Texas School for the Blind and Visually ImpairedOutreach Programswww.tsbvi.edu | 512-454-8631| 1100 W. 45th St. | Austin, Texas 78756

TETN #13906 NUBS Compared to UEB

October 18,20121:30-3:30 PM

Presented by:Susan Osterhaus, TVI, Certified Secondary Mathematics and English Teacher, State Wide Mathematics Consultant, TSBVI Outreach Programs, SusanOsterhaus@tsbvi.edu Maylene Bird, TVI and COMS, Certified Secondary Mathematics and Biology Teacher, birdm@tsbvi.edu Jeri Cleveland, TVI, Certified Elementary, Secondary English, and Master Reading Teacher, Curriculum Teacher, clevelandj@tsbvi.edu Sue Mattson, Certified Braille Transcriber/ Adapted Materials Specialist, mattsons@tsbvi.edu Texas School for the Blind & Visually Impaired

Developed forTexas School for the Blind & Visually ImpairedOutreach Programs – www.tsbvi.edu/outreach

NUBS Compared to UEBSusan Osterhaus, Maylene Bird, Jeri Cleveland, and Sue Mattson

LiteraryJeri and Sue

Definitions EBAE – English Braille American Edition –Our current braille code. A set of rules

that govern the transcription of literary braille. An explanation of the rules for the use of contractions, composition signs and directions for formatting literary and general materials.

Braille Formats: Principles of Print-to-Braille Translation – rules applied to the transcription of textbooks and instructional material.

Definitions BANA – Braille Authority of North America – Their mission is to assure literacy for

tactile readers through standardization of braille and/or tactile graphics. Established in 1976, this group includes national consumer organizations, braille producers, the Library of Congress, transcribing organizations, and others.

ICEB – International Council on English Braille - Their purpose is to coordinate and improve standards for braille usage for all English-speaking users of braille.

Definitions UEB – Unified English Braille – a unified code, developed by ICEB. BANA will

vote on a resolution to adopt UEB next month to replace EBAE. NUBS – Nemeth Uniform Braille System – a unified braille system, developed by

Dr. Abraham Nemeth. No longer under consideration by BANA.

The Call for Unification Started in 1991 with a memo written to BANA by

Drs. T.V. Cranmer and Abraham Nemethhttp:// www.iceb.org/cranem.html

BANA recently published three articles outlining their reasons for supporting a unified braille code

o The Evolution of Braille: Can the Past Help the Future (Part 1, Part 2, and Part 3)http://www.brailleauthority.org/

1

One Unified Code from Three Literary braille Nemeth & Chemical notation Computer braille

(Braille Music is not included)

The Evolution of TechnologyPrint and Braille

Impact of Technology on Print The use of color Varieties of emphasis: bold, italics, underline, fonts, size and color Formatting Extension of symbols and their meanings Non-linear – superscripts and subscripts

Continued Office and home computers, laptops and printers have allowed everyone to be a

publisher Print no longer confined to paper; it’s electronic: we blog, text, tweet and Skype

o Computerso E-readers: Kindle, Nook, iPad, etc.o Smart phones

Continued Technology has impacted braille production positively

o Computer assisted translationo Embosserso Improvements in scanners and OCR softwareo Refreshable braille displays

The 1991 Article to BANA Written by Dr. T. V. Cranmer and Dr. Abraham Nemeth Thesis: The complexity of braille led to an erosion of braille usage.

1. Complexity of Braille Creates Conflict Multiple braille codes Multiple meanings for symbols Multiple symbols with the same meaning

2

Multiple Braille Codes As the braille codes were developed independently of each other they resulted in numerous conflicts.

Figure 1 Image showing from top to bottom the literary, Nemeth, and computer braille code for $1.

Multiple Print Codes Prose Computer programming languages Accounting ledgers Chemical formulas

Multiple Meanings - Print Examples!

Exclamation point Factorial sign in Mathematics

. Period Decimal point Multiplication

Continued@

The “at sign” in an email address: johndoe@example.com An accounting or a business invoice abbreviation meaning “at the rate of”

3

More Examples< and >

“Less than” and “greater than” in math Angle brackets Also called chevrons

Symbols Out of ContextBANA recently used the following example as the reason for pointing out that there are 3 symbols for a dollar sign in braille:Ke$haIsn’t this symbol also out of context for a print reader?

