Planning for Tier 2 Math Intervention r t i Cristianne Lane, M.Ed. Margo Healy, M.Ed. Evelyn Johnson, Ed.D. Lee Pesky Learning Center.

Planning for Tier 2 Math Intervention

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Cristianne Lane, M.Ed.Margo Healy, M.Ed.

Evelyn Johnson, Ed.D.

Lee Pesky Learning Center

Introduction

Where we have been... Where we are heading...

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Training Goals:

• Examine Tier 1 math challenges that may impact Tier 2.

• Identify Tier 2 math resources.

• Provide direction for prioritizing, diagnosing, and planning Tier 2 math instruction.

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Agenda:

• Tier I Math Instruction• Tier 2 Purpose and “Must Haves”

Assessment ToolsTargeted InstructionTime and IntensityProgress Monitoring

• Examples

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Your Materials:

• PowerPoint slides packet

• Yellow handouts for reflection exercises and activities

• Green handout for video assessment clip

• Articles (to be passed out later during fact fluency discussion)r

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Sources:

• Common Core State Standards• What Works Clearinghouse • Doing What Works• Research Journals• RTI Action Network• Center on Instruction• National Center on Response to

Intervention• National Council of Teachers of

Mathematicsr t

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Tier 1

• National “Issues”• Professional Development• Shifting to the Common Core

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Dr. David AllsoppUniversity of South Florida

• Former Middle School Teacher• Special Education Department Chair• Co-developer of MathVIDS and The

Learning Toolbox

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Dr. David AllsoppUniversity of South Florida

Special Education Department ChairFormer Middle School Teacher“RTI and Improved Math Achievement”

Co-developer of MathVIDS and The Learning Toolbox

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iAllsopp is going to talk about 3 topics:

1. Teacher preparation

2. The limited research base for math intervention

3. RTI as a powerful problem-solving process

Knowledgeable Teachers

Professional development opportunities:•MTI classes•MathVIDS.com•Webinars on RTI and math websites•Khan Academy•Mentors in your district•Every Child Ready for Math (K)

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Knowledgeable Teachers...

know the learning progressions!

Sources:•Common Core State Standards

– Deconstructed standards– Learning Progressions

•NCTM Focal Points•Books and Journals

– Adding it Up r t

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r t

iCCSS Domain Progression

K 1 2 3 4 5 6 7 8 HS

Counting & Cardinality

Number and Operations in Base TenRatios and Proportional

RelationshipsNumber & Quantity

Number and Operations – Fractions

The Number System

Operations and Algebraic Thinking

Expressions and Equations Algebra

Functions Functions

Geometry Geometry

Measurement and Data Statistics and ProbabilityStatistics & Probability

CC Process Standards: Math Practices

• Make sense of problems and persevere in solving them.

• Reason abstractly and quantitatively.• Construct viable arguments and critique the

reasoning of others.• Model with mathematics.• Use appropriate tools

strategically.• Attend to precision.• Look for and make use of structure.• Look for and express regularity in repeated

reasoning.

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Strong Mathematiciansr

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SkillsSkills

ProceduresProcedures

ProcessProcess

ApplicationApplication

XContentContent UnderstandingUnderstanding

Genesis of RTI – Public Health Model

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How do you know if it is a Tier 1 issue or a Tier 2 issue?

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Tier 1: Debrief(page 1 of yellow packet)

• National “Issues”• Professional Development• Shifting to the Common Core

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Agenda:

• Tier I Math Instruction• Tier 2 Purpose and “Must Haves”

Assessment ToolsTargeted InstructionTime and IntensityProgress Monitoring

• Examples

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Tier 2 “MUST HAVES”

• Strong Assessment Tools• Targeted Instruction• Time and Intensity• Progress Monitoring

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Tier 2 “MUST HAVES”

#1 Strong Assessment Tools•Screeners

•Diagnostic Tools

•Progress Monitoring (formative)

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Johnson Smith Harris 22r t

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iWhat is Screening?

