1. Assessment within a Response to Intervention Model: Tools and Ideas Karen Karp Amy Lingo

2. Topics Overview of RtI Model, a multi-tiered intervention approach
Universal Screeners:
What do the data tell us and not tell us?
Designing and implementing strategies for tiers of intervention

3. 3-Tiered Support Model - UNIVERSAL Tertiary Prevention:
Specialized & individualized
strategies for students who don’t respond to Tier 2 supplementary support - INTENSIVE
~5%
Secondary Prevention:
Supplementary strategies
for students who do not respond to core instruction - TARGETED
~15%
Primary Prevention:
High quality engaging core instruction
- UNIVERSAL
~80% of Students

4. Has RtI implementation closed the gap?
Note here on the bottom line (the 10th percentile that would be inclusive of some of the special education population) that since 2004 When rti support models and the use of supplemental interventions were mandated that the line is relatively flat. Why is that? Let’s look at eighth grade

5. Are we doing any better at 8th grade?

6. Mathematics Performance on NAEP 2013
4th grade
At or Above Proficient: 45% (+5%) of all students and 18% (+1%) of students with disabilities
Below Basic: 18% (-4%) of all students and 45% (=) of students with disabilities
8th grade
At or Above Proficient: 39% (+4%) of all students and 9% (=) of students with disabilities
Below Basic: 21% (-6%) of all students and 65% (=) of students with disabilities
So to meet proficiency on the NAEP – 83% of students with disabilities need to move up in 4th grade (with as you see more than half of that group at the below basic level) and 91% of the students in 8th grade need to move up to proficiency (with approximately ¾ of that group at the below basic level)
You have to ask – do we think worksheets or a generic computer program can make that happen? (I am not talking about delivering high quality instruction via technology – but the generic programs I see in use are not instructive)
National Center for Education Statistics, 2013

7. What about RtI? Why isn’t it Helping?
A recent study revealed that teachers providing Tier 2 mathematics instruction to elementary and middle grade students largely used worksheets (Foegen & Dougherty, 2010; Swanson, Solis, Ciullo & McKenna, 2012)
In our travels to classrooms many others use a one-size- fits-all generic computer program.
Why would we think that students who don’t function well in a class of 25 students can work independently to learn the mathematics?
Unfortunately this goes back to the attempt to buy one program for all students who struggle

8. Components of A Strong RtI Model
Incorporates a regular screening process
Includes evidenced based practices
Instructs with preventative methodology
Integrates progress monitoring
Uses diagnostic assessment to align intervention
Newman-Gonchar, R., Clarke, B., & Gersten, R. (2009). A summary of nine key studies:Multi-tier intervention and response to interventions for students struggling in mathematics. Portsmouth, NH: RMC Research Corporation, Center on Instruction.

9. Tier 1 - Universal Mathematics Instruction
Implementation of core mathematics instruction
Instruction with methodology addressing both conceptual and procedural understanding.
Implementation of instruction with fidelity

10. Identification of Students Through Screening
Universal Screener
Building level team to facilitate the implementation of the screening and progress monitoring
Use benchmarks or growth rates to identify students at low, moderate, or high risk for developing mathematics difficulties.

11. is given a Universal Screening
Student Body
is given a Universal Screening
X X X X X X X X X X X X X X X X X X X X X X X X X

12. (What we hear schools are using)
Universal Screenings
(What we hear schools are using)
AIMSWeb
Think Link
G-MADE
MAP
Universal Screening: Determines which students may have possible mathematics difficulties.
This is not an endorsement of the products, but a listing of those described by schools.

13. MAP: Adaptable Computer Based Assessment
NWEA Measures of Academic Progress® (MAP®) tests present students with engaging, age-appropriate content. As a student responds to questions, the test responds to the student, adjusting up or down in difficulty. With each assessment a student will get approximately 50% of the questions correct to get an accurate RIT score.
The result provides detailed information for teachers, parents and administrators to use in the classroom to drive instruction, interventions, and enrichment.

