tier 2 mathematics intervention regina hirn karen karp amy lingo project abri university of...

Tier 2 Mathematics Intervention

Regina HirnKaren KarpAmy Lingo

Project ABRIUniversity of Louisville

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

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









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.

X X X X X X X X X X X X X X X X





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

11

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

A

R

C

E

U

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


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


Talk Aloud-Verbalization


Drawing-Visual Representation


Difference in Solutions


Student Decision-making


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.

Hedden’s Continuum - CSA

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.

Thank you

Contact information.

Regina Hirn [email protected] Karen Karp

[email protected] Amy Lingo [email protected]

tier 2 mathematics intervention regina hirn karen karp amy lingo project abri university of...

Documents

universal screening

probability slide

fidelity slide

identification of students

tiered model slide

instructional decisions

individual students

students ways of thinking