• Understanding mathematics
• Computing Fluently
• Applying concepts to solve problems
• Reasoning logically
• Engaging and communicating with mathematics

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• Grous and Ceulla (2000) reported the following
  can increase student learning and have a positive
  effect on student achievement
• Increasing the extent of the students
  opportunity to learn (OTL) mathematics content.
• Focusing instruction on the meaningful
  development of important mathematical ideas.
• Providing learning opportunities for both
  concepts and skills by solving problems.   
• Giving students both an opportunity to discover
  and invent new knowledge and an opportunity to
  practice what they have learned.
• Incorporating intuitive solution methods,
  especially when combined with opportunities for
  student interaction and discussion.

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• Using small groups of students to work on
  activities, problems, and assignments (e.g.,
  small groups, Davidson, 1985 cooperative
  learning, Slavin, 1990 peer assisted learning
  and tutoring, Baker, et al., 2002).
• Whole-class discussion following individual and
  group work.
• Teaching math with a focus on number sense that
  encourages students to become problem solvers in
  a wide variety of situations and to view math as
  important for thinking.
• Use of concrete materials on a long-term basis
  to increase achievement and improve attitudes
  toward math.

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Let's turn to Alabama and Georgia
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Alabama SBR Math SPDG-Supported Activities
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GOAL 1 Through the implementation of SBR
instructional strategies within the framework,
there will be a 20 percent reduction in the
achievement gap between students with and without
disabilities in the area of math and age
appropriate progress in pre-literacy/reading and
math.
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Alabama State Department

• MATH INITIATIVE
• 2008-2009

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Overview

• 12 school districts participated in 2007-2008.
  An additional 4 school districts participated in
  2008-2009 (16 total).
• 31 schools participated in 2007-08, and 42
  schools participated in 2008-2009including 11
  new schools.
• 170 teachers participated in 2007-08, and 281
  participated during 2008-2009including 68 new
  teachers.
• Over 7700 students were entered into VPORT,
  with 4,659 students having two data points in at
  least one Vmath assessment so far in the
  2008-2009 school year.
• Of those with two data points, 838 were
  indicated as special education students.

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• Voyager Expanded Learning Math Intervention
  Program
• A targeted, systematic program that provided
  students more opportunity and support to learn
  mathematics.
• Vmath is informed by Curriculum-Based
  Measurement and provides daily, direct,
  systematic instruction in essential skills needed
  to reduce achievement gaps and accelerate
  struggling math students to reach and maintain
  grade-level performance.
• V-math is designed to complement all major math
  programs by providing an additional 30-40 minutes
  of daily, targeted concept, skill, and
  problem-solving development.

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• Each level of Vmath contains 10 individual
  modules covering the basic strands of elementary
  mathematics.
• The content of these modules is aligned with
  grade-level expectations for the NCTM Content
  Standards.

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• 5 Keys to Successful VMath Implementation
• Amount of Instruction
• 5 days per week 40 minutes per day
• One lesson per day (some lessons will be l l/2 to
  2 days, if time is less than 40 minutes or
  students need extra time).
• Start within 4 weeks of school start data.
• Use of Assessments
• Initial Assessment prior to instruction at the
  beginning of the year
• Computational Fluency Benchmark Assessments 3
  times per year.
• Computational Fluency Progress Monitoring
  Assessments mid-module.

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• Pre-Tests and Post Tests Beginning and end of
  each module.
• Final Assessment after instruction at the end
  of the year.
• Quality of Instruction
• 3 hours of initial training on using scripted
  dialogue to scaffold instruction implementing
  small-group instruction, administering
  assessments, using VmathLive, and using VPORT.
• Principal/Coach reviews teacher instruction,
  teacher completes self-analysis.

