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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

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Improving Mathematics Learning in Special Education Settings

Pat O’Connell Johnson

Team Leader

Math and Science Partnerships

United States Department of Education

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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.


  • 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.


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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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 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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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.

Instructional Practices


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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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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

Improving Basic Mathematics Instruction: Promising Technology Resources for Students with Special Needs

National Center on Response to Intervention

The ACCESS Center

National Center on Student Progress Monitoring

LD Online


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Special Education Resources for Math Improvement

OSEP-funded State Personnel

Development Grants

States with grants that focus on Math








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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 -- for PD models in every state – for math resources -- Doing What Works web site


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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