2. Fewer Braille ReadersThe article states: Professionals resist teaching braille because:

It is too complex Down-play usefulness of braille in favor of electronic devices

Other Contributing Factors Complexity of braille confused with tactile skill Not enough time devoted to actual braille reading in school – braille under the

fingertips Lack of professional training and support for teachers, transcribers and parents Inadequate Nemeth code instructional materials Four sets of braille rules

Stated Goals for a Unified Braille Code Reduce complexity of braille. Reduce conflicts in braille. Accurately represent printed materials in braille.

Considering a Unified CodeA unified braille code must have the following balance of characteristics:

Read-ability Write-ability Think-ability Translate-ability

Read-ability Reading should become quick and automatic

4

Interpretation of characters with multiple meanings can be quickly inferred from context

Express mathematics and technical material as well as literaryWrite-ability

Writing should be quick and automatic Code should not get in the way of the meaning

Think-abilityCognitive Load“Think of the cognitive load. I must physically touch each one of those characters keeping in mind how the placement of one might affect the meaning of another. Meanwhile the problem must be held in my very limited short-term memory space.” –Amanda Lacy

How many modes and indicators are too many?

Translate-ability Flows back and forth between print and braille

o Easyo Accurate

Supports independence

Limitations of a Unified Code Can’t solve all the problems Won’t eliminate all ambiguity Only as good as the supporting documents Won’t eliminate the need for well-trained transcribers Won’t eliminate the need for more training and support for teachers

Can We Learn From The PastThe War of the Dots In 1911, Miss L. Pearl Howard and Mrs. Elwyn H. Fowler, representing the Uniform Type Committee traveled the country and conducted tests in 36 states; they tested 1200 readers. http://www.afb.org/warofthedots/book.asp

Literary Examples A joke Recipe ingredients Text styles Dictionary entry

5

Personal data

TechnicalSusan and MayleneDefinitions

STEM fields - an acronym for the fields of study in the categories of Science, Technology, Engineering, and Mathematics.

XML - Extensible Markup Language - defines a set of rules for encoding documents in a format that is both human-readable and machine-readable.

MathML – Mathematical Markup Language - an application of XML for describing mathematical notations and capturing both its structure and content. It aims at integrating mathematical formulas into World Wide Web pages and other documents. MathML = Math Accessibility

The Way it Was Before the 1960s, blind children were usually educated in residential schools for

the blind. All their teachers knew how to read braille, could create braille materials, and

read the students’ materials. Transcribers could only produce braille by hand, either using a Perkins

braillewriter or a slate and stylus. Multiple copies could be produced only using a thermoform machine.

Beginning of Change Much changed in the 1970s. Public Law 94-142 provided that blind children

should be educated in the “least restrictive environment.” This law accelerated the trend toward blind children being educated in the public schools. This lead to an increased need for braille transcribers.

Braille code for mathematics changed several times during the first half of the twentieth century, but by 1972, the Nemeth Code for Science and Mathematics Notation was the standard.

What’s In Place Todayhttp://www.brailleauthority.org /

Nemeth Code for Science and Mathematics Notation, 1972 Braille Code for Chemical Notation, 1997 Computer Braille Code (CBC), 2000 EBAE – English Braille American Edition, 2002 Guidelines and Standards for Tactile Graphics, 2010 Braille Formats: Principles of Print to Braille Transcription, 2011

6

Where are We Going? Now with various combinations of Internet media, speech output, braille displays,

scanning and OCR, braille translation software, and braille embossers, blind people can read, in a matter of moments, virtually anything created by anyone, with the exception of the STEM fields. However, Expanding Audio Access to Mathematics Expressions by Students with Visual Impairments via MathML is coming.

Nevertheless, braille under the fingertips is still a requirement for the majority of blind individuals working in the STEM fields.

Comments from a teacher who has lived some of this historyComparing Nemeth, UEB, and NUBS from the perspective of a math and vi teacher

Prior to the Nemeth Code, the Taylor Code was used, but it did not support higher mathematics.

The Nemeth Code is logical and supports print mathematics quite successfully. In 1978, the highest level of mathematics taught at the Texas School for the Blind

was a two-year pre-algebra class. In 2011, a female braille student at the school scored a 5 on the AP Calculus exam – highest score possible!

Math requirements have continued to grow more rigorous, and we expect that trend to persist. At present in Texas, graduation requirements for a general education high school diploma are 4 credits in both upper level math and science.

We are now seeing the first generation of adult braille users that were educated by TVIs who only learned Nemeth Code, as opposed to the Taylor Code. These young adults learned Nemeth Code from the beginning and many are showing great success in college, graduate school, and specifically in the STEM fields.

