session 2 tier 2 – category of the problem 1. © amanda vanderheyden, do not reproduce without...

Session 2

Tier 2 – Category of the Problem

1

© Amanda VanDerHeyden, Do Not Reproduce Without Permission

How-To Classwide Math


Intervention Plan- 15 Min per Day• Protocol-based classwide peer tutoring,

randomized integrity checks by direct observation

• Model, Guide Practice, Independent Timed Practice with delayed error correction

• Group performance contingency• Teachers encouraged to

– Scan papers for high error rates– Do 5-min re-teach for those with high-error rates– Provide applied practice using mastery-level

computational skill


• Usually the higher-performing student, goes (models) first.• Rotating high performers helps maintain motivation


Measurement Plan

• Weekly probe of Intervention skill• Weekly probe of Retention of previously

mastered computational skills• Monthly probe using GOM approach to

monitor progress toward year-end computational goals

• To this you might add an application measure


Sample Sequence

Kindergarten, 1st Semester


Kindergarten, 2nd Semester



Intervention Plan

• Class Median reaches mastery range for skill, next skill is introduced

• Following promising results at one site in 2002-2003, lead to implementation district-wide grades 1-8 for all children by 2004-2005.

Instructional Criteria• MATH

– K: • 0-7 Count Objects, Circle Number• 0-5 Count Objects, Write Number• 0-4 Identify Number, Draw Circles• 0-5 Rapid Discrimination (sorting)

– Grades 1-3• 0-19 dc/2 min Frustration• 20-39 dc/2 min Instructional• 40+ dc/2 min Mastery


Instructional Hierarchy: Stages of Learning

Acquisition Proficiency Generalization Adaption

Learning Hierarchy

Instructional Hierarchy

Slow and inaccurate

ModelingExplicit instructionImmediate corrective feedback

Accurate but slow

Novel practice opportunitiesIndependent practiceTimingsImmediate feedback

Can apply to novel setting

Discrimination trainingDifferentiation training

Can use information to solve problems

Problem solvingSimulations

Haring, N. G., & Eaton, M. D. (1978). Systematic instructional procedures: An instructional hierarchy. In N. G. Haring, T. C. Lovitt, M. D. Eaton, & C. L. Hansen (Eds.) The fourth R: Research in the classroom (pp. 23-40). Columbus, OH: Charles E. Merrill.


Acquisition

Fluency

Generalization


To gain the steepest growth, introduction of new skills should happen here– Core Instruction- Not manipulated

But fluency building should happen here with an instructional level skill– Intervention Focus was here

Finally, problem-solving/ application practice should occur here with a mastery level skill– Core Instruction- Not Manipulated but could be


Class-wide Math Intervention


Decision making

• Review data to make decisions:

DATA OUTCOME 1: Class median is below mastery range and most students gaining digits correct per week.

ACTION: Consider implementing intervention for an additional week and then review progress again.


Decision making DATA OUTCOME 2: Class median is below

mastery range and most students are not gaining digits correct per week:

ACTION: Check Integrity first and address with training if needed. Consider implementing intervention for an additional week with incentives or easier task and then review progress again.


Decision making

DATA OUTCOME 3: If the class median is above mastery range then consider:

ACTION: Increasing task difficulty and continuing classwide intervention.

ACTION: For students performing 1 SD below the class mean, consider Tier 3.


Results


Tier 1 Screening Indicates Class-wide Problem


Tier 2: Class-wide Intervention

Teacher F Mult 0-12

0

20

40

60

80

100

120

10/2

4/20

03

10/3

1/20

03

11/7

/200

3

11/1

4/20

03

11/1

8/20

03

Weeks

Dig

its

Co

rrec

t Tw

o M

inu

tes


Increased Difficulty- Intervention Continues


Contextually-Relevant Comparisons and Use of Trend Data


5th Grade Math Intervention


Instructional range

Frustrational range

Pre-post changes to performance detected by CBM

Each bar is a student’s performance


Fourth Grade


Computation Gains Generalized to High Stakes TestImprovements

(Gains within Multiple Baselineshown as pre-post data)


Gains within Multiple Baseline (shown as pre-post data)


District-Wide RCT 4th & 5th Graders


treatment

control

• Effects on year-end scores significant at fourth grade. Effects strongest for students who were lowest performing on the prior year’s test score.

