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Document Sample
RtI Interventions for Students with
Math Delays
Pre-conference Presentation prepared for:
Florida Federation Council for Exceptional Children
October 8, 2009
Mary Little, Ph.D.
Shelby Robertson, Ph.D.
RtI Teaching Learning Connections, UCF
Session Outcomes:
• Describe current research related to instruction in
mathematics to meet needs of students with
disabilities (SWDs),
• Gain awareness of research-based programs,
methods, instruction, and resources to meet diverse
needs of students,
• Engage session participants in levels of learning for
students in math, and
• Share resources, products, and professional
development available in Florida, through support of
the BEESS and in collaboration with multiple
agencies, universities, and school districts.
Introductions
• Locate the page entitled, “About Me”.
• Fill in your personal information.
• Complete the three lines.
What is
RtI-Teaching Learning Connections?
The purpose is to identify, disseminate, and facilitate high
fidelity implementation of current and emerging research-
based instructional practices in curriculum, instruction, and
assessment within the framework of Response to Intervention
(RtI) to educational personnel in Florida.
A Project of the Florida Department of Education
In Collaboration with the University of Central Florida
Why
Math?
Why
Now?
Current Needs
• US Students not performing as well as students
in other developed countries (USDOE, 2000)
• Fourth graders have shown no measurable gains
(NCES, 2004)
• Students with disabilities not achieving rigorous
standards to achieve a high school diploma.
(NLTS, 2000)
Rationale for Change
Daily, mathematics is used throughout our lives.
The ability to compute, problem solve, and apply
concepts and skills in mathematics influences
decisions and life choices. From personal,
professional, and societal perspectives, the
mastery of mathematical skills of number sense
and problem solving are necessary. This is
especially evident in technology-rich societies,
where number sense and problem solving skills
have increasing importance, as technology
enhances both the opportunities for, yet the
demands of, advanced levels of proficiency in
mathematics.
~Witzel & Little, 2009
Rationale: Student Data
According to NAEP 2007:
•Fourth grade students with disabilities had a significant increase in math
scores between 2003 and 2007.
•African American eighth grade students showed a significant increase in
math scores.
•Hispanic eighth grade students showed a significant increase in math
scores.
What do the 2009 FCAT
Results Reflect?
In 2009, 67% of students in grades 3-10 are demonstrating
mathematics skills at or above grade level.
Our Goal, as Math Leaders
in Florida…..
To continue to plan, build understanding,
and make or adjust implementation
decisions regarding curriculum,
instruction, and assessment of the Next
Generation Sunshine State Standards in
Mathematics and RtI.
So, how do we meet these challenging
and changing goals?
Why
Math?
How?
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Strategies to Date
• Completed a thorough review of research
and meta-analyses of math resources,
programs, and methods that:
• Addressed skills and competencies revised national
standards (NCTM)
• Included students with disabilities in the research
sample, and
• Demonstrated positive results that are generalizable to
classrooms in Florida.
Findings
• Specific, explicit instruction is necessary by
a knowledgeable, competent teacher.
• Direct instruction and self-instruction were
most effective methods.
• Metacognitive strategies improve student
learning.
• Multiple student active engagement
strategies improves student learning.
• CAI and peer tutoring showed greater effect
sizes.
• Most research was completed in the domain
of basic skills.
• (Kroesbergen & Van Luit, 2007.)
National Research Databases
The What Works Clearinghouse was established in 2002
by the U.S. Department of Education's Institute of
Education Sciences to provide educators, policymakers,
researchers, and the public with a central and trusted
source of scientific evidence of what works in education.
The What Works Clearinghouse (WWC) collects, screens,
and identifies studies of effectiveness of educational
interventions (programs, products, practices, and
policies).
http://ies.ed.gov/ncee/wwc/
The Center on Instruction, a
partnership of five organizations,
provides resources and expertise to
the Regional Comprehensive Centers
in reading, mathematics, science,
special education, and English
language learners.
http://www.centeroninstruction.org/
NCTM is a public voice of mathematics education,
providing vision, leadership, and professional
development to support teachers in ensuring
mathematics learning of the highest quality for all
students.
