An Emerging Model: Three-Tier Mathematics Intervention Model : An Emerging Model: Three-Tier Mathematics Intervention Model
Special Education Research Project (SERP)-Mathematics:
Diane Pedrotty Bryant, Project Director
Brian R. Bryant, Assessment Director
This model is based on the 3-Tier Reading Model
Vaughn Gross Center for Reading & Language Arts
© University of Texas System/Texas Education Agency: www.texasreading.org
The Characteristics of Students with Mathematics Disabilities (MD) : The Characteristics of Students with Mathematics Disabilities (MD) Procedural difficulties
Immature strategies use
Errors in math problem execution
Memory problems
Poor long-term memory retrieval skills
Working memory deficits
Visual/spatial deficits
Weak visual/spatial representations
Low number sense
Number magnitude comparison confusion
Poor number naming and writing
Core Educational Problem: Assessment : Core Educational Problem: Assessment Limited availability of technically adequate measures for identification and to monitor response to intervention of Tier 2 students in the primary grades
Need to develop technically adequate measures for early mathematics number, operation, and quantitative reasoning skills and concepts
Measures can contribute to an understanding of predictors of early mathematics performance, inform mathematics instructional decisions, and change mathematics outcomes for students who are at risk for mathematics difficulties
(Chard, Clarke, Baker, Otterstedt, Braun, & Katz, 2005)
What is the 3-Tier Mathematics Intervention Model? : What is the 3-Tier Mathematics Intervention Model? Is an assessment & intervention model designed to meet the instructional needs of students in grades K - 2 who are identified as struggling with mathematics
• Provides a framework for providing instruction and using assessment data to inform decision-making
Is a response-to-intervention model (developing)
Focuses on standards-based intervention (number & operation)
What are the Components of the 3-Tier Mathematics Intervention Model? : What are the Components of the 3-Tier Mathematics Intervention Model? Tier 1: Core classroom instruction for all students (45-60 minutes-observed in K-4)
Tier 2: Intervention for approximately 10 - 30% of identified students (15-20 minutes-10 - 12 weeks - 3 to 4 days a week)
Tier 3: Intensive intervention for approximately 5-8% of identified students (may include special education students; probably another 20 minutes?)
What are the Components of the 3-Tier Mathematics Intervention Model? : What are the Components of the 3-Tier Mathematics Intervention Model? Tier 1
Seems to be based on National Science Foundation instructional recommendations, teacher created lessons, basal based instruction, NCTM Standards (based on observations)
Focus on instructional adaptations (content, delivery, materials, activity): Tier 1 + adaptations-keep your eye on Tier 2
What are the Components of the 3-Tier Mathematics Intervention Model? : What are the Components of the 3-Tier Mathematics Intervention Model? Tier 2 (probably Tier 3-developing)
Includes differentiated instruction in number and operation (developing)
Includes explicit instruction in small, homogeneous groupings
Has levels of instructional need within Tier 2
Includes intervention lessons on number and operation (developing)
Tier 3
More intensive instruction; delivery, grouping, content
How is Assessment Conducted in the 3-Tier Mathematics Model? : How is Assessment Conducted in the 3-Tier Mathematics Model? Texas Early Mathematics Inventories (TEMI)
Kindergarten: Quantitative Recognition (subitizing), Numeral Naming (1-20), Magnitude Comparisons (1-20; bigger/same), Number Sequences (1-20) (screening, midpoint)
First Grade: Place Value (ones/tens), Magnitude Comparisons (1-99; smaller/same), Number Sequences (1-99), Add/Subtract Arithmetic Combinations (to 18) (screening, midpoint)
Second Grade: Place Value (ones/tens/hundreds), Magnitude Comparisons (1-999; smaller/same), Number Sequences (1-999), Add/Subtract Arithmetic Combinations (to 18) (screening, midpoint)
All Grades: SAT-10 (pre/post; outcome measure)
How is Assessment Conducted in the 3-Tier Mathematics Model? : How is Assessment Conducted in the 3-Tier Mathematics Model?
