Identifying and Assisting Elementary and Middle School Students Struggling with Mathematics The presentation will begin shortly.

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Welcome and Overview Lydotta M. Taylor, Ed.D. Research Alliance Lead, REL Appalachia The EdVenture Group

What is a REL? A REL is a Regional Educational Laboratory. There are 10 RELs across the country. The REL program is administered by the U.S. Department of Education, Institute of Education Sciences (IES). A REL serves the education needs of a designated region. The REL works in partnership with the region’s school districts, state departments of education, and others to use data and research to improve academic outcomes for students. 8

What is a REL? 9

REL Appalachia’s Mission Meet the applied research and technical assistance needs of Kentucky, Tennessee, Virginia, and West Virginia. Conduct empirical research and analysis. Bring evidence-based information to policy makers and practitioners: – Inform policy and practice – for states, districts, schools, and other stakeholders. – Focus on high-priority, discrete issues and build a body of knowledge over time. Follow 10

Introductions and Webinar Goals Lydotta M. Taylor, Ed.D. 11

Speakers Russell Gersten, Ph.D. Instructional Research Group John Woodward, Ph.D. University of Puget Sound 12

Webinar Goals Equip elementary and middle school teachers and curriculum coaches with: – IES-approved, research-based recommendations for identifying students struggling with mathematics. – Guidance on strengthening mathematics instruction and support of these students. 13

Agenda 1.What is Response to Intervention (RtI)? 2.Why use RtI in mathematics instruction? – Case for RtI and Early Intervention in Mathematics – Case for RtI in the Intermediate Grades 3.Recommendations for identifying and assisting students struggling with mathematics – Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools 4.Applying the Practice Guide in the Classroom 5.Wrap Up and Closing Remarks 14

What is Response to Intervention (RtI)? Russell Gersten, Ph.D. Director, Instructional Research Group

Tier I: Core Class Instruction Tier I is defined differently by experts. Only common feature: Universal screening of all students. Other possible components: Ongoing professional development for classroom teachers on how to use research. Differentiated instruction. High quality mathematics instruction. Scientifically based mathematics instruction. 16

Tier II: Small Group Intervention Tier II is individual or small-group intervention in addition to the time allotted for core mathematics instruction. Tier II includes curriculum, strategies, and procedures designed to supplement, enhance, and support Tier I. Can backtrack and/or elaborate/reinforce classroom curriculum. Progress monitoring of students “at-risk” on a monthly or weekly basis. 17

Updates on Current Research Since the Practice Guide 1.Some of the most effective Tier II interventions involve grade level materials (e.g., work of Lynn Fuchs and colleagues). 2.Some evidence that measures of working memory can be used to help with placement. 3.Typically, takes many data points (perhaps 10-12) to determine if a child is making sufficient progress. 18

Q & A What is Response to Intervention (RtI)?

Why Use RtI in Mathematics Instruction? Russell Gersten, Ph.D.

Case for RtI and Early Intervention in Mathematics

Predictive Power of Early Mathematics Achievement 1.Longitudinal research studies: From Kindergarten to Fifth Grade. 2.Students who enter Kindergarten low in mathematics and fail to learn much mathematics have a high likelihood of remaining weak mathematics students. 3.Mathematics in Kindergarten is a better predictor than reading of later academic outcomes. 4.Attention during Kindergarten is a solid predictor of future mathematics success or failure. Source: Morgan, P., Farkas, G., & Wu, Q. (2009) Duncan, G. J. et al. (2007) 22

Beginning of Math Proficiency: Theory 1.Attention (+) – Persistence (+) – Impulsivity (-) 2.Mental Number Line – Ability to quickly and accurately compare magnitudes  Estimation  This is a core component of number sense 3.Working memory critical as early as the end of first grade. Source: Geary et al. (2012) 23

Case for RtI in the Intermediate Grades

Why Intervention in Grades 3-5 is Important Fractions represents a new level of abstraction for students. Mathematically, this level of abstraction is critical for success in algebra. Recent longitudinal research supports this view: – By 5th grade, understanding of fractions is the best predictor of algebra success. Source: National Mathematics Advisory Panel (2008) Siegler et al. (2012) 25

Why Intervention is Important (continued) Fractions critical to success in algebra. Algebra a gateway to career success. So in many ways, FRACTIONS are the gateway in grades 3-7! 26

National Assessment of Education Progress Results Many American students are unable to solve fractions problems in middle or even high school – Example: NAEP Grade 8 in 2007 (Pass rate = 49%) In which of the following are the three fractions arranged from least to greatest? Most think that the reason for poor performance on these items is that students never understood the mathematical ideas relating to fractions. 27

Poll the NAEP What is the correct set of numbers? A B C D E 28

Q & A Why Use RtI in Mathematics Instruction?