Founded in 1920, NCTM is the world’s largest
mathematics education organization, with 100,000
members and 250 affiliates throughout the United
States and Canada.
http://www.nctm.org/
Effective Professional Development
Critical Questions:
-What are characteristics of “effective”
professional development for continuous
improvement that results in improved
student achievement.
-How will we measure the impact of
professional development?
FDOE Strategic Plan (2006)
• Increase supply of highly effective teachers
• Set, align, and apply academic, curricular, and testing
standards
• Improve student learning & independence
• Improve the quality of instructional leadership
• Increase quantity and quality of educational options
• Align workforce education programs with skill
requirements of the new economy
• Align financial resources with performance
• Improve student opportunities for access and
advancement
Bureau of Exceptional Education and Student
Services:
State Performance Plan
(2005-2010)
• 1-Increase percent of SWDs graduating with a
regular diploma
• 2-Improve percent of SWDs who complete school
(decrease drop outs)
• 3-Increase the participation and performance of
SWDs on state assessments
• (See rest of SPP for additional Indicators, Activities,
Timelines, and Resources.)
ASK HIGHLIGHTS
2008-2009 Grant Year
Potential Impact on Students With/Without
Disabilities:
•Students Without Disabilities = 25,683
•Students With Disabilities = 6,979
Total Potential Impact on Students = 32,662
Measure of Knowledge
2008-2009 Grant Year
• Total Number of Participants = 49
• Pre Test Average Score 74.8%
• Post Test Average Score 96.45%
Potential Impact on Florida
AYP and Math Proficiency
62% scoring at or above grade level
4 districts reflected Math Proficiency in the
subgroup of “Students With Disabilities
(SWD)”
• Dixie County
• Glades County
• Lafayette County
• Sumter County
2007 Measurable Targets-BEESS
State Performance Plan
• Gap between all students and SWDs who graduate
with a standard diploma will decrease to 26%
• The dropout rate for SWDs will decrease to 4.0%
• 96% of SWDs will participate in statewide
assessments
• 37% of school districts will meet AYP targets in
math
• 62% of SWDs in grades 3-10 will demonstrate
proficiency in math
• NCTM
Process
Federal Standards and
Focal Points
• Next
State Generation
Standards
Legislation
Triangle from Heather
39
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Response to Intervention
1) providing high-quality instruction/intervention matched to student
needs
2) using learning rate over time and level of performance to
3) make important educational decisions
(Batsche, et al., 2005)
Problem-solving is the process that is used to develop effective
instruction/interventions.
RtI: Three Tiered Model of School Supports
Multi-tiered Approach
1. The first tier (universal) consists of the core curriculum and general education
program which is based on evidence-based practices. The initial task in this process
is to assure that the core curriculum is effective for a major portion of the students.
2. After demonstrating that the core curriculum results in success for most students,
the second tier (supplemental) consists of supplemental instruction in addition to
the core curriculum to support the small groups of students who continue to
struggle. Tier two interventions are delivered in a small group format using
strategies known to be effective in addressing these learners.
3. Tier three (intensive) interventions are designed to be individualized, long-term
interventions for students who have not responded to Tier I and Tier II
interventions that have been delivered with a high degree of fidelity.
At all tiers, the four-step, PS/RtI process is used to maximize outcomes for students.
Problem-solving Process
• Problem-solving process with RtI:
– PROBLEM IDENTIFICATION: What is the problem?
– DEVELOP AN PLAN TO ADDRESS “WHY”: Why is it occurring?
– CLASSROOM IMPLEMENTATION: What are we going to do?
– COLLECTING, ANALYZING, SHARING RESULTS:
Is it working?
http://floridarti.usf.edu/intro_course
Critical Questions
• How do we meet the instructional needs in mathematics for
all students to achieve?