• CBMS showed strong effects, both grades.

• Integrity varied by class and variations explained effects

36

Overall

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For Vulnerable Students

38

For Vulnerable Students

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Conclusions

• Low-performing students more prone to have week(s) of missing data.

• Probability of failure was reduced at a greater rate for students who receive free and reduced lunch, students receiving special education, and for African American students.

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And Ed Shapiro was right, but these data are preliminary

• New decision rule to select students in need of Tier 2 or 3 intervention

• Class Median= Mastery, Any child in frustration range at any point during intervention– Sens: .46; Spec = .91

• Class Median= Mastery, Any child 1SD below class mean– Sens: .73; Spec= .66

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How to Tier 2

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Kindergarten, 1st Semester

© Amanda VanDerHeyden, Do Not Reproduce Without Permission43

Kindergarten, 2nd Semester


1st Grade


2nd Grade


3rd Grade


4th Grade


5th Grade


6th Grade


7th Grade


8th Grade



Count Objects- Write Number

• Two forms available. Easier form has answers from 1-10. More challenging form has answers from 1-20.

• Classwide or Individual Administration• 1 minute• Scored as correctly written numbers per

minute


Count Objects- Write Number


Tier 2 Assessment

• Evaluate effects of– Incentives on performance (can’t do/won’t do

assessment)– Brief instructional trials on performance– GOAL- identify intervention that will improve

performance and can be delivered efficiently (e.g., small groups)


Tier 2 Intervention

• Identify instructional-level task– Develop logical hierarchy (VanDerHeyden, 2005)– Identify difficulty level for which child responding is

accurate most of the time

• Emphasize multiple opportunities to respond– Use response cards– Use choral responding

• Provide Immediate Corrective Feedback• Provide rewards for skill gains each session


Counts in order to 10

Accurate Number Names to 5

Fluent Number Names to 5

Accuate Number Names to 10

Fluent Number Names to 10

Identifies Number of Objects in a Set to 10

Define the Behaviors/skills


Response Card Intervention


Not at Risk

screening

incentives

intervention

At Risk

Let’s Talk about Another Pitfall

• Overemphasizing intervention selection and under-emphasizing intervention management

60

Integrity Failures are Sentinel Events

• Untreated integrity problems become student learning deficits, schoolwide learning problems, and false positive decision errors

• Integ problems affect dose and quality of the treatment (an intervention implemented with fidelity is a functionally different intervention than one implemented inconsistently

• Integ positively correlated with student learning gains, amount of intervention covered

• Even veteran sites require monitoring and follow-up

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Sometimes it’s the Simple Things• Proximity to trainer• Child availability for intervention sessions• Intervention error (e.g., modeling too

rapidly, failing to give feedback)• Materials available• No one’s watching• Tracking and troubleshooting

implementation failures• Remember, intervention failures should be

rare 62

Just like your mama told you: INTEGRITY MATTERS

59% Integ 96% Integrity

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64VanDerHeyden, McLaughlin, Algina, Snyder (in press). AERJ

TIER 3

What is the causal variable?

Components of Tier III

• Precise measurement on a frequent basis

• Individualized and intensive interventions

• Meaningful multi-disciplinary collaboration regarding individual kids

Materials

• Assessment materials (basic skill builders)• Digital timer• Treasure Chest• Excel for Graphs• Criteria for Decision Making• Intervention Materials

Instructional Criteria• MATH

– K: • 0-7 Count Objects, Circle Number• 0-5 Count Objects, Write Number• 0-4 Identify Number, Draw Circles• 0-5 Rapid Discrimination (sorting)



