Transcript Mathematics for Students with Learning Disabilities

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
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.
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
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.
Number Sense
As important to math as phonological awareness is to reading
(Gersten and Chard, 1999).
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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
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?
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 Piaget’s theory
• The order of development and the age of
onset may be incorrect (Demby; Miller)
Connected Teaching
• CRA instruction
• Fluency
• Direct
Instruction
• Applications
• Use of strategies
Best Practices
1.
2.
3.
4.
Advance Organizer
Model
Guided Practice
Independent
Practice
5. Feedback
6. Maintenance and
Generalization
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.
Implement CRA instruction in
your classroom. Here’s 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
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
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?
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
- 3 cars
___ cars
6 groups of
x 3 apples
___ 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.
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
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?