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 National Dropout Prevention Center for Students with Disabilities Clemson University
Drs. Judy and Howard Schrag Third Party Evaluators Alabama and Georgia
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
Let’s examine the evidence: SBR Math Interventions
Foundations for SuccessNational Mathematics Advisory Panel Final Report, March 2008
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 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
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 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 13
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. 14
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 • 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. 16
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. 17
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 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. 19
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 Please visit us online at: http://www.ed.gov/MathPanel 21
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
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.
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.
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.
MATH INITIATIVE 2008-2009 Alabama State Department
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.
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.
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.
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.
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.
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.
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).
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.
II. Outcome Evaluation Student Math Achievement Scores on State Testing – Statewide Longitudinal Assessment of Participating Students with Disabilities
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 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 • 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 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 • 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 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 • 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%.