© Amanda VanDerHeyden, Do Not Reproduce Without Permission Using RtI to Advance Learning in Mathematics Amanda VanDerHeyden Education Research and Consulting,

7 Years Highly effective teachers show gain of 1.5 grade equivalents. Ineffective teachers show gains of.5 grade equivalents. These gains are independent of other risk factors associated with demographics. 2

Subtle Tension Schools want –scores to increase –vulnerable children to show gains –to avoid negative AYP labels –parents/communities to have confidence in schools –all children to have access –meet legal obligations Families and Caregivers want their children –to be happy at school –to learn skills that will help them succeed in college and beyond –to develop life-long love for learning –to grow into well- rounded, independent citizens 3

What do Families Want? Improved learning Transparent decisions Active system problem- solving Efficient use of resources What was my child’s score? What did you do differently? What effect did it have? What are we doing next? 4

Fool’s Gold If you are poor, of minority ethnicity, or a boy, you have a much higher probability of going to special ed and a much higher risk of academic failure. Special education placement does not improve outcomes for kids in the high- incidence categories and, in fact, is associated with risk. 5

Grade level corresponding to age 1 2 3 4 Reading grade level 4 3 2 1 5 2.5 5.2 At Risk on Early Screening Early Screening Identifies Children At Risk of Reading Difficulty Low Risk on Early Screening This Slide from Reading First Experts J From Reading First 6

Grade level corresponding to age 1 2 3 4 Reading grade level 4 3 2 1 5 2.5 5.2 Early Intervention Changes Reading Outcomes At Risk on Early Screening Low Risk on Early Screening 3.2 Control With research- based core but without extra instructional intervention 4.9 Intervention With substantial instructional intervention This Slide from Reading First Experts J From Reading First 7

New Assumptions with RtI Most children should successfully respond to intervention. Most children in a class should score at benchmark levels given adequate instruction. Intervention failure should be a rare event. Where it is not rare, implementation error should be the first suspect. © Amanda VanDerHeyden, Do Not Reproduce Without Permission

Instructing without assessment or intervening without assessment data is akin to driving without a map. With data, any solution becomes a hypothesis to be tested. We need to focus more on supporting solution implementation and evaluating solutions to be sure they work. Effective teachers, administrators, and schools are defined by the results they produce. © Amanda VanDerHeyden, Do Not Reproduce Without Permission

What does RtI Mean for your Child? High-performing? –Use data to enrich and challenge, smarter allocation of resources means more available for enrichment –Children ready for advanced coursework Average student? –Children ready for advanced coursework Low performing? –Accelerated growth, reduction of risk for failure, mastery of essential skills

Data = Fuel To determine risk To evaluate systemic problems To plan instructional changes system-wide To plan intervention for individual, small groups, or whole classes as supplement to core To evaluate intervention effects and inform referral decisions

Multi-Tiered Academic Interventions Tier I: Universal screening and progress monitoring with quality core curriculum: All students, Tier II: Standardized interventions with small groups in general education: 15% to 20% of students at any time Tier III: Individualized interventions with in-depth problem analysis in general education : 5% of students at any time

Tier I

Types of Math Knowledge Conceptual - the understanding that math involves an interrelated hierarchical network that underlies all math-related tasks Procedural - the organization of conceptual knowledge into action to actually perform a mathematical task (Hiebert & Lefevre, 1986). Which comes first? –Sequence may be specific to the domain or the individual (Rittle-Johnson & Siegler, 1998; Rittle- Johnson, Siegler, & Wagner, 2001) –But the two are clearly interrelated.

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Challenges Ratio of 6:1 NAEP data show improvements but not for ethnic minorities and low SES students Lack of streamlined resources Insufficient instructional time allocated to mathematics Math proficiency related to income post- graduation, success in college Students who are not proficient and enroll in remedial classes post-secondary are less likely to graduate

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Slavin & Lake (2008) 87/256 reviewed studies met rigorous inclusion criteria 13 categorized as examining curricula 36 categorized as computer- assisted instruction 36 categorized as instructional process + 0.10 + 0.19 + 0.33

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Conclusion If you want to change math learning outcomes, you have to change the quality of the instructional interaction between student and teacher So what are the characteristics of quality core instruction in mathematics?

