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Planning for Tier 2 Math Instruction
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Evelyn Johnson, Ed.DCristianne Lane, M.EdMargo Healy, M.Ed
Introductions
Logistics
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Project SponsorIdaho Department of Education Special Education DivisionRichard Henderson, [email protected]
SESTAGina Hopper, [email protected]
Training Goals:
• Provide direction for screening, assessing, planning, delivering and monitoring Tier 2 math instruction through a five step process approach.
• Examine data and apply the process.
• Share ideas, thoughts, resources, etc., with each other.
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Agenda:Introduction
– RTI Purpose/Components/Systems– Beliefs
The Process– Screening, Sorting and Assessing– Grouping Students and Allocating Resources– Delivering Instruction– Monitoring Progress– Reflecting and Responding to Intervention
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Sources:
• What Works Clearinghouse and Doing What Works
• Research Journals• RTI Action Network, Intervention Central• National Center on Response to Intervention
• National Council of Teachers of Mathematics
• Common Core Mathematics Standardsr t
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Introduction:
• RTI Purpose• RTI Components and Systems• Beliefs
Warm‐Up
You run into a parent of a student at the grocery store who asks, “I keep hearing about RTI. What is it?”
How would you explain what RTI is to a parent?
What might you add to that definition if you are talking to colleague?
What is RTI?
Response to intervention (RTI) integratesassessment and intervention within amulti‐level prevention system to maximizestudent achievement and reducebehavioral problems.
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Genesis of RTI – Public Health Model
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RTI is a System of Instruction
Tier I instruction is strong and comprehensive (80% proficient).
Tier II interventions focus on specific skills/concepts to respond to the specific needs of individual students. Students are usually taught in small groups, but identified individually by reliable formal and informal assessments.
RTI
If RTI is a SYSTEM of Instruction...
What are some systems that need to be in place for RTI to be effective and efficient?
Beliefs Set the Foundation and Guide the Process
Introducing...Gildo Rey Elementary in Auburn, WA
• 84% free and reduced lunch, 37% ELL• Over 85% pass rate on state reading and math tests
• Here is what they believe about their students...
Teachers at Gildo Rey Believe:
• All of our kids are all of our kids!• It’s all about relationships.• All of our kids can meet the standard.• Nobody gets to give up, opt out or fail.• “Without data, you’re just another person with an opinion.”
• Every decision comes down to “What is best for our kids?”
Gildo Rey’s Beliefs about Instruction
• Laser focus on the standards• Intentional, direct instruction• Teach to mastery and then review forever• Assume it will take MANY repetitions before achieving mastery
• Reading and math are the focus and the priority
Agenda:Introduction
– RTI Purpose/Components/Systems– Beliefs
The Process– Screening, Sorting and Assessing– Grouping Students and Allocating Resources– Delivering Instruction– Monitoring Progress– Reflecting and Responding to Intervention
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Step #1: Screening, Sorting and Assessing
• Purpose• Choosing a screening tool • Setting a cut score (decision point)• Collecting and organizing results• Determining who needs further assessments
• Administering more targeted assessments• Analyzing results
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iWhat is Screening?
Screening results are confirmed by further testing
Screening results are confirmed by further testing
Screens identify an initial risk poolScreens identify an initial risk pool
Brief assessment of ALL studentsBrief assessment of ALL students
All Students
+ Screen
True Positive
False Positive
‐ Screen
No further testing
19Johnson Smith Harris
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iAccurate
EfficientReliable
Screeners Must Be…
Other Information:• ISAT scores• Grades/report cards• Placement tests• EOC tests
Choosing a Screener
• What does the screener assess? • Is the screener norm‐referenced or criterion‐referenced?
• Is the screener accurate, efficient and easy to understand?
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iCCSS Domain Progression
K 1 2 3 4 5 6 7 8 HS
Counting & Cardinality
Number and Operations in Base Ten Ratios and Proportional Relationships
Number & 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 Probability Statistics & Probability
Strong Mathematiciansr
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Skills
Procedures
Process
Application
XContentContent UnderstandingUnderstanding
Norm‐referenced vs. Criterion‐referencedNorm‐referenced(percentile scores are available that rank students from the 1st to the 99th percentile)
Considers how a student performs relative to a sample of comparable students
Criterion‐referenced(often mastery measures)
Considers how a student performs relative to expected performance on grade level material
Normal Distribution Curve
502510
Example: Setting a cut score...
