Improving Mathematics Learning in
Special Education Settings
Pat O’Connell Johnson
Team Leader
Math and Science Partnerships
United States Department of
Education
Outline of Presentation
• Overview of National Math Panel’s
Review Process
• Selected NMP recommendations
• Implications of selected NMP
recommendations for Special Education
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National Math Panel
• What is the best available
scientific evidence to advise on
improvements in the
mathematics education of the
nation’s children, up to and
including Algebra?
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Basis of the Panel’s work
• Review of 16,000 research studies and related
documents.
• Public testimony gathered from 110 individuals.
• Review of written commentary from 160
organizations and individuals
• 12 public meetings held around the country
• Analysis of survey results from 743 Algebra I
teachers
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Areas of Major Findings and
Recommendations
–Curricular Content
–Learning Processes
–Teachers
–Instructional Practices
–Materials
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Curricular Content
• A focused, coherent progression of mathematics
learning, with emphasis on key topics should be the
norm.
• . LESS IS MORE. DEPTH OVER BREADTH!
• Revisiting topics year after year without closure should
be avoided.
• Automatic recall of math facts is important.
• Proficiency with fractions (including decimals, percent,
and negative numbers) is key.
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Curricular Content
Critical Foundations and Benchmarks are
described in the Report and should guide:
• Classroom Curricula
• Mathematics Instruction
• Textbook Development
• State Assessments
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Curricular Content
Implications for Special Education
• Meet with math directors to determine how the state
and district math frameworks match these
recommendations, and how they are operating with
special education students in various settings.
• Identify supplementary resources or materials that
could be used to reinforce math learning.
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Curricular Content
Implications for Special Education
• Be aware of need for “focused, coherent progression of
learning”—first things first. Students must master one skill
before moving on to the next skill.
• Access to math content must be provided to all students.
Accommodations for providing access may be necessary.
 Environmental
 Instructional Delivery
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Learning Processes
Scientific Knowledge on Learning and Cognition
Applied to the Classroom :
• Most children develop considerable knowledge of
mathematics before they begin kindergarten.
• Children from families with low incomes, low levels of
parental education, and single parents often have less
mathematical knowledge when they begin school than do
children from more advantaged backgrounds. This tends
to hinder their learning for years to come.
• There are promising interventions to improve the
mathematical knowledge of these young children before
they enter kindergarten.
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Learning Processes
• Mathematics performance and learning of
groups that have been traditionally
underrepresented in mathematics’ fields can
be improved by interventions that address
social, affective, and motivational factors.
• The curriculum must simultaneously develop
conceptual understanding, computational
fluency, and problem solving skills. Debates
regarding the relative importance of these
aspects of math knowledge are misguided.
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Learning Processes
• Difficulty with fractions (including
decimals and percent) is pervasive
and a major obstacle to further
progress in math.
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Learning Processes
Children’s beliefs about learning are related to their
mathematics performance.
• Children’s beliefs about the relative importance of effort
and ability can be changed.
• Experiential studies have demonstrated that changing
children’s beliefs from a focus on ability to a focus on
effort increases their engagement in mathematics
learning, which in turn improves mathematics’ outcomes.
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Learning Processes
Implications for Special Education
• EFFORT MATTERS! Success is not a matter of inherent
talent, but persistence. This is important for adults and
children to understand. NEVER say, I wasn’t good at
math!
• Early childhood programs need to include a focus on
numeracy: Pull out “Shoots and Ladders” and blocks in
various shapes, etc.
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Learning Processes
Implications for Special Education
• Sufficient opportunities /time must be provided for
students to learn content at a proficient level.
• Math programs need to include social and emotional
support systems in order for some students to be
successful.
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Teachers and Teacher Education
Mathematically Knowledgeable Classroom Teachers
Have a Central Role in Mathematics Education.
• Evidence shows that a substantial part of the variability in
student achievement gains is due to the teacher.
• The mathematics content knowledge of elementary and
middle school teachers must be strengthened as one
means for improving teacher effectiveness in the
classroom. Most elementary and middle school teachers
have not been well-prepared to teach mathematics.
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Teachers and Teacher Education
• Teacher Education programs and licensure tests for
early childhood teachers, including special education
teachers at this level, should fully address the topics of
whole number, fractions, and the appropriate geometry
and measurement topics, as well as the skills and
concepts leading to the topics.
• Research on teacher incentives generally supports their
effectiveness, but more study is needed.
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Teachers and Teacher Education
Implications for Special Educations
• Review licensure practices to assure that
teachers with strong math background are
certified.
