Instructional Strategies for Teaching
Mathematics to Culturally and
Linguistically Diverse Students with
Disabilities
by Barbara Acosta
Elementary and Middle Schools Technical
Assistance Center (EMSTAC)
Three Strikes Against Them -or Special Abilities?
“These kids are
poor, they don’t
speak English,
and they’re
LD.”
“My job is to
protect them
from failure.”
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All children develop basic
mathematical concepts.
Children with mild disabilities
may have other qualities/gifts
e.g.
– powers of visual
observation
– flexible or “lateral” thinking
– multiple intelligences
Cognitive benefits of additive
bilingualism can include
mathematics reasoning
What are Learning Disabilities?
(26) SPECIFIC LEARNING DISABILITY-
(A) IN GENERAL- The term 'specific learning disability' means a
disorder in one or more of the basic psychological processes
involved in understanding or in using language, spoken or
written, which disorder may manifest itself in imperfect ability to
listen, think, speak, read, write, spell, or do mathematical
calculations.
(B) DISORDERS INCLUDED- Such term includes such conditions
as perceptual disabilities, brain injury, minimal brain dysfunction,
dyslexia, and developmental aphasia.
(C) DISORDERS NOT INCLUDED- Such term does not include a
learning problem that is primarily the result of visual, hearing, or
motor disabilities, of mental retardation, of emotional
disturbance, or of environmental, cultural, or economic
disadvantage.
IDEA 1997(from http://www.ideapractices.org/lawandregs.htm)
AREAS OF DISABILITY
A child is eligible for special education services if s/he
demonstrates a severe discrepancy between
achievement and intellectual ability in:
– Oral expression
– Listening comprehension
– Reading comprehension
– Written expression
– Basic reading skill
– Mathematics calculation
– Mathematics reasoning
Math Learning Challenges
Language & Cultural
Challenges
 math language
 cultural background
knowledge
 reading
 vocabulary
 word problems
Disability-Related
Challenges
 Visual and auditory
perceptual
 spatial/temporal
 memory
 language
 ADD/ADHD
Challenges related to disability

figure/ground

– lose their place on page,
skip parts of problems
– cannot locate relevant info
on page
– auditory: cannot perceive
counting patterns, trouble
skip-counting

– may misread numbers
– writes reversals (2,3,5,6,9)
and 13 for 31 etc.
– trouble recog. Coins, telling
time
– diff. Increases as math
moves from concrete to
abstract symbols
auditory discrimination
– cannot perceive number
endings (eg, 60 vs 16)
– may say numbers correctly
but misperceive what she
hears
visual discrimination

spatial/temporal
–
–
–
–
locating position in space
regrouping
concept of time
multistep computation &
word problems
Is mathematics a language?
If a straight line be cut
at random, the square
on the whole is equal
to the squares on the
segments and twice
the rectangle
contained by the
segments. (Euclid,
Elements, II.4,
300B.C.)
(a+b)2=a2+b2+2ab
Make this into a number
sentence...

There are three times
as many girls as boys.

3g = b
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One of the greatest
challenges for all
students
Problems can occur
in both L1 and L2
particularly difficult
for ELLs with
language
processing
disabilities.
Math Register
Word Problems
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Distractors and complex language can cause
problems for any child.
Students with reading difficulties or mental
impairment often have difficulty distinguishing
essential vs. non-essential information.
Particularly true for subtraction word problems.
L1 word problems with distractors may be just as
hard
Particularly troublesome for learning an L2
Lessons that DON’T work
Teaching
“key words”
Elmer has twelve
stuffed toys in all.
Five of his toys are
bears and the rest
are dogs. How many
of Elmer’s toys are
dogs?
Practices that DON’T work

Excessive practice
– Once the student has understood
the concept, a few exercises should
be sufficient for mastery.
– For kids with mild disabilities, they
may need to revisit short practices
several times.
– If the student does NOT
understand, practicing will only
cause frustration
What Teachers Can Do
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Scaffold language and/or use L1
Balance cognitive and language
demands
Tap into multiple intelligences
Connect with home culture and prior
knowledge
Use cooperative learning and peer
tutoring
Teach problem-solving strategies
Provide language support
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When possible, combine math and language
development objectives, but keep one or the other as
the central focus for each lesson
When teaching content in English, simplify language
When teaching English, focus on academic language
Incorporate ESL objectives into lesson plans
(see ESL standards
http://www.tesol.edu/assoc/k12standards/it/01.html)
If teaching in native language, be sure to teach
correct terminology
Scaffolding Math
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Identify academic language to teach
Determine the background knowledge
that students need to understand the
concept.
Simplify language, not content.
Provide models and demonstrations.
Use graphic organizers and other
visuals
Kopriva, R., and Saez, S. (1997). Guide to scoring LEP student responses to
open-ended mathematics items . Washington, DC: Council of Chief State School Officers,
SCASS LEP Consortium Project.
Connect to home culture &
prior knowledge

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Know your students as individuals
Treat differences as assets
– Talk about them
– Compare and contrast them
– Use them in learning

Adapt or develop materials with
appropriate cultural experiences
Tap in to Multiple Intelligences
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linguistic
logico-mathematical
musical-rhythmic
visual-spatial
bodily-kinesthetic
interpersonal
intrapersonal
naturalist
existential
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visual imagery, graphic
organizers
song, drumming, poetry,
rhyme
manipulatives
cooperative
groups/peer tutoring
classification of
problems
layered curriculum
Learn math through problemsolving
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Have students write their own word
problems and find the answer.
Exchange and have a partner solve.
Have students discuss and explain to
each other how they found the answer.
Learning Problem-Solving in
Groups
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Start with groups of four students and present four
problems.
Give each student a different role: eg
–
–
–
–
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explaining the problem
demonstrating how to address it
working through the problem
stating the answer.
This helps students conceptualize the steps to
problem-solving
Working together in groups provides support when a
student gets stuck. (Cocking & Chipman, 1988)
Why Peer Learning?

Traditional whole
class
– When teacher lectures,
students are not talking
– not enough opportunity to
develop communication
skills
– students are passive,
may become disengaged
– teacher “owns”
knowledge

Peer Learning
– students practice
communication through
analyzing, discussing
and problem-solving.
– Students from other
cultures often feel more
comfortable speaking in
small groups
– may demonstrate
understanding of
mathematical concepts in
small groups before they
can in large class
Effective cooperative learning
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is much more than simply placing students
into groups;
responsibility for learning rests with the
students, not with the teacher;
groups are provided the task of exploring
meaning, working through a process, and
solving problems through consensus, without
outside help;
each group member is given a clear role.
“all children
should be taught
as though they
were gifted”

-- Assets School,
Hawaii

High achievement is
affected more by
teacher
effectiveness than
student background.
Every child has
intelligence waiting
to be mined
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