23Johnson Smith Harris

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iSuggested Screening Process

24Johnson Smith Harris

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iScreeners Must Be…

• ISAT scores• Grades/report cards• Placement tests• EOC tests• Benchmarks• CBMs• K registration

screening

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iDiagnostic tools allow us to...

K 1 2 3 4 5 6 7 8 HS

Counting & Cardinality

Number and Operations in Base TenRatios and Proportional

RelationshipsNumber & Quantity

Number and Operations – Fractions

The Number System

Operations and Algebraic Thinking

Expressions and Equations Algebra

Functions Functions

Geometry Geometry

Measurement and Data Statistics and ProbabilityStatistics & Probability

Strong Mathematiciansr

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SkillsSkills

ProceduresProcedures

ProcessProcess

ApplicationApplication

XContentContent UnderstandingUnderstanding

Probe Examples Handout

(pages 5-7 in your yellow packet)

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Diagnostic Tools: K-1st

Two essential aspects in the development of proficiency in mathematics with predictive validity:

•Knowledge of magnitude of numbers•Counting efficiently and strategically

Geary 2004, Kalchman, Moss, & Case 2001

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Magnitude of Number:

Which is bigger? (1-20 for K, 0-99 for 1st)

1st grade example: 37 48

Strategic Counting:Counting from numbers other than 1, counting backward (missing #)

1st grade example:28 29 _____ 67 ____ 69r t

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Additional Recommendations for K-1st :

• Number Identification (K)

• Basic Arithmetic Facts (beginning at the middle of first grade)

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Possible Diagnostic Tools (K-1):– Primary Math Assessment (PMA)– Number Knowledge Test (NKT)– Monitoring Basic Skills Progress (MBSP)– AIMSweb Test of Early Numeracy

and/or Number Fly Early Math Probes*

• Missing Number• Number ID• Oral Counting• Quantity Discrimination

* free on Intervention Central

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Elementary Math: (2-6th)• Computation• Concepts and Applications

Secondary Math:• Basic Skills and Concepts/Applications• Algebra Foundations• Content Analysis• Translations

Project AAIMS

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Possible Diagnostic Tools:

easyCBM (K-8)Primary Math Assessment (PMA)Math Navigator (2-10)Monitoring Basic Skills Progress (K-6)AIMSweb (K-8)Number Fly Early Numeracy (K-3)Project AAIMS (basic skills and algebra)

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Digging Deeper!

Assessing Math Concepts preK-3rd

(Kathy Richardson)

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K-2, 3-5, 6-8, 9-12

Digging Deeper! r

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NCTM Assessment Handbooks K-2, 3-5, 6-8, 9-12

Example on page 8 of your yellow packet

Pros and Cons...

What are the pros and cons using student interviews or authentic assessment tasks?

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Table Discussions (bottom of page 1, yellow packet)

What diagnostic tools do you have?

Is there a balance between skills and concepts?

What might you need?

What are your next steps?

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Elementary: Word prob. X and Div. Understanding + and - Facts Fractions

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Middle School

+ and – X and Div. Fractions Charts Word Prob. Word Prob. GraphsWord prob. X and Div.

Understanding + and - Facts Fractions

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Fractions!

Only 55% of 8th grades could solve a word problem involving the division of fractions.

National Center for Education Statistics, 2006

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Word prob. X and Div. Understanding + and - Facts Fractions

A 2006 research study...

Conducted at Vanderbilt University asked algebra teachers to describe the major deficiencies that they see in students who enter algebra classes ill-prepared to learn.

What do you think were the two major issues?

