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.”

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 DISABILITYA 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

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

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...

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

Math Register

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

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 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 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

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 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

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

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.

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)

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 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