Losing the Nemeth Code could set math education for the blind back 40 years. If and when the time is right, NUBS (Nemeth Uniform Braille System) may be the

better Unified Braille Code.

The Learning of Mathematics Highest level of math achieved in high school was shown to be linked with

successful completion of a college degree in any field of study (Adelman, 1999 and Hill, 2006)

higher level of high school math = higher likelihood of completing college degree Working memory is acknowledged to hold 7± 2 items or bits of information at a

time (Kalet, 2005). Working memory can only hold this information for about 15-20 seconds (McGee

& Wilson, 1984). Automaticity: the ability to perform a skill automatically or unconsciously Fluency in reading is affected by automaticity; if reading more symbols is

required to distinguish numbers from letters, fluency can suffer.

7

Upper Cell Numbers The fundamental shortcoming in the development of UEB is the use of upper cell

numbers which creates conflict with many other symbols in both literary and mathematical notation.

Use of numbers in the upper part of the braille cell greatly adds to the length of mathematical expressions, especially in algebra, linear algebra, and calculus, where alphabet-number combinations are frequent (20 – 35% more characters than Nemeth Code) (Knowlton & Wetzel, 2006).

Figure 2 An image showing an equation in UEB, Nemeth, and NUBS. 3a+4x=10 where 3 and 4 are coefficient and a and x are variable.

8

Lower Cell Numbers Nemeth Code’s use of lower cell numbers allows the upper part of the braille cell

to be used for mathematical functions, critical to the overall successful use of the code for mathematics (Supalo, 2012).

UEB’s use of upper cell numbers introduces ambiguity by using the same symbols for numbers and letters; this creates a need for a second symbol to distinguish between them.

Figure 3 An image title Composite Functions with the equation f-1(x) = g(h(x)) in UEB, Nemeth, and NUBS.

Concerns from a Blind Computer Programmer English itself is far from unified. Practicality of braille unification in the United States Use of upper numbers in UEB Computer Braille Code (CBC)

-- Chris Gray, www.unifiedbrailleforall.com

Why We Think UEB is Problematic Upper cell numbers Numerous new indicators Longer expressions Insertion of braille grouping symbols that do not appear in print Use of terminology that is not used by mathematics teachers Ambiguity of how to write fractions dependent upon the presence of variables.

9

Published ResearchWetzel and Knowlton JVIB, April – May 2006

“The participants clearly stated that any changes to the code that would make braille more difficult to read would not be in the best interest of the current population, many of whom could be greatly hampered by learning a code that these professionals considered to be more complex.”

“… the [UEB] study lacked input from professional braille users in the fields of mathematics and computer science.”

Wetzel and Knowlton cont. “There is a significant question remaining as to the impact of eliminating multiple

contractions in a passage. It is a question that should be addressed before global changes to the braille code are made. These issues can be most effectively addressed by conducting further research.”

“Perhaps some of the most significant research on any braille code needs to address a vast array of cognitive issues that are related to learning and using braille as a reading and writing system.”

Wetzel and Knowlton cont. “The field would benefit from studies that address limits to short-term memory

(working memory) as they apply to the reading, recall, and writing of braille.” “Writing braille is an area of research that is yet to be addressed.” “When one looks at the results collectively, it is clear that much more research is

necessary before professionals will have sufficient knowledge to make wise decisions regarding changes to the braille codes.”

Wetzel and Knowlton cont. “To date, no studies have addressed the transcription and comprehension of

graphic material in braille. A unified code needs to address this kind of information in addition to pure literary text.”

UEB would be more expensive to produce than EBAE or Nemeth Code due to longer passages.

Arithmetic computation “required 17% more characters and algebra required 20%-35% more characters.” This would mean more expense to produce the books. Arithmetic and algebra books are the longest ones.

Other Available ResearchHolbrook and MacCuspie, JVIB Sept. 2010

Study of UEB involving 5 adult participants

NUBS Sampler Questionnaire, Summary of Responses, Feb. 2011 960 samplers distributed, results based on 236 valid surveys

10

Suggestions Consider development of better and more uniform TVI personnel preparation

programs and higher state certification requirements. This has been researched by Pogrund & Wibbenmeyer (2008) and published in JVIB.

Include a whole semester of study in Nemeth Code TVI preparation programs and test it on the certification test for TVI’s.

Do the serious work necessary to retain the Nemeth Code for math and science with an update to the Nemeth manual which was published in 1972 and has never been updated to include corrections.