• What instructional methods, strategies, and resources are
available for the classroom teacher to meet these diverse
needs?
• How do we enhance our current teaching methods to meet
more of our students’ needs in math?
Multiple Solutions
• Differentiating the
Curriculum
• Implementing various
Levels of Learning
• Actively Engaging
Students in their
Learning
• Using Instructional and
Assistive Technology
Differentiated Instruction
“…allows all students to access the same classroom
curriculum by providing entry points, learning
tasks, and outcomes that are tailored to students’
needs.”
~Hall, Strangman, & Meyer (2003)
Principals of Differentiating
Instruction
• The teacher is clear about what is important in subject matter.
• All students participate in respectful work.
• The teacher understands, appreciates, and builds on students’ differences.
• Assessment and instruction are inseparable.
• The teacher adjusts content, process, and product in response to students’
readiness, interests, and learning profile.
• Students and teachers are collaborators.
• The goals of a differentiated classroom are maximum growth and individual
success.
• Flexibility is the hallmark of a differentiated classroom.
Differentiated Instruction
(Tomlinson, 2001)
The Purpose of
Differentiating Instruction
• Helps address individual learning needs of a
student.
• Offers various methods of instruction or
materials used for learning.
• Customized to the way individual students
learn and how each student is reliably
assessed.
Differentiate Instruction
• When a student experiences difficulty,
move back to the previous level for additional
practice
• Allow the use of manipulatives or
representational drawings to solve problems
• Allow students choose level (CRA) to solve a
problem
Differentiate Instruction
• Students not showing mastery at representational
level returns to using concrete objects before
creating a representational table.
• Students not showing mastery at the abstract level
return to representational.
• (Students not showing mastery should be returned
to the level that allows them to reach mastery after
repeated practice.)
• Assure that mastery is reached at each level of CRA
before moving on
Differentiated Instruction
Differentiated instruction
involves a wide range of
techniques and support
systems that assure that ALL
students participate and are
successful in the general
curriculum.
Instruction in Algebra
ASK Professional Development
Developed by a cadre of math and special educators
from school districts, educational agencies,
universities and FDOE.
Aligned with Next Generation Sunshine State
Standards and national math standards (NCTM).
Piloted and researched in Florida's classrooms for
students with and without disabilities.
ASK Instructional Strategies
ASK provides professional development for math and ESE teachers:
uses the theoretical framework of levels of learning
mathematics (CRA),
infuses researched meta-cognitive strategies
(mnemonic devices, self-monitoring skills, graphic
organizers, etc.),
includes accommodations and technology to meet the
needs of all learners,
includes classroom progress monitoring.
Standards Addressed
• Understanding patterns, relations, and functions
• Representing and analyzing mathematical situations and
structures using algebraic symbols
• Using mathematical models to represent and understand
quantitative relationships, and
• Analyzing change in various contexts (NCTM, 2001)
Levels of Learning
“We know it is important that students learn to
achieve at an abstract level of problem
solving. This is achieved by starting students
with concrete learning and progressing to
representational learning. Students will then
develop strategies, enabling them to problem
solve on an abstract level. This model was
designed for K-12 students and is known as
CRA.”
~Witzel, Mercer, & Miller, 2003
Multiple Solutions
• Differentiating the
Curriculum
• Implementing various
Levels of Learning
• Actively Engaging
Students in their
Learning
• Using Instructional and
Assistive Technology
Levels of Learning
Are you familiar with the
Levels of Learning when
teaching mathematics?
Take several minutes to
sort the activities with the
appropriate Level of
Learning.
Solve This Problem
+
Car and Cycle Expo is coming up soon. Because of
space, there is a limited amount of vehicles able to
register. The total number of wheels is 48 and the
total number of vehicles is 17.
How many cars are able to register?
