1. Tier 2 Mathematics Intervention Regina Hirn Karen Karp Amy Lingo
Project ABRI
University of Louisville

2. Topics Overview of RtI Model, a multi-tiered intervention approach
Core mathematics instruction prior to Tier 2 intervention
General screening characteristics
Diagnostic interview: a component of assessment
(audio example)
Research-based intervention recommendations

3. RtI: 3-Tiered Model Tertiary Prevention: specialized & individualized
strategies for students with continued failure
~5%
Secondary Prevention:
supplementary strategies
for students who do not respond to primary
~15%
Primary Prevention:
school-wide or class-wide systems for all students and staff
~80% of Students

4. 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.

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

6. 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.

7. 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

8. (What we hear schools are using)
Universal Screenings
(What we hear schools are using)
DIBELS
AIMS Web
Think Link
GRADE
MAP
Universal Screening: Determines students with possible mathematics difficulties.
This is not an endorsement of the products, but a listing of those described by schools.

9. 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

10. In-Depth Assessment Math Numbers and Operations Algebra Geometry
Measurement
Data Analysis and Probability

11. Math Content and Processes
Numbers and
Operations
Algebra
Geometry
Measurement
Data and
Probability
Problem
Solving
Reasoning and
Proof
Communication
Connections
Representation 11

12. U C A E R

13. 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

14. What Does It Mean to Understand Mathematics?
Understanding is the measure of quality and quantity of connections between new ideas and existing ideas
Knowing ¹ Understanding (students may know something about fractions, for example, but not understand them)
Richard Skemp named the ends of the continuum of understanding
What to do and why
Relational understanding
Just doing it
Instrumental understanding

15. Implications for Teaching
The need to replace the question “Does the student know it?” with the question “How does the student understand it?”
Early number concepts
Computation
Copyright © Allyn and Bacon 2010

16. Diagnostic Interview - Example
Philip, R. & Cabral, C. (2005). IMAP: Integrating mathematics and pedagogy to illustrate children’s reasoning. San Diego State University Foundation: Pearson.

17. Student Teacher Interaction
Philip, R. & Cabral, C. (2005). IMAP: Integrating mathematics and pedagogy to illustrate children’s reasoning. San Diego State University Foundation: Pearson.

18. 3 3/8
Philip, R. & Cabral, C. (2005). IMAP: Integrating mathematics and pedagogy to illustrate children’s reasoning. San Diego State University Foundation: Pearson.

19. Procedural Error
Philip, R. & Cabral, C. (2005). IMAP: Integrating mathematics and pedagogy to illustrate children’s reasoning. San Diego State University Foundation: Pearson.

20. Talk Aloud-Verbalization
Philip, R. & Cabral, C. (2005). IMAP: Integrating mathematics and pedagogy to illustrate children’s reasoning. San Diego State University Foundation: Pearson.

21. Drawing-Visual Representation
Philip, R. & Cabral, C. (2005). IMAP: Integrating mathematics and pedagogy to illustrate children’s reasoning. San Diego State University Foundation: Pearson.

22. Difference in Solutions
Philip, R. & Cabral, C. (2005). IMAP: Integrating mathematics and pedagogy to illustrate children’s reasoning. San Diego State University Foundation: Pearson.

23. Student Decision-making
Philip, R. & Cabral, C. (2005). IMAP: Integrating mathematics and pedagogy to illustrate children’s reasoning. San Diego State University Foundation: Pearson.

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

25. Recommendations for identifying and supporting students struggling in mathematics
Recommendations are based on strong, moderate and low levels of evidence resulting from comprehensive reviews of current research literature.
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/.

26. 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

27. 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

28. 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.

29. 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.

30. Hedden’s Continuum - CSA

31. Effective Practices for Teachers
Explicit Instruction
A range of instructional examples, a sequence from concrete-representational-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.

32. Thank you
Contact information.
Regina Hirn
Karen Karp
Amy Lingo