• Support intensive, content-based, on-going
professional development for teachers. Teachers
can’t teach what they don’t understand. Join with
math colleagues to support and plan these
efforts.
• Consider using well-trained math specialists in
schools where math performance is low.
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Instructional Practices
• All encompassing recommendations
that instruction should be
exclusively student-centered or
teacher-directed are not supported
by research.
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Instructional Practices
• Research on a number of
cooperative learning approaches
indicate that one approach, Team
Assisted Individualization(TAI), has
been shown to improve students’
computational skills
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Instructional Practices
Formative assessment enhances mathematics
achievement, particularly when:
• Information is used to determine focus of instruction
• Expert teachers offer advice
• Computer-assisted instruction or peer tutoring is a
component
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Instructional Practices
Research on students who are low achievers, have
difficulties in mathematics, or have learning
disabilities related to mathematics tells us that the
effective practice includes:
• Explicit methods of instruction available on a regular basis
• Clear problem solving models
• Carefully orchestrated examples/ sequences of examples.
• Concrete objects to understand abstract representations and
notation.
• Participatory thinking aloud by students and teachers.
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Instructional Practices
Use of technology shows promise when:
• Computer-assisted instruction supports drill and practice
• Well designed tutorials are delivered through computer-assisted
instruction
• Learning is supported by the careful, targeted application of
computer programming
More research is needed
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Instructional Practices
Implications for Special Education
• There are instructional strategies and interventions that
have evidence of effectiveness, and they are compatible
with the RTI framework. This should be considered in
your schools.
• Meet with your math colleagues to ensure that these
strategies are being used in schools that are struggling
with mathematics.
• Teachers should be encouraged to use real-life contexts in
teaching math concepts to make math learning
meaningful.
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Instructional Practices
Implications for Special Education
• The use of frequent progress monitoring, providing
ongoing feedback to measure students’ performance is
imperative to success.
• Explicit instruction (step-by-step strategy) is especially
effective for students with learning disabilities. This
includes thoughtful planning and selection of examples
to support instruction.
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Instructional Materials
• U. S. mathematics textbooks are far too long -- often 7001000 pages. Mathematics textbooks are much smaller in
many nations with higher mathematics achievement than
the U.S. Excessive length makes our books unnecessarily
expensive and tends to undermine coherence and focus.
• Publishers must ensure the mathematical accuracy of their
materials.
• Instructional Software has generally shown positive effects
on student achievement as compared with instruction that
does not incorporate such technologies.
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Instructional Materials
Implications for Special Education
• Due to the comprehensive nature of
math textbooks, teachers must adapt
instructional materials to meet students’
needs.
– Use advanced organizers—outline of
content to be taught.
– Provide copies of pages with highlighted text
of important key words, concepts, directions.
– Break assignments into short sections.
– Avoid using cluttered worksheets.
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Special Education Resources
for Math Improvement
OSEP-funded Technical Assistance Centers
– Center for Implementing Technology in Education
http://www.cited.org/index.aspx
http://www.cited.org/index.aspx?page_id=152
Improving Basic Mathematics Instruction: Promising
Technology Resources for Students with Special
Needs
– National Center on Response to Intervention
http://www.rti4success.org
– The ACCESS Center
http://www.k8accesscenter.org/training_resources/math.asp
– National Center on Student Progress Monitoring
http://www.studentprogress.org/
– LD Online
http://www.ldonline.org/indepth/math
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Special Education Resources
for Math Improvement
OSEP-funded State Personnel
Development Grants
http://www.signetwork.org/activities.html#profd
ev
States with grants that focus on Math
AL
AZ
DE
GA
IA
ID
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IN
MI
MS
MT
NC
NM
NY
OH
OK
PA
SD
WV
In Sum:
• The Report provides a roadmap of what is known
from research.
• Areas of controversy that are address:
-- Early learning in math is important
--”Math Wars”
--Spiral Curriculum
--Less is more, but not how most state math
standards look.
--Teachers need to understand content, and
special education teachers need to take that
knowledge and adapt it for students.
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Where you can go for help
– www.ed.gov/MathPanel
– www.ed-msp.net -- for PD models in every
state
– www.NCTM.org – for math resources
– http://dww.ed.gov -- Doing What Works
web site
– www.Centeroninstruction.org
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Where you can go for help?
Pat O’Connell Johnson
Team Leader
Math and Science Partnerships
Office of Elementary and Secondary
Education
Patricia.Johnson@ed.gov
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