Advocacy Resources · Braille Use · Education Resources · Nemeth Code (for math) · Nemeth Code (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.”