Securing Nemeth Code Instruction

As noted in earlier blogs in this series, many braille-reading students in the U.S. have been caught in some states’ inexplicable move to UEB Technical (a move that: (1) is not supported by the resolution bringing UEB to this country, (2) is not supported by student data, and (3) poses a great risk of harm to students). While thirty-two states teach Nemeth Code by default, ten states have no default, seven default to the unproven UEB Technical code, and two have not published officials stances on the question. While it can be difficult, there ARE ways to secure Nemeth Code instruction, even in states that use UEB Technical as the default code for braille math.

Taking control in the Old Dominion state (Virginia)

The term “dominion” refers to a supreme authority or absolute control. To many parents of blind/low vision children in Virginia (the “Old Dominion State”), the process of advocating for Nemeth Code instruction for their children feels like a battle against a supreme authority that requires all braille readers to use UEB Technical. I know Virginia parents who have chosen to homeschool their children or move to another state in order to provide their children access to Nemeth Code instruction and use.

Multiple parents in multiple school districts have reported to me that they have been told that (1) schools cannot get textbooks in Nemeth Code and (2) the district “must” teach UEB Technical so that students may take the required end-of-course tests, Standards of Learning tests (SOL tests). However, these claims are, at best, misleading.

Textbooks using Nemeth Code abound

As noted in Current Status of Nemeth Code Use in the United States, thirty-two states in the U.S. recognize Nemeth Code as the default for braille math instruction. Another ten fully support both Nemeth Code and UEB Technical. These forty-two states that fully support Nemeth Code are large states and include nine of the ten largest states in the country. In contrast, the UEB Technical default states contain less than ten percent of the nation’s population. Additionally, while the National Library Service (NLS) offers transcriber certifications in UEB literary, Nemeth Code, and Music Braille, there is no certification in UEB Technical (though Canada offers a “Letter of Proficiency,” and a “Completion Certificate” is available from UEBOnline.org). Given that Nemeth Code is fully supported in the vast majority of states, including large states like California, Texas, and New York, it seems highly unlikely that any school district in the United States would have difficulty finding Nemeth Code textbooks—and those textbooks have likely been transcribed by individuals who hold certification in this area, something that is not possible for UEB Technical textbooks.

Virginia DOES offer Nemeth Code on some SOL tests

The Virginia Examiner’s Manual for Fall 2020, Spring 2021, & Summer 2021 Non-Writing Tests (End-of-Course Mathematics Algebra I, Geometry, Algebra II) notes that, for students with a documented need for hard copy tests**, “The braille test is available in UEB with UEB Technical and UEB with Nemeth.” Additionally, the Virginia Examiner’s Manual for Spring 2021 Non-Writing Tests (Grades 4 and 5 and Grade 3) contain the same language. Thus, claims that Nemeth Code is not available on SOL tests are not factually correct.

[**Note: ALL braille readers should have hard copy braille for math. This is because, without hard copy braille, braille readers must use refreshable braille displays to read electronic braille; the braille display serves as the corollary to the print user’s monitor to display content. However, the one commercially available multi-line refreshable braille display, the Canute 360, is very new and only supports a few file types; it cannot be used with screen reading software used by high-stakes online tests. Thus, in practice al terms, braille users can read only one line at a time. In math, many problems are set forth in a multi-line display (addition, subtraction, multiplication, division, fractions, etc.). Without hard copy braille, braille readers would not be able to view most math problems as a whole.]

Many SOL alternatives offer Nemeth Code

Virginia also provides many alternatives to the SOL tests for all students in the state. Such as PSAT, SAT, SAT Subject tests, ACT, AP exams, International Baccalaureate (IB), and Cambridge International exams. In many cases, these alternatives are better for all students because they reduce the number of tests a student needs to take (and thus reduce student time spent in the testing environment). Substitute Tests Approved for Awarding Verified Credit (most recently revised on March 18, 2021) provides:

  • For Math, PSAT tests, SAT tests, SAT Subject tests, AP tests, and CLEP tests all qualify as SOL alternatives. As noted in Nemeth Code Used for All College Board Tests Involving Math and Science, all of these tests are available ONLY in Nemeth Code. Thus, withholding Nemeth Code instruction significantly limits the availability of SOL alternative tests which would be available to a blind student in Virginia.
  • It is worth noting that the ACT (a nationwide college entrance exam that is currently available in both Nemeth Code and UEB Technical) is not permitted to serve as an SOL Alternative test in the following subjects: Earth Science, Biology, or Chemistry). Thus, Braille-reading students who do not know Nemeth Code have few SOL alternative tests in these areas.
  • Another possible test, the Cambridge International Examination, is prepared in UEB only; its “How to apply for modified papers” notes: “there are no longer any special codes for maths and computer braille, one code is used for all.” (from Information on modified papers). Additionally, there are only three schools in the entire state of Virginia which are listed as “Cambridge schools” on the website., one in Dumfries, one in Manassas, and one in Nokesville.
  • Regarding the International Baccalaureate tests, the focus is on “minimizing bias, particularly for those with assessment access requirements,” so it is likely that the student’s braille needs will be paramount. From Assessment principles and practices

