Perspectives of Teenagers and Adults Who are Legally Blind on Their Knowledge and Preference for Either Nemeth or UEB for Mathematics

By Edward C. Bell, Ph.D., and Arielle M. Silverman, Ph.D.

Edward C. Bell, Ph.D., is the director of the Professional Development and Research Institute on Blindness at Louisiana Tech University.

Arielle Michal Silverman, Ph.D., is the founder and principal consultant of Disability Wisdom Consulting in Silver Spring, Maryland.

Abstract

Seventy-one legally blind teens and 123 legally blind adults in the United States were asked about their experiences learning two braille notations for mathematics: the Nemeth Code for Mathematics and Science Notation (Nemeth Code) and Unified English Braille (UEB). About 70% of both teens and adults reported having been introduced to Nemeth Code. About 70% of teens and about one-third of adults reported having been introduced to UEB. In open-ended comments, participants expressed that a lack of Nemeth Code knowledge among teachers of the visually impaired (TVIs) is a major barrier to proper instruction. Participants also described a pattern of not teaching braille math notation to students with residual vision, and some adult participants who had residual vision as children expressed a wish that they had been taught braille math codes. While opinions were mixed regarding the switch from Nemeth Code to UEB in the United States, several concerns about the switch were raised, including concerns about the learning curve as well as a preference for the efficiency of Nemeth Code. Results underscore the importance of training TVIs who are knowledgeable and comfortable teaching UEB and Nemeth Code and the importance of braille for participation in math and science fields.

Keywords

Nemeth Braille, UEB Math, teacher preparedness, math instruction, math codes for the blind

 

In late 2012, the Braille Authority of North America, the official governing body for braille in the United States, adopted the Unified English Braille (UEB) Code as the recognized standard code for literary braille in the United States, replacing what had been referred to as English Braille, American Edition (EBAE). This requires retraining for all current braille readers and all individuals whose job it is to teach, produce, procure, grade, and/or support braille instruction.

Math is a critical skill for all youth to learn, and at times, it has been a challenge for some students with visual impairments. The reasons for the challenge are wide and varied and may include lack of proper accommodations, students being held to low expectations, and students being taught by teachers who are not prepared with proper math skills. Another obstacle for blind students learning math today is the debate over the use of Nemeth Code for Mathematics and Scientific Notation (Nemeth Code) or switching to UEB Math. There are advantages and disadvantages to both sides, but there is a deficit of research about which code will be more efficacious for mathematics in braille. This study reports on the perspectives and experiences of blind and visually impaired teenagers and adults related to the use of Nemeth Code or completing math through UEB.

Mathematical Challenges for Blind and Visually Impaired Students

Before examining the differences between UEB Math and the Nemeth Code, one must first understand what challenges mathematics presents to blind and visually impaired students and the effects of these challenges on their education. One obstacle this population faces is the errors and omissions present in math textbooks (Smith & Smothers, 2012). These errors can be numerous and often pertain to the Nemeth Code (Smith & Smothers, 2012). In these textbooks, tactile graphics are sometimes omitted as well (Smith & Smothers, 2012). Often, textbooks are also received late or not received at all (Smith & Smothers, 2012). These errors are not only present in textbooks but may be present in the math worksheets received by blind and visually impaired students as well (Herzberg & Rosenblum, 2014). Worksheets may also contain variation in formatting and Nemeth symbol use which may affect how students scan or understand worksheets (Herzberg & Rosenblum, 2014). These erroneous textbooks and worksheets would logically impact the education of blind and visually impaired students. Since they are not receiving the same material as their sighted peers, they are not receiving equal educations. They are having to learn concepts while also navigating around and trying to make sense of Nemeth errors.

Another area in which there are sometimes errors is that of tactile graphics. Often when tactile graphics are created, there are sometimes inconsistencies in formatting and labeling (Herzberg & Rosenblum, 2014). This may cause blind and visually impaired students to take longer to scan and navigate a worksheet (Herzberg & Rosenblum, 2014). Some tactile graphics are also created in a way that makes them challenging or unintelligible for blind students. At times, these graphics are not depicted in the same way that they are shown in print, which may cause misinterpretation by this population (Smith & Smothers, 2012). Some graphics are omitted entirely (Smith & Smothers, 2012). Omitted tactile graphics and those with errors ultimately could affect blind and visually impaired students’ spatial understanding and ability to read graphics. 