Braille Code Comparison

Math and Science Samples of UEB, Nemeth, and NUBS Part 2

o Examples 1 & 2o Example 3o Examples 4 & 5o Example 6

Part 1

How will UEB Incorporate: Braille Code for Chemical Notation, 1997 Guidelines and Standards for Tactile Graphics, 2010 Braille Formats: Principles of Print to Braille Transcription, 2011

Number Line Graph x=1

Figure 4 Image of the equation x=1 in print.

Figure 5 Image of the equation x=1 in Nemeth.

Figure 6 Image of the equation x=1 in UEB.

11

ReferencesAdelman, C. (1999). Answers in the Tool Box: Academic Intensity, Attendance

Patterns, and Bachelor's Degree Attainment. Jessup, MD: ED Pubs.

Gray, C., (2012, April 28). Presentation at BANA meeting.

Hill, R. (2006, May 1). On The Transition in Mathematics from High School to Michigan State University [Online]. Available: http://www.math.msu.edu/~hill/

Holbrook, M.C., & MacCuspie, P.A. (2010). The Unified English Braille Code: Examination by science, mathematics, and computer science technical expert braille readers. Journal of Visual Impairment & Blindness, 104, 533-541. 

Kalet, J.W. (2005). Introduction to psychology (7th ed.). Belmont, CA: Thomson & Wadsworth.

Knowlton, M., & Wetzel R. (2006). Analysis of the length of braille texts in English Braille American Edition, the Nemeth code, and Computer Braille Code versus the Unified English Braille Code. Journal of Visual Impairment & Blindness, 100, 267-274.

McGee, M. G., & Wilson, D. W. (1984). Psychology: Science and application. New York: West Publishing Company, 168-170.

Pogrund, R.L. & Wibbenmeyer, K. (2008). Interpreting the meaning of the terms certified and highly qualified for teachers of students with visual impairments. Journal of Visual Impairment & Blindness, 102, 5-15.

Supalo, C. (2012, April 28). Presentation at BANA meeting.

Wetzel, R., & Knowlton, M. (2006a). Focus group research on the implications of adopting the Unified English Braille Code. Journal of Visual Impairment & Blindness, 100, 203-211.

Wetzel, R., & Knowlton, M. (2006b). Studies of Braille Reading Rates and Implications for the Unified English Braille Code. Journal of Visual Impairment & Blindness, 100, 275-284.

NUBS ReferencesNemeth, Dr. A., (2008, Oct. 15). NEMETH UNIFORM BRAILLE SYSTEM, Condensed

Version.

UEB ReferencesInternational Council on English Braille. (2010, June). The Rules of Unified English

Braille. Australia: Round Table on Information Access for People with Print Disabilities Inc.

International Council on English Braille. (2008, Oct.). Unified English Braille, Guidelines for Technical Material.

12

1. JokeQ: What did the tie say to the hat?A: You go on ahead, and I’ll hang around!

Uncontracted Braille

,q3 ,what did the tie say to the hat8,a3 ,you go on ahead1 and ,I'll hang around6

Contracted Braille

,q3 ,:at did ! tie say 6! hat8

,a3 ,y g on ah1d1 & ,I'll hang >.d6

UEB

;,q3 ,:at did ! tie say to ! hat8

;,a3 ,y g on ah1d1 & ,i'll hang >.d6

NUBS

;,q: ,what did ! tie say 6! hat8;,a: ,y g on ah1d1 & ,I'll hang >.d6

13

2. List of Ingredients6 medium Portobello mushrooms¼ C. goat cheese½ C. roasted sweet red peppers2 T. olive oilSalt and pepper to tastePreheat oven to 350º

Uncontracted Braille

#f medium ,Portobello mushrooms#a/D ,c4 goat cheese#a/b ,c4 roasted sweet red peppers#b ,t4 olive oil,salt and pepper to taste,preheat oven to #cej;dg

Contracted Braille

#f m$ium ,Portobello mu%rooms#a/d ,c4 goat *eese#a/b ,c4 roa/$ sweet r$ pepp]s#b ,t4 olive oil,salt & pepp] 6ta/e,preh1t ov5 6#cej;dg

UEB

#f m$ium ,portobello mu%rooms#a/d ;,c4 goat *eese#a/b ;,c4 roa/$ sweet r$ pepp]s#b ;,t4 olive oil,salt & pepp] to ta/e,preh1t ov5 to #cej"9NUBS#6 m$ium ,Portobello mu%rooms#1_/4 ;,c] goat *eese#1_/2 ;,c] roa/$ sweet r$ pepp]s#2 ;,t] olive oil,salt & pepp] 6ta/e,preh1t ov5 6#350@]

14

3. Text Styles: bold, italics and underline

In The Hunger Games, Suzanne Collins creates a dystopian society with disturbing parallels to life in the U.S. Find three quotes from the book that illustrate the meaning of “dystopian”.