Bottom line

Braille reading students in Virginia do not need to use UEB Technical in order to have access to high-quality textbooks, SOL tests, or SOL alternatives. In fact, students who know only UEB Technical and who have not mastered Nemeth Code are at a severe disadvantage in both post-secondary school options and in SOL alternative test options.

UEB Technical is limiting; Nemeth Code is freeing and empowering.

Nemeth Code Used for All College Board Tests Involving Math and Science

College Board supports only Nemeth Code

The College Board offers Braille tests ONLY in UEB and with Nemeth Code for math. Braille test materials are available in Unified English Braille (UEB) with Nemeth Code for math. Students approved for braille will receive a braille test book, Guide to the Nemeth Code, and Braille Reference Information for use with the math test.” From Accommodations and Supports Handbook, Spring 2021.

Given the lack of availability of UEB Technical from the College Board, students who are not permitted to learn Nemeth Code will be unable to take the following tests:

  • PSAT/NMSQT® (the ONLY means by which a student may compete to become a National Merit Scholar)
  • SAT®
  • SAT Subject Tests™
  • Advanced Placement® (AP®) Exams
  • CLEP® (College Level Examination Program)
  • ACCUPLACER® (widely used by post-secondary schools to “assess student readiness for introductory credit-bearing courses”)
  • PSAT™ 10
  • PSAT™ 8/9

College Board tests are widely-used

This will place these students at a severe disadvantage in their pursuit of post-secondary education.

PSAT (Preliminary SAT)

As noted above, the PSAT is the ONLY method of entering the competition to be named a National Merit Scholarship semi-finalist, finalist, or winner. Achieving this distinction can result in National Merit Scholarship funds as well as scholarships from private and school sources. Additionally, “National Merit Scholar” is a valuable addition to any college application.

SAT (formerly, Scholastic Aptitude Test)

The SAT is a commonly-used college entrance exam. It is used by scholarship-granting organizations as well.

AP (Advanced Placement) examinations

AP exams are end-of-course tests through which a student may earn college credit (depending on the student’s score and the attending school’s AP credit-granting policy).

Note that pursuing AP study is favored by colleges. When deciding whether to limit a student to UEB Technical, ask: Will those colleges understand that the blind student couldn’t take the AP Calculus exam because the district never taught the student Nemeth Code—the code needed to access AP exams?

Also, AP exams cost less than one hundred dollars, but a student may earn three to eight credits by passing the test. This can save a significant amount of money for the students’ families. Will schools be willing to pay for a comparable college course for students unable to take an AP exam because Nemeth Code instruction was withheld from them?

CLEP (College Level Examination Program)

CLEP exams provide students a way to get college credit similar to that of AP exams. While CLEP exams are not typically tied to high school courses like AP exams are, the remain valuable tools for securing college credit for entry-level courses. In fact, an online program, Modern States, offers free course materials for AP and CLEP examinations. Blind students should not miss out on these college credit opportunities simply because their schools decline to teach them Nemeth Code.

Accuplacer

Accuplacer is an exam used by many community colleges, four-year colleges, and universities to place students in the proper class. The subject areas of Accuplacer are Reading, Writing (really, editing), Math, and WritePlacer Essay (composition).

Students who cannot take the Accuplacer exam will likely be placed in lower-level classes than is appropriate. As noted above, failing to prepare a student to take exams that could waive the need for entry-level college courses puts that student in the position of taking additional classes that might not have been needed had the student had the opportunity to “test out” of those classes. This, in turn, will increase the expense of college as well as the time needed to matriculate to a degree.

Consider students’ current and future needs

Please note that even students who are permitted to learn Nemeth Code (but are also forced to learn UEB Technical) are harmed. They are burdened with needlessly learning two math codes: one to please their school and one to serve them for life. The push toward UEB Technical forces braille-reading students to learn and use a math code which is region-specific and which restricts the student’s post-secondary education options. States and school districts are not placing this demand on non-disabled students; print readers are allowed to continue using two codes: one for literary and one for math.