These errors in both Nemeth and tactile graphic preparation may point to under-preparation of teachers of blind and visually impaired students. In various studies, teachers feel like parts of their training in the Nemeth Code is lacking in some way (Rosenblum & Smith, 2012). This is especially true in concepts of higher level math (Rosenblum & Smith, 2012). These sentiments of under-preparation may lead to teachers feeling intimidated to teach their students some concepts. In regard to UEB Math, teachers also noted feeling that they did not have enough resources to prepare them or their students for the possible transition to this new code (Sunggye, Rosenblum, & Campbell, 2017). This lack of resources and preparation could have a significant impact on the quality and completeness of the education received by blind and visually impaired students.

This impact can be seen when looking at how blind students compare to their sighted peers in regards to their grade level in math. According to one study, 70% of blind students are one grade level behind where they should be in math, and 30% are five grade levels behind(Gulley, Smith, Price, Prickett, & Ragland, 2017). These statistics illustrate how blind students are not being given adequate educations in mathematics compared to their sighted peers. These unequal educations could limit employment opportunities for blind students.

Nemeth vs UEB Math

One issue that is complicating the education of blind and visually impaired students is the ongoing debate in the United States about whether to teach mathematics using the Nemeth Code or UEB. This debate may present a big problem for students, as different codes are used in different states. This could cause a student who moves from one state to another to potentially begin learning math using one code and have to learn a completely new code later in life (Bell, 2016). This could obviously cause undue stress and confusion for a student. For this reason, it is important to determine through the use of research which code is superior to the other. Since the adoption of UEB is relatively recent in the United States, not much research has been done on this topic. There has been some research, however, which can help us understand the benefits and challenges inherent in each method.

One element that must be considered when examining this debate is the presence of resources for teachers who are learning how to instruct students. As stated above, teachers often feel underprepared to teach the Nemeth Code (Rosenblum & Smith, 2012). However, this sense of under-preparation seems to also be present in regard to UEB (Sunggye, et al. 2017). Also, since UEB is relatively new to the United States and Nemeth has been present for a number of decades, Nemeth may have more curricular materials which can be utilized. Regardless, teachers do not feel adequately prepared to thoroughly teach either code, which shows that there are curricular deficits that may need to be addressed.

Another important aspect of this debate is the differing amounts of space taken up by each code. Studies show that UEB Math takes up more space than Nemeth (Wetzel & Knowlton, 2006).   Braille already takes up much more space than print, especially in hard copy. In order to do math, hard copy textbooks and homework assignments done with the Perkins braillewriter and braille paper are often required. Additionally, braille math textbooks already consist of multiple volumes. Increasing the number of volumes required for a math textbook could be cumbersome and inconvenient for teachers and students. Also, the relative newness of UEB means that there are not as many textbooks available in this medium. Since math textbooks can already be difficult for students to acquire, this could present additional problems for students and teachers. Not to mention the fact that many textbooks that are already in the Nemeth Code will have to be reproduced in UEB.

The biggest argument in favor of UEB Math is that it does not require a student to learn a whole new code (Steinle, 2016). This would reduce the number of symbols a student would have to learn and theoretically make learning math simpler for them (Bogart, 2009). According to Steinle (2016) the benefits of a single code become evident when working in advanced math where word problems and scenarios are part of the equation. Teachers also cite the fact that a symbol does not change meaning in UEB Math based on what context it’s in as sometimes happens in the Nemeth Code (Wetzel & Knowlton, 2006). Also, the purpose of UEB is to unify all English braille. If UEB Math was utilized, students from all English-speaking countries would be doing math using the same code (Bogart, 2009).  

However, UEB Math comes with its own set of complications. The first is that it presents a significant learning curve for those students and adults who have already learned Nemeth (Wetzel & Knowlton, 2006). It could be somewhat disruptive to a child’s education to be learning new mathematical concepts while simultaneously learning a new mathematical code. There is also the problem of teachers not having access to enough transcribers who are well versed in this code (Sunggye et al.2017). Also, some teachers worry about whether UEB is easily translatable by computers and whether it is useful for completing mathematical equations (Wetzel & Knowlton, 2006).     