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The Findings:

1. Lack of understanding of fractions, ratio and proportion.

2. The inability to transfer word problems into mathematical expressions or equations.

Zimmer, Christina, Hamilton, & Weber Prine, 2006r

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Tier 2 “MUST HAVES”

• Strong Assessment Tools• Targeted Instruction• Time and Intensity• Progress Monitoring

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Tier 2 “MUST HAVES”

#2 Targeted Instruction•General Components of Tier 2 Math Instruction•Recommendations from What Works Clearinghouse

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Explicit and Systematic Instruction:(page 2 of yellow handout)

• Modeling, Explanations, Think alouds,• Scaffolded, guided practice• Cumulative Review• Immediate Corrective Feedback• Visual Representations and Models• Motivation What Works Clearinghouse and Doing What Works Recommendation

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Math Video

MathVIDS.com: Division with Fractions

Explain to your partner why it works to invert and multiply when you are dividing fractions.

2 divided by 1/3

Debrief with Rubric

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Tier 2 “MUST HAVES”

#2 Targeted Instruction•General Components of Tier 2 Math Instruction•Recommendations from What Works Clearinghouse

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Tier 2 “MUST HAVES”

#2 Targeted Instruction•General Components of Tier 2 Math Instruction•Recommendations from What Works Clearinghouse

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iRecommendations from

What Works Clearinghouse:

Interventions should focus intensely on in-depth understanding of whole numbers (K-5) and rational numbers (grades 4-8).Interventions should include instruction on solving word problems that is based on common underlying structures.Interventions at all grade levels should devote about 10 minutes in each session to building fluent retrieval of basic facts.

Recommendation #1:

Provide in-depth intervention focused on•whole numbers (K-5) and •rational numbers (4 and above)

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Whole Number Skills:“Number sense,” counting strategies, place value, addition, subtraction, multiplication, division operations

Rational Number Skills: operations with fractions, decimals, ratios and percentages

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What do you know about this number?

6

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Number Sense:

“Number sense also means literally a ‘sense of number’ –an understanding of numbers so complete that a child knows that 6 is half of 12, and that it’s also 3 doubled, 1/3 of 18, 2 sets of 3 or 3 sets of 2, 1 more than 5 and 1 less than 7, and that if you add 10 to it, you’ll get 16. Now that is real number sense.”

Catherine Jones Kuhnsr

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Models: Match to Concepts

– Number lines– Tree diagrams– Ones, tens, hundreds blocks/charts– Arrays– Strip diagrams – Tables

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C-R-A Progression

Abstract

Representational

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Examples?

4x + 3 = 15

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Concrete:

8= 2x - 2

Representational:

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C-R-A Progression

Abstract

Representational

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Video Clip: Making Math Real

University of California at Berkley

Math intervention:kindergarten through pre-algebra

After viewing we will debrief the clip with your rubric.

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Table Discussions(top of page 3 of yellow packet)

• Do you have interventions for whole or rational numbers?

• Do your interventions use consistent models that match the concepts?

• Do your interventions follow the C-R-A progression?r

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WWC Recommendation

Teach the underlying structures of word problems.

Activity: Look at your handout of math problems on page 9 of your yellow packet. What support might struggling students need with these problems?

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Page 9 of your yellow packet

John had 470 baseball cards in his collection. He lost 152 of them when his family moved from Florida to New York. How many does he have now?

John has 470 cards in his baseball card collection. 152 cards are of his favorite team, the New York Yankees. How many are not New York Yankee cards?

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Change ProblemsThere is a passage of time and a change occurs

Beginning Change Ending

-152 470 cards

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Part-Part-WholeLarge group always equals the sum of the parts

470 cards

152 Yankees

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Compare Problems

John has 470 cards in his baseball collection. Joann has 50 less cards than John. How many cards does Joann have?

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Compare Problems

John has 470 cards

Joann has?

50

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Ratios and Proportions...

Are an extension of rational numbers and are central to mathematics development and the concept of multiplicative thinking that is critical to secondary mathematics and algebra readiness.

(National Mathematics Advisory Panel, 2008)

Understanding ratios plays a fundamental role in the study of linear functions in algebra, particularly slope. (Cheng, 2010)r t

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Carlos is on the school’s track team. He takes 54 minutes to run 6 miles. How long did it take him to run 2 miles?

