RTI in Mathematics: The Perspective from NCTM David Chard Ben Clarke John Woodward Russell Gersten, Moderator October 1

1. RTI in Mathematics: The Perspective from NCTMDavid ChardBen ClarkeJohn WoodwardRussell Gersten, ModeratorOctober 19, 2011 Funded by U.S. Department of Education

2. The Center on Instruction is operated by RMC Research Corporation in partnership with the Florida Center for Reading Research at Florida State University; Instructional Research Group; Lawrence Hall of Science at the University of California-Berkeley; the Texas Institute for Measurement, Evaluation, and Statistics at the University of Houston; and The Meadows Center for Preventing Educational Risk at the University of Texas at Austin.The contents of this PowerPoint were developed under cooperative agreement S283B050034 with the U.S. Department of Education. However, these contents do not necessarily represent the policy of the Department of Education, and you should not assume endorsement by the Federal Government.The Center on Instruction requests that no changes be made to the content or appearance of this product.To download a copy of this document, visit www.centeroninstruction.org. 2011 Funded by U.S. Department of Education

3. Question 1:Are you familiar with the NCTM policy on Interventions? • If YES, CLICK on the check • If NO, CLICK on the X Funded by U.S. Department of Education

4. NCTM Position Without identifying specific interventions, we endorse the use of increasingly intensive and effective instructional interventions for students who struggle in mathematics. Teachers must use a variety of formative assessments to target strategic instructional techniques that are tailored to meet individual students’ needs. When implementing appropriate interventions for all mathematics learners, teacher must possess strong backgrounds in mathematical content knowledge for teaching, pedagogical content knowledge, and a wide range of instructional strategies.

5. NCTM Position Without identifying specific interventions, we endorse the use of increasingly intensive and effective instructional interventions for students who struggle in mathematics. Teachers must use a variety of formative assessments to target strategic instructional techniques that are tailored to meet individual students’ needs. When implementing appropriate interventions for all mathematics learners, teachers must possess strong backgrounds in mathematical content knowledge for teaching, pedagogical content knowledge, and a wide range of instructional strategies.

6. Key Points to Consider • NCTM emphasizes that effective interventions: • Should include explicit instruction based on student need; • Should strengthen both conceptual understanding and procedural knowledge; • Rely on teachers with knowledge of mathematics content and evidence-based strategies; • Require that teachers are certified and trained in mathematics.

7. Response to Intervention • Reauthorization of IDEA (2004) allowed for RTI to be included as a component in special education evaluations • Premised on the use of research based interventions and student response to intervention • Students who respond are not identified as learning disabled • Students who do not respond are referred for a complete evaluation and potential identification as learning disabled

8. Response to Intervention • Linked closely to an early identification and prevention model of delivery • Provides for the delivery of tiered services across traditional boundaries (e.g. Special and General Education) • Most often implemented by schools using a schoolwide model of instruction

9. TIER 1: Core Class Instruction Tier I is defined differently by experts Only common feature: Universal screening of all students Other possible components: Ongoing professional development for classroom teachers on how to use research Differentiated instruction High quality mathematics instruction Scientifically based mathematics instruction TIER 1 TIER 2 TIER 3

10. TIER 2: Small Group Instruction Tier 2 is individual or small-group intervention in addition to the time allotted for core mathematics instruction. Tier 2 includes curriculum, strategies, and procedures designed to supplement, enhance, and support Tier 1. Can backtrack and/or elaborate/reinforce classroom curriculum. Progress monitoring of students “at risk” on a monthly or weekly basis TIER 1 TIER 2 TIER 3

11. TIER 3: Intensive Intervention Tier 3 is specifically designed and customized individual or small-group mathematics instruction that is extended beyond the time allocated for Tier 1 and Tier 2. NOTE: Some states/districts use 3 tiers and other states use 4 tiers. TIER 1 TIER 2 TIER 3

12. Key Features of Tier 2 and 3 • Progress monitoring and diagnostic assessments • Standard protocol interventions • Instructional design considerations • Individualized problem solving

13. RtI in Practice • To get started • Screening to determine risk status • Research based interventions • To expand • Progress monitoring assessments • Diagnostic assessments • To support • Math specialists • Professional development

14. Question 2:Has your state or region begun to implement RTI in mathematics? • If YES, CLICK on the check • If NO, CLICK on the X Funded by U.S. Department of Education

15. NCTM Position Paper • Struggling students should be identified through appropriate assessments • Success in understanding important mathematical ideas is central • Interventions should rely on substantive teacher knowledge and evidence based strategies • Progress monitoring through formative and summative assessments including diagnostic interviews should capture “conceptual and procedural knowledge”

16. Formative and Summative Assessments • The NCTM Position Paper is an important reminder in the context of traditional special education assessment • Far too many models of assessment rely on procedural competence alone

17. The Limits of Procedural Assessment • 2493 • 1556 • 937

18. After an Individual Interview, We Learn This is How the Student Solved the Problem • 2493 • 1556 • 937 8 1 1

19. “When I get big numbers like this, I just split them in half. Then I start here [on the right]” 8 1 24 93 - 15- 56 9 37 1 1 student thinking

20. There is a Difference 15 8 13 8 1 8 - = clerical error 15 8 13 8 2 0 - Understanding error =

21. The Devil is in the Details: What It Means to Count Correct Digits 38 r 2 12 458 • 458 • -36.. • 98 • -96 • 2 Digits and the Traditional Algorithm

22. An Alternative Algorithm 8 10 10 10 Decent Number Sense Many Digits 12 458 -120 338 -120 218 -120 98 -96 2 38 r 2

23. An Alternative Algorithm 12 x 4 = 48 therefore 12 x 40 = 480 12 x 3 = 36 therefore 12 x 30 = 360 Student thinking Much Better Number Sense Fewer Digits 8 30 12 458 38 r 2 • -360 • 98 • -96 • 2

24. Proficiency and/or Good Number Sense? Consider These Subtraction Problems 407 - 153 14 - 7 52 - 29 210 - 195

25. Good Number Sense and Flexible Thinking Consider These Subtraction Problems Know the fact automatically Doubling Strategy Through 10s Traditional Algorithm Left to Right 407 - 153 14 - 7 Strategies 52 - 29 Traditional Algorithm Add up Renaming 210 - 195 Add up Renaming

26. Question 3:Does the NCTM position fit with current RtI policy in your state or region? • If YES, CLICK on the check • If NO, CLICK on the X Funded by U.S. Department of Education

27. Questions? Thank you for attending our webinar. We will be posting the archived webinar file and the PowerPoint presentations to our website in the next few days. Your feedback is important to us. Please take our survey, available by clicking on the link Ruth Dober has put into the Chat Box or by going to http://www.surveymonkey.com/s/Z3ZSD7B. Funded by U.S. Department of Education