All of these findings, when taken together, illustrate the benefits and flaws of both the Nemeth and UEB Math codes. However, there are two main problems both codes seem to be presenting for teachers and students. The first is that teachers feel underprepared to teach both. When it comes to Nemeth, this problem is more common in higher level math. Teachers feel under prepared to teach their students algebraic and geometric concepts, leaving students to fall behind their peers. UEB Math, however, is relatively new, and teachers have few resources to draw from to learn how to educate their students. For Nemeth, various curriculum and supplementary tutorials are present, but there are not as many materials about UEB Math. The second issue is that the fact that a student may have to switch between two codes part way through their education is troubling. It is in the best interest of students and teachers to resolve this debate soon, as the use of both codes could cause undue stress for students. UEB requires students to only learn one code and it is being used by all English-speaking countries. However, it takes up more space, does not have many educational resources, and it may cause logistical issues. It also presents a significant learning curve for students, teachers, and adults who have used and taught Nemeth for most of their lives. Both codes have compelling arguments for and against them. This argument, however, is one that may need to be resolved soon, at the risk of complicating the lives of teachers and students.

The Current Study

Data for this study were taken from the Access to Math Survey, which took place in late 2016. For this analysis, both teens and adults were asked about their knowledge and training in Nemeth and UEB Math codes. They were also asked open-ended questions about barriers to learning braille math codes in general and their feelings about the switch from Nemeth to UEB in the United States. We present a mixed-methods analysis of both quantitative and qualitative results.

Research Questions

RQ1: What have been teens’ experiences with learning Nemeth or UEB for math?
RQ2: What do teens perceive as the barriers related to learning math?
RQ3: What have been the experiences of adults in learning Nemeth or UEB for math?
RQ4: What do adults perceive as the barriers in learning math?

Methods

Participants

For the teen survey, 71 individuals between the ages of 9 and 18 provided valid responses. The average age of these 71 youth was 14.62 years (SD = 2.6, Range = 9-18). These individuals were 43 females (60.56%) and 28 males (39.44%), who resided in 33 different states (AL, AZ, CA, CO, CT, FL, GA, IA, IL, IN, KY, LA, MD, MI, MN, MO, NC, ND, NJ, NV, NY, OH, OR, PA, SD, TX, UT, VA, VT, WA, WI, and WV) and one participant who was from British Columbia, Canada.

These teens were 39 White or Caucasian (54.93%); nine Asian American, Asian (12.68%); nine Hispanic, Latino (including Puerto Rican) (12.68%); one Native American, Alaska Native (1.4%); five African American, black (5.63%); three who said Other (4.23%); and six who preferred Not to Answer (8.45%).

Teens were asked what grade they were currently in, and 11 were in elementary school (15.49%), 16 in middle or junior high (22.54%), and 44 in high school (61.97%). More specifically, four were in 4th grade (5.63%), seven were in 5th (9.86%), three were in 6th (4.23%), six were in 7th (8.45%), seven were in 8th (9.86%), five were in 9th (7.04%), 12 were in 10th (16.90%), 15 were in 11th (21.13%), and 12 were in 12th grade (16.90%).

For the adult sample, we obtained valid responses from 123 adults. The adults ranged in age from 18-73 years with an average age of 35.90 (SD = 14.16). There were 80 females (65.04%) and 43 males (34.96%) in the sample. The participants resided in 36 different states: AL, AR, AZ, CA, CO, CT, DC, FL, GA, IA, IL, IN, KS, KY, LA, MA, MD, ME, MI, MN, MO, MT, NC, NE, NH, NJ, NM, NY, OH, OR, PA, TN, TX, VA, WA, WI, and WV.

Ninety-one participants (73.98%) were white or Caucasian, 11 (8.94%) were Asian American, eight (6.50%) were Hispanic, one (.81%) was Native American, four (3.25%) were African American or black, one (.81%) reported their ethnicity as “other”, and seven (5.69%) did not report their ethnicity.

The adults were asked what year of college they had most recently completed. Eight (6.5%) said first-year student, ten (8.13%) said sophomore or AA degree, eight (6.5%) said junior, 24 (19.51%) said senior or completed bachelor’s degree, 15 (12.2%) said post-baccalaureate coursework, 33 (26.83%) said master’s degree, 16 (13%) said doctoral degree, and eight (6.5%) said “other”.

