1. Teaching Math to Students with Visual Impairments Gaeir Dietrich High Tech Center Training Unit of the California Community Colleges De Anza College

2. Tips for Teaching Math

3. Be wary of assumptions Blindness covers a range Blindness covers a range –Most blind folks have some sight –Many do see color Not all blind people read Braille Not all blind people read Braille –In fact, many CC students do not Not all students who read Braille read Nemeth math Braille Not all students who read Braille read Nemeth math Braille

4. Nemeth Braille for Math Numbers Numbers –1234567890 –#1234567890 Symbols Symbols –x² + 2x + 2 = 10 –x^2"+2x+2.k #10

5. Nemeth Code Information Texas School for the Blind and Visually Impaired Texas School for the Blind and Visually Impaired –http://www.tsbvi.edu/math/math- nemeth.htm Resources for students and teachers Resources for students and teachers

6. What will be true Likely to have very good listening skills Likely to have very good listening skills Likely to need one-on-one tutoring Likely to need one-on-one tutoring Likely to require extra time on tests Likely to require extra time on tests

7. Some Issues Will not see what you project on- screen or write on board Will not see what you project on- screen or write on board Will not see a show of hands Will not see a show of hands Often prefer sitting near the front so they can hear Often prefer sitting near the front so they can hear Prefer a seat that is easy to find Prefer a seat that is easy to find

8. What you can do Order books as early as possible Order books as early as possible –Consider adopting a book for 3+ years Provide campus alternate media personnel with electronic files for tests Provide campus alternate media personnel with electronic files for tests Educate yourself about the issues Educate yourself about the issues Be creative Be creative Verbalize, verbalize, verbalize! Verbalize, verbalize, verbalize!

9. Use Meaningful Words Use concrete terms Use concrete terms Meaningless! Meaningless! –“Here is the equation.” –“We start with the equation and factor.” –“Set both factors equal to zero and solve to get the result.” Avoid Avoid –This, that, here, there, thing

10. In the following example, you would say everything! Don’t just write it; verbalize it! 6x 2 = 53x + 9 Subtract 53x and 9 from both sides 6x 2 – 53x – 9 = 0 Trinomial factoring gives us (6x + 1)(x – 9) = 0 Set both factors equal to zero 6x + 1 = 0 and x – 9 = 0 Solve each equation…etc.

11. Alternate Formats

12. Braille options Brailling math is expensive and time- consuming Brailling math is expensive and time- consuming –Algebra books can cost $25,000+ –Calculus books can cost $50,000+ Consider “independent study” with a book already in Braille Consider “independent study” with a book already in Braille

13. For the CCCs Alternate Text Production Center (ATPC) Alternate Text Production Center (ATPC) –www.atpc.net ATPC produces Braille and tactile graphics free for the CCCs ATPC produces Braille and tactile graphics free for the CCCs Must have syllabus to begin project Must have syllabus to begin project –Does only those chapters required –The more advance notice, the better

14. Nemeth Braille Resources American Printing House for the Blind hosts the Louis Database American Printing House for the Blind hosts the Louis Database –Anyone can search for Braille materials –www.aph.org Hadley School for the Blind Hadley School for the Blind –Free courses –www.hadley-school.org/Web_Site/ 2_b_ae_and_hs_program.asp

15. Other Resources FIPSE grant project to produce audio- tactile statistics workbook FIPSE grant project to produce audio- tactile statistics workbook Looking for campuses to participate Looking for campuses to participate –Contact: Annette Gourgey at CUNY –laprofessore@hotmail.com

16. Creating Nemeth on Campus Scientific Notebook documents can be translated into Nemeth math Braille Scientific Notebook documents can be translated into Nemeth math Braille –www.mackichan.com –From other equation editors, save as LaTeX –Take into Scientific Notebook and save –Open with Duxbury Braille Translation Software (www.duxsys.com)

17. Tactile Diagrams PIAF paper PIAF paper –“Pictures in a Flash” (www.optelec.com) –Microcapsule paper –Can start from any computer file

18. Graphics Printer Tiger Embosser Tiger Embosser –Embosses graphics in raised dots (www.viewplus.com) –Creates Dots Plus

19. Commercially Available Wikki Stix Wikki Stix –www.wikkistix.com Sewell Raised Line Drawing Kit Sewell Raised Line Drawing Kit –www.maxiaids.com Non-slip abacus (Cranmer Abacus), Braille ruler, protractor, compass, Cubarithm Non-slip abacus (Cranmer Abacus), Braille ruler, protractor, compass, Cubarithm –www.aph.org MathWindow MathWindow –www.mathwindow.com

20. Other Tactile Strategies Be creative! Be creative! Magnet boards Magnet boards –Letters and numbers can be purchased –Symbols can be cut from magnetic sheets Corkboard for graphics Corkboard for graphics –Glue thread to make a grid –Push-pins and string for graphing

21. Be Creative! Manipulatives Manipulatives –Many standard K-12 manipulatives will work Collage Collage –Puff paint –Cut-outs –Real objects

