Mathematics for Students with Learning Disabilities

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Mathematics for Students with Learning
Disabilities

• Background Information
• Number Experiences
• Quantifying the World
• Math Anxiety and Myths about math
• The Concepts (How they are formed)
• Connected Teaching

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Background Information

• For every ___ years of schools, students with
  disabilities gain 1 year of math achievement.
• What grade level of math do most high school
  students with learning disabilities top out at?
• Most students with disabilities are not
  knowledgeable of needed consumer math skills
  (Algozzine et al., 1987).
• Students with learning disabilities learn
  arithmetic through hills and valleys (Cawley,
  Parmar, Miller, 1997).
• Many elementary school preservice teachers show a
  distaste for mathematics.

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Overall concerns for students with learning
disabilities

• Abstractness of numbers
• Low number sense
• Poorly formed ideas and algorithms
• (requiring systematic instruction over
  constructivism)
• Overgeneralization or incorrect use of algorithms
• Poor recall of facts and procedures
• Generalization and maintenance
• (increases with difficulty of problems)
• different presentation confuses

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Number Experiences

• A concept is an idea or mental image. Children
  develop concepts from physical objects through
  mental abstractions.
• How can we help young children experience the
  importance of numbers?
• Arithmetic is used to refer to manipulations with
  numbers and computations while mathematics is
  concerned with thinking about quantities and
  relationships among them (Polloway Patton,
  1993). To learn mathematics children must be
  taught the relationships between quantities and
  shown relevance behind arithmetic.

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Number SenseAs important to math as phonological
awareness is to reading (Gersten and Chard, 1999).

• Numerals to objects
• Which is larger? 8 or 18
• Which is closer to ___?
• Counting
• Counting on
• Backwards on
• Place Value
• Writing numerals to match oral word and writing
  number words to match numeral
• Note Use frames to teach number patterns
• 2 4 6 8 12 14 16 20

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Anxiety and Myths about math

• Most elementary school children have positive
  experiences with mathematics and arithmetic.
• Do adults have positive experiences with math?
• Females score on average with males in math until
  secondary school (Xin, 2000). When males and
  females take the same math course in 11th grade
  they share a positive attitude about math in the
  12th grade. However, why do more men take
  advanced high school courses and score high in
  math achievement tests by the 12th grade?

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The Concepts (How they are formed)

• Sensorimotor- objects exist out of sight (0-2)
• Preoperational- ability to think in symbols (2-7)
• Concrete- manipulatives offer medium for
  instruction(7-11) conservation of objects
• Formal operations- abstract problem solving (11)
• Much research challenges Piagets theory
• The order of development and the age of onset may
  be incorrect (Demby Miller)

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Connected Teaching

• CRA instruction
• Fluency
• Direct Instruction
• Applications
• Use of strategies

• Best Practices
• Advance Organizer
• Model
• Guided Practice
• Independent Practice
• Feedback
• Maintenance and Generalization

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CRA instruction

• 62 of primary teachers use manipulatives while
  only 8 of secondary teachers use hands-on
  materials (Howard, Perry, Lindsay, 1996). Why?
• Concrete - from fingers to objects
• Representational - from objects to pictures
• Abstract - from pictures to numerals
• What programs cover some of these components?
  Touch math, etc.

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Implement CRA instruction in your classroom.
Heres how

• Choose the math topic to be taught
• Review abstract steps to solve the problem
• Adjust the steps to eliminate notation or
  calculation tricks
• Match the abstract steps with an appropriate
  concrete manipulative
• Arrange concrete and representational lessons
• Teach each concrete, representational, and
  abstract lesson to student mastery (accuracy
  without hesitation)
• Help students generalize learning through word
  problems and problem solving events

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Algorithms and Fluency

• Students apply algorithms properly after they
  learn the concept.
• Why do shortcuts and algorithms not work as well
  when learning is new or the concept is difficult?
• Fluency measures can only be used with
  instruction after students show mastery.
• Fluency programs
• Great Leaps Math
• Precision Teaching
• Teacher Made probes

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Direct Instruction

• Explain how you can apply direct instruction to
  teaching the 6 times multiplication table.
• What other mathematics areas would be appropriate
  for direct instruction?

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Word Problems

• Students with disabilities do not paraphrase or
  visualize word problems. There is a connection
  between reading comprehension difficulties and
  poor performance solving for word problems.
  (Montague, Bos, Doucette, 1991)
• How can we help? Examples
• 7 cars 6 groups of
• - 3 cars x 3 apples
• ___ cars ___ apples
• after seeing this pattern, leave some blanks for
  students to fill in. Then list needed information
  to solve, followed by extraneous info. Once
  students show mastery, have them write their own
  word problems.

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Word Problems (cont)

• Teach word problems as problem solving situations
  that need to be interpreted
• Teach strategies for recognizing types of
  problems
• i.e., focus on reading comprehension strategies
• KWL
• RAPQ
• Word walls for vocabulary

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Sum it Up

• What activities can we do in the classroom to
  help children prepare to think in symbols and
  numbers?
• What is the difference between elementary or
  middle school boys and girls?
• What is CRA instruction?
• When should a teacher use fluency or algorithms
  to solve math problems?