Procedures

Both the teen and adult participants completed an online survey between November and December 2016. Participants were recruited from the listservs of two national consumer organizations. Compensation was provided through a drawing of a number of gift cards. For the teen sample, participants had to be enrolled within the last year in grades eight through 12 or have graduated within the past year. For the adult sample, participants had to be 18-65 years. In both samples, participants had to be legally blind or visually impaired, residents of the United States, and have participated in the public education setting. The overall survey included demographic questions, interest in STEM-related courses, familiarity with braille math, availability of accommodations, mentorship, access to digital math platforms, and aspirations for a career.

For purposes of this paper, both the teens and adults were asked about their knowledge of Nemeth Code and UEB. For each code, they were asked whether or not they knew the code at all, and if they did, whether they would rate their skill level as beginner, intermediate, or advanced. Then the participants were asked how old they were when they were first exposed to each code and how they were taught each code. Finally, both the teens and adults were presented with three open-ended questions: (1) What do you think are the biggest barriers to Nemeth literacy? (2) If you did not learn either Nemeth or UEB, do you wish you had learned one of these codes? Why or why not? And (3) What do you think about the switch from Nemeth to UEB Math in the United States? The teens were asked a fourth open-ended question: “In general, are there ways in which your braille math experience could have been improved?”

Results

Teen Participants

Braille Math Knowledge. Of the 68 participants who answered the braille questions, 49 of them (72%) reported learning Nemeth Code. Of these 49 individuals, nine rated their knowledge as beginner-level (18%), 16 rated their knowledge as intermediate-level (33%), and the remaining 24 rated their knowledge as advanced-level (49%). When asked at what age they were first introduced to Nemeth Code, the average age was 7.78 years old (SD = 2.70; Range = 3-16).
Regarding UEB Math code, of the 65 participants who responded, 45 had learned the code (69%). Nineteen of these participants rated their knowledge as beginner-level (29%), 15 rated their UEB knowledge as intermediate-level (33%), seven rated their knowledge as advanced-level (16%), and four did not answer. They were introduced to UEB at an average age of 12.93 years old (SD = 3.54, Range = 3-18).

When asked how they learned Nemeth Code, UEB, or both, 37 individuals (73%) said they were taught by a teacher of the visually impaired (TVI), six individuals (11%) said they were self-taught, and seven individuals (14%) said they learned both independently and through a TVI.

Comments on Braille Math Codes

Because this survey sought to obtain information from the lived experiences of participants, what follows are the direct perspectives of those participants. These data do not necessarily represent factual information regarding Nemeth or UEB, but rather, the perspectives of participants related to their experiences with braille and math. Teen participants were next asked, "What do you think are the biggest barriers to Nemeth Code literacy? What would help more students learn it?” Interestingly, there were about as many participants who said learning Nemeth was easy as those who said learning Nemeth was difficult. Many comments were related to their teachers not knowing the code. Some examples of comments made were:

  • I believe that the biggest barriers for Nemeth literacy are not enough practice.
  • I believe that the sooner a blind student is introduced into the Nemeth code, the easier STEM subjects will be easier to understand for the student.
  • availability of instructors who know it well enough.
  • I think the barriers to Nemeth Code learning is that students are being told that they aren't able to do math and other STEM related subjects.
  • Students aren't also encouraged to learn Braille when they really should be.
  • I think that if someone created a fun and interactive way to learn the Nemeth Code, students would be happy to learn Nemeth.
  • It's too hard to use both Nemeth and Braille (literacy) in the same document on an APEX.
  • Technology like my BrailleNote is hard to use Nemeth code because my refreshable display is one line.
  • What would have helped me more is if the TVI would have learned the symbols that I needed for my math classes ahead of time and then taught them to me before that class, instead of teaching them to me as the class was going on (by classroom aide).
  • Grasping concepts of graphs presented textbooks. A good graph made by vision para was easier than those produced in braille books.
  • I think that, if it was translated better into print by computers, TVIs and sighted teachers would encourage blind students to use it more in the classroom.
  • Since it is not easily translatable through current technology, not many people take it seriously.
  • Lack of understanding by TVIs and lack of willingness to teach it to young students.

