1. Generating Nemeth Braille Output Sequences from Content MathML Markup
Sam Dooley Pearson Assessment Su Park

2. Braille math is hard! Blind students need high-quality braille math
Advanced preparation is costly and takes time
Software translation can be problematic
Real-time two-way translation is non-existent

3. Producing Braille Math
Online equation editor software component
Real-time translation from math into braille
Accessible to both sighted and blind users
Nemeth Braille
Content MathML

4. Braille Output Demo Numbers Arithmetic Equations Fractions Radicals
Exponents
Functions

5. W3C MathML (1998) World Wide Web Consortium (W3C)
XML element/attribute vocabulary
Typical K-12 and higher ed. math
Presentation and content markup

6. Nemeth Braille (1952) Abraham Nemeth (AFB, APH, BANA)
Tactile encoding for print math
Math for technical publications
Presentational math structures
Consistent with content markup

7. Presentation v. Content
Presentation encodes signs/symbols
Content encodes functional structure
"x^2+1" v. "1346, 45, 23, 5, 346, 2"
"x^2+1" v. (plus (power x 2) 1)

8. Equation Editor (2002) WYSIWYG entry for math expressions
Keyboard input into Content MathML
Content MathML to Presentation MathML
Display MathML in a browser (MathJax)

9. Content to Presentation
Math operators determine notations
Operator-based XML transformations
Minimal contextual dependencies
Presentation links back to content
(plus x 1) v. "x + 1"

10. Content to Braille Operators determine braille symbols
Operator-based transforms to braille
Additional contextual dependencies
Flattening to linear output format
(plus x 1) v. "1346, 346, 2"

11. Structure Braille determined by operator alone
No influence from surrounding markup
Operation, comparison, symbols, etc.
Arrows, shapes, circled/squared ops

12. Context Surrounding markup affects encoding
Nested fractions and radicals
Superscripts and subscripts
Over and under scripts

13. Kerning Adjacent markup affects encoding Spacing rules
Numeric indicators
Alphabetic indicators
Multipurpose indicators

14. Braille Output Testing
Content MathML segments (948)
Most from the Nemeth reference
Machine-generated Nemeth output
Displayed on a braille terminal
Hand-generated alternate text
Spoken by a screen reader
Output verified by a blind user
Within a day and a half
Defects identified and reported

15. Further work Address remaining defect fixes
Limits, derivatives, integrals
Combining text and math content
Spatial arrangements
Tactile graphics

16. Applications Web-based translation tools Stand-alone translation tools
Online high-stakes assessment
Real-time classroom translation

17. To Be Continued …
Generating Content MathML Markup from Nemeth Braille Input Sequences Sam Dooley, Dan Brown, Edgar Lozano