Expanding RtI
Procedures to Math
Math RtI Pilot
Lincoln Public Schools
Math: The Next Frontier
RtI procedures can be expanded to math
without great difficulty
Similar goal: prevent and/or intervene early
with students who struggle in math
Less comprehensive research is available
about the specific, component skills and the
hierarchy of skills in math
3 Tiers of Intervention
TIER 1
School-wide Interventions
ALL
TIER 2
Targeted group interventions
TIER 3
Tier Non-Classroom
High intensity interventions
Systems
RTI Three Tier Model
Needed to Solve Problem
Tier III
Amount of Resources
Tier II
Tier I
INTENSITY OF PROBLEM
RTI Three Tier Model
Needed to Solve Problem
Amount of Resources
Tier I
High-quality, scientifically
based instruction, differentiated
to meet their needs, and students are
screened on a periodic basis
to identify struggling learners
who need additional support.
INTENSITY OF PROBLEM
RTI Three Tier Model
Tier II
Needed to Solve Problem
Amount of Resources
Increasingly intensive instruction
matched to student’s needs
on the basis of levels of
performance and
rates of progress.
Tier I
Students not making
adequate progress in the
core curriculum
INTENSITY OF PROBLEM
RTI Three Tier Model
Tier III
Students receive
individualized, intensive interventions
that target the students' skill deficits
Needed to Solve Problem
for the remediation of existing
problems and the prevention
Amount of Resources
of more
Tier II severe problems.
Tier I
INTENSITY OF PROBLEM
Focus of This Pilot Project
Three Tier instructional RTI model
Determine use of screening procedures
Measurement using frequent progress
monitoring measures
Math Calculation Skills
Not just math fact skills although fact fluency
contributes to multi-skill calculation success
What interventions work, how does the
progress translate to the classroom
Pyramids of Interventions
& High Performing Schools
Why?
Some students need more time for learning
Some need more support for learning
How?
Use systematic, school-wide processes that ensure
students are treated equitably
Use timely procedures to identify needs so additional
time and support can be provided
Provide, not just offer, directive interventions
Monitor individual student progress
DuFour, DuFour, Eaker & Karhanek, 2004
What is Math Achievement?
Five strands according to the National Research
Council (2001)
Understanding (mathematical concepts, operations and
relations)
Computing (using math procedures)
Applying (formulate problems and strategies for solving
them)
Reasoning (using logic to explain & justify solutions
and extend from known to unknown)
Engaging (seeing math as sensible, useful and doable)
What is Math Achievement? (cont’d)
Two broad areas according to the Learning
Disability literature (Geary, 2003, 2004)
Mathematics calculations (recalling basic facts, fact
fluency, recalling procedures, steps to be followed,
properties and rules for calculations, attending to and
following signs and symbols)
Mathematics problem-solving (understanding math
vocabulary, reading word problems, sorting essential
from nonessential information, using a multi-step plan
to solve problems, choosing the correct calculation to
solve problems)
Screening
Two levels:
Level 1: Universal, general screening
Level 2: Specific, Tier 2 screening
Universal screening
For all students:
PLC teams can request prior report data through
the trained data coach or principal in their
building to identify below grade level math
students (based on four quarters from previous
year’s report card)
During the pilot, this may be limited to students
in specific grade levels
Person(s) responsible: PLC Team with
Administrative Input
Tier 2 Screening
Multiple data sources
For the students with 1’s and 2’s in math computation and
numeration (and number sense for Kdg.) on previous report cards,
the PLC team would analyze their Math Cards and use teacher/PLC
team recommendations for further screening
Possible procedures: look at the consistency of the non-proficient
grades (1’s and 2’s), patterns on the Math Spreadsheet, the number
of re-teachings, as well as rank ordering students by degree of need
Person(s) responsible: PLC Team and may include psychologist
and/or coordinator
Additional screening for normative standing
Administer three math probes and use the median score
Math probes selected for Grades 1-5
Monitoring Basic Skills Progress (MBSP)
Advantages:
Brief math calculation checks
Multiple skills included in each probe
Already developed and available
Widely used and cited
Sufficient numbers of probes to avoid a learning
effect and to measure progress over time
MBSP Alignment with Curriculum
Lead math teachers found good
alignment between the MBSP probes
and the LPS math curriculum at each
grade level
Instruction for some of the skills occurs
later in the year so there is sufficient
ceiling in the probes
The items on each probe are arranged
randomly sampling the whole year of
skills
Sample MBSP Computation Problems
Gr. 1: 6 52 7 8
-3 +12 +0 1
+0
Each probe has 25 problems
2 minute per probe at grades 1 & 2
3 minute per probes at grades 3 & 4
5 minute per probes at grade 5
30 alternate forms per grade level
Administering MBSP
Directions
Practice
Scoring MBSP
The probes will be scored by total digits
correct for the calculation probes, and
problems correct for the application probes.