14. What is RIT?
RIT or “Rasch Units” are units of measurement involving the difficulty of individual items. They estimate a particular student’s achievement.
The RIT scale measures achievement growth over time. As a student goes to the next grade level, RIT scores “grow” with them. For example if a grade 2 student had a 200 point RIT score and then 210 at grade three, it means that his/her academic performance increased by 10 RITs.
RIT scores should not be used to compare one student with another. Instead, RIT scores assess if a student has “grown” academically. The scores represent individual performance on individual items so similar scores as other students doesn’t necessarily mean similar achievement.

15. NWEA Norms

16. Normative Data

17. MAP Data for Instruction Tier 1
RIT Bands for instructional flexible grouping

18. Individual Student Report Summary (over time)

19. Student Graph
District average graph
Student graph
Norm group graph

20. Sample Math Question from MAP
Work the problem on scratch paper.
Click on the best answer.
Click the Go on button.
Talking Points:
This shows what a math question might look like. You will have scratch paper at your computer if you need to use it to help you solve the problem.
Once you have worked the problem, click on the best answer from the list. Then click the Go on button at the bottom of the screen. Remember, you may change your answer as many times as you want, but once you click Go on you cannot go back to this question.
MAP® Student Presentation
Revised 7/2012
© 2012 Northwest Evaluation Association™

21. Individual Student Report

22. In-Depth Assessment determines:
Students Identified by the Universal Screening are given more in-depth mathematics assessment.
X X X X X X X X X X X X X X X X
In-Depth Assessment determines:
Tier of Support
Specific Areas of Need
Plan of Intervention

23. In-Depth Assessment CCSS- Math Domains Counting and Cardinality
Operations and Algebraic Thinking
Number and Operations in Base 10
Number and Operations- Fractions
Geometry
Data and Measurement

24. Focus on Skills

25. Focus on Skill

26. Focus on Sense Making

27. The Two Worlds Collide: Sense Making Meets Skill
Petit, Laird,& Marsden, 2010

28. Diagnostic Interview
Gathers in-depth information about an individual student’s knowledge and mental strategies.
Provides evidence of prior knowledge, naïve understandings and students’ ways of thinking about concepts.
Focuses on a task or problem where students are asked to either verbalize their thinking or demonstrate ideas through models or drawings
Emphasizes the collection of evidence
Is not a teaching opportunity
Uses errors to identify barriers to understanding, to inform instructional decisions

29. What might a student’s brain look like?
What if one student had a good understanding of a concept and the other student had just memorized it (or lacked the ability to efficiently memorize – like a student with disabilities)?

30. Relational understanding: Focus on how and why
Build on prior knowledge
Discuss relationships between strategies and ideas
Instrumental understanding:
Focus on how
Develop isolated skills, concepts, rules, and symbols
Doing math problems without understanding
From Teaching Student Centered Mathematics (2014) (Volumes I - III)

31. Link Sheet Equation Story problem or Situation
Model, Picture, Illustration
My Explanation of the Operation
Van de Walle, J., Karp, K., & Bay Williams, J. (2013). Elementary and Middle School Mathematics: Teaching developmentally. New York: Pearson.

32. Student work 5 + 8 = 13 Equation Word Problem Model/Illustration
There were 5 birds on the feeder. Then 8 more birds flew to the feeder. How many birds are now on the feeder?
Model/Illustration
Explanation
First I had 5 birds. Then I needed to combine them with 8 more birds. I added so all together I have 13 birds.
5 + 8 = 13
Van de Walle, J., Karp, K., & Bay Williams, J. (2013). Elementary and Middle School Mathematics: Teaching developmentally. New York: Pearson.

33. Middle School Level Algebraically Graphically Numerically in Tables
Verbal Description
Van de Walle, J., Karp, K., & Bay Williams, J. (2013). Elementary and Middle School Mathematics: Teaching developmentally. New York: Pearson.

37. How to design a diagnostic assessment
Identify what students need to know CCSS
Give a task
Record and/or make notes
Have materials available for students to use
The difference between a regular task and a diagnostic interview is that you are sitting and listening to the student talk about their thinking and how they are solving the task. Questions are used to probe and materials and other representations are used to see the depth of understanding. You never walk away wondering why.