Norm‐referenced vs. Criterion‐referencedNorm‐referenced
Student PercentileRanking
Macy 92 %ileBailey 74 %ileRuby 65 %ileDeclan 50 %ileTim 44 %ileWill 40 %ileTroy 35 %ileMindy 20 %ileKris 18 %ileMark 10 %ile
Criterion‐referenced
Student Raw score
Percent Correct
Tom 48 98%John 43 88%Sandra 37 76%Matt 30 61%Mike 24 49%Joe 16 33%Annie 14 29%Sara 10 20%
Screening: 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
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Additional Recommendations for K‐1st from the researchers:
• Number Identification (K)
• Basic Arithmetic Facts (beginning at the middle of first grade)
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Examples of K‐1 Screening Tools Listed on Intervention Central:
–Monitoring Basic Skills Progress (MBSP)
–AIMSweb Test of Early Numeracy–EasyCBM–STAR
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐Primary Math Assessment (PMA) –Idaho
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Elementary‐High School• Number and Operations• Content in other domains (e.g. Geometry)• Concepts and Application
Examples of Screening Tools (all grades):STAR, 1st ‐ 12th
AIMSweb (M‐COMP and M‐CAP), K‐ 8th
Math Navigator, 3rd ‐10th
EasyCBM, K ‐ 8thr t
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Organizing Data
Examples:Data boardsSpreadsheets
Student FALL
Student Winter
Student Spring Harry Potter 48 Harry Potter 48 Harry Potter 48
Hermoine Granger 44 Hermoine Granger 45 Hermoine Granger 46
Ron Weasley 44 Ron Weasley 42 Ron Weasley 44
Neville Longbottom 43 Neville Longbottom 42 Ginny Weasley 44
Oliver Wood 38 Oliver Wood 39 Luna Lovegood 43
Ginny Weasley 37 Luna Lovegood 38 Oliver Wood 42
Vincent Crabbe 36 Ginny Weasley 36 Vincent Crabbe 42
Luna Lovegood 36 Vincent Crabbe 35 Neville Longbottom 41
Cho Chang 29 Cho Chang 35 Cho Chang 39
Gilderoy Lockhart 28 Draco Malfoy 35 Draco Malfoy 39
Draco Malfoy 27 Gilderoy Lockhart 28 Gilderoy Lockhart 39
Gregory Goyle 26 Poppy Pomfrey 28 Poppy Pomfrey 39
Dudley Dursley 25 Gregory Goyle 27 Gregory Goyle 37
Helga Hufflepuff 23 Dudley Dursley 27 Dudley Dursley 34
Minerva McGonagall 23 Helga Hufflepuff 23 Helga Hufflepuff 32
Poppy Pomfrey 22 Minerva McGonagall 23 Minerva McGonagall 27
Screening
Mock Screening Data Example
Your Screening Data
Your Screener• What skills/concepts does your screener assess?
• Is the screener norm‐referenced or criterion‐referenced?
• Is the screener accurate, efficient and easy to understand?
• What is your decision rule (cut score)?• How will/did you organize your data?• Have you identified students who need more targeted assessments?
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iSuggested Screening Process
Step 1: Review Screening ResultsStep 1: Review
Screening Results
All Students
Step 2: Identify Students who don’t meet benchmarks
Step 2: Identify Students who don’t meet benchmarks
Does Not Meet Benchmark
Meets Benchmark
Step 3: Determine Severity of Discrepancy
Step 3: Determine Severity of Discrepancy
Moderate to Significant Discrepancy
Near Benchmark
Continue
Step 4: Conduct Targeted
Assessments to Inform
Intervention
Step 4: Conduct Targeted
Assessments to Inform
Intervention
Determine Nature of Discrepancy
IndividualStudent andProgramPlanning
39Johnson Smith Harris
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iMore targeted assessment tools
allow us to...
