Teaching Math to Students with Disabilities

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Teaching Math to Students with Disabilities

• Present Perspectives

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Math is hard (Barbie, 1994)

• US 15 year olds ranked 24th (among 29 developed
  nations) in the 2003 International Student
  Assessment in math literacy and problem solving
• 7 of US students scored in the advanced level in
  the 2004 Trends in Math and Science Study
• Almost half of America's 17 year olds did not
  pass The National Assessment of Educational
  Progress math test
• 2006 Hart/Winston Poll found that 76 of
  Americans believe that if the next generation
  does not work to improve its skills it risks
  becoming the 1st generation who are worse off
  economically than their parents

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How did we get here?

• Math skills have received less attention than
  reading skills because of the perception that
  they are not as important in real life
• Ongoing debate over how explicitly children must
  be taught skills based on formulas or algorithms
  vs a more inquiry-based approach
• Teacher preparation general concern about
  elementary preservice training programs
• Little reference to students with disabilities in
  NCTMs standards
• Debate over math difficulties vs math
  disabilities

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Developmental dyscalculia

• developmental difficulties or disabilities
  involving quantitative concepts, information, or
  processes
• Dyscalculia is where dyslexia was 20 years ago it
  needs to be brought into the public domain
• Jess Blackburn, Dyscalculia Dyslexia Interest
  Group

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What defines mathematical learning disabilities?

• Genetic basis
• Presently only determined by behavior (which
  behaviors knowledge of facts? procedures?
  conceptual understanding? Speed and accuracy?)
• Depending on the criteria incidence can include
  from 4 to 48 of students
• Mathematical difficulties vs. mathematical
  disabilities different degrees of the same
  problem or different problems?

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National Mathematics Advisory Panel

• Established in 2006
• To examine
• Critical skills skill progressions
• Role appropriate design of standards
  assessment
• Process by which students of various abilities
  and backgrounds learn mathematics
• Effective instructional practices, programs
  materials
• Training (pre and post service)
• Research in support of mathematics education

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NCMT final Report (2008)

• Curricular content
• Focused must include the most important topics
  underlying success in school algebra (whole
  numbers, fractions, and particular aspects of
  geometry and measurement)
• Coherent effective, logical progressions
• Proficiency students should understand key
  concepts, achieve automaticity as appropriate
  develop flexible, accurate, and automatic
  execution of the standard algorithms, and use
  these competencies to solve problems

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What is the structure of mathematical learning
disabilities?

• Issues with retrieval of arithmetic facts
• Difficulties understanding mathematical concepts
  and executing relevant procedures
• Difficulties choosing among alternate strategies
• Trouble understanding the language of story
  problems, teacher instructions and textbooks

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Math instruction issues that impact students who
have math learning problems

• Spiraling curriculum
• Teaching understanding/algorithm driven
  instruction
• Teaching to mastery
• Reforms that are cyclical in nature

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Promising approaches to teaching mathematics to
students with disabilities

• Math Expressions
• Saxon
• Strategic math Series
• Touch Math Number Worlds Curriculum
• Montessori methods and materials
• What works clearing house

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Resources for teaching math

• Illuminations
• MathVids

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Teaching Math to Students with Disabilities

• Strategies

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Application of effective teaching practices for
students who have learning problems

• Concrete-to-representational-to-abstract
  instruction (C-R-A Instruction)
• Explicitly model mathematics concepts/skills and
  problem solving strategies
• Creating authentic mathematics learning contexts

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Concrete-to-Representational-to-Abstract
Instruction (C-R-A Instruction)

• Concrete each math concept/skill is first
  modeled with concrete materials (e.g. chips,
  unifix cubes, base ten blocks, pattern blocks)
• Representational the math concept is next
  modeled at the representational (semi-concrete)
  level (e.g. tallies, dots, circles)
• Abstract The math concept is finally modeled at
  the abstract level (numbers mathematical
  symbols) should be used in conjunction with the
  concrete materials and representational drawings.