Braille for Math? Tell Me More

Yes, as noted in A Brief Introduction to Braille in the United States, braille readers have access to specialized mathematical and scientific notation using braille. As noted in the BANA resolution that adopted Unified English Braille in the U.S., “Braille Authority of North America (BANA) adopts Unified English Braille to replace the current English Braille American Edition in the United States while maintaining the Nemeth Code for Mathematics and Science Notation, 1972 Revision…” (emphasis added). However, Unified English Braille (UEB) does contain some mathematical notations, and, despite the clear, unequivocal language of the resolution, some individuals have attempted to replace Nemeth Code with the technical materials for UEB. To better understand the “educational landscape” of which braille to use for math, it is helpful to provide some background.

Foundations of braille math

Braille numbers in the English-speaking world are based on the first ten letters of the alphabet. The dot formations for numbers one through nine are the same shape is the letters “a” through “i;” the number zero corresponds to the dot formation of the letter “j.” In literary braille, the only difference between these letters and these numbers is the placement of a special notation, the “numeric indicator,” directly before the brailled numbers. In contrast, Nemeth Code uses “dropped” numbers; while the dot shape still corresponds to letters, those dots are “dropped” to the bottom of the cell. Thus, in Nemeth Code, readers have two means by which to distinguish numbers from letters.

Pitfalls of “raised” numbers

Before Nemeth Code, the U.S. used a math code similar to UEB Technical, called the Taylor Code. Like UEB Technical, the Taylor Code used “raised” numbers.

Instructional issues

In my experience as a teacher of students with blindness/low vision, I have found that students learn dropped numbers (what Nemeth Code uses) far more easily than the “raised” numbers used in UEB Technical and the Taylor Code. For beginning and emergent braille learners, raised numbers are too much like letters, and students often take a two-step approach to decoding their numbers: they first identify the “letter” after the numeric indicator, then they “count” to the number associated with the letter. For example, if they identify the number as being associated with the letter “g,” they count – a, b, c, d, e, f, g – in order to identify the number as 7. Not only is this time-consuming and inefficient, the students usually use their fingers to “count” and thereby lose their place in the braille.

Delayed instruction

For many years, teachers actually withheld instruction in braille math (of any kind) until students had “mastered” the literary braille code (usually by second- or third-grade). Thus, most braille readers were prevented from learning any written math until halfway through elementary school—putting them years behind their sighted peers and feeding into the myth that blind students are poor in math. With Nemeth Code, it is easier to teach numbers as separate entities from letters, and students can pick up the braille more quickly, more efficiently, and at younger ages.

Efficiency in reading and writing

The use of numbers in the upper portion of the braille cell creates the need for numerous and duplicative number indicators and letter indicators in many mathematical equations. In other words, because it uses “raised” numbers, UEB Technical is much longer than Nemeth Code. This additional length leads to slower reading and slower writing. It doesn’t take a teaching certificate to understand that slowing a student down in reading and writing math probably doesn’t increase the student’s love for the subject.

Benefits of “dropped” numbers

When the U.S. switched from the Taylor Code to Nemeth Code, blind students started excelling in math. They took higher-level math classes, and more than ever before pursued and attained undergraduate and graduate degrees in math and science. Other countries, including Australia, have been using UEB Technical for more than a decade. They are not showing the kind of growth in blind math students that the U.S. has shown. It saddens me to think that some want to abandon a robust and efficient code and take up one that has not shown itself to be even as good as Nemeth Code (and definitely has no proof of being better than Nemeth Code). Our children’s education is too important to forgo proven methods of equitable STEM access in favor of unproven methods.

Print readers benefit from “switching codes;” why shouldn’t braille readers?

I always find it interesting that some individuals bemoan “two codes” and the need for “code switching” as a reason to eliminate the robust and effective Nemeth Code and replace it with UEB Technical, which is, at best, unproved to provide the robust foundation students need to pursue STEM opportunities in education and employment.

In print, we have two codes: Classic Latin Alphabet letters and Arabic numbers. The print writing systems for letters and for number don’t even have didn’t even have the same origin. Yet these codes are so efficient, we hardly recognize them as different codes. For English language print users, it is most efficient to use Roman letters and Arabic numerals.

Does consistency outweigh utility?

Imagine someone trying to force all print readers to change to Arabic letters or to Roman numerals for the sake of “consistency.”

What would that do to academic performance by print readers?

The education sector would never consider subjecting print readers to such a change.

If it ain’t broke, don’t fix it

Some individuals believe that braille readers should be subjected to this type of change—even though there is no data showing that UEB Technical improves the efficiency or attainment level of braille users anywhere on the planet. They promote this view even though (1) there are decades of evidence of the benefits of Nemeth Code use and (2) there is no evidence that the use of UEB Technical is superior to Nemeth Code in meeting students’ educational needs for efficient and effective tools to access STEM materials in education and in employment.