Example of Proportion Diagram:If Then

54

minutesX

minutes

6 miles

2 milesr

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Word Problems:

Over 50% of students with math disabilities also have reading disabilities.

Barbaresi et al., 2005

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Additional Strategies:

• Reading the problem more than once• “Think alouds”• Pre-teaching key vocabulary• Encouraging visualizing or drawing• Paraphrasing or restating the problem

orally• Crossing out extraneous information or

underlining critical information

(Learning Toolbox website has more ideas)r t

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Table Discussions(bottom of page 3 of yellow packet)

• Do you have interventions for teaching word problems?

• Do your interventions teach the underlying structure of word problems?

• Do your students need additional strategies for reading the problems?r

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WWC Recommendation

Interventions at all grade levels should devote about 10 minutes in each session to building fluent retrieval of basic facts.

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Learning Progression for Single-Digit Addition

From Adding It Up: Helping Children Learn Mathematics, NRC, 2001.

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Models

• Number lines

• Arrays

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Fact Fluency:

Read one of the two documents, discuss with a partner who read the other:

The fact fluency article (The Educator)

IES Practice Guide, Recommendation 6

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Table Discussions(page 4 of yellow packet)

Please reflect upon the articles, and discuss your fact fluency interventions.

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Tier 2 “MUST HAVES”

#2 Targeted Instruction•General Components of Tier 2 Math Instruction•Recommendations from What Works Clearinghouse

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•Does the program use consistent models and visual representations?•Is the program explicit and systematic?•Are their opportunities to verbalize thought processes?•Does the program follow the C-R-A progression?•Does the program have a frequent cumulative review?

Resources and Programs: Use your rubric to evaluate programs!

(page 2 of your yellow packet)

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Sources for Program Recommendations:

• What Works Clearinghouse• Book: Understanding Response to

Intervention in Mathematics: Proven Methods and Applications – R. Gersten and R. Newman-Gonchar

• Book: Response to Intervention – P. Riccomini and B. Witzel

• Major Publishers• NCTM• Center on Instruction

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Tier 2 “MUST HAVES”

• Strong Assessment Tools• Targeted Instruction• Time and Intensity• Progress Monitoring

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Scheduling Intervention Time:

Middle and high schools reported that they:Used elective periods or study hallAdded an additional class period Pulled students from core classesProvided extended learning time

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Middle School Example

ReadingWritingMath—coreMath-- differentiated by needScience/Social StudiesPE/Music/Computer LabElective/Study Hall

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Elementary Schools:

Intervention/enrichment blocks (30 min)

After lunch recess:11:45-12:00 story12:00-1:00 math1:00-1:15 recess1:15- 1:45 P.E. /Music/Library

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Tier 2 “MUST HAVES”

• Strong Assessment Tools• Targeted Instruction• Time and Intensity• Progress Monitoring

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Tier 2 “MUST HAVES”

#4 Progress Monitoring

•Mastery Measures

•General Outcome Measures

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Progress Monitoring:

• Mastery Measures (program measures)– Measures that tell us if students are

learning the specific skills being taught in the intervention.

• General Outcome Measures– Tend to be more broad and consistent with

what is being measured schoolwide

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Examples:

Implementing Response to Intervention video series (YouTube):• Boulevard Elementary School• Russell Middle School• Tigard High School

Center on Instruction and Doing What Works have school examples on their websites.

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What are three “take aways” from today’s training?

Please pick one to share with the group.

Thank You!Contact:

Dr. Evelyn [email protected]

Cristianne [email protected]

Statewide Special Education Technical Assistance (SESTA)

Gina Hopper, Director

208.426.4363

[email protected]

Katie Bubak,Statewide

Consultant

208.426.3257

[email protected]

Training materials can be found at www.idahotc.com

Project Sponsor

Idaho Department of EducationSpecial Education Division

Richard Henderson, [email protected]