Texas School for the Blind & Visually Impaired

1. Texas School for the Blind & Visually Impaired Tactile Math Booster Presented by: Maylene Bird, Jeri Cleveland, Sue Mattson, Glenda Torrence and Patrick Van Geem AER International 2014

2. Texas School for the Blind & Visually Impaired Refresh Your Nemeth Braille Code Maylene Bird, TVI and COMs Glenda Torrence, TVI

3. Why did we do this? • Why? Braille Examples: 2+3 = ch 2+3 = 5 Mistakes by students, mistakes found in textbooks, commonly found errors or ones we always have to look up. It is important to preserve our Nemeth Code. It is important for our students to learn math. Math has it's own special set of symbols and can not be treated as a literary code.

4. Common Errors and Forgotten Signs • Top 3 errors noted by TVIs. • Symbols we often forget. • Miscellaneous items. Picture of woman pondering: "Where is the guzinto sign?"

5. Long Division • 4284 divided by 6 equals 714. Notes: In print this symbol is the vinculum; correctly read as: 4284 divided by 6.

6. Top 3 List • Spacing: To space or not to space • Dot 5 • Numeric indicator We will start with a list of frequently seen Nemeth Code errors.

7. To Space Or Not To Space • (5, 6)

8. Space before and after signs of comparison • 2+9 = 11 • 3<7 • 5>1 We know the equal and > and < are signs of comparison. Space before and after..

9. Remembering > and < • How to remember < and > symbols on the Braille writer. (Print students have the alligator) • Greater than: • Right hand dots: 4, 6 • Left hand dot: 2 • Less than: • Right hand dot: 5 • Left hand dots: 1, 3

10. Alligator for Print • x is not equal to 4 • y is less than or equal to15 • r is greater than or equal to 25

11. Signs of Comparison Continued A chart comparing popular male cartoon figures in the following categories: White shirt, Blue pants, Seth McFarlane, Good show.

12. To space or not to space: Signs of Comparison continued Note: Notice space before and after these signs of comparison congruent, approximately equal to, parallel and perpendicular.

13. To space or not to space: Signs of Comparison (Continued) • The ratio x to y. • x ꞉ y • 1 ꞉ 2 ꞉꞉ 2 ꞉ 4 The word 'to' is spelled out, uncontracted, and not hooked to the variable 'y'. Problem 15 reads one is to 2 as 2 is to 4.

14. Spacing Continued • A is a subset of B. • x is an element of Real numbers. • {x | 3 ≤ x < 10} • The symbol for “therefore” An example for 19 is: All men are mortal, Socrates is a man, therefore Socrates is mortal.

15. Intersection and Union Symbols • Find A∩B

16. Braces and Brackets • Parenthesis (7) • Braces {7} • Brackets [7] There is no particular significance in the use of square brackets instead of parentheses. Brackets and curly-braces are used when there are nested parentheses, as an aid to keeping track of which parentheses go with which. When working with nested parenthesis, the order will always be: parenthesis, brackets, and braces as shown: {[( )]}.

17. Braces and Brackets • {x | -5 ≤ x < 5} • [-5, 5) Number 21 is set builder notation. Another way to represent 21 is shown in 22. The is interval Notation using bracket and parenthesis. It is also represented by the number line on the next slide.

18. Graphing Set Notation Students can graph over the tic marks, but the correct way is to leave them uncovered. Caution students to at least leave the first tic mark at -5 uncovered. The full cell above the number line signifies shaded/filled in circle. Notice there are no number signs used on the line graph.

19. Braces and Brackets • [5-(3+4)] = ? • {-2, 0, 2} Number 23 is just PEMDAS (Please excuse my dear aunt Sally Number 24 is another set; finite set with 3 elements.

20. Dot 5 • Normal level of writing is on the baseline. Subscripts are below the baseline and exponents are elevated. The term superscript is used to define any letter, sign, or symbol written above the baseline.

21. Exponents/Superscripts(dots 4, 5) • 90⁰+90⁰ = 180⁰ • x²+6x+3² • x²+1 • Use dot 5 when ti is followed by another symbl. Do not use if it is followed by a space.This should read: 1 over x squared equals five

22. Subscripts (dots 5,6) • H2O • 2H3PO4 → H4P2O7 + H2O↑ Number 30 reads: 2H3PO4 yields H4P2O4 plus H2O gas • (x1, y1) Don't use a dot 5 if a subscript indicator is not used. {X followed by a subscript a is when you do use a subscript indicator}. When you have an x subscripted by a letter then use subscript indicator.

23. Reference • The Braille Code for Chemical Notation 1997 available through the American Print House for the Blind

24. Exceptions to the Dot 5 Rule • x2 , x3 • x12 + 9 • x12+9

25. Slope • No dot 5 is used here for the slope equation. • Rule: if a letter is followed by a numeric subscript then do not use dot 5.