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Begin with Number Sense Numbers represent quantity and have magnitude One number may be bigger than another number or quantity Numbers have a fixed order with numbers later in the sequence representing greater quantities –Begins with counting in sequence, counting objects, comparing quantities, adding and subtracting numbers. Leads to understanding of associative, commutative, and distributive property and place value. Griffin (2004)

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Integrate Instruction for Procedural and operational fluency with conceptual understanding e.g., emergence of the “count-on” strategy as children’s understanding of ordinality and associative property develop –Estimate, discuss solutions, verify solutions, practice application

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Sequence Skills Logically and Provide Adequate Instructional Time “a mile wide and an inch deep” Make tough decisions about which skills are essential and ensure mastery of those skills NMP says –whole number add/sub by grade 3 –mult/div by grade 5 –Operations with fractions, decimals, percentages –Operations with pos/neg integers –Operations with pos/neg fractions –Solving percentages, ratios, and rates to balance equations

Match Instruction to Learner Competence Opportunities to Respond; Practice to Mastery Build Fluency

Increased range of stimuli Response Variation- Build response set Improve Maintenance

Student Competence Goal of Intervention Intervention Example Acquisition TaskEstablish 100% correct Cover, copy, and compare Independent Task Build fluencyFlashcards, timed performance with incentives, response cards Mastery TaskEstablish robust application Guided practice intervention

What is Balanced Math Instruction? Math Proficiency Ensure acquisition of key concepts in math Build conceptual understanding to fluency Provide opportunities to generalize skills to novel problems Opportunities to predict, estimate, verify, and discuss solutions

Common Core Content Standards Streamlined “Asking a student to understand something means asking a teacher to assess whether the child has understood it.” Hallmark of understanding: student can explain why a mathematical statement is true or where a rule comes from. © Amanda VanDerHeyden, Do Not Reproduce Without Permission

Roadmap to Lesson Planning Do students understand? Can they do it? How will you –Establish conceptual understanding? –Build fluency? –Provide applied practice and discussion? © Amanda VanDerHeyden, Do Not Reproduce Without Permission

Tier 1: Screening 3 times per year More frequently if problems are detected Probably two probes required Computation probes work well-- consider state standards Math Screening 2 minutes. Scored for Digits Correct per 2 min

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Tier 2: Can’t Do/Won’t Do Assessment “Can’t Do/Won’t Do” Individually-administered Materials –Academic material that student performed poorly during class assessment. –Treasure chest: plastic box filled with tangible items. 3-7 minutes per child

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Response to Intervention Before Intervention During Intervention Avg. for his Class Intervention in Reading #Correct Intervention Sessions Each Dot is one Day of Intervention

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Screening tells you How is the core instruction working? What problems might exist that could be addressed? Most bang-for-the-buck activity Next most high-yield activity is classwide intervention at Tier 2.

Mult 0-9 4 th Grade Fall Screening

Start with a Helicopter View 45

Second Grade Math 46

Third Grade Math 47

Where system problems are detected, deploy system interventions and: Verify Rapid Growth in all Classes 48

Look for Lagging Classes– and Respond 49

Teacher 1Teacher 2Teacher 3Teacher 4Teacher 5Teacher 6Teacher 7Teacher 8Teacher 9 Teacher 10 Teacher 11 Teacher 12 50

Set System Goals- Track- And Respond 51

How Can MTSS Help? Organize small groups based on student proficiency (acquisition, fluency, generalization) Use Classwide intervention to build fluency in pre-requisite skills (I’ll explain) Use intensive, individualized interventions to conduct acquisition interventions following functional academic assessment (I’ll show you how) Use screening data to connect instructional strategies to student proficiency © Amanda VanDerHeyden, Do Not Reproduce Without Permission

School-Wide Problem? Examine core instruction materials and procedures –Instructional time –Research-supported curric materials –Calendar of instruction –Understanding and measurement of mastery of specific learning objectives © Amanda VanDerHeyden, Do Not Reproduce Without Permission