Instead of stripping braille readers in the U.S. of Nemeth Code, a proven tool that promotes STEM opportunities and achievement for braille readers, it makes more sense to follow the plain language of the BANA resolution and maintain Nemeth Code in the States. This will allow our students to have the STEM access they need, and we can monitor the impact of UEB Technical in the countries where it has been in place for years. If, at some point, there is evidence that UEB Technical promotes STEM achievement for blind students, BANA might revisit its 2012 resolution and any data can be evaluated to determine if a switch to UEB Technical should be implemented in the United States.

Please check out the next installment in this series, “Current status of Nemeth Code use in the United States.”

Current Status of Nemeth Code Use in the United States

As set forth in A Brief Introduction to Braille in the United States, the moved to Unified English Braille (UEB) was not intended to include braille notation for either math or science: “Braille Authority of North America (BANA) adopts Unified English Braille to replace the current English Braille American Edition in the United States while maintaining the Nemeth Code for Mathematics and Science Notation, 1972 Revision…” (emphasis added) BANA resolution that adopted Unified English Braille in the U.S.

Nevertheless, in some states, a few individuals began advocating for UEB Technical and the resulting complete abandonment of Nemeth Code in favor of UEB Technical. This position is clearly contrary to the plain language of the BANA resolution that brought UEB to the United States in the first place. Proponents of this UEB Technical stance also fail to provide any data showing that UEB Technical is as good as, much less better than, Nemeth Code, the braille math code used with great success in the U.S. for decades.

Where the states stand

According to my research, as of June 16, 2021:

  • Thirty-two (32) states denote Nemeth Code as the default code for math and science (technical) subjects: Alabama, Arizona, Arkansas, California, District of Columbia, Georgia, Idaho, Illinois, Indiana, Iowa, Kansas, Louisiana, Maryland, Michigan, Minnesota, Mississippi, Missouri, Nebraska, Nevada, New Jersey, New Mexico, New York, Ohio, Oklahoma, Oregon, South Carolina, Tennessee, Texas, Washington (state), West Virginia, Wisconsin, and Wyoming
  • Seven (7) states set UEB for Technical Materials as the default code: Delaware, Maine, Massachusetts, North Carolina, Rhode Island, Virginia, and Utah
  • Ten (10) states have stated that they do not have a default code, will support both Nemeth Code and UEB for Technical Materials, and charge the IEP team with making the decision: Alaska, Colorado, Connecticut, Florida, Hawaii, Kentucky, New Hampshire, North Dakota, South Dakota, and Vermont.
  • Two (2) states either do not have a final decision, or I was unable to get information on their decision: Montana and Pennsylvania. [Regarding Pennsylvania, while a draft plan was published in 2015, that plan has not been finalized, so there has not been a final decision reached. At this time, Pennsylvania produces textbooks in both UEB with Nemeth Code and in all UEB, see AIM Request Form.]

At first glance, it seems that the majority of U.S. states (64%), including many states with large populations, have decided to follow BANA guidance and retain Nemeth Code as the default code for braille reading students. However, it is concerning that eighteen (18) states are ignoring BANA guidance and either implementing the unproved UEB Technical code or placing it on equal footing with the proven Nemeth Code. In the print world, this is akin to eighteen states stripping the default use of Arabic numerals and replacing them with Roman numerals because, “We use Roman letters, and it is too difficult for students to have to switch to another code for math.”

Problems with using two math codes

Moreover, the use of both Nemeth Code and UEB Technical poses numerous problems:

Adverse educational impact on students

Families needing to move to or from different states for economic or security reasons risk putting their children behind in math due to the need to learn a new Braille math code.

Nemeth Code and UEB Technical are fundamentally different, so much so that most children who are fluent in one code will have a learning curve if forced to use a different code—and they will lose valuable instructional time in STEM content course due to the need to learn a new code to read those materials

  • Such a child may well fall months behind in math classes due to a lack of familiarity with the different code.
  • This will be particularly difficult for children of military families, who will almost certainly move several times throughout their school careers.
    • Certainly states should not wish to become “that state” or “one of those states” that military personnel with blind children know they need to avoid.
  • This change could also be particularly difficult for children from families of lower socioeconomic means due to a need to relocate more often for financial and/or personal safety reasons.
    • Many times, these students do not have strong family support in the area of Braille education—because of lack of parental time, energy, education, etc.
  • A move away from the national standard of Nemeth Code could render these children so bereft of STEM educational opportunities that they might never recover from the lost time taken to learn new codes instead of learning math and science content.
  • There is no reason to set up a system that will automatically place Braille readers at an academic disadvantage upon relocation

Availability of educational materials

Abandoning Nemeth Code will create a problem with accessible math textbooks. All current math textbooks have been produced in Nemeth Code, and there is no certification for UEB Technical transcription in the US.

