Response to Intervention (RtI) & Mathematics

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Mathematics Supports for Students in a Response to Intervention Model

Dr. Erica LembkeDepartment of Special Education

University of Missourilembkee@missouri.edu

Overview

• RtI in Mathematics—How does it look?• Curriculum-Based Measurement (CBM) in

Mathematics• Assessment—Making Connections• Evidence-Based Interventions in Mathematics

Critical Elements: Center on Response to Intervention

Poll #1

Which of the essential elements do you feel is most difficult to implement in mathematics?

a. Screening

b. Progress monitoring

c. Data-based decision making

d. Mathematics intervention

Basic Steps in Depth

Basic Steps in the RtI Process

Step #1: Implementation of Evidence-based Core Instruction for all Students, including Differentiated Instruction

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What is the most important part of instruction and intervention?

The teaching is the most important part.• Be deliberate and intentional about your teaching.

• Maximize every instructional minute.

• Understand and ask, “What are the elements of an effective teaching practice?”

Effective Teaching Components

Evidence-based teaching practices are the key to high-quality instruction and intervention. Practices include

• an objective for the lesson (concrete and measurable), including a rationale;

• motivational activities to get students interested in and excited about the lesson;

• modeling;• guided practice;• independent practice; and• assessment.

Treatment Fidelity

One of the key triggers in RtI is a lack of response to validated instruction implemented with integrity.

• Check on fidelity of implementation. • How can this be done?• Use checklists, observation, discussion, video, etc.

The purpose of fidelity checks is to create open dialogue regarding what is effective and what needs to be altered.

• Fidelity checks should be an open process.• There should be no surprises.

Fidelity of implementation is critical to intervention success.

• How is implementation fidelity monitored in schools in which you are working, or is it monitored?

• How can implementation fidelity become a routine part of a school environment?

• How can implementation fidelity lead to more open dialogue and better instructional methods?

• How would the example work in your building?

Basic Steps in the RtI Process

Step #2: School-wide Screening and Benchmarking• All students are screened (three times per year is most

prevalent) to determine which students are suspected to be at risk.

• One suggestion is a Curriculum-Based Measurement (CBM) tool. There will be more about CBM in a moment.

• CBM data systems give one data source to help determine students who fall into tiered levels (based on national norms).

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Basic Steps in the RtI Process and Considerations

Step #3: Progress Monitoring for Students at RiskStudents receiving Tier 2 (supplemental) or Tier 3 (intensive) supports are progress monitored on a frequent basis. Goals are set, data is graphed, and decisions are made based upon the data.

• Considerations include how often and what tool is used.

• Guidelines are as follows:

• Students in Tier 2 are progress monitored every other week.

• Students in Tier 3 are monitored weekly.

• More frequent data leads to better decisions made more frequently.

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How do assessments fit together?

1 to 3 times per yearOutcome tests

District testCBM benchmarking

The question answered: How is this studentdoing compared to peers or

benchmarks?

Weekly or monthlyProgress monitoring using CBM

for students deemed at-risk after triangulation of data

The question answered: Is the student benefitting from the instruction being provided?

Weekly or monthlyDiagnostic tests (unit or

chapter tests, teacher-made tests)The question answered: What specific skills are

mastered or need to be reinforced?

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CBM: Overall Indicators

Curriculum-Based Measurement (CBM) assessments serve as indicators of academic proficiency, just like• temperature, in degrees, serves as an indicator of overall

wellness;

• weight, in pounds, serves as an indicator of overall health; and

• a litmus test serves as an indicator of a solution’s acidity.

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CBM: An Index of Academic Health

Num

ber o

f Cor

rect

Dig

its

Fact Fluency

Place value

Word Problems

Conceptual understanding

Math CBM and Measures Used For Monitoring

• Early Numeracy• Oral Counting

• Missing Number

• Number Identification

• Quantity Discrimination

• Math Computation

• Math Concepts & Applications

Math CBM and Early Intervention

• It is important to identify students who are at-risk in math early.

• There is a relationship between number sense and deficit areas in LD (Geary, 1993; McCloskey and Macaruso, 1995).

• What measures can we use to screen and progress monitor students in early elementary grades?

Examples of Options for Early Numeracy Indicators

• Measures in most systems include number identification, quantity discrimination, missing number, mixed numeracy, next number, and number of items.

• Most measures in early numeracy are individually administered for 1–3 minutes.

• Teachers score the measures later.

Examples of Sources for CBM Early Numeracy Measures

• Lembke and Foegen measures number identification, quantity discrimination, missing number, and mixed numeracy.

• The instrument is available at no cost at www.progressmonitoring.org. Click on “RIPM Research” then “Early Numeracy.”

• The instrument provides both screening and progress monitoring measures.