Teens were next asked, "If you did not learn either Nemeth or UEB Math, do you wish that you had learned one of these codes? Why or why not?” They commented:

  • I wish to learn Math in UEB because it's becoming the new standard, and at some point I will stop being able to read Large Print.
  • I didn't learn unified English braille math because I prefer Nemeth.
  • Yes so that I could read math problems. I hope to learn Braille for the sake of being literate in both mediums;
  • I feel it might be helpful in the future. I wish I could master both because it increases me and my career choice.
  • I don't like UEB math. Nemeth is better.
  • I know Nemeth Code and prefer it to UEB.
  • UEB is easier to use and transcribe.
  • I do wish that I would learn one of these codes because, then I would not fall behind when I am in class.

Teens were then asked, "What are your feelings about the switch from Nemeth Code to UEB Math code as the primary code used in the United States?" Opinions were generally mixed, with some concerns raised about the impact of the switch. While some did not have an opinion, here are comments from those who did:

  • I have not learned the UEB code.
  • I think it is better because you only need to learn one code and not two. We have to learn the UEB symbols just because people use them to write things instead of spelling out the words so we should just do UEB.
  • I like it because it makes it more reading is different than math. It's more separated like print.
  • I think it would be frustrating at first because I am used to using the Nemeth code to write mathematics and scientific notations. However, I feel that there is a reason why UEB is going to be taught.
  • The one thing that worries me is that the books will have Nemeth while UEB is being used. Such a switch would cause a lot of confusion for blind people and for blind students.
  • Nemeth has been used for decades, and a switch would not be simple or immediate.
  • Students raised on Nemeth would have extreme difficulty learning UEB math. I have tried to teach myself UEB math, and have been attempting to get it to translate with technology for a little over a year, and have so far been unsuccessful. In addition, the thousands of stem textbooks in hard copy Braille cannot be reproduced in UEB because it would be wasteful, harmful to the environment, and not cost or time-efficient.
  • I feel it's bad for students who haven't learned UEB math, but for everyone knew it will be a great unification.
  • I believe that the changes from Nemeth to UEB as the primary code used in the united States has its positive and negative side. I believe that the positive side to this change is that everyone will learn the same code but I believe that the negative side is that an older student will have to get used to using UEB in the future compared to a student in elementary school that can learn UEB since the beginning.
  • Highly detrimental because the entire math code and since most states use Nemeth, it causes confusion for transcribers to have to transcribe for both and students to have to relearn a whole new set of symbols.
  • I think that, overall, Nemeth code is much more efficient. For example, the UEB open parenthesis takes two symbols to create, while the same symbol in Nemeth takes only one.
  • I don't like it because UEB is practical but UEB math is not

The teen participants were then asked, "In general, were there ways in which your braille math experience could have been improved?" They reported:

  • Sometimes the symbols were hard to identify.
  • When I would ask a teacher to help me, they wouldn't know what to do. They would look it up on the internet and tell me the dots for the symbol. This was okay, but I had to wait a long time.
  • I think if the front of the books included a special symbols page with the math symbols that will be used in that book that would have to be introduced to sighted students.
  • When I was in fourth grade, my teacher taught fractions. Because fractions are displayed horizontally in Braille but vertically in print, it is difficult to visually picture adding the two top portions or two bottom portions of fractions together.
  • It seems relatively uncommon for a blind person to think visually, but nonetheless my shaky foundation with basic fractions, long division et cetera led to three years of difficulty with variables, pre-algebra, and so on.
  • An increase in the emphasis on visual concepts would be beneficial for blind students. This is not limited to fractions, but also to tactile graphics and special orientation, which I know a lot of blind students have difficulty with.
  • Spatial orientation really helps students understand volume and surface area, among other things, while at the same time increasing their ability to use sounds and other markers to figure out their environments. So it is beneficial to learn spatial orientation for both educational and practical reasons.
  • Tactile graphics can be confusing, frustrating, or absolutely brilliant when understood properly.
  • One common misconception among young blind students is that all tactile graphics are drawn exactly as they are in print, and that they are all exactly to scale. This is not necessarily true, and having a solid foundation in understanding tactile graphics leads to success in higher education, including geometry... Which is generally the most feared mathematics class among blind students.
  • Having actually been taught it by a TVI rather than having to self-study. The majority of my issues with braille are the lack of graphs I was provided in middle school, which is hindering me now as a high school student who wants to study physics in college.
  • Yes, I would say so. If I had already gone through a special Nemeth Code course, I probably would be more confident in my skills in math and maybe even do better with math in general.
  • It would be more helpful if the teachers of math could get materials to the braillist ahead of time so that I have my materials ready ahead for the TVI to help with.
  • Yes, if I was actually receiving Nemeth instruction during Math class. Not 45 minutes during the day at random times.