Uncontracted Braille

,in .,the .,hunger .,games1 ,Suzanne ,Collins creates a .dystopian society with disturbing parallels to life in the ,u4,s4 ,find .three quotes from the book that illustrate the meaning of 8dystopian04

Contracted Braille Textbook Formats Font Attributes_. Single bold indicator

_- Single underline indicator

,' Termination indicator

,9 .,! .,Hung] .,game's1 ,Suzanne ,coll9s cr1tes a _.dy/opian society ) 6turb+ p>allels 6life 9 ! ,u4,s4 ,f9d _- ?ree ,' quotes f ! book t illu/rate ! m1n+ ( 8dy/opian04

15

UEB.7 Italics passage indicator

.' Italics passage terminator

^1 Boldface word indicator

_1 Underlined word indicator

,9 .7,! ,hung] ,game's1.' ,suzanne ,coll9s cr1tes a ^1dy/opian society ) 4turb+ p>allels to life 9 ! ,u4,s4 ,f9d _1?ree quotes f ! book t illu/rate ! m1n+ ( 8dy/opian04

NUBS..; Begin Italics phrase.' End Italics phrase_; Bold one word@; Underline one word,9 ..;,! ,HUNG] ,GAMES.'1 ,SUZANNE ,COLL9S CR1TES A _;DYSTOPIAN SOCIETY ) 4TURB+ P>ALLELS 6LIFE 9 ! ,U4,S4 ,F9D @;?REE QUOTES F ! BOOK T ILLU/RATE ! M1N+ ( ,8DYSTOPIAN,04

16

4. Dictionary entry using diacritic marks

dystopian (dĭs-tōʹ-pē-ən)1. dystopian of or pertaining to or resembling a dystopia2. dystopian as bad as can be; characterized by human misery.

Uncontracted Braille

dystopian 7d^is3/t_o3p_e35n7#a4 dystopian of or pertaining to or resembling a dystopia#b4 dystopian as bad as can be2 characterized by human misery4

Key:/ accent mark^ (45) breve_ (456) macron5 (26) schwa e

17

Contracted Braille

dy/opian dystopian 7d^is3/t_o3p_e35n7#a4 dy/opian ( or p]ta9+ 6or resembl+ a dy/opia #b4 dy/opian z bad z c be2 "*iz$ 0human mis]y4

Key:/ accent mark^ (45) breve

_ (456) macron5 (26) schwa ə

Contracted Braille Diacritics

UEB

dy/opian dystopian "<d@+is-t@-o^.b-p@-e-_5n">#a4 .1dy/opian ( or p]ta9+ to or resembl+ a dy/opia#b4 .1dy/opian z bad z c be2 "*iz$ by human mis]y4

18

Key:^.b accent mark

@+ breve

@- macron

_5 schwa ə

Used: Version I: June 2010 UEB Rule book pg. 47, Sec. 4.4.1

NUBS

DY/OPIAN dystopian

;(D<i_"aS-T<O:^/-P<E:-_5N)

#1] _;DYSTOPIAN ( OR P]TA9+ 6OR RESEMBL+ A DYSTOPIA

#2] _;DYSTOPIAN Z BAD Z C BE2 "*IZ$ 0HUMAN MIS]Y4

19

5. Name and address, including emailTexas School for the Blind and Visually Impaired1100 W. 45th St.Austin, Texas 78756(512)-454-8631clevelandj@tsbvi.edu or mattsons@tsbvi.edu

Uncontracted Braille

,texas ,school for the ,blind and

,visually ,impaired

#aajj ,W4 #deth ,st4

,austin1 ,texas #ghgef

7#eab7-#ded-hfca

_+clevelandj@tsbvi.edu_:

_+mattsons@tsbvi.edu_:

Contracted Braille

,Texas ,s*ool =! ,bl & ,Visu,y

,impair$

#aajj ,w4 #de? ,/4

,au/91 ,texas #ghgef

7#eab7-#ded-hfca

_+clevelandj@tsbvi.edu_:

