What’s New in the Nemeth Code
Authors: Susan A. Osterhaus, Statewide Mathematics Consultant, Outreach Program, Texas School for the Blind and Visually Impaired, TSBVI, and Member of the BANA Nemeth Code Technical Committee; Maylene Bird, Secondary Mathematics Teacher, Comprehensive Programs, Texas School for the Blind and Visually Impaired, TSBVI.
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In the spring 2024 issue of TX SenseAbilities, the authors announced that The Nemeth Braille Code for Mathematics and Science Notation 2022 was officially posted to the BANA (Braille Authority of North America) website in both PDF and BRF formats. The purpose of the revision was to modernize the code and clarify the application of existing and newly adopted rules using Nemeth within the UEB Code. The new code book consists of 498 print pages, containing 26 Rules and 4 Appendices. The purpose of this article is to highlight the changes since the 1972 edition.
Note: The authors advise that a hard copy braille document is best for reading examples of spatial and multi-line equations. Therefore, please see the BRF file attached below with all examples transcribed into braille. SimBraille images are included in the article for the sighted reader; however, this may be of little value when read using a braille display.
New BANA Nemeth Code Documents
There are five new rule books, errata, or guidelines that reflect the changes to the Nemeth Code. This review is confined to the rule book itself. The first four documents can all be found on the BANA website:
- The Nemeth Braille Code for Mathematics and Science Notation 2022
- Nemeth Braille Code Errata
- Chemical Notation Using the Nemeth Braille Code 2023
- Graphing Calculator Guidelines, 2018
The fifth document is the Guidelines and Standards for Tactile Graphics, 2022. In this revision, technical material is transcribed in Unified English Braille (UEB) as well as the Nemeth Code in UEB Contexts.
Important Appendix A Code Changes
The revised Nemeth Rule Book provides a comprehensive look at updates to the code. Appendix A contains all the code changes made after 2018 and consists of five succinct print pages. The authors strongly suggest checking the list of changes that are outlined by each rule before completing transcriptions. This article focuses on specific changes that significantly impact the teaching and transcribing of K–12 materials, including examples of these changes.
Rule 2: Nemeth Braille Indicators
Under Rule 2, the most significant changes are as follows:
- Added Opening and Closing Switch Indicators to the list of indicators
- Added Single-Word Switch Indicator construction and use
- Changed from Carried Number Indicator to two different Regrouping Indicators— Broadened to include Addition, Subtraction, Multiplication, and Division
Those who have kept up with the Guidance should already be familiar with the switch indicators, but the regrouping indicators are brand new, and the carried number indicator has been eliminated. For those transcribing elementary math materials, this is a game-changer.
Rule 4: Code Switching—A Must Read!
As stated above, the reader should already be familiar with the switch indicators, but there has been quite a bit of confusion about when, how, and where they should be used. Rule 4 gives extensive examples to help clarify these questions. As a reminder, these are the three switch indicators:
- Opening Nemeth Code indicator (UEB indicator)
- Nemeth Code terminator
- Single-word switch indicator
In this article, SimBraille is used to indicate the braille dot configurations for the switch indicators for sighted readers. However, this may be of little value for those using a screen reader, which will only see the examples as an image. Therefore, please see the attached BRF with all SimBraille examples in “real” braille starting at this point in the article.
Single-Word Switch Indicator
The use or non-use of the single-word switch indicator appears to have often been interpreted differently than intended by the BANA Nemeth Committee. The following statement should clarify Rule 4.6.8 c.
“When only one narrative word, hyphenated word, or abbreviation without an associated value occurs between two Nemeth expressions or symbols, the single-word switch indicator (dot 6, dot 3) is used to indicate that the word is in UEB. The indicator is unspaced from the affected word. Contractions are used in the subsequent word as needed. The indicator is used whether or not the word contains contractions. The effect of the single-word switch indicator is terminated by a space.”
Examples of the Use of the Single-Word Switch Indicator
The following examples are taken directly from the 2022 Nemeth Code rule book. Notice the placement and use of the Opening and Closing Switch Indicators. Remember to use the attached BRF file for these same examples in hard copy braille.
Rule 25: Spatial Arrangements
Rule 25 has quite a few significant additions and changes that are worth mentioning and illustrating with examples. The first change below occurs in elementary math, while the remaining apply to high school level math.
- Symbols for carried numbers (regrouping numbers) above and below the arrangement
- Augmented matrix guidance
- Symbols for vertical and diagonal ellipses
- Transcription of matrices with blank entries and single dot entries
- Systems of equations are spatial
- Transcriber-Inserted Grouping Symbol
Regrouping Indicators
The regrouping indicators are as follows:
- For numbers above the arrangement (varying in length)
- For numbers below the arrangement (varying in length)
Example of Regrouping Numbers
The following example is taken directly from the 2022 Nemeth Code rule book. Notice that the new regrouping indicators are formed from the old carried number indicator consisting of dots 2-3-5-6 with the addition of either dots 1-2-6 (directly over) or dots 1-4-6 (directly under) at the beginning.
Example of a Matrix with Ellipses
The following example is taken directly from the 2022 Nemeth Code rule book. The horizontally placed ellipses have not changed, but the vertical ellipses (dots 1-4-6, dot 3, dot 3) and the diagonal ellipses (dots 5-6, dot 3, dot 3) are brand new.