Recommendations for Identifying and Assisting Students Struggling with Mathematics Russell Gersten, Ph.D.

Response to Intervention Practice Guide

Panelists Russell Gersten (Chair) Sybilla Bechmann Ben Clarke Anne Foegen Laurel Marsh Jon R. Star Bradley Witzel 32

Practice Guides Mandate Create a framework for establishing/refining instruction that is clear and practical. Include action-based recommendations that can be implemented in practice. Take risks: don’t equivocate! Create a coherent document: common themes should underlie the various specific suggestions. 33

Practice Guide Structure Recommendations How to carry out the recommendations Levels of evidence Potential roadblocks and suggestions 34

Evidence Rating Each recommendation receives a rating based on the strength of the research evidence. Strong Moderate Low simply means no rigorous evidence, not contradictory evidence or negative (i.e., minimal evidence)… 35

Evidence Rating RecommendationLevel of Scientific Evidence 1. Universal screening (Tier I)Moderate 2. Focus instruction on whole number for grades K-5 and rational number and whole number for grades 4-8 Low 3. Systematic, focused instructionStrong 4. Solving word problemsStrong 5. Visual representationsModerate 6. Building fluency with basic arithmetic factsModerate 7. Progress monitoring of all students receiving intervention or at risk Low 8. Use of motivational strategiesLow 36

Poll Item Which level of evidence is the biggest surprise for you? Why? 37

Setup for this Segment Target areas where evidence is most provocative Give a flavor of some of the Recommendations Set the stage for next set of presentations/panelists 38

Universal Screening and Progress Monitoring No evidence that progress monitoring (conventional) is linked to effective intervention. Some promising ideas for universal screening measures – Increased use of number line estimation and magnitude comparison. – Consideration of screeners that provide diagnostic and placement information. Source: Gersten et al. (2009) Siegler & Pyke (2013) 39

Predictive Power of Mathematics Measures Measures using a number line seem to be strongest predictors. They are better than general mathematics achievement measures. Source: Siegler & Pyke (2013) 40

Sample Grade 2 Estimation Item 41

Magnitude Comparison Requires students to name the larger of two visually presented numbers from 0 to 20 in Kindergarten and 0 to 99 in 1st grade. Administered in Kindergarten and 1st Grade Example Items - Grade 1 Prompt: “Each box has two numbers in it. Look at the numbers. I want you to tell me which number is bigger.”

What to Teach in Intervention (for Recommendation 2) Instruction includes: – Procedures – AND concepts – AND word problems There is a reciprocal relationship between understanding principles and mathematical ideas and competence with procedures. – The better you are with one aspect, the better you become with the other. – Panel urges the integration of both understanding principles and ideas with competence. Source: Riddle-Johnson & Siegler. (1998) Singapore Mathematics, Inc. (2003) 43

What to Teach Intervention content closely aligned to the Common Core BUT May need to include related material from earlier grades 44

Recommendation 3 Instruction during the intervention should be systematic and include models of proficient problem-solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review. Level of Evidence: Strong 45

What Seems Most Essential in the Supportive Research Extensive practice with feedback. Let students provide a rationale for their decisions. Instructors and fellow students model approaches to problem solving. Source: Schunk & Cox (1986) Tournaki (2003) 46

Unresolved Issues with Explicit Instruction How to support students’ talking about mathematics. How to capitalize on helping students learn from hearing peers explain their mathematical reasoning. 47

Recommendation 5 Intervention materials should include opportunities for the student to work with visual representations of mathematical ideas and interventionists should be proficient in the use of visual representations of mathematical ideas. Level of Evidence: Moderate 48

Life on the Number Line 49

Use a Visual Fraction Model 50

Sample 1: Developing an Understanding of Fractions ConcreteVisual Representation 51