Establish priorities for improvement and determine timeline Add a supplemental instructional program with weekly PM Examine and respond to implementation effects each month. Share w/ feeder pattern & connect to long-term effects. © Amanda VanDerHeyden, Do Not Reproduce Without Permission

School-Wide Problem? © Amanda VanDerHeyden, Do Not Reproduce Without Permission

Demographics should become more proportionate in failure or risk groups over time. Percentage of students “on track” should improve (look at percent enrolling in and passing algebra, AP enrollments and scores, Percent taking and meeting ACT benchmarks). © Amanda VanDerHeyden, Do Not Reproduce Without Permission

Grade-wide Problem? Examine core instruction procedures Begin class-wide supplement and PM weekly Conduct vertical teaming with preceding and subsequent grade levels to identify strategies to ensure children attain grade- level expected skills in future. © Amanda VanDerHeyden, Do Not Reproduce Without Permission

Small Group Problem Use Tier 2 time to provide more explicit instruction following standard protocol. Monitor weekly. Exit students based on post-intervention performance not in the risk range on lesson objectives and screening criterion. When most children are responding well, identify children for Tier 3. © Amanda VanDerHeyden, Do Not Reproduce Without Permission

About 90% of children should respond successfully to Tier 2 intervention Successful responders should surpass screening criterion at higher rates on subsequent screenings. Successful responders should pass high- stakes at higher rates than before use of Tier 2 strategies. © Amanda VanDerHeyden, Do Not Reproduce Without Permission

Individual Problem? Conduct individual assessment to establish targets, identify effective intervention, and specify baseline. Prepare all materials Monitor weekly and troubleshoot to accelerate growth © Amanda VanDerHeyden, Do Not Reproduce Without Permission

Most children participating in Tier 3 should respond successfully. More than 5% of screened pop is a red flag. Focus on integrity of intervention. Growth should be detectable within two weeks. Troubleshoot interventions that aren’t working. © Amanda VanDerHeyden, Do Not Reproduce Without Permission

Successful responders to Tier 3 should fall into risk range on subsequent screenings at lower rates. Successful responders should pass high- stakes at higher rates. Unsuccessful responders should qualify for more intensive instruction at higher rates. Responders/nonresponder should be proportionate by demographics. © Amanda VanDerHeyden, Do Not Reproduce Without Permission

Let’s Talk about Two Pitfalls Loosely Defined Model Over-assessment 67

Your Model is “Too Loose” If Results are inconsistent across schools and/or over time There are long delays between decisions There are cases without a final decision 68

Assess Smarter First, select the best measures and understand what the “hit” rate is No measure is perfect and adding more measures may not (most likely will not) increase the “hit” rate What do I mean by a “hit” rate? 69

“Hit” Rates Summarize Accuracy of Decisions 70

Users Must Weigh The costs of false positive errors and false negative errors for each decision. –For Screening Decisions – A priority is placed on avoiding false negative errors typically. –As a result, many screening systems burden systems with high false-positive error rates. –High error rates cause users to lose momentum and can attenuate intervention effects systemwide. –Collecting “more data” does not necessarily improve the hit rate. 72

Schools are Drowning in Data and the Same Children Still Can’t Read (or Count) Are we making a difference? Are we changing the odds? 73

Take an Assessment Inventory 74

Verify Screening Adequacy 75

Exploit Existing Data and Respond- First, Verify Core 76

Decision “Hit Rates” Can be Examined to know if Use of an assessment or intervention improves outcomes over time (increases the odds of student success) You can compute the probability of passing or failing the high-stakes test if a student has passed or failed a screener (called the post-test probability) e.g., VanDerHeyden, A. M. (2010). Determining early mathematical risk: Ideas for extending the research. Invited commentary in School Psychology Review, 39, 196-202. 82

Bad Decisions are Not Benign Parent/School Bonding Community Support Play Rest Field Trips Special Projects Art Music LiteracyMathematics Social Skills Language and Writing 83

