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
1 𝑥 2 =5
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 Miss-cellaneous
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, 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 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
Susan's Math Page (
Abacus Videos (
National Braille Association (
Braille Authority of North America (

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

51. Define Sizes

52. Define Styles

53. Set Preferences

54. Duxbury
Create document in MS Word using the BANA Braille 2014 template or
On an existing document apply the BANA Braille 2014 template
Format using the style pane
Save and open in Duxbury

55. BANA Braille 2014 Template

56. Math Issues Build a support system Teachers Transcribers
Online resources

57. Other Problems Communicate with teachers Lead Time
How much time do you have from receiving assignment until it is needed by student?
Difficult to overcome misinformation
Communicate with teachers

58. Hardware
Graphic Embossers
Tigers
Phoenix

59. Conclusion
"We cannot hope that many children will learn mathematics unless we find a way to share our enjoyment and show them its beauty as well as its utility."
--Mary Beth Ruskai, University of Waterloo
Ontario, Canada

60. Texas School for the Blind & Visually Impaired
Supporting Tactile Learners
Jeri Cleveland, TVI
(Curriculum Teacher, TSBVI)

61. Tactile Learners
Your tactile learners do not have to be

62. Do Your Students Feel Like:
Villain: "You must read the graphic!
Heroine: "I can't read the graphic!"

63. Tips for Supporting Tactile Learners in Mathematics
Excellent posture
Systematic exploration
3-D to 2-D (Flat Stanley)
Text before graphics
Familiar Features

64. Tips (continued)
Perspective and dimensionality
Shared language

65. References
Lost in Space poster, Retrieved online from
Villain and heroine photo, Retrieved online from /02/29/love-derailed-lindseymarks- damsel-in-distress-engagement-session- featuring-brent-the-villain/

66. Tactile Graphic Document Production
for
School-based Mathematics Worksheets
Texas School for the Blind and Visually Impaired
Outreach Programs
Texas School for the Blind and Visually Impaired
Austin, Texas 78756

67. Criteria for Including a Tactile Graphic
TSBVI
Criteria for Including a Tactile Graphic
Introduce at an early age.
All required information included.
Omitting vs Admitting diagrams.
Complex Diagrams (meaningful?)
Include if it is used to answer questions.

68. Planning and Editing More meaningful in text form?
TSBVI
Planning and Editing
More meaningful in text form?
What is information is conveyed?
Planning Components
Editing Content
What production method is used?
Planning Process Sheet

69. Object Components Area (no less then .25” width/height)
TSBVI
Object Components
Area (no less then .25” width/height)
Line (1,3, and 6 point)
Points (no less than .13” diameter)
Label (only horizontal labeling)

70. What is order of these elements?
TSBVI
What is order of these elements? 2 1 1 2 3 4 4 5 3 5

71. Order of Elements in a Tactile Graphic
TSBVI
Heading, Titles, and Numbered Figures
Illustration Captions
Questions and Answer Choices
Transcriber’s Notes
Keys Content and Format Order
Area
Lines
Points
Letters
Placement of Tactile Graphics
Label Placement
Order of Elements in a Tactile Graphic

72. Content Information Title Caption Question Answer Choices (5-5) (3-1)
TSBVI
Content Information
Title
(5-5)
Caption
(3-1)
Question
(1-5)
Answer Choices
(3-5)

73. Transcriber’s Notes Title Transcriber’s Note Symbol (begin 7-5) Key:
TSBVI
Transcriber’s Notes
Title
Transcriber’s Note Symbol (begin 7-5)
Key:
(7)
Area Keys
(.50” wide)
Letter Keys
Transcriber’s Note Symbol (end)

74. Tactile Graphic Illustration
TSBVI
Tactile Graphic Illustration
Title
Y-axis Content
Axis Line
(3-4.5 pts)
Numbering
Coordinate Line
(1 pt)
Objects
(.25” width)
X-axis Content

75. Readability Text Content Transcriber’s Notes Tactile Graphics
TSBVI
Readability
Text Content
Follow the BANA Braille Formatting Standards
Transcriber’s Notes
Short and at students grade level.
Tactile Graphics
Follow the BANA Tactile Graphics Guidelines

76. TSBVI
CCS
Consistency
Continuity
Standardization

77. Thank you!
Tactile Math Booster
A Production of TSBVI, 2014