38. Diagnostic Interviews – Knowing students’ thinking
Select tasks that are close to what you expect the children to be able to do – start easy and ramp up if you are not sure
Ask questions to prompt why they are doing something – or to ask them to explain their thinking or use models or drawings to demonstrate their ideas
Be neutral – watch your body language - avoid clues or leading questions
Wait silently - Do not interrupt – Do not teach
Take notes, keep student work, take photos
Say – show me, tell me, do…, try…, can you do that another way?
Karen

39. Diagnostic Interviews
Collect in-depth information about an individual student’s knowledge and mental strategies.
Provide evidence of students’ prior knowledge, naïve understandings and ways of thinking
Focus on a task/problem where students are asked to verbalize their thinking and/or demonstrate ideas through multiple representations
Is not a teaching opportunity
Use errors to identify barriers to understanding and to inform instructional decisions
Van de Walle, J., Karp, K., & Bay Williams, J. (2010). Elementary and Middle School Mathematics: Teaching developmentally. New York: Pearson.

40. Diagnostic Interview Task
Ask the student to write the number that shows: 3 ones, 1 hundred and 5 tens
Karen

41. Student Work
Karen

42. Progress Monitoring: Assessment
Procedural measures: skills, algorithms Typically multiple-choice format

43. Assessment
If assessments only measure skill, it is difficult to determine what a student knows.
If you cannot determine what a student knows, it’s difficult to plan an instructional sequence.
Barb

44. Progress Monitoring Conceptual measures May not require computation
Focuses on reasoning
Emphasizes Big Ideas
May be multiple choice but the multiple choice options are linked to thinking, not just the answer
May open-response items, scored with a metric/rubric

45. Interventions Following Diagnostics
Use of screening information
Use of diagnostic interview
Create a plan for intervention

46. Recommendations for identifying and supporting students struggling in mathematics
Recommendations are based on strong and moderate levels of evidence resulting from comprehensive reviews of current research
Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., & Witzel, B. (2009). Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools (NCEE ). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from ed.gov/ncee/wwc/publications/practiceguides/.

47. General Screening and Intervention Recommendations
Screen all students
Choose appropriate instructional materials
Intervention with explicit instruction
Modeling
Talk aloud (verbalization)
Guided practice
Feedback (correction of errors)
Frequent review of progress
Problem solving instruction based on common underlying structures
Visual representations
Strong
Moderate
Low

48. Screening and Intervention Recommendations
10 minutes per session devoted to fluency building of basic mathematics facts
Progress monitoring
Integration of motivational strategies
Strong
Moderate
Low

49. Recommendations for students identified as low-achieving
On a regular basis; and
For the purpose of building computation and problem solving proficiency;
Explicit instruction including opportunities for asking and answering questions
Think aloud opportunities regarding decisions during problem solving
Dedicated time to foundational skills necessary for grade level mathematics learning
National Mathematics Advisory Panel. Foundations for Success: The Final Report of the National Mathematics Advisory Panel, U.S. Department of Education: Washington, DC, 2008.

50. Recommendations from research involving small group interventions
Explicit instruction
Concrete--Semi-concrete--Abstract approach
Modeling
Underlying mathematical structures
Examples (consideration of range and sequence)
Independent work with immediate corrective feedback
Visuals (drawings & diagrams)
Note: The interventions may be effective for other student groupings. This listing specifically targets small groups.
Newman-Gonchar, R., Clarke, B., & Gersten, R. (2009). A summary of nine key studies: Multi-tier intervention and response to interventions for students struggling in mathematics. Portsmouth, NH: RMC Research Corporation, Center on Instruction.

51. CSA – Concrete Semi-Concrete Abstract
Van de Walle, J., Karp, K., & Bay Williams, J. (2013). Elementary and Middle School Mathematics: Teaching developmentally. New York: Pearson.

52. Effective Practices for Teachers
Explicit Instruction
A range of instructional examples, a sequence from concrete-semi-concrete-abstract
Verbalization by the students and the teacher
Use of visual representation
Multiple heuristic strategies
Formative assessment information provided to teachers
Peer-assisted learning (1:1 tutoring)
Cross age (more effective)
Within classroom same grade, role exchange
Performance based
Jayanthi, M., Gersten, R., Baker, S. (2008). Mathematics instruction for students with learning disabilities or difficulty learning mathematics: A guide for teachers. Portsmouth, NH: RMC Research Corporation, Center on Instruction.

53. Thank you
Contact information.
Karen Karp
Amy Lingo