26. Dot 5 continued… • Dot 5 at the beginning or with a space in front of it indicates something immediately following will be modified.

27. The Numeric Indicator The last of the big three.

28. Non use of the Numeric Indicator • Computation problem written in spatial arrangement do not use a number sign. • Problems written horizontally start with a number indicator unless preceded by …

29. Non-use of Number Indicator • Don't use the number indicator when a number follows the opening parenthesis

30. Non-use of Number Indicator • No Number Indicator in front of an Opening Fraction indicator

31. Use of Number Indicator • The distance from the Earth to the Sun is about 92,955,807. • (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11) If a long number cannot fit on 1 line, begin the number on a new line or even a new page. There is a way to split a number, but it is highly discouraged. A hyphen (3, 6) is inserted after a comma and a new numeric indicator is placed at the beginning of a new line. On problem 47 the numeric indicator is not required before the 9.

32. Miscellaneous The next items are to refresh your memory about other areas of mathematics and the Nemeth symbols. The photo shows 5 staff members of TSBVI dressed as beauty queen contestants. The constants represented: Mis-behave, Mis-understood, Mis-fit, Mis-apprehension, Mis-cellaneous, and Mis-do. Miss-cellaneous

33. Infinity and Beyond 48. No special spacing required--it follows rules in the context in which it is used. 6,250 49. The infinity symbol is a full braille cell, dots 1, 2, 3, 4, 5, 6.

34. Repeating Decimals • Notice how a repeating decimal is written in Nemeth. 50. Use dots (1, 5, 6) when only 1 number is repeating. 51. If more than 1 digit repeats, you must note where the repeating sequence starts with a dot 5 and use the over the top symbol and bar symbol. It ends with a termination symbol.

35. Tally Marks • A tally mark in Nemeth is dots 4, 5, 6. They are grouped 5 in a row with a space between groups of 5.

36. Absolute Value

37. Square Roots and Radicals Problem 55 depends on the math level; if you ask for 2 square roots (plus or minus). 56. The index of the cube root is written first and then the radical (root) sign and the number under the radical (in this case the 8 which is called the radicand). Remember to terminate the radical sign after both!

38. Mixed Numbers and Complex Fractions In problem 57 do not forget the (4, 5, 6) before closing the fraction! Note the opening fraction indicator in number 58.

39. Line Graphs 59. Notice that the tic marks are not covered by the graphing {dots (2, 3, 5, 6)}. The X dots (1, ,3, 4, 6) above the line graph signifies the unshaded circle. Remember you do not need number to labels the numbers on number line.

40. Dedication • Dedicated to Dr. Abraham Nemeth • October 16, 1918 to October 2, 2013.

41. References AAWB-AEVH-NBA Advisory Council to the Braille Authority (1979). The nemeth braille code for mathematics and science notation, 1972 revision. Louisville, KY: American Printing House for the Blind. Braille Authority of North America, (1997). Braille code for chemical notation 1997. Louisville, KY: American Printing House for the Blind. Craig, R.H. (1987). Learning the nemeth braille code; A manual for teachers and students. Louisville, KY: American Printing House for the Blind. Laudenslader, E., (1972). Braille handbook for nemeth code of braille mathematics and scientific notation. San Francisco State College. Roberts, H., Krebs, B.M., & Taffet, B., (1978). An introduction to braille mathematics. Washington, DC: Library of Congress.

42. Emails and Other links • Maylene Bird(birdm@tsbvi.edu) • Glenda Torrence(torrenceg@tsbvi.edu) • Susan's Math Page(http://www.tsbvi.edu) • Abacus Videos(http://www.tsbvi.edu.com/user/VideoTSBVI) • National Braille Association(http://www.nationalbraille.org/NBAResource/FAQs/(askanexpert) • Braille Authority of North America(http://www.brailleauthority.org/)

43. Texas School for the Blind & Visually Impaired Braille Production Sue Mattson, Braille Transcriber/ Adapted Materials Specialist

44. Theme • "Do not let what you cannot do interfere with what you can do!" --John Wooden

45. Unraveling the Problems • Nemeth Braille Code • Reference materials • Software issues • Compatibility problems • Math issues • Uncomfortable with math

46. The Nemeth Braille Code • It isn't rocket science • 63 palpable braille characters (64 including the space) • It evolved out of rules of speech

47. Software Issues • Understanding the multiple layers of software use • Knowing what programs to use and how they work together • Windows updates and the impact on your work

48. Related Problems • File formats and how to handle them • PDFs, Word files … • Type of documents • Electronic copies, hard copies

49. MS Word and Math Type • Using Math Type with MS Word • An equation editor • Installs a tab on the Word Ribbon • Keyboard short cuts are easily customizable • Commonly used in schools • Not expensive

50. MathType Equation Editor