Concrete
Representational
Abstract
C-R-A
“We know it is important that students learn
to achieve at an abstract level of problem
solving. This is achieved by starting students
with concrete learning and progressing to
representational learning. Students will
then develop strategies, enabling them to
problem solve on an abstract level. This
model was designed for K-12 students and is
known as C-R-A.”
~Witzel, Mercer, & Miller, 2003
Concrete Level
Definition:
A teaching method that
uses actual objects such as
people, shoes, toys, fruits,
cubes, base-ten blocks, or
fraction tiles.
What concrete items have you
used in your classroom to
teach math concepts?
Representational Level
Definition:
IIIII-III=II
A teaching method that uses
pictures, tally marks, diagrams, OR
and drawings. These pictorial ♥♥+♥=♥♥♥
representations relate directly to
the manipulatives and set up the
student to solve numeric
problems without pictures.
From your experiences what
can you use that are
representational in your
Abstract Level
Definition:
A teaching method that uses
written words (including 10‐a=5
Braille), symbols (such as
variables or numerals),
verbal expressions, or sign Sam put 18 pencils in
language. 3 equal groups. How
many pencils are in
each group?
From your experiences what
can you use that are abstract
in your classroom?
“It is better to solve one problem
five different ways than to solve
five problems one way.”
~Polya, 1945
Reflection on Learning
• Reflect on your
learning related to
the levels of learning
(C-R-A).
• Record your
reflections in the
Math Journal.
Research Findings
“Studies that involved teaching algebra revealed
that C-R-A instruction was more effective than
traditional abstract-level instruction.”
~Witzel, 2001
Research Findings
“Students who learned how to solve algebra
transformation equations through C-R-A
outperformed peers receiving traditional
instruction.”
~Witzel, Mercer, & Miller, 2003
How do we meet the needs of all students?
Federal Legislation
~ taken from IES-WWC
~ taken from IES-WWC
Multiple Solutions
• Differentiating the
Curriculum
• Implementing various
Levels of Learning
• Actively Engaging
Students in their
Learning
• Using Instructional and
Assistive Technology
Actively Engaging Students
in Their Learning
“Many excellent teachers have discovered that their
students can be more successful when they are
engaged in doing mathematics— writing about
mathematics, modeling mathematical situations,
discussing mathematics, exploring mathematical
ideas—rather than watching their teacher do
mathematics.”
~Engagement As A Tool For Equity, NCTM, 2008
77
Actively Engaging Students in their Learning
Use of Technology
http://nlvm.usu.edu/en/nav/index.html
National Council of Teachers of Mathematics
http://illuminations.nctm.org/
FDLRS Tech
What do we know?
• Can be used K-12
• Works for all students
• Can be used alone or combined
• Possible to use any or all in assessment
• Provides greater depth to learning
• More likely students will retain knowledge longer
• Can revert back to lower level when a student
experiences difficulty (Mercer & Miller, 2001)
Let’s look at an example…
www.mmdatasurvey.com
Now, what should we
do with the data?
Analyze your data as a class…
Or add it to Mr. Wright’s real time
data…
Break Time
See you in 15 minutes!
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Multiple Solutions
• Differentiating the
Curriculum
• Implementing various
Levels of Learning
• Actively Engaging
Students in their
Learning
• Using Instructional and
Assistive Technology
Use of Technology
Technology
Within an effective educational setting,
technology can enable students to become:
• Capable information technology users
• Information seekers, analyzers, and evaluators
• Problem solvers and decision makers
• Creative and effective users of productivity tools
• Communicators, collaborators, publishers, and
producers
• Informed, responsible, and contributing citizens
~(NETS, 2004)
Think-Pair-Share
• What technology and
instructional websites
do you currently use
to assist your students
with:
• -fluency and learning
of basic facts?
• -algebra/math skills?
Digital Natives
Schools are stuck in the
20th century. Students
have rushed into the 21st.
How can schools catch up
and provide students with a
relevant education?