Diagnostic/Progress Monitoring (all students): individually administered/fluency (2nd grade screening-whole class) (group administration in development)
Progress Monitoring of Lessons: Bi-weekly for Tier 2 & Weekly for Tier 3 (developing)
Outcome: whole class (2 sessions for K) (in development)
Slide10 : PM Measures Numeral Naming (K Only)
0-20
Slide11 : Quantity Recognition (K Only)
1-6 PM Measures
Slide12 : Magnitude Comparisons
K: 0-20, bigger #, same
1: 0-99, smaller #, same
2: 0-999, less, equal PM Measures
Slide13 : Numeral Sequences
K: 0-20
1: 0-99
2: 0-999 PM Measures
Slide14 : Place Value PM Measures 1: 1-99
2: 1-999
Slide15 : Addition/Subtraction
Combinations, to/from 18 (1 & 2 only) PM Measures
Slide16 : Reliability
Immediate Alternate Forms (Content Sampling)
K (n=43) 1 (n=52) 2 (n=55)
QR: .89 (C)
NN: .89 (C)
MC: .91 (D) .90 (C) .88 (B)
NS: .83 (D) .94 (B) .91 (C)
PV: .86 (B) .75 (D)
ASC: .93 (B) .83 (C) Results
Slide17 : Validity
Concurrent Criterion-Prediction
TEMI (Form A) Correlations w/SAT-10
SAT-10 [K], (1) & 2
[Math] (Math) MPS MP Total
QR: .54
NN: .48
MC: .65 .64 .52 .43 .53
NS: .56 .58 .56 .56 .62
PV: .65 .51 .57 .59
ASC: .55 .53 .59 .62 Results
Core Educational Problem: Intervention : Core Educational Problem: Intervention Limited evidenced-based interventions demonstrating efficacy for improving mathematics performance in early mathematics skills and concepts
Need to develop, refine, and evaluate interventions to teach students in kindergarten, first, and second grades who have been identified as Tier 2 for mathematics difficulties
Number and operations is cited as the most important area of NCTM’s (2000) Principles and Standards for School Mathematics (Clements & Sarama, 2004)
Automaticity is identified as “desirable” at an early stage of formal mathematics education (Cumming & Elkins, 1999)
Tier 2: Types of Boosters : Skill Building/ Practice
PR/VR/AR Fluency Building
AR Lower Proficiency Levels Higher T
E
K
S Physical Representation
Visual
Representation
Abstract Representation Tier 2: Types of Boosters
Slide20 : Framing the lesson*
Previewing
Modeling w/think alouds
Guided practice
Independent practice
Checking for understanding
Error correction and feedback
Progress monitoring Effective Instruction
for Booster Sessions * © 2005 Psycho-Educational Services
Procedures & Features of Tier 2 Intervention : Procedures & Features of Tier 2 Intervention
Groupings: homogeneous grouping with 2 - 4 students per group; 3 levels within in grade level
(2) Duration: 4 - 5 times per week for 15-20 minutes
(3) Lesson Design: sequential, scaffolded, stacked, scripted interventions;
explicit, strategic, “think aloud;” error correction
(4) Instructional Content: See Framework handout; mathematics vocabulary
(e.g., greater than/less than)
(5) Representations: physical (concrete), visual (pictorial), abstract (numbers)
(6) Materials: number charts, 5- and 10-frames, counters, cubes,
number lines (horizontal/vertical), base-ten materials, dot cards
(7) Progress monitoring
Slide22 : Levels* of
Progress Monitoring Activity
Level Maintenance/
Generalization
Level Content I
Level Content II
Level What was learned this month, and can it generalize to the larger instructional content?
Monthly testing using Forms B, C, and D of Content Measures What was learned this week; was it maintained and can it generalize to a testing format?
Booster Probes What was learned this trimester?
Pre-, Mid-, and Post-testing using Form A of Content Measures What was learned today?
Independent Practice progress monitoring: a set of techniques for assessing student performance on a regular and frequent basis (R. Quenemoen, M. Thurlow, R. Moen, S. Thompson, A. Blount Morse) * © 2005 Psycho-Educational Services
How Can Your District Get Started? : How Can Your District Get Started? Tier 1
Ensure that core instruction includes effective practices for struggling students
Help teachers identify ways to adapt instruction and to monitor performance
Identify an amount of time to require mathematics instruction (60+ minutes)
Help teachers balance instruction
Examine textbooks for the presence of practices that support struggling students’ needs (practice, scaffolds, grouping)
How Can Your District Get Started? : How Can Your District Get Started? Tier 2 & 3
Identify the standards you wish to emphasize as part of Tier 2 instruction (number & operation)
Identify the assessment measures to be used and when they will be administered; include fluency; include how to interpret assessments and plan instruction accordingly
Identify who will provide Tier 2 & 3 instruction & how often
Identify the interventions to be used
Help teachers integrate Tier 2 into their day (amount of time, practices: student work stations)
Elevate the importance of math instruction
Provide coaching assistance
Implementation Questions : Implementation Questions How do you know if Tier 1 (core) instruction is not working? Assess all students 3 times a year; students not showing appropriate progress may qualify for Tier 2 instruction (cut score < 16th percentile)
What should Tier 2 instruction look like? See previous Tier 2/3 instruction slide for example
How do we know if Tier 2/3 instruction is working (are students responding to instruction)? Progress monitor students regularly
Implementation Questions : Implementation Questions How long is Tier 2 instruction implemented? 10-12 weeks; reassess if progress move to Tier 1; if limited progress conduct another 10-12 weeks of Tier 2; if no progress consider Tier 3
How often should we progress monitor students? Tier 2, bi-weekly; Tier 3 - weekly - recommendation
How do I assess fidelity? Use a checklist containing expectations for Tier 2 to decide if intervention practices are being used with fidelity; see Instructional Decision Making booklet - administrator’s pages
http://www.texasreading.org/utcrla/materials/serp_prereferral_booklet.asp
What Are Helpful Resources? : What Are Helpful Resources? Baker, S., Gersten, R., & Lee, D. (2002). A synthesis of empirical research on teaching mathematics to low-achieving students. The Elementary School Journal, 103, 51-73.
Chard, D., Clarke, B., Baker, B., Otterstedt, J., Braun, D., & Katz, R. (in press). Using measures of number sense to screen for difficulties in mathematics: Preliminary findings. Assessment Issues in Special Education.
Clark,B., & Shinn, M.R. (in press). A preliminary investigation into the identification and development of early mathematics curriculum-based measurement. School Psychology Review.
Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4-15.
Gersten, R., & Chard, D. (1999). Number sense: Rethinking arithmetic instruction for students with mathematical disabilities. The Journal of Special Education, 33, 18-28.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, & B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
Special issue of JLD-July issue-Gersten & Jordan