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

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

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.

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?"

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

To Space Or Not To Space (5, 6)

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..

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

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

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

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.

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.

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.

Intersection and Union Symbols Find A∩B

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: {[( )]}.

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.

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.

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.

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.

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

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.

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

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

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.

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

The Numeric Indicator The last of the big three.

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 …

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

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

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.

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

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.

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.

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.

Absolute Value

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!

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.

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.

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

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.

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/)

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

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

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

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

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

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

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

MathType Equation Editor

Define Sizes

Define Styles

Set Preferences

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

BANA Braille 2014 Template

Math Issues Build a support system Teachers Transcribers Online resources

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

Hardware Graphic Embossers Tigers Phoenix

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

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

Tactile Learners Your tactile learners do not have to be

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

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

Tips (continued) Perspective and dimensionality Shared language

References Lost in Space poster, Retrieved online from http://www.imdb.com/title/tt0058824/ Villain and heroine photo, Retrieved online from http://www.carolynscottphotography.com/2 012/02/29/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

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.

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

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)

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

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

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)

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)

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

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

TSBVI CCS Consistency Continuity Standardization

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