Instructional Criteria- Updated

• Grades 2-3– 28-61 dc/2 min

• Grades 4-5– 48-98 dc/2 min

– Burns, VanDerHeyden, & Jiban (2006)

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Within-child Variables

•Temperament

•Ability/biology

•Early deficits or insults

•Learned Coping Strategies

Environmental Variables

• Task demands

•Quality of Instruction

• Learning opportunities

• Motivation

Child-Environment Fit

CHILD PERFORMANCE/SUCCESS/ADAPTATION

Largely Unalterable Alterable

• Acquisition Interventions– Designed to establish correct responding– Cover, copy, compare; modeling; immediate

corrective feedback/guided practice; prompt hierarchies; Incremental Rehearsal

• Instructional Skill Interventions– Designed to build fluency– Timed trials with reinforcement; goal setting; rapid

advancement of task content; delayed feedback/error correction; Task interspersal

• Mastery Level Interventions– Designed to teach generalization– Guided practice applying learned skill; variation of

materials during intervention

Functional Assessment

• Consider logical sequence of skills• Identify target skills

– Watch the child do the task– Ask the child to “think out loud”– Ask the child to teach you how to do it

• Examine effect of reduced task difficulty, use of incentives, and brief instruction (modeling and guided practice)

• Two key questions-– Does child understand concept?– Can child complete problem-solving steps?

Instructional Hierarchy: Stages of Learning


Learning Hierarchy


Slow and inaccurate

ModelingExplicit instructionImmediate corrective feedback

Accurate but slow

Novel practice opportunitiesIndependent practiceTimingsImmediate feedback

Can apply to novel setting

Discrimination trainingDifferentiation training

Can use information to solve problems

Problem solvingSimulations

Haring, N. G., & Eaton, M. D. (1978). Systematic instructional procedures: An instructional hierarchy. In N. G. Haring, T. C. Lovitt, M. D. Eaton, & C. L. Hansen (Eds.) The fourth R: Research in the classroom (pp. 23-40). Columbus, OH: Charles E. Merrill.

Instructional Hierarchy for Conceptual KnowledgePhase of Learning


Examples of appropriate instructional activities

Explicit Instruction in basic principles and concepts

Modeling with math manipulatives

Immediate corrective feedback

Independent practice with manipulatives

Immediate feedback on the speed of responding, but delayed feedback on the accuracy.

Contingent reinforcement for speed of response.

Instructional games with different stimuli

Provide word problems for the concepts

Use concepts to solve applied problems

Instructional Hierarchy for Procedural KnowledgePhase of Learning Acquisition Proficiency Generalization Adaption

Examples of appropriate instructional activities

Explicit instruction in task steps

Modeling with written problems

Immediate feedback on the accuracy of the work.

Independent practice with written skill

Immediate feedback on the speed of the response, but delayed feedback on the accuracy.

Contingent reinforcement

Apply number operations to applied problems

Complete real and contrived number problems in the classroom

Use numbers to solve problems in the classroom

Phase of Learning for Math

ConceptualAcquisition Proficiency Generalization Adaption

ProceduralAcquisition Proficiency Generalization Adaption

© Matthew Burns, Do Not Reproduce Without Permission

• Step 1: Build conceptual understanding• Step 2: Build procedural fluency• Check acquisition (accuracy),

independence (fluency), and application

Assessing Conceptual KnowledgeConcept Oriented CBM

• Monitoring Basic Skills Progress-Math Concepts and Applications (Fuchs, Hamlett, & Fuchs, 1999).

• Focal Point Assessments (Witt, 2008) isteep.com

• Math Applications (Connell, 2008).

Assessing Conceptual KnowledgeConcept Oriented CBM

• Monitoring Basic Skills Progress-Math Concepts and Applications (Fuchs, Hamlett, & Fuchs, 1999).

• 18 or more problems that assess mastery of concepts and applications

• 6 to 8 minutes to complete

Conceptual Assessment

• Ask students to judge if items are correct– 10% of 5-year-old children who correctly

counted did not identify counting errors in others (Briars & Siegler, 1984).