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• Differentiation
• Small group instruction
• Use Initial Assessments and PRE-Tests to
  identify strengths and weaknesses in math
  content.
• Differentiate instruction using VmathLive.
• Classroom Management
• Small group area identified Vmath scheduled.
• Overhead projector Smartboard or teacher
  computer with projector available to teach
  lessons.
• Web-accessible computers for VmathLive
  designated.

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• Evaluation of VMath
• I. Process Evaluation
• 1. Classroom visitations to gather on-going
  implementation data during Year 2 of the SPDG.
• 88 of the Classrooms implemented VMath 5 days
  a week (12 - Not Available)
• Number of minutes per day of VMath 30
  minutes 59 37.5 4 45 minutes 18 less
  than 45 minutes 8 (11 - Not Available)
• Group size 1-6 65 7-12 14 13 7
  (Not Available 13)
• Delivery Approach 55 - In-class 21 -
  Pull-Out Specialist pull/push 13 (11 - Not
  Available).

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• Progress Monitoring
• Initial Assessment prior to instruction at the
  beginning of the year
• Computational Fluency Benchmark Assessments 3
  times per year.
• Computational Fluency Progress Monitoring
  Assessments mid-module.
• Pre-Tests and Post Tests Beginning and end of
  each module.
• Final Assessment after instruction at the end
  of the year.

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II. Outcome Evaluation Student Math Achievement
Scores on State Testing Statewide Longitudinal
Assessment of Participating Students with
Disabilities
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Third Grade Computational Fluency

• On average, Third Grade students increased their
  Computational Fluency scores from 18.9 to 51.7.
• The percent of students needing intensive focus
  on computational fluency decreased from 92 to
  44.

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Third Grade Modules
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Third Grade Computational FluencySpecial
Education Students

• On average, Third Grade students increased their
  Computational Fluency scores from 15.7 to 37.7.
• The percent of students needing intensive focus
  on computational fluency decreased from 96 to
  72.

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Third Grade ModulesSpecial Education Students
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Fourth Grade Computational Fluency

• On average, Fourth Grade students increased
  their Computational Fluency scores from 37.5 to
  56.4.
• The percent of students needing intensive focus
  on computational fluency decreased from 35 to
  19.

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Fourth Grade Modules
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Fourth Grade Computational FluencySpecial
Education Students

• On average, Fourth Grade students increased
  their Computational Fluency scores from 25.6 to
  40.2.
• The percent of students needing intensive focus
  on computational fluency decreased from 62 to
  51.

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Fourth Grade ModulesSpecial Education Students
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Fifth Grade Computational Fluency

• On average, Fifth Grade students have increased
  their Computational Fluency scores from 31.9 to
  37.9.
• The percent of students needing intensive focus
  on computational fluency increased from 3 to 6.

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Fifth Grade Modules
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Fifth Grade Computational FluencySpecial
Education Students

• On average, Fifth Grade students increased their
  Computational Fluency scores from 29.5 to 35.6.
• The percent of students needing intensive focus
  on computational fluency increased from 5 to 12.

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Fifth Grade ModulesSpecial Education Students
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Sixth Grade Computational Fluency

• On average, Sixth Grade students increased their
  Computational Fluency scores from 41.5 to 51.5.
• The percent of students needing intensive focus
  on computational fluency decreased from 23 to
  16.

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Sixth Grade Modules
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Sixth Grade Computational FluencySpecial
Education Students

• On average, Sixth Grade students increased their
  Computational Fluency scores from 39.2 to 42.6.
• The percent of students needing intensive focus
  on computational fluency increased from 31 to
  34.

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Sixth Grade ModulesSpecial Education Students
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Seventh Grade Computational Fluency

• On average, Seventh Grade students increased
  their Computational Fluency scores from 33.3 to
  47.
• The percent of students needing intensive focus
  on computational fluency decreased from 65 to
  47.

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Seventh Grade Modules
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Seventh Grade Computational FluencySpecial
Education Students

• On average, Seventh Grade students increased
  their Computational Fluency scores from 34.1 to
  46.8.
• The percent of students needing intensive focus
  on computational fluency decreased from 57 to
  48.