22. Electronic Solutions

23. Hardware Calculator Orion TI-36X Orion TI-36X –Hand-held, talks –American Printing House for the Blind www.aph.org

24. Software Calculator Audio Graphing Calculator Audio Graphing Calculator –Computer software, talks –ViewPlus Technology www.viewplus.com –Note: Graphs can be printed on Tiger Embosser or to PIAF paper

25. Computer Options Virtual Pencil Algebra Virtual Pencil Algebra –Auditory output and input –Set up through its own interface –www.hentermath.com Math ML with MathPlayer Math ML with MathPlayer –Auditory output for Web pages (free!) –Works with screen readers (JAWS, Window Eyes, Super Nova) –Set up in MathType –www.dessci.com WinTriangle WinTriangle –Auditory output and input –Set up in MathType –www.wintriangle.com

26. General Resources Texas School for the Blind and Visually Impaired (TSBVI) Texas School for the Blind and Visually Impaired (TSBVI) –www.tsbvi.edu/math Blindmath List Blindmath List –www.nfbnet.org/mailman/listinfo/ blindmath Chisenbop Finger Counting Chisenbop Finger Counting –www.cs.iupui.edu/~aharris/chis/chis.html Calculus Calculus –http://163.238.35.147/CalculusForTheBlind/inde x.html

27. Tips for General Interaction

28. When a blind person enters the room Speak to the person by name Speak to the person by name Identify yourself Identify yourself If the person will be remaining in the room, let him/her know who else is there If the person will be remaining in the room, let him/her know who else is there Always speak directly to the blind person, not to his/her companion Always speak directly to the blind person, not to his/her companion

29. When you encounter a blind person Greet the person by name. Greet the person by name. Tell the person who you are. Tell the person who you are. –After a while, the person may learn your voice, but don’t assume they’ll recognize you. –It’s not polite to play guessing games when only one person is guessing! Make it clear when the conversation is at an end or you are leaving. Make it clear when the conversation is at an end or you are leaving.

30. When talking with a blind person Look directly at the blind person. Look directly at the blind person. –A person can hear when you are speaking directly to him/her Speak in a normal tone. Speak in a normal tone. Feel free to use words like “look” and “see.” Feel free to use words like “look” and “see.” –Blind people also say “see you later.”

31. When assisting a blind person If you think the person needs help, ask. If you think the person needs help, ask. –Offer assistance; don’t just assume the person needs help. Ask the blind person directly how you can help him/her. Ask the blind person directly how you can help him/her. –Do not ask the person who is with the blind person.

32. When explaining things to a blind person Use very specific, concrete language. Use very specific, concrete language. –Avoid words like “this,” “that,” “here,” “there” –Especially avoid “thing” –“Get that thing over there” is a meaningless statement for a blind person. To show the person something tactually, ask the person if you may take his/her hand. To show the person something tactually, ask the person if you may take his/her hand.

33. When giving directions to a blind person Make sure that you use specific language. Make sure that you use specific language. –Left/right –In front/behind –Degrees of a circle –Clock face –Compass directions Always give directions from the blind person’s orientation. Always give directions from the blind person’s orientation.

34. When guiding a blind person Never grab the person’s cane or dog or arm. Never grab the person’s cane or dog or arm. Let the blind person take your arm. Do not grab his/her arm. Let the blind person take your arm. Do not grab his/her arm. When guiding a blind person, let him/her take your elbow. When guiding a blind person, let him/her take your elbow. –Most blind people will prefer to take your left elbow (i.e., they will grasp your elbow with their right hand).

35. When the person has a dog Never distract a working dog. Never distract a working dog. Never call to the dog or use its name when it’s working. Never call to the dog or use its name when it’s working. Never grab a dog’s harness. Never grab a dog’s harness. Never give commands to the dog. Never give commands to the dog. Never feed the dog. Never feed the dog.

36. Interacting with the dog If you would like to pet a guide dog, ask the handler’s permission. If you would like to pet a guide dog, ask the handler’s permission. Never encourage the dog to interact with you unless the handler tells you it’s okay. Never encourage the dog to interact with you unless the handler tells you it’s okay. Sometimes handlers will use attention as a behavior modification tool. Sometimes handlers will use attention as a behavior modification tool. –Interacting with the dog without permission can interfere with its training.

37. Understanding the dog Guide dogs undergo strict training, but the training continues with the blind handler. Guide dogs undergo strict training, but the training continues with the blind handler. –Do not be disturbed when you see a handler correcting his/her dog. Remember that these dogs are working dogs, not pets!! Remember that these dogs are working dogs, not pets!!

38. In conclusion… "Since mathematics is an experience of the mind anyway, it should be doable for the student. The student probably has a way of creating 'pictures' in his/her mind already. You just have to figure out which descriptors to use to promote understanding in pre-algebra and algebra.” --Claudia, for the Teacher2Teacher service

39. Feel free to contact me Gaeir (rhymes with “fire”) Dietrich Gaeir (rhymes with “fire”) Dietrich gdietrich@htctu.net gdietrich@htctu.net 408-996-6043 408-996-6043 www.htctu.net www.htctu.net