Example of a Transcriber-Inserted Grouping Symbol
The following example is taken directly from the 2022 Nemeth Code rule book. The Transcriber-Inserted Grouping Symbol (dot 6, dot 3, dots 2-3-4-5-6) is new and is used when an explanation or comment refers to more than one print line in a series of mathematical expressions to which no grouping sign as a whole applies. See the example to understand this more clearly. See Rule 25.10.1 for details of spacing and formatting.
A Couple of Not-So-New Reminders
Use of UEB Numerals
Numerals at the corners of pages and the new page indicators that occur mid-page are transcribed in UEB. Titles for figures, tables, sections, etc., are transcribed in UEB. UEB numerals may be used with freestanding, unmodified numbers, ordinals, and plurals. (See Rule 4.6). When teaching the Nemeth Code to a pre-K student or older adventitiously blind student, it is best not to use UEB numerals. It is fine to use UEB whole numbers in word problems with older/experienced Nemeth readers.
There are no contractions or short-form words in Nemeth with UEB. When encountering words within mathematical expressions, they must be uncontracted.
Examples of When to Use UEB Numerals
The following examples are taken directly from the 2022 Nemeth Code rule book. You must use UEB for the section title, but you may use UEB for unmodified numbers in UEB context. Note that in Example 4-25, UEB has been illustrated; however, Nemeth numbers could have been used.
One or More Words in Mathematical Context
“When one or more words are part of an equation or math expression, they are as much a part of the technical notation as are the variables (letters), numbers, signs of operation, etc. The entire expression is placed inside the Nemeth switches. No contractions are used in the words. Spacing rules of the Nemeth Code are followed.” (See Rule 4.6.8 b)
Examples of Words in Mathematical Context
If the words are part of the equation or inequality where other Nemeth symbols, such as operation signs and comparison signs, are used, you must place all the words, etc., inside Nemeth. When words are just used in a sentence, use the single-word switch indicator between math expressions where appropriate.
Nemeth Resources
If you need further assistance, the following resources are recommended:
- APH Nemeth Tutorial. This tutorial is available at no cost, and it is interactive and accessible. However, it has not been updated, and all text is written in Grade 1 EBAE. Nevertheless, it is useful for practicing isolated Nemeth Symbols without switch indicators.
- Nemeth at a Glance: A Math Resource, Grade Level Chart, and Evaluation Tool, February 2017. This book is available at a cost of $78. It is available in a hard copy print or a digital version. It was the first book to introduce Nemeth within UEB contexts and is an excellent resource, but it does not include all the latest updates.
- Nemeth Braille Code for Instructors and Paraeducators Online Courses. This online course is available at no cost and was designed as a companion to Nemeth at a Glance. However, it consists of videos only and needs updating to include all the latest additions and updates. All dot configurations are verbalized, and it is useful for persons who prefer videos.
- Nemeth Reference Sheets from the National Braille Press are available in print and braille for $18 each or $30 for the set. These have been updated to include the switch indicators. The braille version includes a raised line drawing of each corresponding print symbol.
- NFB Course in Nemeth Code Transcribing Course Manual, 2025. This manual is authored by Lindy Walton, a consultant to the BANA Nemeth Code Technical Committee, and adheres very closely to the new Nemeth Code book. It is available at no cost in PDF and BRF formats.
All of the following resources were written before the publication of the 2022 Nemeth Code Rule Book; however, they are in the process of being updated to correct any changes that have been made. These are all available at no cost, and they are fully accessible.
- Learning and Teaching the Nemeth Code within UEB Contexts: A Step-by-Step Guide (2022) provides opportunities to build Nemeth Code skills and learn about strategies and resources for teaching the Nemeth Code. The book contains multiple examples of STEM materials transcribed into braille. Many universities are using this resource in pre-service training of TSVIs.
- Nemeth in a Box for Middle School Students contains seven lessons that teachers of students with visual impairments or others (e.g., paraprofessionals, family members) can use to review and/or introduce Nemeth Code symbols at the middle school level and review math concepts in a fun way.
- Project INSPIRE: Increasing the STEM Potential of Individuals who Read Braille. Project INSPIRE created six free, self-paced courses for TVIs, paraprofessionals, braillists, transcribers, and others who support braille learners focusing on the Nemeth Code.
- The Nemeth Braille Code Curriculum consists of the step-by-step Pre-K to Second Grade Nemeth Curriculum, the engaging Nemeth Code Focused Lessons, and the user-friendly Nemeth Symbol Library.
Free Nemeth Reference Sheets
These reference sheets don’t contain all the updates, but they contain quite a few valuable math symbols that are useful for quick reference, and they are available at no cost to the reader.
APH offers both a large print version and a braille version available on federal quota funds. Each booklet contains a list of Nemeth math symbols, along with a verbal description of what each symbol represents.
Gloria Bennett and Susan Osterhaus have several free downloadable versions in PDF or BRF. These include the topics of Algebra I, Geometry, Algebra II, and Set Notation. Each print reference sheet includes a list of Nemeth math symbols (in print, SimBraille, and ASCII), along with a verbal description of what each symbol represents.
Emails and Other Links:
For additional information regarding the Nemeth Code and teaching mathematics in general to students who are blind or have low vision, please feel free to contact the authors at:
Susan Osterhaus: [email protected]
Maylene Bird: [email protected]
Also see Susan’s page on Paths to Literacy for information on a variety of Math topics.