Examples of Sources for CBM K–8 Measures

Review sites such as the National Center for Intensive Intervention or the Center on RTI for screening and progress monitoring tools and charts.

The addresses are as follows:• intensiveintervention.org

• rti4success.org

Questions for Discussion

• Which math measures will we use or are we using?

• When will we implement math screening and progress monitoring?

Basic Steps in the RtI Process and Considerations

Step #4: Discussion and Decision Making about the Data with Grade-level, Content-specific, or School-wide Teams

• Decision-making rules should be established.

• For instance, after six data points are collected over six weeks, use the trend line or 4-point rule to make a decision about the current plan.

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Decision Making: Progress Monitoring Data

Every four to six weeks, examine the trend of data or the four most recent consecutive data points compared to the goal line.

• If trend or four points are below the goal line, make an instructional change.

• If trend or four points are above the goal line, consider past data to determine if the student can be moved to a lower tier or if the goal can be raised.

• If trend or four points are the same as the goal, stay the course.

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Weeks of Instruction

Prob

lem

s C

orre

ct in

7 M

inut

es

Four-Point Method

X

most recent 4 points

goal-line

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Weeks of Instruction

Prob

lem

s C

orre

ct in

7 M

inut

es

Four-Point Method

X

goal-line

most recent 4 points

Discussion of Data and Decision Making

• Use decision-making rules.• Use guiding questions to discuss data with

your grade-level team.

Basic Steps in the RtI Process and Considerations

Step #5: Implementation of Evidence-based Interventions for Students at RiskConsiderations are as follows:

• How will fidelity be monitored?

• How will interventions be scheduled?

• How will they be chosen?

• How will skills be targeted (diagnostic)?

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Diagnostics

• Align instruction and intervention to curriculum.

• Examine results from your common assessments.

• Implement mathematics interviews.

• Analyze errors.

• Maximize unit tests, “mad minute” assessments, and diagnostic information gleaned from CBM measures.

Intervention: A Closer Examination

What does instruction and intervention look like at each tier?

Tier 1

• All students

• Differentiated instruction

• Co-teaching

• Research-based core program

Tier 2 (more strategic interventions to meet student goals)

• Fewer students

• Review of core components

• Supplemental, evidence-based program

Tier 3 (intensive interventions to meet student goals)

• Small group of students or individualized instruction

• Intensive, systematic, and explicit program

Tiers 2 and 3: What are my choices?

Standard Treatment Protocol• “Standard” refers to “the same.”• “Treatment” refers to “intervention.”• “Protocol” refers to “for everyone in the same way.”• Students receive the same intervention for a fixed period

of time, rather than individualized intervention unique to the learning needs of each child.

Problem-solving Model• Unique and individualized instruction is provided and is

based on student needs.• Instruction varies by student.

What are the pros and cons of each?

The Foundation: High-Quality, Direct Instruction Techniques

There will be more about standard treatment protocol and the problem solving model in a moment.

First, what are universal teaching practices or strategies that need to be in place for all students, especially our students in Tiers 2 and 3?

• Think of effective teaching or lesson components.

• Write down three.

Mathematics Intervention Resources

• Intervention briefs are available for review at Evidence-Based Intervention Network at ebi.missouri.edu.

• Helping Your Child Learn Mathematics http://www.ed.gov/parents/academic/help/math/math.pdf

• Lesson plans from NCTM http://illuminations.nctm.org/

Mathematics Interventions

Key documents are as follows:• National Mathematics Advisory Panel Report

• Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools (Gersten, Beckmann, Clarke, Foegen, Marsh, Star, & Witzel, 2009)

Mathematics Interventions

Other key documents are as follows: • Improving Mathematical Problem Solving in

Grades 4-8

• Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students

• Effective Mathematics Instruction (National Dissemination Center

for Children with Disabilities)

• National Math Panel fact sheet

Mathematics Interventions

Other key documents are as follows: • A Summary of Nine Key Studies: Multi-Tier

Intervention and Response to Interventions For Students Struggling in Mathematics (Newman-Gonchar, Clarke, & Gersten, 2009)

• Mathematics Instruction for Students with Learning Disabilities or Difficulty Learning Mathematics: A Synthesis of the Intervention Research (Gersten, Chard, Jayanthi, Baker, Morphy, & Flojo, 2008)

Poll # 2

Of the following resources for intervention, which one will you explore next?

a. Lessons plans from NCTM Illuminations

b. EBI Network mathematics briefs

c. National Math Panel report

d. A practice guide from the What Works Clearinghouse

Reflecting on Key Findings from Recent Reports

What are the practices we need?• Visual and graphic depictions

• Systematic and explicit instruction

• Student self instruction

• Structured, peer-assisted learning activities

• Formative assessment data provided to teachers and/or students

VISUAL AND GRAPHIC DEPICTIONS

Sequencing of Skills

• Use concrete-semiconcrete-abstract (CSA).

