Collaboration for Effective Educator
Development, Accountability, and Reform
Course Enhancement Module on Multi-Tiered Systems of Support in
Mathematics: Part 1—Introduction
H325A120003
CEM Overview
Part 1: Introduction
Part 2: Universal Intervention
Part 3: Supplemental Intervention
Part 4: Intensive Intervention
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Participant Goals
By the end of this section, participants
will be able to:
 Discuss the importance of science, technology,
engineering, and mathematics (STEM) education
 Identify essential concepts in mathematics
 Identify areas where students commonly struggle
 Identify the essential components of a multi-tiered
system of support
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Part 1: Introduction
Importance of STEM education
Guiding principles in math
Common Core State Standards (CCSS)
and essential math concepts
How students learn math
Students with math disabilities
Multi-tiered systems of support (MTSS)
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Note
Part 1 uses content and resources from:
 The National Center on Intensive Intervention (NCII)
www.intensiveintervention.org
 The National Center on Response to Intervention
http://www.rti4success.org/
 National Council of Teachers of Mathematics
www.nctm.org
 Innovation Configuration for Mathematics
(CEEDAR)
 The National Math Advisory Panel Report (2008)
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Why Is Mathematics
Education So Important?
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The Importance of STEM Education
 Prepares all students for college and career
 Is vital to meeting the needs of the future job
market
 Eliminates disparities in math achievement
(National Council of Teachers of Mathematics [NCTM], 2014)
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Nation’s Report Card (2013)
http://nationsreportcard.gov/reading_math_2013/#/student-groups
(National Assessment of Educational Progress, 2013)
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Nation’s Report Card (2013)
Students Scoring Basic or Below Basic in Math
Student Subgroup
Grade 4
Grade 8
All students
58%
64%
Students with disabilities
83%
92%
English language learners
86%
95%
http://nationsreportcard.gov/reading_math_2013/#/student-groups
(National Assessment of Educational Progress, 2013)
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Sample NAEP Grade 4
Math Question
Fourth-grade students
scoring at the basic
level should be able to
solve a problem like
this:
http://nces.ed.gov/nationsreportcard/itmrl
sx/default.aspx
(National Assessment of Educational Progress, n.d.)
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STEM Education: The
President’s Charge
The United States’ international math
status is significantly lower than other
well-developed countries.
Implications for the nation’s future
Implications for our quality of life
(National Mathematics Advisory Panel, 2008)
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Interactive
Activity
STEM Education
Video from www.whitehouse.gov,
retrieved from http://www.youtube.com/watch?v=f9NxFeCFApM&feature=player_detailpage,
as posted by Mavericks Space Foundation, 2010
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STEM Education: Job
Outlook
3:1 increase in STEM jobs
(National Science Board, 2008)
“Close to half of all seventeen year olds cannot read or do math at the
level needed to get a job at a modern automobile plant. Barring some
other special knowledge or talent that would allow them to earn a
living as, say, a plumber or artist, they lack the skills to earn a middleclass paycheck in today’s economy.”
- Labor economists Richard Murnane and Frank Levy
(National Mathematics Advisory Panel, 2008, p. 3)
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Income by Graduation Status
National Center for Education Statistics. (2014). The condition of education 2014 (NCES
2014-083). Annual Earnings of Young Adults.
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STEM Education: Life Skills
Many Americans lack life skills that
involve math.
Many have difficulty with fractions,
which are essential for algebra.
Algebra is “gateway.”
(National Mathematics Advisory Panel, 2008)
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Importance of STEM
Education: College Success
Success in math is essential for college.
High school math beyond Algebra II is
highly correlated with college attendance
(Horn & Nuñez, 2000; Horowitz, 2005).
College graduates produce multiple
benefits for society.
(National Mathematics Advisory Panel, 2008)
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STEM Education:
Addressing Disparities
 College is a social escalator
(Pascarella & Terenzini, 1991).
 College graduation rates differ
between those who have and
have not taken Algebra II.
 High school science and math course
completion can relieve or eliminate the
achievement gap.
 Math is for ALL.
