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Texas School for the Blind & Visually Impaired

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Tactile Math Booster

Presented by:

Maylene Bird, Jeri Cleveland, Sue Mattson, Glenda Torrence and Patrick Van Geem

AER International 2014

Refresh Your Nemeth Braille Code

Maylene Bird, TVI and COMs

Glenda Torrence, TVI

- 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.

- Top 3 errors noted by TVIs.
- Symbols we often forget.
- Miscellaneous items.
Picture of woman pondering: "Where is the guzinto sign?"

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

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

- (5, 6)

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

- 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

- x is not equal to 4
- y is less than or equal to15
- r is greater than or equal to 25

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

Note: Notice space before and after these signs of comparison congruent, approximately equal to, parallel and perpendicular.

- 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.

- 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.

- Find A∩B

- 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: {[( )]}.

- {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.

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.

- [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.

- 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.

- 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

- 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.

- The Braille Code for Chemical Notation 1997 available through the American Print House for the Blind

- x2 , x3
- x12 + 9
- x12+9

- 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.

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

The last of the big three.

- Computation problem written in spatial arrangement do not use a number sign.
- Problems written horizontally start with a number indicator unless preceded by …

- Don't use the number indicator when a number follows the opening parenthesis

- No Number Indicator in front of an Opening Fraction 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.

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

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.

- 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.

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

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!

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

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.

- Dedicated to Dr. Abraham Nemeth
- October 16, 1918 to October 2, 2013.

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.

- 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/)

Braille Production

Sue Mattson, Braille Transcriber/

Adapted Materials Specialist

- "Do not let what you cannot do interfere with what you can do!" --John Wooden

- Nemeth Braille Code
- Reference materials

- Software issues
- Compatibility problems

- Math issues
- Uncomfortable with math

- It isn't rocket science
- 63 palpable braille characters (64 including the space)
- It evolved out of rules of speech

- 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

- File formats and how to handle them
- PDFs, Word files …

- Type of documents
- Electronic copies, hard copies

- 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

- 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

- Build a support system
- Teachers
- Transcribers
- Online resources

- Lead Time
- How much time do you have from receiving assignment until it is needed by student?
- Difficult to overcome misinformation

- Communicate with teachers

- Graphic Embossers
- Tigers
- Phoenix

- "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

Supporting Tactile Learners

Jeri Cleveland, TVI

(Curriculum Teacher, TSBVI)

- Your tactile learners do not have to be

- Villain: "You must read the graphic!
- Heroine: "I can't read the graphic!"

- Excellent posture
- Systematic exploration
- 3-D to 2-D (Flat Stanley)
- Text before graphics
- Familiar Features

- Perspective and dimensionality
- Shared language

- Lost in Space poster, Retrieved online from http://www.imdb.com/title/tt0058824/
- Villain and heroine photo, Retrieved online from http://www.carolynscottphotography.com/2012/02/29/love-derailed-lindseymarks-damsel-in-distress-engagement-session-featuring-brent-the-villain/

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

TSBVI

- Introduce at an early age.
- All required information included.
- Omitting vs Admitting diagrams.
- Complex Diagrams (meaningful?)
- Include if it is used to answer questions.

TSBVI

- More meaningful in text form?
- What is information is conveyed?
- Planning Components
- Editing Content
- What production method is used?
- Planning Process Sheet

TSBVI

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

TSBVI

1

2

2

1

3

4

4

5

5

3

TSBVI

- Heading, Titles, and Numbered Figures
- Illustration Captions
- Questions and Answer Choices
- Transcriber’s Notes
- Keys Content and Format Order
- Area
- Lines
- Points
- Letters

TSBVI

Title

(5-5)

Caption

(3-1)

Question

(1-5)

Answer Choices

(3-5)

TSBVI

Title

Transcriber’s Note Symbol (begin 7-5)

Key:

(7)

Area Keys

(.50” wide)

Letter Keys

Transcriber’s Note Symbol (end)

TSBVI

Title

Y-axis Content

Axis Line

(3-4.5 pts)

Numbering

Coordinate Line

(1 pt)

Objects

(.25” width)

X-axis Content

TSBVI

- 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

TSBVI

- Consistency
- Continuity
- Standardization

Tactile Math Booster

A Production of TSBVI, 2014