K 1 2 3 4 5 6 7 8 HS
Counting & Cardinality
Number and Operations in Base Ten Ratios and Proportional Relationships
Number & 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 Probability Statistics & Probability
Examples of More Targeted Assessment Tools:
• Basic skills tests from other grade levels• Pre and post‐tests from programs (e.g. unit tests)• Item analysis of screener or other tests• More targeted probes • Kathy Richardson’s Assessing Math Concepts (K‐3)• NCTM’s Mathematics Assessment Samplers• The Direct Mathematics Assessment sample items
Item Analysis: Math Navigator
Student Beg. PlaceValue % correct
Add. & Sub.Facts % correct
UnderstandingAdd. & Sub.% correct
Mult. & Div. Facts% correct
Fractions
% correct
Charts & Graphs% corrrect
17 100 83 83 67 67 87
18 83 100 83 67 50 33
19 83 100 67 67 33 87
20 83 67 67 50 33 0
21 67 67 83 67 33 17
22 50 67 67 50 17 50
23 50 67 33 33 17 33
24 67 67 67 67 33 33
25 33 50 67 17 17 67
26 67 67 67 50 33 67
27 33 33 0 17 33 17
28 17 67 33 33 17 17
29 33 67 67 50 33 33
30 33 67 67 33 33 33
31 33 50 33 33 33 0
32 17 33 17 0 33 0
More Examples:
• More targeted probes: Easy CBM examples Grade 3, number and operations, pages 2‐5Grade 6, algebra, pages 6‐9
• Kathy Richardson K‐3, student interviewsGrouping Tens (place value), page 10
• NCTM Assessment Sampler, K‐12 performance tasks Grade 6‐8 example, page 11
• Direct Math Assessment Toolkit Binder
Entry ...and Exit Criteria!
Examples of Tier 2 Math Planning Templates from Meridian:
– Fractions and Decimals, page 12‐13
More Targeted Assessment Data
• Mock Data Example
• Your Data– If you already administered more targeted assessments, what did you learn?
– If not, what tools might you use?
The Process
Step 1: Screening, Sorting and Assessing Step 2: Grouping Students and Allocating
ResourcesStep 3: Delivering InstructionStep 4: Monitoring ProgressStep 5: Reflecting and Responding to
Intervention
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Grouping Students
• Based on the mock data, what groups seem to emerge?
• How many students you can serve also depends on how you are able to allocate resources (time, personnel, space, etc.)
Allocating Resources Activity:From Beginning ...to Ideal!
(see grid, page 14)
• Time (see next 3 slides)• Personnel• Instructional Resources/Materials • Group Configurations• Instructional Settings
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
Meridian High School Example
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Middle School Example
ReadingWritingMath—coreMath‐‐ differentiated by needScience/Social StudiesPE/Music/Computer Lab rotationElective or Study Hall
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Elementary School Example:What is a possibility???
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/library1:45‐2:20 social studies/science2:20‐2:30 clean up and dismissal
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Step 2: Wrap Up
Examining your resources and your data, how will you serve your students who need tier 2 intervention?
The Process
Step 1: Screening, Sorting and Assessing Step 2: Grouping Students and Allocating
ResourcesStep 3: Delivering Instruction*Step 4: Monitoring ProgressStep 5: Reflecting and Responding to
InterventionW (We will address this last today)r t
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The Process
Step 1: Screening, Sorting and Assessing Step 2: Grouping and Allocating ResourcesStep 3: Delivering InstructionStep 4: Monitoring ProgressStep 5: Reflecting and Responding to
Intervention*
*Note: We will spend more time on reflecting in March...
Progress Monitoring Tier 1
Purpose:• To determine whether a student is making sufficient progress in gen. ed. curriculum
• To provide a classroom by classroom measure of student progress (school level)
• To monitor students who have exited intervention programs to ensure continued progress/ trigger re‐entry to intervention
What is the purpose of monitoring progress in Tier 2?
Progress Monitoring Tier 2
Purpose: • To determine when a student is ready to exit intervention
• To determine when an intervention needs to be changed
• To monitor a student’s progress through the intervention process over time to document a need for more intensive intervention
Strong progress monitoring relies on:
• Reliable and valid measures• Measures that are tied to important general outcomes – not just focused on mastery measurement
• Measures that are sensitive to student growth
• Measures that are administered frequently (recommended practice of 1 – 4 times per month depending on the age/grade level of the student)
Progress Monitoring Tools
• 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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Progress Monitoring Tools
Progress Monitoring Tools in Tier 2Review the tool to ensure that the mastery measure is aligned to the content of the intervention.• For students who require intervention that is significantly
below grade level, the general outcome measure may not be sensitive to student growth.
• For this student, the data from mastery measures that accurately measure the intervention content will help to show progress.
• Both general outcome measures and mastery measures inform the student’s progress in tier 2 (SLD).
Real Life Progress Monitoring Dilemma:
Benson is in fifth grade and the data indicate he does not have a solid grasp of place value concepts. The number and operations CBM for his grade level does not have questions that correspond directly to what he is learning in his math intervention class regarding place value.
