tier 2 mathematics intervention regina hirn karen karp amy lingo project abri university of...
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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
Tertiary Prevention:specialized & individualizedstrategies for students with
continued failure
Secondary Prevention:supplementary strategies
for students who do not respond to primary
Primary Prevention:school-wide or class-wide
systems for all students and staff
~80% of Students
~15%
~5%
RtI:3-Tiered Model
Components of A Strong RtI Model
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.
Tier 1 - Universal Mathematics Instruction Implementation of
core mathematics instruction
Instruction with methodology addressing both conceptual and procedural understanding.
Implementation of instruction with fidelity
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.
Student Bodyis given a Universal Screening
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Universal Screenings(What we hear schools are
using)
DIBELSAIMS WebThink Link
GRADEMAP
Universal Screening: Determines students with possible mathematics difficulties.
This is not an endorsement of the products, but a listing of those
described by schools.
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Students Identified by the Universal Screening are given more in-depth
mathematics assessment.
In-Depth Assessment determines:Tier of Support
Specific Areas of Need Plan of Intervention
In-Depth Assessment
MathNumbers and Operations
AlgebraGeometry
MeasurementData Analysis and
Probability
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MeasurementMeasurement
RepresentationRepresentation
AlgebraAlgebraNumbers and Numbers and OperationsOperations
Data and Data and ProbabilityProbability
CommunicationCommunication
GeometryGeometry
Reasoning and Reasoning and ProofProof
ProblemProblemSolvingSolving ConnectionsConnections
Math Content and Processes
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
What Does It Mean to Understand Mathematics?
Understanding is the measure of quality and quantity of connections between new ideas and existing ideas
Knowing 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
Instrumentalunderstanding
Implications for Teaching
Copyright © Allyn and Bacon 2010
The need to replace the question “Does the student know it?” with the question “How does the student understand it?”
Early number concepts
Computation
Diagnostic Interview - Example
Philip, R. & Cabral, C. (2005). IMAP: Integrating mathematics and pedagogy to illustrate children’s reasoning. San Diego State University Foundation: Pearson.
Student Teacher Interaction
Philip, R. & Cabral, C. (2005). IMAP: Integrating mathematics and pedagogy to illustrate children’s reasoning. San Diego State University Foundation: Pearson.
3 3/8
Philip, R. & Cabral, C. (2005). IMAP: Integrating mathematics and pedagogy to illustrate children’s reasoning. San Diego State
University Foundation: Pearson.
Procedural Error
Philip, R. & Cabral, C. (2005). IMAP: Integrating mathematics and pedagogy to illustrate children’s reasoning. San Diego State University Foundation: Pearson.
Talk Aloud-Verbalization
Philip, R. & Cabral, C. (2005). IMAP: Integrating mathematics and pedagogy to illustrate children’s reasoning. San Diego State University Foundation: Pearson.
Drawing-Visual Representation
Philip, R. & Cabral, C. (2005). IMAP: Integrating mathematics and pedagogy to illustrate children’s reasoning. San Diego State University Foundation: Pearson.
Difference in Solutions
Philip, R. & Cabral, C. (2005). IMAP: Integrating mathematics and pedagogy to illustrate children’s reasoning. San Diego State University Foundation: Pearson.
Student Decision-making
Philip, R. & Cabral, C. (2005). IMAP: Integrating mathematics and pedagogy to illustrate children’s reasoning. San Diego State University Foundation: Pearson.
Interventions Following Diagnostics
Use of screening information
Use of diagnostic interview
Create a plan for intervention
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 2009-4060). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from http://ies. ed.gov/ncee/wwc/publications/practiceguides/.
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
StrongModerateLow
Screening and Intervention Recommendations
10 minutes per session devoted to fluency building of basic mathematics facts
Progress monitoring Integration of motivational strategies Strong
ModerateLow
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.
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.
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.
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