(National Mathematics Advisory Panel, 2008)
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Standards-Based Movement
Six Principles of the StandardsBased Movement






Equity
Curriculum
Teaching
Learning
Assessment
Technology
(Van de Walle et al., 2013)
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Principles and Standards
(NCTM, 2000)
Five Content
Standards





Number and Operations
Algebra
Geometry
Measurement
Data Analysis and
Probability
(Van de Walle et al., 2013)
Five Process
Standards





Problem Solving
Reasoning and Proof
Communication
Connections
Representation
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Quest for Coherence
(NCTM, 2006)
Curriculum focal points for
prekindergarten through grade
8 mathematics: A quest for
coherence (NCTM, 2006)
BIG ideas identified
Three focal points along with process
skills and connections are fundamental
at each grade level
(Van de Walle et al., 2013)
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Birth of the Common Core
State Standards
Common
Core State
Standards
Five content
standards
Five process
standards
Coherence
(CCSSO, 2010)
11 content
domains
8 practice
standards
Watch the CCSS VIDEO
(Van de Walle et al., 2013; Council on Great City Schools, 2013)
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Characteristics of
Successful Math Programs,
Teachers, and Students
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Activity: Successful Schools,
Teachers, and Students
Directions:
1. Move into your assigned group.
•
Choose one person to be the recorder and one person to be the reporter.
2. Travel to each chart as directed, read the topic on the
chart, and record your ideas on the chart paper.
3. After you visit all three charts, return back to your original
chart.
4. Read all of the additional ideas that have been added by
the other teams and be ready to share out to the large
group.
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Math Guiding Principles
I. Teachers must understand and demonstrate
mastery of the mathematics content they
teach.
II. Teachers must understand how students
learn math content.
III. Teachers must understand how
assessment guides and informs instruction.
(VanDerHeyden & Allsopp, 2014)
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Knowledge of Math Content
Teachers must demonstrate:
 Competency in understanding the underlying
concepts for the content they teach
 Understanding of math concepts and skills
across domains
 Understanding of and engagement in the eight
critical practices (CCSS)
 Understanding of effective teaching practices
specific to the mastery of math
(VanDerHeyden & Allsopp, 2014)
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Teacher’s Knowledge
(Hill, Ball, & Schilling, 2008)
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Understanding Underlying
Concepts
Teachers must…
 Understand key ideas and skills
 Articulate prerequisite skills
 Explicitly connect the known to the new
 Explain why a problem worked
 Establish mastery objectives
 Select tools that align with key ideas to facilitate
understanding
(VanDerHyden & Allsopp, 2014)
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Understand the Developmental
Nature of Mathematics
 Teachers must also demonstrate understanding
of math concepts and skills across domains
and how they build on each other.
 11 domains (CCSSO, 2010):
1. Counting and Cardinality
2. Operations and Algebraic
Thinking
3. Number and Operations in
Base Ten
4. Number and Operations–
Fractions
5. Measurement and Data
(Van de Walle et al., 2013)
6. Geometry
7. Ratios and Proportional
Relationships
8. The Number System
9. Expressions and Equations
10. Functions
11. Statistics and Probability
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Handout
1
Eight Math Practices
K–8 students should be able to:
 Make sense of problems and
persevere in solving them
 Use appropriate tools
strategically
 Reason abstractly and
quantitatively
 Attend to precision
 Construct viable arguments and
critique the reasoning of others
 Look for and make use of
structure
 Model with mathematics
 Look for and express regularity in
repeated reasoning
http://www.corestandards.org/Math/Practice/
(Van de Walle et al., 2013)
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How Mathematical
Thinking Develops
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Math Proficiency
What is math proficiency?
Math proficiency means understanding key
concepts with automaticity, developing
“flexible, accurate, and automatic execution
of standard algorithms, and [using] these
competencies to solve problems” (NMAP, 2008).
For example, to prepare students for algebra, teachers must
“simultaneously develop conceptual understanding,
computational fluency, and problem-solving skills” (NMAP,
2008).
