Improving Mathematics Learning in Special Education Settings

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Improving Mathematics Learning in Special
Education Settings

• Pat OConnell Johnson
• Team Leader
• Math and Science Partnerships
• United States Department of Education

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Outline of Presentation

• Overview of National Math Panels 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 nations children, up to and
  including Algebra?

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Basis of the Panels 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 learningfirst 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

• Childrens beliefs about learning are related to
  their mathematics performance.
• Childrens beliefs about the relative importance
  of effort and ability can be changed.
• Experiential studies have demonstrated that
  changing childrens 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 wasnt 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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Implications for Special Education
Learning Processes

• 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
  cant teach what they dont 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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Implications for Special Education
Instructional Practices

• 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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Implications for Special Education
Instructional Practices

• 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 700-1000 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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Implications for Special Education
Instructional Materials

• Due to the comprehensive nature of math
  textbooks, teachers must adapt instructional
  materials to meet students needs.
• Use advanced organizersoutline 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_id152
• 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/tr
  aining_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.htmlprofdev
• States with grants that focus on Math
• AL IN NY
• AZ MI OH
• DE MS OK
• GA MT PA
• IA NC SD
• ID NM WV

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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 OConnell Johnson
• Team Leader
• Math and Science Partnerships
• Office of Elementary and Secondary Education
• Patricia.Johnson_at_ed.gov

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