• Provide three examples of the same equation and asking them to circle the correct one

• Provide a list of randomly ordered correct and incorrect equations and ask them to write or circle “true” or “false” (Beatty & Moss, 2007).

Conceptual Assessment

Problem 1Please use a picture to solve the problem

3 x 4 = ___

Problem 2Please use a picture to solve the problem

5 x 6 =___

Next 4 slides from Burns 2010

To Establish the Skill

• Use manipulatives to demonstrate• Ask child to explain what it means• Vary answer format • Ask equivalence, more-less, and true/false

questions• Add a within-stimulus prompt or cue• Once accurate, begin procedural fluency

Common Procedural Errors

• Not attending to operation, wrong operation

• Regrouping errors in addition, subtraction, and multiplication

• Dysfluency in basic computations• Misalignment of columns- place value

errors (e.g., long division)

Strategies

• Model, guided practice

• Provide Cues (e.g., use graph paper for column alignment, use highlighter to highlight operation)

• Use cover, copy, compare intervention

• Use within-stimulus prompt

• Build fluency on component skills

Cover-Copy-Compare

Match?

= 3

An Interpreted Example…

3

5

2

An Interpreted Example…

35

2

Interspersal

• Mix challenging with easier tasks (1:1, 1:3, 1:5)

• Effects for completion of challenging problems and preference

3

+ 1 2

+ 2

6

+ 3

1

+ 2

3

+ 2

Incremental Rehearsal

• Drill “unknown” item mixed in with “known” items

• Present 9 known flashcard problems to 1 unknown in 1:1 rotation.

• When an unknown is correct 9 times in session, it becomes a known

• When a known is missed three times, it becomes an unknown again

• Good effects for retention

Unknown

• 16 x 8 = 128

16 x 8

2 x 3


16 x 8

2 x 3


1 x 5


10 x 5

16 x 8

2 x 3


1 x 5


10 x 5


2 x 10

16 x 8

Unknown

Known 1

Unknown

Known 1

Known 2

Unknown

Known 1

Known 2

Known 3

Unknown

Known 1

Known 2

Known 3

Known 4

Unknown

Known 1

Known 2

Known 3

Known 4

Known 5 © Amanda VanDerHeyden, Do Not Reproduce Without Permission

Unknown correct 5 times = KnownNext Session, Unknown becomes Known 1

Amanda’s Show and Tell


Some Lessons Learned• We often measure too much and too much

of the wrong things.• We do not begin with a plan in mind of

what the most critical “big ideas” are and make these explicit for students.

• Students are not provided with adequate time to practice to mastery.

• We do not connect instructional strategies to student proficiency.

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Lessons Learned• We fail to attend to the basics

– Adequate time, intention, systematic advancement of content based on mastery of prior content, explicit connection of computations to conceptual understandings past and future, providing sufficient demonstrations and checking for student understanding

• We de-value fluency in computational skills and bigger ideas like quantity discriminations with proportions

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• We think of “application” as only word problems

• If we graph expectations for mathematical learning across years of school, it is not a linear upward trend. We expect too little at the lower grades and try to make up for lost time later on.

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For More Information• Amanda VanDerHeyden

– [email protected]– 251-300-0690

• www.isteep.com and www.gosbr.net • www.rtinetwork.org• www.nasdse.org (blueprints)• Keeping RTI on Track: How to Identify, Repair and Prevent

Mistakes That Derail Implementation• http://www.shoplrp.com/product/p-300620.html• Or 1-800-341-7874• http://www.jeabjaba.org/abstracts/JabaAbstracts/26/26-597.Htm

(Fixsen & Blasé, 1993)• Hattie (2009). Visible Learning.

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mailto:[email protected]

http://www.isteep.com/

http://www.gosbr.net/

http://www.rtinetwork.org/

http://www.nasdse.org/

http://www.shoplrp.com/product/p-300620.html

http://www.jeabjaba.org/abstracts/JabaAbstracts/26/26-597.Htm

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