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Welcome. Scientifically Based Math Interventions June 16, 2009 Alabama SPDG Ms. Abbie Felder, Director Curtis Gage, Education Specialist Alabama Department of Education. Georgia SPDG Dr. Julia Causey, Director Georgia Department of Education Dr. Paul Riccomini

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slide2

Scientifically Based Math Interventions

June 16, 2009

Alabama SPDG

Ms. Abbie Felder, Director

Curtis Gage, Education Specialist

Alabama Department of Education

slide3

Georgia SPDG

Dr. Julia Causey, Director

Georgia Department of Education

Dr. Paul Riccomini

National Dropout Prevention Center for Students with Disabilities

Clemson University

slide4

Drs. Judy and Howard Schrag

Third Party Evaluators

Alabama and Georgia

slide5

Our

Agenda

slide6

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
slide8

Let’s examine the evidence:

SBR Math Interventions

presidential executive order april 2006
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.

10

basis of the panel s work
Basis of the Panel’s 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

11

slide12

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.

12

curricular content
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 content14
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 content15
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

15

learning processes
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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slide18

Learning Processes

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

18

instructional practices
Instructional Practices

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

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

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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.

20

for more information
For More Information

Please visit us online at:

http://www.ed.gov/MathPanel

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slide22

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
slide23

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.
slide24

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.
slide27

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.

slide29

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 2008-2009—including 11 new schools.
  • 170 teachers participated in 2007-08, and 281 participated during 2008-2009—including 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.
slide30

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.
slide31

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.
slide32

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.
slide33

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.
slide34

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.
slide35

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).
slide36

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.
slide37

II. Outcome Evaluation

Student Math Achievement Scores on State Testing – Statewide

Longitudinal Assessment of Participating Students with Disabilities

third grade computational fluency
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%.
third grade computational fluency special education students
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%.
fourth grade computational fluency
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%.
fourth grade computational fluency special education students
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%.
fifth grade computational fluency
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%.
fifth grade computational fluency special education students
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%.
sixth grade computational fluency
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%.
sixth grade computational fluency special education students
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%.
seventh grade computational fluency
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%.
seventh grade computational fluency special education students
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%.
eighth grade computational fluency
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%.
eighth grade computational fluency special education students
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%.
slide62

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.

slide63

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.
slide64

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 student’s mastery of foundational math skills.
  • Ongoing assessment to inform instruction and measure student progress
slide69

II. Outcome Evaluation

Student Math Achievement Scores on State Testing – Statewide

Longitudinal Assessment of Participating Students

slide70

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.
math in georgia
Math in Georgia
  • SPDG Context
    • Georgia Performance Standards rollout
    • Dropout Prevention/Graduation Project
georgia performance standards math
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)
georgia spdg goals
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

georgia s spdg
Georgia’s 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
georgia spdg
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
collaboration coaches duties
Collaboration Coaches’ Duties

Attend to Essential Implementation Tasks

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essential tasks to facilitate in school implementation
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

essential tasks to facilitate in school implementation83
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

essential tasks to facilitate in school implementation84
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

schools implementing srb math
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
cohort 1 baseline data
Cohort 1 Baseline Data
  • Georgia High School Graduation Test
    • Percent Passing Math
      • 5-20 % = 6 High Schools
      • 25-40% = 5 High Schools
      • > 40 % = 2 High Schools
  • Georgia Criterion Referenced Competency Test
    • Percent Passing Math
      • < 20% = 1 Middle School
      • 25-40% = 10 Middle Schools
      • > 40% = 7 Middle Schools
expanding the training
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
slide88

Components of Effective Mathematics Programs

Mathematics Curriculum & Interventions

Assessment & Data-Based Decisions

100% Math Proficiency

Teacher Content & Instructional Knowledge

slide89

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 teachers—what they know and do –that makes them more effective.
    • National Mathematics Advisory Panel (2008)

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basis for math instruction
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

specific instructional strategies
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

specific areas targeted
Specific Areas Targeted

Computational Fluency

Conceptual Development

Basic Fact Automaticity

Problem Solving & Application

Essential Vocabulary

Student Success

slide93

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)

93

formative data
Formative Data
  • Formative Data
    • Individualized based on each school’s 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
summative data
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)
summative math data
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
formative data98
Formative Data
  • Specific to each school’s 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
formative data examples
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
formative results examples
Formative Results Examples

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

  • Cook County Middle School: ASCEND Math Lab
formative data examples101
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 >50% of students with matched scores from January to March improved
coffee county examining teacher practices
Coffee County: Examining Teacher Practices
  • Pilot Survey of 6th Grade Teachers
    • Use of 12 targeted strategies from Riccomini’s training on differentiating in math
    • Six teachers participated in the survey
    • Twelve strategies/methods from the training were identified on the survey
instruction methods strategies on survey
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
2009 statewide crct results
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

students with disabilities
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
students with disabilities108
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
lessons learned next steps
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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