~Prensky, 2005
Knowledge of the Teacher
Digital Natives (Students) Digital Immigrants (Teachers)
Multiple multimedia information sources rapidly Slow controlled information release, limited sources
Parallel process & multi‐task Singular process and single or limited task
Processing order Processing order
Picture, Video & Sound—Text Text—Picture, Video & Sound
Random access to interactive media Linear, logical sequential access
Interact/network simultaneously to many Interact/network simultaneously to few
Comfortable in virtual and real spaces Comfortable in real spaces
Prefer interactive/network approach to work Prefer students to work independently
“Just in time” learners “Just in case” learners
Instant access, rewards & gratification Delayed/differed access, rewards & gratification
Learning is relevant, instantly useful and fun Learning is to teach to the curriculum guide and standardized tests
~ Prensky, 2005
“If this tool doesn’t dramatically change the way we
teach mathematics and the mathematics we teach,
then we must seriously question our professional
integrity.”
~Frank Demana, Ohio State University professor, 1995
Questions to consider…
• How do you incorporate the use of technology in
your mathematics classroom?
• What evidence have you seen that technology
deepens students’ mathematical understanding?
• How have your instructional design and the
teaching of lessons changed because of
technology?
http://nlvm.usu.edu/en/nav/index.html
National Council of Teachers of Mathematics
http://illuminations.nctm.org/
FDLRS Tech
Think-Pair-Share
• How does the use of the levels of learning
meet the learning needs for students?
• How else can we accommodate for students’
needs to meet the learning needs for all
students?
• What are some classroom accommodations
and technology that you use in Math?
Diverse Abilities
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Accommodations and Technology
Exploration
Accommodations
Accommodations involve a wide
range of techniques and support
systems that assure that ALL
students participate and are
successful in the general curriculum.
The Purposes of
Accommodations
• Helps address individual learning needs
of a child
• Offers various methods of instruction or
materials used for learning
• Customized to the way individual
students learn and how each child is
reliably assessed
Accommodations
Accommodations may be provided in five
general areas:
• Instructional methods and materials
• Assignments and classroom assessments
• Time demands and scheduling
• Learning environment
• Use of special communication systems
Accommodations
Examples:
– Flexible scheduling
– Flexible responding
– Additional time
– Clarification of word or phrase for
general directions
– Dictionaries
Accommodations
Think about accommodations students
might use in the classroom.
Take 2 minutes and write 1
accommodation on each post it.
Assess with a purpose.
You can either take action, or
you can hang back and hope
for a miracle. Miracles are
great, but they are so
unpredictable.
~Peter Drucker
Assessment
Assessment has to guide
teaching and must be
decided before teaching.
~Ortiz, 2004
Reflection Questions
• How are the actions of a
teacher like a doctor?
• How is this related to
assessment?
Assessment Standards
The Assessment Standards for
School Mathematics (NCTM,
1995) presented six standards
about exemplary mathematics
assessment.
Assessment Standards
• Reflect the mathematics that students
should know and be able to do
• Enhance mathematics learning
• Promote equity
• Be an open process
• Promote valid inference
• Be a coherent process
Assessment and Evaluation
• Assessment
– The process of gathering evidence
• Evaluation
– The process of using evidence gathered during
assessment to determine the work of,
assigning a value to, or making a judgment
about…
Types of Assessment
• Formal and informal
• Pre-assessment, Progress monitoring,
Summative
Name as many assessments as you can in the time
provided.
How do you use these assessments in your
classroom?
Types of Assessment
• Rubrics
• Teacher made assessments
• Observations
• Open ended questions
• Journals
Teacher Made Assessments
• Rubrics
• Portfolios
• Projects
– Individual
– Group
• Tests and Quizzes
• Checklist
• Cooperative Learning Activities
Questions to Consider
• Do I gather enough evidence before
making judgments or evaluating my
students?
• Do I really understand what my students
know, can do, and feel?
(NCTM, 2003)
Time to Practice on Your
Own
Your
turn
to
shine!
THINK-PAIR-SHARE
•What do you
understand the
“levels of learning”
to be?