  • The National Library Service (NLS) provides certification for braille transcriptionists in UEB literary, Nemeth Code, and Music Braille
  • UEB literary was adopted throughout the nation on January 1, 2016, but now, more than five years later, there is still no certification program for UEB Technical materials

Students receiving math and science textbooks and tests in UEB Technical are, necessarily, receiving materials that have been transcribed by an individual who is NOT certified in UEB Technical transcription (because none exists)

  • This situation puts students at high risk of receiving poor quality math transcription.

Post-secondary educational consequences

Colleges and universities in UEB Technical states would be forced to choose between following the national BANA Nemeth Code model or taking the UEB Technical detour.

  • If these institutions do the former, students in UEB Technical states will be ill-equipped to pursue STEM opportunities at any post-secondary institution that follows BANA’s Nemeth Code guidance.
  • If these institutions do the latter, few, if any, out-of-state students will choose to attend their post-secondary institutions due to the high learning curve of switching to a new math and science code.

Additionally, scores of current Nemeth Code-using students would find that their in-state schools are now hostile learning environments due to the abrogation of BANA-recommended Nemeth Code.

  • This could require vocational rehabilitation agencies serving the blind to be required to spend hundreds of thousands of extra tuition dollars to send these students to out-of-state schools where they may pursue higher education opportunities without the need for remediation in math code.

Post-secondary employment consequences

UEB Technical state high school and college graduates will be ill-prepared to enter the post-secondary workforce in any STEM field due to what will become their lack of Nemeth Code knowledge.

It is highly doubtful that the employment sector would abandon the ubiquitous, useful, compact, and BANA-approved Nemeth Code for a limited number of rogue institutions providing only UEB Technical.

Increased expense and depletion of limited resources

Switching to UEB Technical is duplicative and expensive.

For decades, all math and science materials have been produced in Nemeth Code.

  • Supporting two codes will mean that all materials will need to be produced in each code.
  • Supporting two codes will mean that all materials will need to be available in each code.
  • This could well lead to shortages in materials.

Teachers of Students with Blindness/Visual Impairment will have LESS time to instruct children

  • TSBVIs [teachers of the blind and visually impaired] are in short supply as it is; we should not be creating additional, unnecessary drains upon their time.

A Brief Introduction to Braille Currently Used in the United States

Many people know that individuals who are blind/have low vision can use a nonvisual means for reading and writing: Braille. Braille is a code with which we can create expressive written communication and with which we can access written communication created by others. Unlike American Sign Language, braille is NOT a language; it is only a code. Just as print uses lines and curves to represent letters and numbers, braille uses dots to do the same.

While we print readers may not think about it much (or at all), we use different print codes for different purposes. The code we use for most writing is based on Roman letters. For math and science, we use Arabic numbers, Greek letters (at higher levels), and specialized mathematical and scientific notation (subscripts, superscripts, and mathematical operators, just to name a few.). Musical notation has yet a different code—using circles, dots, lines (horizontal and vertical), and curves. Typically-sighted people see these different codes in more environments throughout their lives, so it’s easy to forget how truly diverse and complex the print code is.

Braille has different codes as well. There is a braille code for most writing is typically called “literary braille.” This code is based on the code created by the late Louis Braille, but it has undergone many changes through the years.

Nemeth Code has long been used in the United States to provide blind/low vision students with efficient and robust access to mathematics and science. It was created by the late Dr. Abraham Nemeth, a blind mathematician born in New York City who developed the code to allow him to pursue opportunities in mathematical and science, including a doctorate in mathematics.  

Like literary braille, Music Braille was developed by a young man in France named Louis Braille. He was an accomplished musician and developed this code to enable blind individuals to independently read and write musical notation.

Most recently, in 2016, the United States adopted Unified English Braille (UEB) as the literary braille code in the U.S.: “Braille Authority of North America (BANA) adopts Unified English Braille to replace the current English Braille American Edition in the United States while maintaining the Nemeth Code for Mathematics and Science Notation, 1972 Revision; the Music Braille Code 1997; and the IPA Braille Code, 2008. The official braille codes for the United States will be Unified English Braille, Nemeth Code for Mathematics and Science Notation, 1972 Revision and published updates; Music Braille Code, 1997; and The IPA Braille Code, 2008.” BANA Motion to Adopt UEB, on November 2, 2012.