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Concrete-to-Representational-to-Abstract
Instruction (C-R-A Instruction)

• Concrete each math concept/skill is first
  modeled with concrete materials (e.g. chips,
  unifix cubes, base ten blocks, pattern blocks)
• Representational the math concept is next
  modeled at the representational (semi-concrete)
  level (e.g. tallies, dots, circles)
• Abstract The math concept is finally modeled at
  the abstract level (numbers mathematical
  symbols) should be used in conjunction with the
  concrete materials and representational drawings.

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Concrete-to-Representational-to-Abstract
Instruction (C-R-A Instruction)

• Concrete each math concept/skill is first
  modeled with concrete materials (e.g. chips,
  unifix cubes, base ten blocks, pattern blocks)
• Representational the math concept is next
  modeled at the representational (semi-concrete)
  level (e.g. tallies, dots, circles)
• Abstract The math concept is finally modeled at
  the abstract level (numbers mathematical
  symbols) should be used in conjunction with the
  concrete materials and representational drawings.

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Important Considerations

• Use appropriate concrete objects
• After students demonstrate mastery at the
  concrete level, then teach appropriate drawing
  techniques when students problem solve by drawing
  simple representations
• After students demonstrate mastery at the
  representational level use appropriate strategies
  for assisting students to move to the abstract
  level.

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How to implement C-R-A instruction

• When initially teaching a math concept/skill,
  describe and model it using concrete objects
• Provide students multiple opportunities using
  concrete objects
• Provide multiple practice opportunities where
  students draw their solutions or use pictures to
  problem solve
• When students demonstrate mastery by drawing
  solutions, describe and model how to perform the
  skills using only numbers and math symbols
• Provide multiple opportunities for students to
  practice performing the skill using only numbers
  and symbols
• After students master performing the skill at the
  abstract level, ensure students maintain their
  skill level by providing periodic practice
• Example

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Explicit Modeling

• Provides a clear and accessible format for
  initially acquiring an understanding of the
  mathematics concept/skill
• Provides a process for becoming independent
  learners and problem solvers

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What is explicit modeling?
Teacher
Mathematical concept
Student
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Instructional techniques.

• Identify what students will learn (visually and
  auditorily)
• Link what they already know (e.g. prerequisite
  concepts/skills, prior real life experiences,
  areas of interest)
• Discuss the relevance/meaning of the skill/concept

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Instructional techniques.(cont)

• Break math concept/skill into 3 4 learnable
  features or parts
• Describe each using visual examples
• Provide both examples and non-examples of the
  mathematics concept/skill
• Explicitly cue students to essential attributes
  of the mathematic concept/skill you model (e.g.
  color coding)
• Example

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Implementing Explicit Modeling

• Select appropriate level to model the concept or
  skill (concrete, representational, abstract)
• Break concept/skills into logical/learnable parts
• Provide a meaningful context for the
  concept/skill (e.g. word problem)
• Provide visual, auditory, kinesthetic and tactile
  means for illustrating important aspects of the
  concept/skill
• Think aloud as you illustrate each feature or
  step of the concept/skill
• Link each step of the process (e.g. restate what
  you did in the previous step, what you are going
  to do in the next step)
• Periodically check for understanding with
  questions
• Maintain a lively pace while being conscious of
  student information processing difficulties
• Model a concept/skill at least three times

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Authentic Mathematics Learning Contexts

• Explicitly connects the target math concept/skill
  to a relevant and meaningful context, therefore
  promoting a deeper level of understanding for
  students
• Requires teachers to think about ways the concept
  skill occurs in naturally occurring contexts
• The authentic context must be explicitly
  connected to the targeted concept/skill
• Example

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Implementation

• Choose appropriate context
• Activate students prior knowledge of authentic
  context, identify the math concept/skill students
  will learn and explicitly relate it to the
  context
• Involve students by prompting thinking about how
  the math concept/skill is relevant
• Check for understanding
• Provide opportunities for students to apply math
  concept/skill within authentic context
• Provide review and closure, continuing to
  explicitly link target concept/skill to authentic
  context
• Provide multiple opportunities for student
  practice

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Now its your turn

• Using your case study information apply at least
  one of the three selected teaching strategy
  (C-R-A, Explicit Modeling or Authentic Concepts)
  to your groups focus student
• Think about the students strengths needs
• Review the students IEP and corresponding
  curricular framework
• Be prepared to share your ideas with the class