Adult Participants

Braille Math Knowledge. Eighty-five of the adults (69.11%) reported learning Nemeth Code, while 38 (34.89%) did not. When asked how old they were when they first learned Nemeth Code, of the 85 who knew it, 54 (63.53%) learned during the elementary school years (ages 5-10); 12 (14.12%) learned during the middle school years (ages 11-14); nine (10.59%) learned during the high school years (ages 15-18); and 11 (12.94%) learned when they were 19 years or older. When asked about their level of Nemeth skill, 15 (17.65%) said “beginner”, 28 (32.94%) said “intermediate”, and 42 (49.41%) said “advanced.”

Fewer participants reported knowing UEB Math: only 39 (31.71%) said yes, and 84 (68.29%) said no. Of the 39 participants who had learned UEB, four (10.26%) learned during elementary years, three (7.69%) learned during middle school years, six (14.38%) learned during high school years, and 26 (66.67%) learned as adults. Fifteen participants (38.46%) rated their knowledge of UEB for technical material as “beginner”, 12 (30.77%) rated their knowledge as “intermediate”, and 12 (30.77%) rated their skill as “advanced”.

When asked how they learned braille math codes, 56 (75.88%) learned from a TVI, eight (9.41%) learned at a residential school for the blind, two (2.35%) learned at an adult training program for the blind, 10 (11.76%) were self-taught, four (4.7%) learned from other teachers or braillists, and five (5.88%) learned from multiple sources.

Open-Ended Comments

When these adults were asked, "What do you think are the biggest barriers to Nemeth Code literacy? What would help more students learn it?" overwhelmingly, these adult participants felt that braille was not being taught if the individual had any usable vision, teachers were not prepared to teach the math code, and the teachers did not value instruction in Nemeth. Some comments include:

  • Lack of places to learn it my math teacher at the school for the blind didn't feel the need to teach it because at the time she believed I had too much vision.
  • I don't think that's fair my vision is considered degenerative it's changed a lot since middle school. The teacher for the visually impaired that was assigned to me in high school really did not see the value in teaching Braille to someone who still had usable vision with an eye condition that would deteriorate gradually over time. Therefore, it seems to me that blindness professionals are not really interested in teaching Braille to those who still have some usable vision but are still considered legally blind.
  • There are too many TVIs that are unwilling to devote the time and resources to teach students who would benefit from it.
  • Because I have some partial vision, my TVIs were convinced I didn't need braille, but once I got into college I had a lot of accessibility problems and definitely could have used braille in my studies.   
  • I asked my school multiple times for braille training but they did not have a TVI in my county. I have spent a lot of time and energy teaching myself braille, which is something most students would not feel inclined to do on their own.
  • Finding people to teach you as an adult. VR and rehabilitation specialist   Discourage use of alternative techniques for adults like braille. We are told to just settle for technology and if it fails, so what. You're not supposed to   Do anything of your life anyhow.
  • Teachers don't know it and don't know how to teach it. Math is scary and braille is intimidating.
  • Most people are falling back on screen readers and other methods of learning. It takes time to write and set up the problems. 
  • It's time consuming and if you make errors, they are difficult to correct if you are using a braillewriter.
  • For some time, a huge barrier to otherwise fluent Braille users learning the Nemeth Code has been the lack of compatibility with Braille note-takers and many other assistive technologies. Only recently, though, have software packages like the Nemeth Tutorial (HumanWare, LTD) made it possible for users of the popular BrailleNote line of products to learn Nemeth fundamentals with Braille and speech feedback. But to actually use that code for writing math materials on such devices only became possible about two years ago. So much to say that the spatial nature of certain aspects of the Nemeth code (and math in general) might make learning this distinct Braille code.
  • It's time-consuming and takes a lot of detailed steps to correctly write it so that you can see the steps.  Most paras and teachers don't have a good grasp of the code and don't know how to correctly transcribe it.
  • Lack of training for the transcriber. The braille transcriber for my school district was not adequately trained to braille math text in Nemeth code.