Solving Similar Problems that Appear Different Difficulties encountered by some students – Extraneous information – Different wording Even though the problems have a common underlying structure. Creates problems for any student who needs intervention. Source: Fuchs et al. (2007) 52

Recommendation 2: What to Teach in Intervention Instructional materials for students receiving interventions should focus in-depth on: – Whole numbers in kindergarten through grade 6 – Rational numbers in grades 4 through 8 – Applications to geometry and measurement Level of Evidence: Minimal 53

Criteria for a Mathematics Intervention Temporarily decreases cognitive load for students. Includes cumulative review. Includes extensive practice. Students have opportunities to explain their reasoning. Use of Number Line and a small set of representations. 54

Tools Progressions for the Common Core State Standards in Mathematics (draft) By: The Common Core Standards Writing Group DRAFT 21 April Supported by the Brookhill Foundation 55

How does Common Core Fit In? How Common Core can guide intervention and assessments (interim, progress monitoring, etc.) 56

Features of Common Core Covers fractions more than 1 and less than 1 concurrently. Word problems integrated with symbols/operations from the start. Ideas (concepts) and procedures linked. Limited array of mathematical models. 57

Recommendation 6 Interventions at all grades should devote about 10 minutes in each session to building fluent retrieval of basic arithmetic facts. Level of Evidence: Moderate 58

Suggestions Provide 10 minutes per session of instruction to build quick retrieval of basic facts. For students in K-2 grades, explicitly teach strategies for efficient counting to improve the retrieval of math facts. Teach students in grades 2-8 how to use their knowledge of math properties to derive facts in their heads. 59

Recommendation 8 Include motivational strategies in Tier II and III interventions. Level of Evidence: Minimal 60

Roadblocks Rewards can reduce genuine interest in mathematics by directing student attention to gathering rewards rather than learning math. Suggested Approach: Rewards have not shown to reduce intrinsic interest. As students become more successful, rewards can be faded so student success becomes an intrinsic reward. 61

Q & A Recommendations for Identifying and Assisting Students Struggling with Mathematics

Applying the Practice Guide in the Classroom John Woodward, Ph.D. Panel Chair Improving Mathematical Problem Solving in Grades 4 Through 8

Evidence Rating RecommendationLevel of Scientific Evidence 1. Universal screening (Tier I)Moderate 2. Focus instruction on whole number for grades K-5 and rational number and whole number for grades 4-8 Low 3. Systematic, focused instructionStrong 4. Solving word problemsStrong 5. Visual representationsModerate 6. Building fluency with basic arithmetic factsModerate 7. Progress monitoring of all students receiving intervention or at risk Low 8. Use of motivational strategiesLow 64

Recommendation 3 Instruction during the intervention should be systematic and include models of proficient problem-solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review. Level of Evidence: Strong 65

Recommendation 4 Interventions should include instruction on solving word problems that is based on common underlying structures. Level of Evidence: Strong 66

What Seems Most Essential in the Supportive Research Extensive practice with feedback. Let students provide a rationale for their decisions. Instructors and fellow students model approaches to problem solving. Source: Schunk & Cox (1986) Tournaki (2003) 67

Unresolved Issues with Explicit Instruction How to support students’ talking about mathematics. How to capitalize on helping students learn from hearing peers explain their mathematical reasoning. 68

Teaching Problem Solving There are many kinds of problems. Word problems related to operations or topics: I have 45 cubes. I have 15 more cubes than Darren. How many cubes does Darren have? Geometry/measurement problems. Logic problems, puzzles, visual problems. How many squares on a checkerboard? 69

Teaching Problem Solving Prepare problems and use them in whole-class instruction. Ensure that students will understand the problem by addressing issues students might encounter with the problem’s context or language. Linguistic issues are a barrier. Cultural background is a big factor. 70

Ensure That Students Will Understand the Problem A yacht sails at 5 miles per hour with no current. It sails at 8 miles per hour with the current. The yacht sailed for 2 hours without the current and 3 hours with the current and then it pulled into its slip in the harbor. How far did it sail? yacht? slip? harbor? 71