Establishing Baseline
Administer 3 math calculation probes
Use the median score (not the mean) as the
baseline.
Individual(s) responsible: Teacher, interventionist,
psychologist and/or coordinator
MBSP probes will also be used for weekly progress
monitoring during intervention
LPS Math Curriculum (Tier 1)
Houghton-Mifflin Math (Harcourt in Kindergarten)
Thorough and research-based
Intensive field-testing before adopted by LPS
Focuses on conceptual understanding as well as skill
practice
60-80 minutes per day, heterogeneous groupings
High expectations for all children
Supported and expected by district leadership
Strict pacing is used to make sure students receive
instruction on essential objectives
LPS Math Curriculum - cont’d
Systematic re-teaching of skills
Required of all classroom teachers for
students who do not meet district
expectations for core objectives
Re-teaching, re-testing & re-learning may
take 50-75 minutes per week
May occur within or outside of math class
Students are then re-tested on the skills
Overview of Intervention (Tier 2)
Tier 2 Math Intervention
Occurs in addition to classroom instruction (outside of regular math
time)
Small groups
Establish baseline for math skills level (e.g., median of 3
probes)
Monitor progress with MBSP weekly probes
Graph weekly data to provide ongoing feedback for teachers
and students
Establish Goal lines with the expectation of one digit
improvement per week
2nd Grade Monitoring Basic Skills Progress: Calculation
20
Number of Digits Correct in 1 minute
16
15
11
10 10
9 9
7
10th% 6
3
2 2
0
9-7
9-14
9-21
9-28
10-5
11-2
10-12
10-19
10-26
Weeks of School Year
Tier 2 - cont’d
When?
Be creative - during unit studies, specials, etc.
How long?
At least three times per week (best practice
would be four-five times per week)
Minimum of 90 minutes per week
Depends on the response to intervention
Who administers interventions?
Certified Non-certified
Re-teaching X
intervention
Toolkit X X
Interventions
Standardized X (If trained)
Math
Interventions
What General Strategies Work?
(Gersten, Chard, Jayanthi, Baker & Lee, 2006)
For low achieving students
(in order of effect sizes large to moderate)
Structured peer-assisted learning in
heterogeneous groupings (.62)
Systematic & explicit instruction (.58)
Formative assessment data provided to
students (.57)
Formative data provided to teachers (.51)
What General Strategies Work?
(Gersten, Chard, Jayanthi, Baker & Lee, 2006)
For special education students
(in order of effect sizes large to moderate)
Systematic & explicit instruction (1.19)
Student think-alouds (.98)
Visual & graphic depictions (.50)
Structured peer-assisted learning in
heterogeneous groupings (.42)
Data provided to students (.33)
Examples of Intervention
Math chapter intervention materials (examples
later)
Math Toolkit
Specific math programs
Math Steps (1-5)
Knowing Math (3-5)
Corrective Math (3-5)
Number Worlds (K-2)
Math Steps
Emphasis is on computation skills
Individualized but not independent skill
practice
Small group intervention
Suggested that Math Steps be integrated with
opportunities for conceptual understanding
to increase deep understanding of the
computational algorithms
Knowing Math
Designed for students in grades 3-5
Conceptually-based math program
For students who are two or more grade
levels below expected levels
Small group intervention
45 minutes, 4-5 days per week
15 weeks of lessons
Number Worlds
Researched based program
Focuses heavily on the concept of number
sense
Appropriate for primary grades
Corrective Math
Grades: 3-5
Provides intensive support for students who have difficulty with
mathematics
Organized into seven strategic modules that provide teacher-
directed instruction on critical skills and concepts which struggling
students often fail to grasp
Highly focused, intervention program consisting of seven modules
that offer quick, targeting intervention to build understanding of: *
Addition * Subtraction * Multiplication * Division * Basic Fractions
* Fractions, Decimals, and Percents * Ratios and Equations
Focuses on core content and breaking this content into a series
of small conceptual steps and embedded skills, Corrective
Mathematics enables you to teach mathematics skills, rules, and
strategies efficiently and effectively.