Survey respondents were next asked, "If you did not learn either Nemeth or UEB Math, do you wish that you had learned one of these codes?" To this, participants commented:

  • I think if they were introduced to it early, and had the TVI in the classroom during the Math lesson, students could become as accustomed to enmesh code right along with their peers learning basic numeracy skills in preschool and kindergarten.
  • I think the low expectations people have about learning and using Braille is probably the biggest barrier to learning Braille.
  • Most people seem to believe that Braille is a slow and inefficient means of reading. I think these types of beliefs makes it difficult for people to learn Braille.
  • Being exposed to it in school, and then having enough time with a good teacher to support ongoing learning.
  • Mandated braille learning as well as a teacher who is skilled in Nemeth.
  • Teaching it to as many blind children early on in the school system as possible. There needs to be much more early intervention, and school systems need to be thinking more carefully before deciding not to teach them braille.
  • I feel that the bar for being able to be more proficient in large print and braille should be fairly higher than it is so that more children are able to learn braille and benefit from it.
  • I think teaching every student the Nemeth Code, from the start of learning braille, probably right after he learns the basic uncontracted literary braille. This should also not be restricted to kids in school, but when adults become blind later in their life as well.
  • I feel that the key to students  becoming fluent in Nemeth Code is being introduced early. In that way, math notation should be treated sort of like another language, such that students can be taught to think in a distinct way from literary materials. This would motivate the association between distinct Braille codes and distinct systems of writing in general, and would serve to prevent confusion similar Braille characters/sequences in dissimilar contexts.
  • Find ways to make it fun to learn and quit criticizing it if you are a teacher.  
  • instruction, good teachers, and other blind mentors with knowledge in this area. Actually having instructors that know what it is and are available to teach it.
  • Those that I have spoken with who want to learn it, do not have teachers that know what it is.
  • It would help if there were more emphasis on teaching braille.  Not only does there need to be emphasis on teaching Nemeth code, but on braille literacy overall.

These adults were then asked, "What are your feelings about the switch from Nemeth Code to UEB Math code as the primary code used in the United States?" Ninety-six participants answered this question. Of these, a majority (54) were opposed to the switch. They said:

  • While I'm still giving it a chance, I'm not yet a fan.
  • While it seems that it may be easier for developers to code for UEB, I find as a skilled braille reader that it is a far busier code to read which can be a discouraging factor for the reluctant and newcomers.
  • I would be very disappointed if they did away with  Nemeth  code  all together.  I think that it would be a terrible idea.   Nemeth code is specifically designed for mathematical notation, so removing the code entirely would prevent a person with blindness from performing mathematical operations.  
  • I would hate that. UEB seems so much more complicated for higher level math problems and has caused me more errors than Nemeth. This is very bad as a chemist where an error in calculation might cause a safety hazard.
  • Our teachers would be further behind the curve than they already are with UEB and I like the Nemeth code for math notation, some symbols such as the "=" look like their print counter-parts, easier to learn.
  • While I understand that this is what is happening in most of the English speaking world, I believe it would be a travesty.  It would place our young blind students at a huge disadvantage related to STEM materials and instruction. 
  • While TVIs are not as proficient in Nemeth Code as they should be, our students would be waiting for TVIs to receive the necessary training to provide instruction and produce materials in UEB for math and science.

However, another thirty-three participants felt neutral or ambivalent. They said:

  • I do not know because, I do not know UEB.  That would be OK.
  • I'm not really familiar with either. I have never tried UEB so I don't quite know how UEB work.
  • I think (in my limited knowledge) that Nemeth code should stay as the primary code for math and science.
  • Not informed enough to comment too much, but in my state, where many students are not in advanced math, it might be an appropriate choice. However, for those in more advanced science and math courses, Nemeth certainly seems more equipped to handle material in those settings, from my limited knowledge of technical UEB.