_+mattsons@tsbvi.edu_:

20

UEB

,texas ,s*ool = ! ,bl & ,visually

,impair$

#aajj ;,w4 #deth ,st4

,au/91 ,texas #ghgef

"<#eab">-#ded-hfca

clevel&j@atsbvi4$u

mattsons@atsbvi4$u

NUBS

,texas ,s*ool =! ,bl & ,visu,y

,impair$

#1100 ;,w4 #45"? ;,st]

,au/9' ,texas #78756

;(512)-454-8631

;clevelandj@atsbvi]edu

;mattsons@atsbvi]edu

21

We have made every effort to be 100% accurate in our representations of each braille system. If there are any errors they are not intentional and will be corrected. We used the June 2010 edition of The Rules of Unified English Braille and the October 2008 edition of Unified English Braille: Guidelines for Technical Material as a reference for the UEB examples, and the 2008 version of the Nemeth Uniform Braille System.If you contact us about an error, include which of the above manual(s) you used and reference the rule and/or page number.

Your comments are welcome. Please send them to: braille.compare@gmail.com

22

Braille Code Comparison, Part 2Math and Science Samples of UEB, Nemeth, and NUBS

Compiled by: Maylene Bird, Jeri Cleveland, Susan Mattson & Susan Osterhaus

As the Braille Authority of North America (BANA) moves closer towards making a decision about the braille code(s) that will be used in the U.S., it becomes increasingly important for all the stakeholders to be familiar with the codes. In November, BANA will vote on their resolution to adopt UEB and retain the Nemeth Code for Mathematics and technical materials.

Unified English Braille (UEB), which encompasses literary, math, science, and computer braille

Nemeth Code for Mathematics and Science Notation (the current math and science code)

Nemeth Uniform Braille System (NUBS), a system that encompasses literary, Nemeth, and computer braille codes

The format is as follows:

Example No. and Subject

Example transcribed in UEB, showing number of cells required (where applicable).Example transcribed in Nemeth, showing number of cells required (where applicable).Example transcribed in NUBS, showing number of cells required (where applicable).

23

Example 1, Spatial Addition

UEB 1st Version

#def"6# cd "333 #dij

UEB 2nd Version

## def "6 cd "33 dij#'

Nemeth NUBS

456 456 + 34 + 34333333 "33333 490 490

24

Example 2, Linear Addition

3 + 5 = 8

UEB 1st Version, 14 cells

#c "6 #e "7 #h

UEB 2nd Version, 12 cells

#c"6#e "7 #h

Nemeth, 10 cells

#3+5 .k #8

NUBS, 8 cells

#3+5 = 8

Example 3, Simple Chemical Formula

UEB, 8 cells

,h;5#b,o

Nemeth, 5 cells

,h2,o

NUBS, 6 cells

;,h2,o

25

Example 4, Simple Numeric Fraction

UEB, 4 cells

#e/h

Nemeth, 5 cells

?5/8#

NUBS, 6 cells

;?5/8#

Example 5, General Fraction

UEB, 9 cells

;;(x./#b)

Nemeth, 5 cells

?x/2#

NUBS, 6 cells

;?x/2#

26

Example 6, Superscripts

UEB, 5 cells

x;9#b

Nemeth, 3 cells

x^2

NUBS, 4 cells

;x^2

UEB, 6 cells

x;9#by

Nemeth, 5 cells

x^2"y

NUBS, 6 cells

;x^2"y

UEB, 9 cells

;;x9<#by>

Nemeth, 4 cells

x^2y

NUBS, 5 cells

;x^2y

27

We have made every effort to be 100% accurate in our representations of each

braille system. If there are any errors they are not intentional and will be

corrected. We used the June 2010 edition of The Rules of Unified English

Braille and the October 2008 edition of Unified English Braille: Guidelines for

Technical Material as a reference for the UEB examples, the Nemeth Code for

Mathematics and Science Notation with the 2007 updates and the 2008

condensed version of the Nemeth Uniform Braille System.

If you contact us about an error include which of the above manual(s) you used

and reference the rule and/or page number.

Your comments are welcome. Please send them to: braille.compare@gmail.com

28

Texas School for the Blind & Visually ImpairedOutreach Programs

Figure 7 TSBVI logo.

Figure 8 U.S. Department of Education, Office of Special Education Programs (OSEP) logo that reads, “Opinions expressed here are the authors and do not necessarily represent the position of the Department of Education.”

29