© 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 Written Permission Materials Needed Computer and software to organize data Student data imported. Clerical person to enter data on- site for tier 1 screen only. Color printer to print graphs + extra color cartridges Probe materials, digital count-down timers Intervention protocols, intervention materials (e.g., flashcard sets, reading materials) Access to copier and some assistance with copying Reinforcers for treasure chest (no more than $500 per school)

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 © 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 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 –Grades 4-6 0-39 dc/2 min Frustration 40-79 dc/2 min Instructional 80+ dc/2 min Mastery

Acquisition Child response is inaccurate Fluency Child response is accurate but slow Generalization Child response is fluent Salient cues, frequent & high-level prompting, immediate feedback, more elaborate feedback, sufficient exemplars of correct/incorrect, controlled task presentation. Intervals of practice, opportunities to respond, delayed feedback, ensure reinforcement for more fluent performance. Cues to generalize, corrective feedback for application and problem-solving, systematic task variation, fading of support. A More Powerful Way to Define Intervention Intensity

© 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.

Tier 1 Screening Indicates Class-wide Problem

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Tier 2: Class-wide Intervention Teacher F Mult 0-12 0 20 40 60 80 100 120 10/24/200310/31/2003 11/7/2003 11/14/200311/18/2003 Weeks Digits Correct Two Minutes

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

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 116

Overall 117

For Vulnerable Students 118

For Vulnerable Students 119

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. 120

Let’s Talk about Another Pitfall Overemphasizing intervention selection and under-emphasizing intervention management 121

© Amanda VanDerHeyden, Do Not Reproduce without Written Permission Common Pitfalls Most interventions fail because they are not implemented correctly Standard protocol interventions facilitate accurate implementation and can work Too much time is spent on problem admiration and dissection

© Amanda VanDerHeyden, Do Not Reproduce without Written Permission Troubleshoot Intervention SupportYesNo Was the intervention developed to ensure that it required minimal classroom time and resources and fit within daily classroom routines? Are materials readily available to the teacher? Was a step-by-step “coach card” provided? Was the teacher shown how to implement the intervention by a “coach?” Did the coach observe implementation of the intervention to ensure that the teacher could use the intervention correctly and had all needed materials? Was weekly follow-up support provided to the teacher after initial training? Are integrity data graphed to show used correctly? Is an administrator involved? From Witt, VanDerHeyden, & Gilbertson, 2004

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 125

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 126

Just like your mama told you: INTEGRITY MATTERS 59% Integ96% Integrity 127

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

To Avoid Pitfalls Specify measures, decision rules, and intervention management procedures Obtain the best data Obtain only the data necessary to make accurate decisions at each stage Plan system interventions where system problems are detected Actively manage intervention implementation 129

Ask What are our system goals? What data are we collecting to reflect progress? How are we responding to lack of progress (how often, what resources)? How do data inform professional development decisions, text/material/resource adoptions, allocation of instructional time? How do data tie into personnel evaluation? 130

Ask Are we changing the odds of success in our schools? What are our special targets and priorities (e.g., numeracy, high-mobility, etc.) Are we operating as efficiently as possible? Are teachers adequately supported (i.e., someone responds to data and goes in to coach and support)? Do our instructional leaders follow data? 131

Avoid Common Mistakes Exploit existing data to know if efforts are working –% at risk fall, winter, spring by grade –% of class-wide problems fall, winter, spring by grade –% of f/r lunch at risk should mirror % of f/r lunch overall, same for ethnicity and sp ed –Reduced risk across grades –Decreased evaluations, proportionate, & accurate Specify what you are going to do about it Implement solution well Follow-up and respond to implementation failures 132

For More Information Amanda VanDerHeyden –amandavande@gmail.comamandavande@gmail.com –251-300-0690 www.isteep.com and www.gosbr.netwww.isteep.comwww.gosbr.net www.rtinetwork.org www.nasdse.org (blueprints)www.nasdse.org 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)http://www.jeabjaba.org/abstracts/JabaAbstracts/26/26- 597.Htm Hattie (2009). Visible Learning. 133

© Amanda VanDerHeyden, Do Not Reproduce Without Permission Using RtI to Advance Learning in Mathematics Amanda VanDerHeyden Education Research and Consulting,

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