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Seventh Grade ModulesSpecial Education Students
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Eighth Grade Computational Fluency

• On average, Eighth Grade students increased
  their Computational Fluency scores from 28.8 to
  35.4.
• The percent of students needing intensive focus
  on computational fluency decreased from 11 to 7.

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Eighth Grade Modules
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Eighth Grade Computational FluencySpecial
Education Students

• On average, Eighth Grade students increased
  their Computational Fluency scores from 28.8 to
  35.4.
• The percent of students needing intensive focus
  on computational fluency decreased from 20 to
  14.

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Eighth Grade ModulesSpecial Education Students
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Transitional Math Four school improvement
schools were selected during Year 2 for
implementation of Transitional Math One
high school in Butler County - Greenville
One high school in Elmore County - Stanhope
Two high schools in Montgomery County Jefferson
Davis and Robert E. Lee The four
participating schools received eight days of
technical assistance a month from two consultants
from SOPRIS West.
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• Transitional Mathematics is designed to help
  students understand operations on whole numbers
  conceptually and addresses the needs of
  struggling students who have scored at or below
  the 40th percentile on national math tests.
• Transitional Mathematics is based on three broad
  design principals
• Ensuring that students have relevant background
  knowledge.
• Using a balanced approach in computational
  practice.
• Addressing the need for careful time management.

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• I. Process Evaluation
• The Transitional Math program uses curriculum
  based student progress monitoring, which services
  as a fidelity tool. In August 2009, the
  TransMath Online Assessment System will be
  launched as
• Individualized student placement based on
  students mastery of foundational math skills.
• Ongoing assessment to inform instruction and
  measure student progress

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Jefferson Davis High School Comparison Comparison
(Dec/May)
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Greenville High School Comparison Comparison
(Dec/May)
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Robert E. Lee High School Comparison Comparison
(Dec/May)
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II. Outcome Evaluation Student Math Achievement
Scores on State Testing Statewide Longitudinal
Assessment of Participating Students
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Lessons Learned/Next Steps

• The value of teacher coaching/support to ensure
  fidelity of instruction and data gathering.
• The importance of providing data driven
  instruction based on individual student needs.

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Georgia SBI Math SPDG-Supported Activities
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Math in Georgia

• SPDG Context
• Georgia Performance Standards rollout
• Dropout Prevention/Graduation Project

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Georgia Performance Standards Math

• Georgia Performance Standards
• Integrated math curriculum algebra, geometry,
  statistics
• Aligns with recommendations from the National
  Math Panel
• New Math Standards
• Phase-in statewide 2005-2011
• Grade 6 in 2005 --K-2 and 7
  in 2006
• Grades 3-5 and 8 in 2007 --Grade 9 began last
  year
• Full implementation 2011
• Intensive statewide training for all math
  teachers
• standards-based math instruction
• Implementation of the Student Achievement Pyramid
  of Interventions (RTI)

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Georgia SPDG Goals

• Improve reading and math achievement
• Increase the number of students with disabilities
  who graduate with a general education diploma
• Decrease the number of students with disabilities
  ho dropout
• Improve Postsecondary outcomes
• Increase recruitment of fully certified special
  education teachers
• Increase parent support of pre-literacy, math,
  and social skills development for young children
  with disabilities
• Embed parent engagement within each goal

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Georgias SPDG

• Focus is dropout prevention and increasing the
  graduation rate for students with disabilities
• Partnering with the National Dropout Prevention
  Center for Students with Disabilities
• Year 1 Data Analysis and Individualized Plans
• Year 2 Training and Implementation

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Georgia SPDG

• Cohort 1 (2007-2009)
• 34 schools (15 HS, 18 MS)
• High School with one or two feeder middle schools
• Geographically distributed throughout the state
• Content
• Research-based dropout prevention strategies
• Partnership with the National Dropout Prevention
  Center for Students with Disabilities