•How can you use
in your classroom?
Application Activity
Lesson Design
At your tables, design a CRA Lesson
using a Math Standard for your grade
level.
(HINT: Feel free to start with a
“favorite lesson”.)
Use the Self-checklist and any of the
concrete items to assist with your
planning. Be prepared to share
with the group!
Your Turn!
Please share your lesson plan:
– Standards
– Grade levels
– Levels of Learning
– Metacognitive Strategies
– Accommodations
– Technology
– Assessments
Lesson Challenge
• You have just been told
that a new student will
be included into your
Math class.
• Will your lessons meet
the learning needs for
the student(s)?
• Revise and/or add, as
needed.
Content and Process Review
ABCDEFGHIJKLMNOPQRSTUVWXYZ
List terms or concepts that start with the
identified letter based on new knowledge
learned and reviewed.
Success Stories!
Teachers in the younger grades concluded that by
spending more time on the representational stage,
they spent far less time reteaching the skill.
Robert, Indian River County
How did the ASK Cadre Teacher’s
Classes do on FCAT?
6th Grade Mathematics
(Matched Student DSS Gain)
State Average: 24
District Average: 6
Average ASK Cadre: 43
79% higher than the state average and
617% higher than the district average
How did the ASK Cadre Teacher’s
Classes do on FCAT?
10th Grade Mathematics
(Matched Student DSS Gain)
State Average: 40
District Average: 43
Average ASK Cadre: 64
60% higher than the state average and
48.8% higher than the district average
Intensive Math at Johnson Middle
School in Manatee County
6th Grade (27 students)
Mean State DSS Gain: 24
Mean District DSS Gain: 6
Mean ASK DSS Gain: 85.4
Intensive Math at Johnson Middle
School in Manatee County
7th Grade (38 students)
Mean State DSS Gain: 126
Mean District DSS Gain: 122
Mean ASK DSS Gain: 203.9
Intensive Math at Johnson Middle
School in Manatee County
8th Grade (26 students)
Mean State DSS Gain: 91
Mean District DSS Gain: 87
Mean ASK DSS Gain: 169.1
All but two of my students
showed better
understanding and
improvement with adding
and subtracting basic facts
and two digit numbers.
Alina, Orange County
Teacher Quote
“By using manipulatives
to demonstrate a math
concept, then draw it
and explain it in
words, students get
that necessary hands
on experience and are
able to transfer that
knowledge to student’s
mind.”
Teacher’s Reflection
“After using C-R-A with my students, I have
definitely seen many advantages and have
decided to incorporate it permanently into
my math instruction.”
What
are
our
next
steps…
Action Planning
Discuss participants implementation plans using C-R-A
by discussing these critical questions:
– How will you use this new knowledge?
– How will you assess its effectiveness in your teaching
practices?
– How will you know it is working for your students?
Products
• Primary Edible Math booklets and CDs
• Secondary Edible Math booklets and CDs
• Cool Tools in Mathematics:Classroom Informal
Assessments for Teachers
• Newsletters
• Math Connections: Learning Gains and Instructional
Decision-making in the Math Classroom
• Metacognitive Strategies book
www.RtITLC.ucf.edu
Keys of Problem Solving (KoPS)
Who?
• Pre-K to 12 teachers who provide or
support instruction of mathematics to
students who struggle with problem
solving.
What?
• KoPS will facilitate teacher knowledge in
the use of research-based instructional
strategies in problem solving.
How?
• KoPS is a two-day statewide professional
development institute designed to
provide teachers with the necessary
resources to increase student ability in
problem solving.
“We cannot hold a torch
to light another's path
without brightening
our own.”
-Ben Sweetland
Contact Us
E-mail
RtITLC@mail.ucf.edu
Toll free 1-866-367-4150
Visit our website
http://www.RtITLC.ucf.edu
Contact
Mary Little, Ph.D. -Principal Investigator
Shelby Robertson, Ph.D. -Project Coordinator
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