Teaching Problem Solving Assist students in monitoring and reflecting on the problem-solving process. Provide students with a list of prompts to help them monitor and reflect during the problem-solving process. Model how to monitor and reflect on the problem-solving process. Use student thinking about a problem to develop students’ ability to monitor and reflect. 72

Teaching Problem Solving This is what we want to AVOID. Read the problem (and read it again). Find a strategy (usually, “make a drawing”). Solve the problem. Evaluate the problem. 73

Provide Prompts or Model Questions What is the story in this problem about? What is the problem asking? What do I know about the problem so far? What information is given to me? How can this help me? Which information in the problem is relevant? Is this problem similar to problems I have previously solved? 74

Provide Prompts or Model Questions What are the various ways I might approach the problem? Is my approach working? If I am stuck, is there another way I can think about solving this problem? Does the solution make sense? How can I check the solution? Why did these steps work or not work? What would I do differently next time? 75

Evidence Rating RecommendationLevel of Scientific Evidence 1. Universal screening (Tier I)Moderate 2. Focus instruction on whole number for grades K-5 and rational number and whole number for grades 4-8 Low 3. Systematic, focused instructionStrong 4. Solving word problemsStrong 5. Visual representationsModerate 6. Building fluency with basic arithmetic factsModerate 7. Progress monitoring of all students receiving intervention or at risk Low 8. Use of motivational strategiesLow 76

Recommendation 5 Intervention materials should include opportunities for the student to work with visual representations of mathematical ideas and interventionists should be proficient in the use of visual representations of mathematical ideas. Level of Evidence: Moderate 77

Sample 1: Developing an Understanding of Fractions ConcreteVisual Representation 78

Visual Representations Teach students how to use visual representations. Select visual representations that are appropriate for students and the problems they are solving. Use think-alouds and discussions to teach students how to represent problems visually. Show students how to convert the visually represented information into mathematical notation. 79

Criteria for a Mathematics Intervention Temporarily decreases cognitive load for students. Includes cumulative review. Includes extensive practice. Students have opportunities to explain their reasoning. Use of Number Line and a small set of representations. 80

Cognitive Load: Problem Solving Through Words Alone Eva spent 2/5 of the money she had on a coat, then spent 1/3 of what was left on a sweater. She had $150 remaining. How much did she start with? 81

Problem Representation Tape Diagrams vs. Pictures Eva spent 2/5 of the money she had on a coat, then spent 1/3 of what was left on a sweater. She had $150 remaining. How much did she start with? 82

Draw a Picture? Eva spent 2/5 of the money she had on a coat, then spent 1/3 of what was left on a sweater. She had $150 remaining. How much did she start with? 83

Tape Diagrams as a Tool Eva spent 2/5 of the money she had on a coat, then spent 1/3 of what was left on a sweater. She had $150 remaining. How much did she start with? 84

Tape Diagrams as a Tool Eva spent 2/5 of the money she had on a coat, then spent 1/3 of what was left on a sweater. She had $150 remaining. How much did she start with? 85

Tape Diagrams as a Tool Eva spent 2/5 of the money she had on a coat, then spent 1/3 of what was left on a sweater. She had $150 remaining. How much did she start with? $150 = 2/5 of the money. That means 1/5 = $75 5 x 1/5 = 5/5, or the whole amount, so 5 x $75 = $375 Eva started with $

Evidence Rating RecommendationLevel of Scientific Evidence 1. Universal screening (Tier I)Moderate 2. Focus instruction on whole number for grades K-5 and rational number and whole number for grades 4-8 Low 3. Systematic, focused instructionStrong 4. Solving word problemsStrong 5. Visual representationsModerate 6. Building fluency with basic arithmetic factsModerate 7. Progress monitoring of all students receiving intervention or at risk Low 8. Use of motivational strategiesLow 87

Recommendation 6 Interventions at all grades should devote about 10 minutes in each session to building fluent retrieval of basic arithmetic facts. Level of Evidence: Moderate 88

Suggestions Provide 10 minutes per session of instruction to build quick retrieval of basic facts. For students in K-2 grades, explicitly teach strategies for efficient counting to improve the retrieval of math facts. Teach students in grades 2-8 how to use their knowledge of math properties to derive facts in their heads. 89

Wrap Up and Closing Remarks Lydotta M. Taylor, Ed.D.

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