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Project Strands
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Project Strands
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Collaboration Coaches Duties
Attend to Essential Implementation Tasks
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Essential Tasks to Facilitate In-school
Implementation

• Identify team members for the school
• Participate in overview training
• Participate in data training
• Collect and analyze data

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Essential Tasks to Facilitate In-school
Implementation

• Examine causes and prioritize needs based on
  school and system data
• Participate in overview of effective practices
  that increase student engagement and school
  completion
• Select intervention framework that best matches
  prioritized need
• Develop a reasonable action plan

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Essential Tasks to Facilitate In-school
Implementation

• Provide training for appropriate school staff on
  the selected intervention
• Develop a timetable for coaching and feedback to
  ensure fidelity of implementation
• Establish checkpoints to evaluate implementation
  of intervention
• Communicate results of implementation

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Schools Implementing SRB Math

• Improving math achievement priority 10 schools
• Lewis Frazier Middle School
• Midway Middle School
• Henry High School
• Henry Middle School
• Rutland Middle School
• Coffee High School
• Coffee Middle School
• Cook Middle School
• Manchester Middle School

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Cohort 1 Baseline Data

• Georgia High School Graduation Test
• Percent Passing Math
• 5-20 6 High Schools
• 25-40 5 High Schools
• gt 40 2 High Schools
• Georgia Criterion Referenced Competency Test
• Percent Passing Math
• lt 20 1 Middle School
• 25-40 10 Middle Schools
• gt 40 7 Middle Schools

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Expanding the Training

• Ten targeted schools math teachers and
  collaboration coaches trained
• Demand spread beyond SPDG schools
• Expanded training beyond SPDG schools
• Open to any school stateside
• Trained several hundred math teachers on
  strategies for teaching students struggling in
  math
• Follow-up webinars for interested participants
• 2010-2011 school year Follow-training will be
  offered to participants from last school year

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Components of Effective Mathematics Programs
Mathematics Curriculum Interventions
Assessment Data-Based Decisions
100 Math Proficiency
Teacher Content Instructional Knowledge
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Teachers and Teacher Education

• Mathematically Knowledgeable Classroom Teachers
  Have a Central Role in Mathematics Education.
• Evidence shows that a substantial part of the
  variability in student achievement gains is due
  to the teacher.
• Less clear from the evidence is exactly what it
  is about particular teacherswhat they know and
  do that makes them more effective.
• National Mathematics Advisory Panel (2008)

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Basis for Math Instruction

• Engaged Time
• Student Success Rate
• Content Coverage Opportunity to Learn
• Grouping for Instruction
• Scaffolded Instruction
• Addressing Forms of Knowledge
• Activating Organizing Knowledge
• Teaching Strategically
• Making Instruction Explicit
• Making Connections

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Specific Instructional Strategies

• Space learning over time
• Interleave worked example solutions and
  problem-solving exercises
• Connect and integrate abstract and concrete
  representations of concepts
• Use quizzes to re-expose students to information

IES Practice Guide (2007). Organizing
Instructional and Study to Improve Student
Learning
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Specific Areas Targeted

• Computational Fluency
• Conceptual Development
• Basic Fact Automaticity
• Problem Solving Application
• Essential Vocabulary
• Student Success

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Instructional Practices

• Research on students who are low achievers, have
  difficulties in mathematics, or have learning
  disabilities related to mathematics tells us that
  the effective practice includes
• Explicit methods of instruction available on a
  regular basis
• Clear problem solving models
• Carefully orchestrated examples/ sequences of
  examples.
• Concrete objects to understand abstract
  representations and notation.
• Participatory thinking aloud by students and
  teachers.

