Instructional Strategies for Teaching Mathematics to Culturally and Linguistically Diverse Students

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• Instructional Strategies for Teaching Mathematics
  to Culturally and Linguistically Diverse Students
  with Disabilities
• by Barbara Acosta
• Elementary and Middle Schools Technical
  Assistance Center (EMSTAC)

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Three Strikes Against Them --or Special
Abilities?

• These kids are poor, they dont speak English,
  and theyre LD.
• My job is to protect them from failure.

• 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

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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/lawand
  regs.htm)

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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

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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

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Challenges related to disability
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• 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
• auditory discrimination
• cannot perceive number endings (eg, 60 vs 16)
• may say numbers correctly but misperceive what
  she hears

• visual discrimination
• 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
• spatial/temporal
• locating position in space
• regrouping
• concept of time
• multistep computation word problems

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5
9
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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.)

• (ab)2a2b22ab

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Make this into a number sentence...

• One of the greatest challenges for all students
• Problems can occur in both L1 and L2
• particularly difficult for ELLs with language
  processing disabilities.

• There are three times as many girls as boys.
• 3g b

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Math Register
square
table
odd
power
rational
times
square root
perfect
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Word Problems

• 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

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Lessons that DONT 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
  Elmers toys are dogs?

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Practices that DONT 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

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What Teachers Can Do

• 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

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Provide language support

• 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/k12
  standards/it/01.html)
• If teaching in native language, be sure to teach
  correct terminology

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Scaffolding Math

• 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

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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.
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Connect to home culture prior knowledge

• 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

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Tap in to Multiple Intelligences

• linguistic
• logico-mathematical
• musical-rhythmic
• visual-spatial
• bodily-kinesthetic
• interpersonal
• intrapersonal
• naturalist
• existential

• visual imagery, graphic organizers
• song, drumming, poetry, rhyme
• manipulatives
• cooperative groups/peer tutoring
• classification of problems
• layered curriculum

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Learn math through problem-solving

• 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.

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Learning Problem-Solving in Groups

• Start with groups of four students and present
  four problems.
• Give each student a different role eg
• 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)

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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

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Effective cooperative learning

• 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.

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• 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