A placement test provides a plan that identifies which modules
need to be covered.
Math Toolkit
Flashcard Intervention for Teaching Math
Facts
Intervention to Increase Accuracy and
Productivity Rates Via Self-Monitoring
and Performance Feedback
Intervention to Increase Accuracy By
Intermixing Easy and Challenging
Problems
Cover-Copy-Compare
Example Math Intervention
1. Greeting and Opening
• students are presented with an opening question, a real
world math problem. Often times this was a graphing
question such as what toppings do you like on your
pizza or who is your favorite teacher?
2. Main Objective of the Day
• re-teaching of 1 or more objective(s) from math
curriculum (objective had already been covered in the
classroom)
• involves pencil and paper practice pages from online
curriculum resource
Example Math Intervention
• Strong use of manipulatives, number lines,
graphics and visual organizers and other teaching
strategies to present the material in a different way
than presented in class
• independent practice with corrective feedback
3. Fluency Practice
• flashcards, math fact games
4. FFF – Fast Fact Friday
5. Intervention varies for each grade.
Sharing Information
Documents and Research Articles on
Docushare
Docushare Discussion Boards
Math Data Log
Pilot Planning Pages
Follow up sessions, December 4 and 11
Topics to include: Kindergarten Interventions and
progress monitoring, Pilot Status
Norming
• During the 2008-09 school year, we will
be gathering district norms on LPS
elementary students using the MBSP
• Probes will be administered on a classroom wide
basis to randomly selected classes throughout the
district
Fall norming: October 13-17, 2008
Winter norming: January 12-16, 2009
Spring norming: April 14-17, 2009
Norming - cont’d
Kindergarten Winter, Number sense 1 min. each
spring only (3 mins. total)
1st grade F, W, S Computation 2 minutes
2nd grade F, W, S Computation 2 minutes
3rd grade F, W, S Computation, 3 minutes,
Application 5 minutes
4th grade F, W, S Computation, 3 minutes,
Application 6 minutes
5th grade F, W, S Computation, 5 minutes,
Application 8 minutes
References
Clarke, B. & Shinn, M. R. (2004). A preliminary investigation into
the identification and development of early mathematics
curriculum-based measurement. School Psychology Review, 33, No.
2, 234-248.
DuFour, R., DuFour, R., Eaker, R., & Karhanek, G. (2004)
Whatever it takes: How professional learning communities
respond when kids don’t learn. Bloomington, IN: National
Educational Services.
Fuchs, L. S, Fuchs, D., Compton, D. L., Bryant, J., Hamlett, C.,
Seethaler, P. (2007). Mathematics screening and progress
monitoring at first grade: Implications for responsiveness to
intervention. Exceptional Children, 73, 311-330.
References - cont’d
Fuchs, L. S., Hamlett, C. L., & Fuchs, D. (1998). Monitoring
Basic Skills Progress: Basic Math Computation (2nd Ed.)
[Computer software, manual, and black-line masters]. Austin,
TX: PRO-ED.
Geary, D. C. (2003). Learning disabilities in arithmetic. In H. L.
Swanson, K. R. Harris, & S. graham (Eds.), Handbook of
Learning Disabilities. New York: Guilford Press.
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. Journal of Special Education, 33, 18-28.
References - cont’d
Gersten, R., Chard, D., Jayanthi, M., & Baker, S. (2006).
Experimental and quasi-experimental research on instructional
approaches for teaching mathematics to students with learning
disabilities. A research synthesis. Signal Hill, CA: Center on
instruction/RG Research Group.
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, D.C.: National Academy
Press.
VanDerHeyden, A. M., Witt, J. C., Naquin, G. & Noell, G. (2001). The
reliability and validity of curriculum-based measurement readiness probes
for kindergarten students. School Psychology Review, 30, 363-382.