What additional tool might you need?
Decision Rules for PM:
• What is the exit criteria?• When is an instructional adjustment warranted?
• What if a student is making progress but still needs support?
• When should a student be referred for a comprehensive evaluation?
PM Data Management in Tier 2
• Time allotted for analyzing data (e.g. collaboration meetings)
• Manage data to provide easy access by teachers
• Manage and analyze data by graphing, color coding, data boards, etc.
• Teachers use data to make decisions for individual students
• Teachers use PM data to evaluate the effectiveness of the intervention
Examples of Data Management Systems
AIMSwebhttp://www.aimsweb.com/
EasyCBMhttp://www.easycbm.com/
CBM focushttp://www.cbmfocus.com/
Activity: Interpreting PM Data
Let’s examine the PM data for students in a Tier 2 math intervention. The following graphs chart progress on fall to spring measures. The blue line is the aimline for the desired 5th grade performance standard.
Conclusion
• Progress monitoring will keep your interventions responsive to student needs
• Progress monitoring will allow for frequent, routine evaluations of the intervention programs
• Progress monitoring will monitor the efficacy of the Tier 2 instructional program
The Process
Step 1: Screening, Sorting and Assessing Step 2: Grouping and Allocating ResourcesStep 3: Delivering InstructionStep 4: Monitoring ProgressStep 5: Reflecting and Responding to
Intervention...more this spring!
Explicit and Systematic Instruction:Handout, page 16
• Modeling, Explanations, Think alouds,• Scaffolded, guided practice (C‐R‐A)• Cumulative Review• Immediate Corrective Feedback• Opportunities for student to verbalize reasoning
• Visual Representations and Models• Motivation
What Works Clearinghouse and Doing What Works Recommendationr
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C‐R‐A Progression
Abstract
Representational
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••
Concrete‐ Representational‐Abstract(Remember the Lizzie problem from your MTI class)
What is a concrete example for this?
4x + 3 = 15
Models: Match to Concepts
–Number lines– Ten Frames – Tree diagrams–Ones, tens, hundreds blocks/charts–Arrays and Area Models– Strip diagrams – Tables
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What Works Clearinghouse (IES Practice Guide):
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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Word Problem Recommendations:
Teach the underlying structures of word problems (WWC)
Eliminate “distracters” (P. Riccomini)
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How is the structure of these different?
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?
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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Change Problems
A passage of time and a change occurs
Beginning Change Ending
‐152 470cards
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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
Joann 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)
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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
54minutes
Xminutes
6 miles
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Eliminating “Distracters” Activity, page 17 in your handouts
Carmella planted an evergreen seedling. It grew 9 inches the first year. Every year after it grew 1 ¾ inches. How tall was the oak tree after 12 years?
What are possible distracters?
Can you rewrite this problem eliminating the possible distracters?
Source: Dr. Paul Riccomini’s CEC webinars
Video Activity
Word Problems:Multiplication Comparison Problems
1. Compare to explicit, systematic instruction model. Does this lesson meet the criteria?2. What are the next steps of this lesson?3. What would tomorrow’s lesson be?
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
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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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Fact Fluency:
Two resources for teachers and parents:
The fact fluency article (The Educator)www.LPLearningCenter.org
IES Practice Guide, Recommendation 6
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Fact Fluency Progression
Counting Strategies
Reasoning Strategies
Automatic Recall!
Fact Fluency Clip
From Math Ed:Origo and Stepping StonesTeaching “reasoning strategies” for fact fluency
Possible Instructional Resources:
• Making an existing program more explicit • Purchasing programs that follow the explicit teaching model
• Elementary and Middle School Mathematics by John Van de Walle
• MTI classes (models)• Some examples on MathVIDS.com and Khan Academy follow the model...
• IES Practice Guides (fraction guide too)
The Process
Step 1: Screening, Sorting and Assessing Step 2: Grouping and Allocating ResourcesStep 3: Delivering InstructionStep 4: Monitoring ProgressStep 5: Reflecting and Responding to
Intervention...more this spring!
Tier 2 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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Wrap Up
What are three “take aways” from today’s training?
Please pick one to share with the group.
Statewide Special Education Technical Assistance (SESTA)
Gina Hopper,Director
208.426.4363
Katie Bubak,Statewide
Coordinator
208.426.4613
Training materials can be found at www.idahotc.com
Project Sponsor
Idaho Department of EducationSpecial Education DivisionRichard Henderson, [email protected]