While a minority, another nine participants expressed positive feelings about the switch, saying:

  • I believe it would simplify learning as there is only one code.  
  • I believe the whole premise of unified English braille was to ensure that anyone using English braille would be using the same code.
  • I believe that keeping Nemeth for code would defeat some of the purpose behind unified English braille.
  • I understand that unified English braille is more cumbersome to transcribe and takes up more space, but I would not be adverse to eliminating Nemeth code.
  • If we don't. Attempts to collaborate with the international community will become more and more difficult and then, eventually impossible. The US will be left further behind in STEM fields then we already are now. I urge the United States to adopt UEB completely because UEB purposes to establish one braille code for all material, whether literal or technical, which Dr. Abraham Nemeth helped create and establish UEB himself. Plus, being a mathematician myself, I use UEB for mathematics, which I prefer UEB over the Nemeth Code due to the fact that I do not need to switch braille codes just because the context is technical. (I have many other reasons too.) I earned both a B.A. and an M.A. for mathematics using UEB. Therefore, I support the United States adopting UEB completely.

Discussion

This study was based on the perspectives of teens and adults who are currently faced with the challenge of the braille code changing for mathematics and the lack of clarity over which code will ultimately predominate the field of education. Because this survey sought to obtain information from the lived experiences of participants, the data that have been provided represent the perspectives of those participants. These data do not necessarily represent factual information regarding Nemeth or UEB, but rather, the perspectives of participants related to their experiences with braille and math. What is clear from these data are that significant discrepancies still exist in the perceptions of participants regarding access to proper instruction in either math code. Teens and adults site teacher lack of preparation and intimidation over braille math as a barrier to their learning. This research further highlights the insecurity that exists over the lack of direction from policy makers and administrators over which code to use. The Nemeth Code of math is preferred by the majority of participants, but many are also excited about the prospect of having greater access to instruction in either math code. Yet, without clear policy directives to provide guidance to administrators and teachers, it is likely that the question over which code is to be used, and indeed whether instruction in braille math is to be improved, is very questionable.

Implications for Practitioners

The take-away message from this study is to highlight what parents, educators, and others can do to increase access to high quality instruction in braille math. The following points that serve to illustrate are taken directly from the words of the participants:

  • It is important for teachers of blind students to be proficient in braille math codes and to teach them to blind students at an early age when possible.
  • There is a need for self-teaching resources for adults to learn braille math codes, such as Nemeth, if they become blind later in life or did not learn braille math codes in school.
  • Switching from Nemeth code to UEB math code could present challenges, especially for young people who are still learning math concepts.
  • Access to lack of instruction in either code is further compounded by lack of direction from leadership as to which code is most appropriate.

References

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Bogart, D. (2009). Unifying the English Braille codes. Journal of Visual Impairment & Blindness, 103(10), 581-583.

Gulley, A. P., Smith, L. A., Price, J. A., Prickett, L. C., & Ragland, M. F. (2017). Process-driven math: An auditory method of mathematics instruction and assessment for students who are blind or have low vision. Journal of Visual Impairment & Blindness, 111(5), 465-471.

Herzberg, T. S., & Rosenblum, L. P. (2014). Print to braille: Preparation and accuracy of mathematics materials in K-12 education. Journal of Visual Impairment & Blindness, 108(5), 355-367.

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Smith, D. W., & Smothers, S. M. (2012). The role and characteristics of tactile graphics in secondary mathematics and science textbooks in braille. Journal of Visual Impairment and Blindness, 106(9), 543-554.

Steinle, K. J. (2016). Personal perspectives on Unified English Braille for mathematics. The Journal of Blindness Innovation and Research, 6(3). Retrieved from https://nfb.org/images/nfb/publications/jbir/jbir16/jbir060312.html. doi: http://dx.doi.org/10.5241/6-ICEB-12

Sunggye, H., Rosenblum, L. P., & Campbell, A. F. (2017). Implementation of Unified English Braille by teachers of students with visual impairments in the United States. Journal of Visual Impairment & Blindness, 111(6), 543-555.

Wetzel, R., & Knowlton, M. (2006). Studies of braille reading rates and implications for the Unified English Braille Code. Journal of Visual Impairment & Blindness, 100(5), 275-284.


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