Instructional Strategies for Teaching Mathematics to Culturally and Linguistically Diverse Students with Disabilities by

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

2. “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 Three Strikes Against Them --or Special Abilities?

3. 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)

4. 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

5. 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 Math Learning Challenges

6. 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 Challenges related to disability 3 2 5 9

7. 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 Is mathematics a language?

8. 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 Make this into a number sentence...

9. Math Register square table odd power rational times square root perfect

10. 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

11. 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? Lessons that DON’T work

12. 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 Practices that DON’T work

13. 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

14. 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

15. 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

16. 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.

17. 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

18. 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 Tap in to Multiple Intelligences

19. 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.

20. 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)

21. 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 Why Peer Learning?

22. 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.

23. “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