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

Identifying and Assisting Elementary and Middle School Students Struggling with Mathematics

The presentation will begin shortly.

2

WebEx Instructions

WebEx Instructions

Attendees can provide non-verbal feedback to presenters utilizing the Feedback tool.

3

WebEx Instructions

Feedback options:

4

5

WebEx Instructions

Responses to poll questions can be entered

in the Polling Panel.

Remember to click “Submit” once you have selected your answer(s).

6

WebEx Instructions

Attendees should utilize the “Q&A” feature to pose questions to the speaker, panelists, and/or host.

The host will hold all questions directed toward the speaker or

panelists, and they will be answered during a Q&A session at the end of

each discussion.

Welcome and Overview

Lydotta M. Taylor, Ed.D.Research Alliance Lead, REL Appalachia

The EdVenture Group

8

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.

9

What is a REL?

10

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.

http://www.RELAppalachia.org

Follow us! @REL_Appalachia

http://www.relappalachia.org/

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

13

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.

14

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

4. Applying the Practice Guide in the Classroom

5. Wrap Up and Closing Remarks

http://ies.ed.gov/ncee/wwc/pdf/practice_guides/rti_math_pg_042109.pdf






What is Response to Intervention (RtI)?

Russell Gersten, Ph.D.Director, Instructional Research Group

16

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.

17

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.

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 & AWhat is Response to Intervention (RtI)?

Why Use RtI in Mathematics Instruction?

Russell Gersten, Ph.D.

Case for RtI and Early Intervention in Mathematics

22

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)

23

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)

Case for RtI in the Intermediate Grades

25

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)

26

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!

27

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?

A. B. C.

D. E.

• Most think that the reason for poor performance on these items is that students never understood the mathematical ideas relating to fractions.

28

Poll the NAEP

What is the correct set of numbers?• A• B• C• D• E

Q & AWhy Use RtI in Mathematics Instruction?

Recommendations for Identifying and Assisting Students Struggling with Mathematics

Russell Gersten, Ph.D.

Response to Intervention Practice Guide



32

Panelists

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

33

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.

34

Practice Guide Structure

• Recommendations• How to carry out the recommendations• Levels of evidence• Potential roadblocks and suggestions

35

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)…

36

Evidence Rating

Recommendation Level of Scientific Evidence1. Universal screening (Tier I) Moderate2. Focus instruction on whole number for grades K-5 and rational number and whole number for grades 4-8

Low

3. Systematic, focused instruction Strong4. Solving word problems Strong5. Visual representations Moderate6. Building fluency with basic arithmetic facts Moderate7. Progress monitoring of all students receiving intervention or at risk

Low

8. Use of motivational strategies Low

37

Poll Item

Which level of evidence is the biggest surprise for you?

Why?

38

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

39

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)

40

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)

41

Sample Grade 2 Estimation Item

42

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.”

38 16 56 39

43

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)

44

What to Teach

Intervention content closely aligned to the Common Core

BUT

May need to include related material from earlier grades

45

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

46

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)

47

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.

48

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

49

Life on the Number Line

50

Use a Visual Fraction Model

• Representation of as a length

• Using the number line to see that

51

Sample 1: Developing an Understanding of Fractions

Concrete Visual Representation

52

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)

53

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

54

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.

55

Tools

Progressions for the Common Core State Standards in Mathematics (draft)By: The Common Core Standards Writing Group DRAFT 21 April 2012

http://ime.math.arizona.edu/progressions

Supported by the Brookhill Foundation

http://ime.math.arizona.edu/progressions

56

How does Common Core Fit In?

How Common Core can guide intervention and assessments (interim, progress

monitoring, etc.)

57

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.

58

Recommendation 6

Interventions at all grades should devote about 10 minutes in each session to

building fluent retrieval of basic arithmetic facts.


59

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.

60

Recommendation 8

Include motivational strategies in Tier II and III interventions.

Level of Evidence: Minimal

61

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.

Q & ARecommendations 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


Low


Low


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.


65

66

Recommendation 4

Interventions should include instruction on solving word problems that is based on

common underlying structures.


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


• 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


• 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


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


Low


Low


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.


77

Sample 1: Developing an Understanding of Fractions

Concrete Visual 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

84

Tape Diagrams as a Tool




85



$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 = $375Eva started with $375.

86

Evidence Rating


Low


Low


87

Recommendation 6

Interventions at all grades should devote about 10 minutes in each session to

building fluent retrieval of basic arithmetic facts.


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.

91

Stakeholder Feedback Survey Access Information

Please visit: https://checkbox.cna.org/REL_AP_Webinar.aspxto provide feedback on today’s webinar event.

https://checkbox.cna.org/REL_AP_Webinar.aspx

https://checkbox.cna.org/REL_AP_Webinar.aspx

Documents

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