(National Mathematics Advisory Panel, 2008)
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Five Domains of
Math Proficiency
Van de Walle, Karp, Bay-Williams, Wray, & Rigelman, 2013
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Understand the Developmental
Nature of Mathematics
(slide graphic from NCTM, 2012, as referenced by Common Core Math Library, n.d. Retrieved from
http://ccssmlibrary.blogspot.com/p/grade-level-math-resources.html)
Interactive K–8 chart
Interactive K-8 chart linked above is LearnZillion (n.d.), retrieved from https://learnzillion.com/common_core/math/k-8
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Students With Math Disabilities
and Struggling Learners
 Number sense
 Working memory
 Phonological processing
 Processing speed
 Executive functioning
 Pattern of strengths and weaknesses
(Compton et al., 2012)
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Math Disabilities
 Dyscalculia: a neurologically based disorder
affecting math abilities, this is evident by a
discrepancy between a student’s general
cognitive functioning (IQ) and math abilities
(academic achievement). The three types of
math disabilities are:
– Semantic memory
– Procedural memory
– Visuospatial memory
 Prevalence: at least 6 percent
 Language difficulties
(Wadlington & Wadlington, 2008)
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Math Disabilities
Math anxiety
Additional factors: motivation, poor
instruction, lack of prerequisite skills
(Video from: www.NLCD.org or http://www.youtube.com/watch?v=HVf_OHK2hHQ)
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Poor Outcomes for
Students With Disabilities
Students with disabilities have a history of poor
outcomes (compared with their non-disabled
peers) in:
 Academic achievement
 Involvement with criminal justice system
 Employment
(National Mathematics Advisory Panel, 2008)
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Multi-Tiered Systems of
Support
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Multi-Tiered Systems of
Support (MTSS)
(Slide graphic and information taken from www.rti4success.org)
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Multi-Level Prevention System
Intensive
level of
prevention
(~ 5% of
students)
Supplementary
level of
prevention
(~15% of
students)
Universal level
of prevention
(~80% of
students)
(Information taken from www.rti4success.org)
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Multi-Level Prevention System
Students with
disabilities and
English language
learners
receive services at
all levels,
depending on need
Intensive level of
prevention
Supplemental level of
prevention
Universal level of
prevention
(Information taken from www.rti4success.org)
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MTSS Framework
Multi-Level Prevention System
Universal
Focus: All students
Instruction: District curriculum and instructional practices that are
evidence-based; aligned with state or district standards; and
incorporate differentiated instruction
Setting: General education classroom
Assessments: Screening, continuous progress monitoring, and
outcome measures
Supplementary
Focus: Students identified (through screening) as at risk for poor
learning outcomes
Instruction: Targeted, supplemental instruction delivered to small
groups
Setting: General education classroom or other general education
location within the school
Assessments: Progress monitoring, diagnostic
Intensive
Focus: Students who have not responded to universal or
supplementary instruction
Instruction: Intensive, supplemental instruction delivered to small
groups or individually
Setting: General education classroom or other general education
location within the school
Assessments: Progress monitoring, diagnostic
(Information taken from www.rti4success.org)
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MTSS: Screening
 Purpose: Identify students who are at risk of
poor learning outcomes
 Focus: All students
 Tools: Brief assessments that are valid,
reliable, and that demonstrate diagnostic
accuracy for predicting learning or behavioral
problems
 Timeframe: Administered more than once per
year (e.g., fall, winter, and spring)
(Information taken from www.rti4success.org)
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Progress Monitoring
 Purpose: Monitor students’ response to primary,
secondary, or tertiary instruction in order to estimate
rates of improvement, identify students who are not
demonstrating adequate progress, and compare the
efficacy of different forms of instruction
 Focus: Students identified (through screening) as at risk
for poor learning outcomes
 Tools: Brief assessments that are valid, reliable, and
evidence-based
 Timeframe: Students are assessed at regular intervals
(e.g., weekly, biweekly, or monthly)
(Information taken from www.rti4success.org)
44
Data-Based Decision Making
 Data analysis is used at all levels of RTI implementation
(e.g., state, district, school, grade level) and at all levels of
prevention (e.g., universal, supplementary, intensive).
 It requires established routines and procedures for making
decisions.
 It also requires explicit decision rules for assessing student
progress (e.g., state and district benchmarks, level and/or
rate).
 Data is used to compare and contrast the adequacy of the
core curriculum and the effectiveness of different
instructional and behavioral strategies.
(Information taken from www.rti4success.org)
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Implementing the MTSS
Framework
 Select and implement evidence-based
practices and procedures.
 Implement essential components and the
identified framework with integrity.
 Ensure that cultural, linguistic, and
socioeconomic factors are reflected in the RTI
framework and its components.
(Information taken from www.rti4success.org)
46
Considerations for English
Language Learners
 Provide interventions that:
– Include high-quality vocabulary instruction
– Take into account the student’s level of
language proficiency
– Address cultural and prior educational
experiences
(Information taken from www.rti4success.org)
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Linguistic and Cultural
Factors to Consider
 Native language
 Current levels of proficiency in first language
and in English
 Early exposure to first language and English
 Country of origin
 Educational and cultural experiences
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(Information taken from www.rti4success.org)
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How CCSS-M Aligns
With MTSS
(Information and graphic from
http://www.intensiveintervention.org/sites/default/files/NCII_Computation_Fractions_Example.pdf )
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Benefits of MTSS
Maximize academic growth
Minimize behavioral
problems
Culturally responsive
(Slide graphic and information taken from www.rti4success.org)
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Interactive
Activity
Reflect and Revise:
Closure Activity
 Take three minutes to reflect on five to eight of
the big ideas you learned from this module.
 Revisit the chart paper.
 Update your definition of “successful math
instruction, teachers, and students.”
 Add or delete ideas in your definitions based on
new information you learned from this module.
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