Session 2 Tier 2 – Category of the Problem 1

© Amanda VanDerHeyden, Do Not Reproduce Without Permission How-To Classwide Math

© Amanda VanDerHeyden, Do Not Reproduce Without Permission 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

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Usually the higher-performing student, goes (models) first. Rotating high performers helps maintain motivation

© Amanda VanDerHeyden, Do Not Reproduce Without Permission

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

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Sample Sequence

© Amanda VanDerHeyden, Do Not Reproduce Without Permission

Sample Sequence © Amanda VanDerHeyden, Do Not Reproduce Without Permission

Kindergarten, 1 st Semester © Amanda VanDerHeyden, Do Not Reproduce Without Permission

Kindergarten, 2 nd Semester © Amanda VanDerHeyden, Do Not Reproduce Without Permission

Intervention Plan Class Median reaches mastery range for skill, next skill is introduced Following promising results at one site in , lead to implementation district- wide grades 1-8 for all children by

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 dc/2 min Frustration dc/2 min Instructional 40+ dc/2 min Mastery –Grades dc/2 min Frustration dc/2 min Instructional 80+ dc/2 min Mastery

Instructional Hierarchy: Stages of Learning AcquisitionProficiencyGeneralizationAdaption Learning Hierarchy Instructional Hierarchy Slow and inaccurate Modeling Explicit instruction Immediate corrective feedback Accurate but slow Novel practice opportunities Independent practice Timings Immediate feedback Can apply to novel setting Discrimination training Differentiation training Can use information to solve problems Problem solving Simulations 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 ). Columbus, OH: Charles E. Merrill.

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Acquisition Fluency Generalization Instructional Hierarchy 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

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Class-wide Math Intervention

© Amanda VanDerHeyden, Do Not Reproduce Without Permission 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.

© Amanda VanDerHeyden, Do Not Reproduce Without Permission 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.

© Amanda VanDerHeyden, Do Not Reproduce Without Permission 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.

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Results

Tier 1 Screening Indicates Class-wide Problem

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Tier 2: Class-wide Intervention Teacher F Mult /24/200310/31/ /7/ /14/200311/18/2003 Weeks Digits Correct Two Minutes

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Increased Difficulty- Intervention Continues

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Contextually-Relevant Comparisons and Use of Trend Data

© Amanda VanDerHeyden, Do Not Reproduce Without Permission 5 th Grade Math Intervention

© Amanda VanDerHeyden, Do Not Reproduce Without Permission

Instructional range Frustrational range Pre-post changes to performance detected by CBM Each bar is a student’s performance

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Fourth Grade

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Computation Gains Generalized to High Stakes Test Improvements (Gains within Multiple Baseline shown as pre-post data)

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Gains within Multiple Baseline (shown as pre-post data)

© Amanda VanDerHeyden, Do Not Reproduce Without Permission District-Wide RCT 4th & 5th Graders

© Amanda VanDerHeyden, Do Not Reproduce Without Permission treatment control

© Amanda VanDerHeyden, Do Not Reproduce Without Permission treatment control

35

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 37

For Vulnerable Students 38

For Vulnerable Students 39

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. 40

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 41

How to Tier 2 42

Kindergarten, 1 st Semester © Amanda VanDerHeyden, Do Not Reproduce Without Permission 43

Kindergarten, 2 nd Semester © Amanda VanDerHeyden, Do Not Reproduce Without Permission 44

1 st Grade © Amanda VanDerHeyden, Do Not Reproduce Without Permission

2 nd Grade © Amanda VanDerHeyden, Do Not Reproduce Without Permission

3 rd Grade © Amanda VanDerHeyden, Do Not Reproduce Without Permission

4 th Grade © Amanda VanDerHeyden, Do Not Reproduce Without Permission

5 th Grade © Amanda VanDerHeyden, Do Not Reproduce Without Permission 49

6 th Grade © Amanda VanDerHeyden, Do Not Reproduce Without Permission

7 th Grade © Amanda VanDerHeyden, Do Not Reproduce Without Permission 51

8 th Grade © Amanda VanDerHeyden, Do Not Reproduce Without Permission

Count Objects- Write Number Two forms available. Easier form has answers from More challenging form has answers from Classwide or Individual Administration 1 minute Scored as correctly written numbers per minute

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Count Objects- Write Number

© Amanda VanDerHeyden, Do Not Reproduce Without Permission 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)

© Amanda VanDerHeyden, Do Not Reproduce Without Permission 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

© Amanda VanDerHeyden, Do Not Reproduce Without Permission 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

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Response Card Intervention

© Amanda VanDerHeyden, Do Not Reproduce Without Permission 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 61

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% Integ96% Integrity 63

64 VanDerHeyden, 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) –Grades dc/2 min Frustration dc/2 min Instructional 40+ dc/2 min Mastery –Grades dc/2 min Frustration dc/2 min Instructional 80+ dc/2 min Mastery

Instructional Criteria- Updated Grades 2-3 –28-61 dc/2 min Grades 4-5 –48-98 dc/2 min –Burns, VanDerHeyden, & Jiban (2006) 69

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 AcquisitionProficiencyGeneralizationAdaption Learning Hierarchy Instructional Hierarchy Slow and inaccurate Modeling Explicit instruction Immediate corrective feedback Accurate but slow Novel practice opportunities Independent practice Timings Immediate feedback Can apply to novel setting Discrimination training Differentiation training Can use information to solve problems Problem solving Simulations 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 ). Columbus, OH: Charles E. Merrill.

Instructional Hierarchy for Conceptual Knowledge Phase of Learning AcquisitionProficiencyGeneralizationAdaption 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 Knowledge Phase of LearningAcquisitionProficiencyGeneralizationAdaption 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 Conceptual AcquisitionProficiencyGeneralizationAdaption Procedural AcquisitionProficiencyGeneralizationAdaption © Matthew Burns, Do Not Reproduce Without Permission

© Amanda VanDerHeyden, Do Not Reproduce Without Permission

Step 1: Build conceptual understanding Step 2: Build procedural fluency Check acquisition (accuracy), independence (fluency), and application

Assessing Conceptual Knowledge Concept 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 Knowledge Concept 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 1 Please use a picture to solve the problem 3 x 4 = ___ Problem 2 Please 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

3 5 2

3 5 2

Interspersal Mix challenging with easier tasks (1:1, 1:3, 1:5) Effects for completion of challenging problems and preference

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

2 x 3

16 x 8

2 x 3 © Amanda VanDerHeyden, Do Not Reproduce Without Permission

1 x 5

16 x 8

2 x 3 © Amanda VanDerHeyden, Do Not Reproduce Without Permission

1 x 5 © Amanda VanDerHeyden, Do Not Reproduce Without Permission

10 x 5

16 x 8

2 x 3 © Amanda VanDerHeyden, Do Not Reproduce Without Permission

1 x 5 © Amanda VanDerHeyden, Do Not Reproduce Without Permission

10 x 5 © Amanda VanDerHeyden, Do Not Reproduce Without Permission

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 = Known Next Session, Unknown becomes Known 1

Amanda’s Show and Tell © Amanda VanDerHeyden, Do Not Reproduce Without Permission

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. 113

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 114

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. 115

For More Information Amanda VanDerHeyden – and (blueprints) Keeping RTI on Track: How to Identify, Repair and Prevent Mistakes That Derail Implementation Or Htm (Fixsen & Blasé, 1993) 597.Htm Hattie (2009). Visible Learning. 116