• Concrete: manipulatives

• Semiconcrete: pictures

• Abstract: number symbols

• Use parallel modeling by relating manipulation of concrete objects or pictures immediately to number symbols.

• Remember that conceptual understanding and automaticity are different skills.

1. “How many rows?”

2. “How many faces in each row?”

3. “ How many in all?”

Schema-Based Strategy Instruction

Schema-based strategy instruction was researched in grades 2–8. For an example, see Xin & Jitendra, 2006.

The goal for schema-based strategy instruction is for students to identify the schema, or type of problem, and use that information to solve the problem.

The four interrelated steps are as follows:• Identify the problem schema (e.g., a “compare” problem).

• Generate a representation for the schema identified.

• Plan how to solve the problem, which includes setting a final goal and subgoals, selecting the appropriate operation, and writing the math sentence or equation.

• Carry out the plan.

Change Problem

Stacy had 43 coins in her coin collection. She lost 20 of them when she moved from one house to another. Now Stacy has __ coins.

43 coins

Beginning set

coins

Ending set

20 coins

Change set

Group problem

Jim has _ baseball cards in his collection. 20 are from the St. Louis Cardinals, and the remaining 15 are Kansas City Royals players.

St. Louis 20 cards

KansasCity

15 cards

Total baseball cards

Smaller sets Larger set

Your Turn

Erica baked 3 dozen chocolate chip cookies, and Gary ate 6 of them. Now Erica has __ cookies to take to the office.

1. Identify the type of schema (change, group, compare).

2. Generate a representation.3. Plan how to solve the problem.4. Carry out the plan.

SYSTEMATIC AND EXPLICIT INSTRUCTION

Direct and Explicit Instruction in Mathematics

• State the objective and rationale

• Review

• Provide teacher-led instruction

• Check for understanding

• Complete guided practice

• Complete independent practice

• Assess

STUDENT SELF INSTRUCTION

Student Self Instruction (see http://nichcy.org/research/ee/math)

• Set goals.• Keep on task.• Check work as you go.• Remember to use a specific strategy.• Monitor your own progress.• Be alert to confusion or distraction and take

corrective action.• Check your answer.

Samples

Montague (1992)

1. Read for understanding.

2. Paraphrase in your own words.

3. Visualize a picture or diagram.

4. Hypothesize a plan to solve the problem.

5. Estimate or predict the answer.

6. Compute the answer.

7. Check to be sure everything is correct.

Miller, Strawser, & Mercer (1996)

1. Read the problem.

2. What is the question the problem asks?

3. To answer the question, do I have to add, subtract, multiply, or divide?

4. What information is not needed?

5. Write out the problem using numbers.

6. Solve the problem.

7. Check the answer.

Samples

Fleischner, Nuzum, & Marzola (1987)

1. ReadWhat is the question?

2. Reread What is the necessary information?

3. Think“Putting together” means addition.“Taking apart” means subtraction.

4. SolveWrite the equation.

5. CheckRecalculate, label, and compare.

Generic

1. Read the problem.

- Circle unknown words and ask.

- Underline cue words.

2. Choose the operation.

3. Write down necessary numbers.

4. Cross out unnecessary information.

5. Write the equation.

6. Solve the problem.

7. Check the answer. Ask yourself, “Does this make sense?”

Poll # 3

Reflecting on elements that are identified from the research findings, in which of the following areas do your students need the most support?

a. Visual and graphic depictionsb. Systematic and explicit instructionc. Student self instructiond. Structured, peer-assisted learning activitiese. Formative assessment data provided to teacher

and/or students

• What are two things you will share with others in your school or district?

• What are two things you will try yourself?• Are there any questions that remain?

Next Steps

Join the following webinars:Tuesdays 3:30-4:30 pm (CST)RtI & TexasTurning Learning Challenges into Advantages

Join Research in Mathematics Education and TEA for a series of webinars on RtI.

Join us:RtI & Behavior Tuesday, May 12, 3:30 – 4:30 pmRtI & Writing Tuesday, May 19, 3:30 – 4:30 pm

Missed the first three webinars? You can view the archived footage online at:http://www.smu.edu/Simmons/Research/RME/Participate/RtIWebinars/RtIExperts

Each free webinar provides 1.0 hour of professional development continuing education credit (CEC).

Follow up and Certificate of Completion• You may contact Dr. Erica Lembke, Associate Professor, Department

of Special Education at University of Missouri at lembkee@missouri.edu

• The Certificate of Completion link will be sent in your follow-up email.

• Please allow 48 hours for the presentation slides and archived footage of today’s webinar to be available at http://www.smu.edu/Simmons/Research/RME/Participate/RtIWebinars/RtIExperts

• If you have further questions, please send an email to rme@smu.edu