Planning for Tier 2 Math Intervention

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Planning for Tier 2 Math Intervention

• Cristianne Lane, M.Ed.
• Margo Healy, M.Ed.
• Evelyn Johnson, Ed.D.
• Lee Pesky Learning Center

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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 Tools
• Targeted Instruction
• Time and Intensity
• Progress 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)

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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 Mathematics

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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

• Allsopp is going to talk about 3 topics
• Teacher preparation
• 2. The limited research base for math
• intervention
• 3. RTI as a powerful problem-solving process

• Special Education Department Chair
• Former Middle School TeacherRTI and Improved
  Math Achievement
• Co-developer of MathVIDS and
• The Learning Toolbox

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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

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CCSS Domain Progression
K K 1 2 3 4 5 6 7 8 HS
Counting Cardinality Counting Cardinality
Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten Ratios and Proportional Relationships Ratios and Proportional Relationships Number Quantity
Number and Operations Fractions Number and Operations Fractions Number and Operations Fractions The Number System The Number System The Number System Number Quantity
Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Expressions and Equations Expressions and Equations Expressions and Equations Algebra
Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Functions Functions
Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry
Measurement and Data Measurement and Data Measurement and Data Measurement and Data Measurement and Data Measurement and Data Measurement and Data Statistics and Probability Statistics and Probability Statistics and Probability Statistics Probability
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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 Mathematicians
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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 Tools
• Targeted Instruction
• Time and Intensity
• Progress 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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What is Screening?
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Suggested Screening Process
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Screeners Must Be

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

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Diagnostic tools allow us to...
K K 1 2 3 4 5 6 7 8 HS
Counting Cardinality Counting Cardinality
Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten Ratios and Proportional Relationships Ratios and Proportional Relationships Number Quantity
Number and Operations Fractions Number and Operations Fractions Number and Operations Fractions The Number System The Number System The Number System Number Quantity
Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Expressions and Equations Expressions and Equations Expressions and Equations Algebra
Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Functions Functions
Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry
Measurement and Data Measurement and Data Measurement and Data Measurement and Data Measurement and Data Measurement and Data Measurement and Data Statistics and Probability Statistics and Probability Statistics and Probability Statistics Probability
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Strong Mathematicians
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• 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 ____ 69

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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)

NCTM Assessment handbooks K-2, 3-5, 6-8,
9-12
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Digging Deeper!
NCTM Assessment Handbooks K-2, 3-5, 6-8,
9-12 Example on page 8 of your yellow packet
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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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Word prob. X and Div.
Understanding and - Facts
Fractions
Elementary
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and
X and Div. Fractions Charts
Word Prob. Word Prob.
Graphs
Word prob. X and Div. Understanding
and - Facts Fractions
Middle School
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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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High School
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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

• Lack of understanding of fractions, ratio and
  proportion.
• The inability to transfer word problems into
  mathematical expressions or equations.
• Zimmer, Christina, Hamilton, Weber Prine,
  2006

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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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Recommendations 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.

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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
  its 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, youll get 16. Now
  that is real number sense.
• Catherine Jones Kuhns

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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
• Concrete

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Examples?

• 4x 3 15

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8 2x - 2

• Concrete

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8 2x - 2

• Representational

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C-R-A Progression

• Abstract
• Representational
• Concrete

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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?

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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

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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
50
Joann has?
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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)

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Carlos is on the schools 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

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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)

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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?

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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
• Ten Frames

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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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Resources and Programs Use your rubric to
evaluate programs!(page 2 of your yellow packet)

• 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?

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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 hall
• Added an additional class period
• Pulled students from core classes
• Provided extended learning time

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Middle School Example

• Reading
• Writing
• Mathcore
• Math-- differentiated by need
• Science/Social Studies
• PE/Music/Computer Lab
• Elective/Study Hall

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Elementary Schools

• Intervention/enrichment blocks (30 min)
• After lunch recess
• 1145-1200 story
• 1200-100 math
• 100-115 recess
• 115- 145 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 todays
  training?
• Please pick one to share with the group.

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Thank You!

• Contact
• Dr. Evelyn Johnson
• ejohnson_at_lplearningcenter.org
• Cristianne Lane
• clane_at_lplearningcenter.org

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Statewide Special Education Technical Assistance
(SESTA)

• Gina Hopper,
• Director
• 208.426.4363
• ginahopper_at_boisestate.edu

• Katie Bubak,
• Statewide Consultant
• 208.426.3257
• katiebubak_at_boisestate.edu

Training materials can be found at
www.idahotc.com
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Project Sponsor
Idaho Department of Education Special Education
Division Richard Henderson, Director rhenderson_at_sd
e.idaho.gov