National Mathematics Advisory Panel (2008)
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Evaluation of SBR Initiatives
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Formative Data

• Formative Data
• Individualized based on each schools focus
  priority
• Used to guide implementation of the action plan
• Collected for targeted at-risk student group
• Discipline Referrals
• Reading Achievement
• Math Achievement
• Social Studies Achievement
• Science Achievement
• Attendance
• English/Language Arts
• Discipline Referrals

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Summative Data

• All Cohort 1 Schools
• Graduation Rate for Students with Disabilities
  and All Students (Collected Oct. 09)
• Dropout Rates for Students with Disabilities and
  All Students (Collected Oct. 09)

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Summative Math Data

• For the 10 project schools with a math focus
• CRCT Math Scores for Middle Schools
• GHSGT Math Scores for High Schools
• Scores will be available late summer

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Formative Data

• Specific to each schools plan and interventions
• Examples
• Lewis Frazier Middle School Transmath
• 18 of targeted students passed CRCT Math 2008
• 44 of the same targeted students passed CRCT
  Math 2009
• Liberty County High School Transmath
• All targeted students with pre/post test data
  improved

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Formative Data Examples

• Midway Middle School
• 59 of students with both pre/post test scores
  improved.
• Rutland Middle School SuccessMaker Math Labs
• 59 of targeted students improved math grade
  level scores, ranging from .54 to 3.07

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Formative Results Examples

• Cook County Middle School ASCEND Math Lab

• COMPUTATION
• Of the targeted group of students
• 57 were SWD
• 71 of all students progressed from the
  Frustration to Instructional or Mastery Level
• 66 of SWD progressed from the Frustration to
  Instructional or Mastery Level

• CONCEPTS/ESTIMATION
• Of the targeted group of students
• 28 were SWD
• 56 of all students progressed from the
  Frustration to Instructional or Mastery Level
• 45 of SWD progressed from the Frustration to
  Instructional or Mastery Level

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Formative Data Examples

• Coffee County Middle School
• Saturday school with math focus
• Math vocabulary and fluency
• AIMSWeb for progress monitoring 6th and 8th gr.
• Numeracy coaches
• Strategies from SPDG training
• Results for 24 sections of 6th grade math
• 79 of the sections had gt50 of students with
  matched scores from January to March improved

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Coffee County Examining Teacher Practices

• Pilot Survey of 6th Grade Teachers
• Use of 12 targeted strategies from Riccominis
  training on differentiating in math
• Six teachers participated in the survey
• Twelve strategies/methods from the training were
  identified on the survey

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Instruction Methods/Strategies on Survey

• Grouping
• Scaffolded Instruction
• General Learning Strategies (Ex. RIDE)
• Math Vocabulary
• Spaced Instructional Review (SIR)
• Interleave Worked Example

• Writing about Math
• Graphic Organizers for Math
• Mnemonic Strategy
• Fluency
• Explicit Methods of Instruction
• Memory Strategies
• Chunking Keyword

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Survey Results
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2009 Statewide CRCT Results

• 6th Grade All Students
• 75 met/exceeded the standard
• 6 percentage point increase from 2008
• 15 percentage point increase since 2006
• Exceeded state target
• 7th Grade All Students
• 84 met/exceeded the standard
• 4 percentage point increase from 2008
• 14 percentage point increase since 2006
• Exceeded state target
• 8th Grade All Students
• 70 met/exceeded the standard
• 8 percentage point increase from 2009
• Exceeded target

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Students with Disabilities

• CRCT Math Scores 08 to 09
• More than a five percentage point increase in
  math scores for grades 6, 7, and 8 for SWD

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Students with Disabilities

• Georgia High School Graduation Test
• Grade 11, first-time test takers
• 08 to 09 for SWD
• 63 met/exceeded standards
• 4 percentage point increase from 2008

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Lessons Learned/Next Steps

• Review of requirements for data collection to
  better ensure uniformity
• Importance of continuing connection with general
  education statewide math initiatives
• Selection of new cohort of schools for Year 3
• Continued follow-up for cohort 1
• other

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Open Discussion