Middle and High School Students with Visual Impairments Describe Their Experiences in Learning a New Braille Code for Mathematics and Science

Abstract

Introduction: When the United States adopted Nemeth Code within Unified English Braille (UEB) Contexts and UEB Math/Science in 2016, students who were using braille had to learn a new code for science, technology, engineering, and mathematics (STEM). In late 2016, Bell and Silverman surveyed students about their initial experiences transitioning to a new braille code. However, to date there has not been additional research that includes students’ perspectives regarding the long-term effect of the transition to a new braille code on their ability to learn. The purpose of this study was to learn about students’ experiences in transitioning to a new braille code, whether students receive STEM braille materials in a timely manner, the technology students use in STEM, and what advice students have for teachers of students with visual impairments. Methods: In the spring of 2021, 11 middle and high school students who use braille for STEM classes participated in one of three focus groups. The data were analyzed using open-coding methods. Results: All participants had initially learned the Nemeth Braille Code for Mathematics and Science Notation and subsequently transitioned to one of the new braille codes. Students typically characterized learning a new braille code as easy. Most of the students had experienced delays in receiving braille materials, which sometimes negatively affected their ability to learn. Students reported using a variety of mainstream and assistive technologies. Discussion: Students should have consistent access to high-quality STEM materials in a timely manner in the braille code that they prefer. The students in this study articulated their preferences and were willing to advocate for themselves to overcome learning challenges in their STEM courses. Implications for Practitioners: Teachers of students with visual impairments can partner with general education STEM teachers and administrators to resolve persistent issues. Teachers can encourage students to voice their preferences and assist students in developing strategies before challenges arise.

Keywords

access braille science technology engineering mathematics visual impairment (blindness and low vision)self-determination

Mathematics skills are essential in everyday life and are often prerequisites to participation in postsecondary education and many fields of employment (Rosenblum et al., 2018; Rotermund & Burke, 2021; Smith, 2017; Torpey, 2012). The study of mathematics fosters problem-solving skills, attention to detail, and the ability to think abstractly (Torpey, 2012). Furthermore, many skilled trade and professional jobs require individuals to use math routinely (Torpey, 2012). Nemeth Code within Unified English Braille (UEB) Contexts and UEB Math/Science provide students who are tactual learners an effective way to access science, technology, engineering, and mathematics (STEM) content and demonstrate their understanding of mathematical concepts (Smith, 2017). Through the use of these braille codes, students can solve math problems in a way that is incrementally similar to their sighted peers.

In 2016 the United States adopted the Nemeth Code within UEB Contexts and UEB Math/Science. Yet, some teachers of students with visual impairments are still learning the new braille codes or have yet to learn the new braille codes (Herzberg & McBride, 2023; Herzberg & Rosenblum, 2022). Teachers of students with visual impairments have also reported a lack of resources to learn and teach the new braille codes (Herzberg & McBride, 2023; Herzberg & Rosenblum, 2022). In late 2016, Bell and Silverman (2019) surveyed 71 students between the ages of 9 and 18 years about their experiences learning a new braille code. The students expressed concerns about (1) learning two braille codes for mathematics, (2) limited access to textbooks in the new braille codes, (3) limited braille instruction, (4) incompatible technologies, and (5) timely access to instructional materials. Some students shared that they were intimidated by mathematics and felt the need to learn a new code negatively affected their ability to learn math (Bell & Silverman, 2019).

There are other barriers to STEM learning for students who are braille users. STEM materials often include formulas, mathematical problems, charts, and diagrams that are not accessible (Emerson & Anderson, 2018). Describing math images to students may be helpful, but that alone does not grant full accessibility (Emerson & Anderson, 2018). Teachers of students with visual impairments have recommended providing students with multiple modalities to access content, including auditory descriptions paired with tactile graphics (Rosenblum et al., 2018). High-quality instruction and multiple opportunities to practice are necessary for students who read braille to become efficient and accurate readers of information displayed in tactile graphics (Kamei-Hannan, 2009; Rosenblum & Herzberg, 2015; Rosenblum et al., 2021). Furthermore, students who are blind are more likely to answer math questions correctly when they are provided descriptions (Ferrell et al., 2017). However, audio descriptions prepared by teachers of students with visual impairments do not always meet National Center for Accessible Media guidelines (Rosenblum et al., 2020). In addition, audio descriptions are sometimes not available in statewide tests (Ferrell et al., 2017).

Braille materials with errors and omissions may impede students’ ability to learn. In order to access materials that include visual representations of STEM concepts or graphs that summarize data, students who read braille should be given substantively equivalent tactile graphics or audio descriptions or both. Yet, in an analysis of 598 graphics in 15 secondary math or science textbooks, Smith and Smothers (2012) found that two textbooks were missing 85% of the graphs. Graphs that were included were often missing key features such as an axis label. Herzberg and Rosenblum (2014) examined 107 math worksheets, including 18 algebra and 15 geometry worksheets, transcribed by teachers of students with visual impairments, transcribers, or paraeducators. Fewer than 5% of the transcriptions were completely accurate, and more than one-third of the tactile graphics had errors in the labels. When students who read braille encounter delays, errors, or omissions, teachers of students with visual impairments can support students in problem-solving, learning to voice their preferences, and advocating for themselves (Cmar & Markoski, 2019; Wolffe et al. 2014).

Students with visual impairments who read braille use a variety of technologies in their STEM learning, including mainstream and assistive technologies. Tuttle and Carter (2022) defined high-tech assistive technology as “any computing device or software used by students with visual impairments” (p. 474). In contrast, low-tech assistive technology included long canes, abaci, and tactile graphic drawing boards such as the Draftsman available from the American Printing House for the Blind. Twelve teachers of students with visual impairments reported information about the technology used by 51 students with visual impairments in Tennessee. Secondary students used a mean of 2.67 (SD = 1.5) high-tech devices (Tuttle & Carter, 2022). The most frequently used mainstream devices were tablets and laptops, and the most frequently used assistive technologies were book readers, screen reading software, refreshable braille displays, and talking calculators.

The purpose of this study was to explore the experiences of middle and high school students who read braille 5 years after the United States transitioned to Nemeth Code within UEB Contexts and UEB Math/Science. The research questions were:
Which braille codes did participants use in their STEM classes?

To what extent did middle and high school students who read braille receive high-quality STEM materials in a timely manner and how did this impact their STEM learning?

What technologies were used by middle and high school students who read braille to access STEM content and demonstrate their learning?

What advice did middle and high school students who read braille have for teachers of students with visual impairments?

Methods

Question Development and Procedures

Focus groups were utilized to obtain an understanding of the students’ experiences and beliefs. This methodology is frequently used in social science research so that participants can discuss their experiences and respond to comments from other focus group members (Krueger & Casey, 2015; Merriam & Tisdell, 2016). The researchers developed a semi-structured set of open-ended questions to guide focus group discussions. A certified teacher of students with visual impairments with a master's degree in mathematics education and a certified teacher of students with visual impairments with considerable experience in teaching braille reviewed the questions. Based on the feedback of these professionals, the questions were modified and finalized. During the focus groups, participants were asked follow-up questions to clarify responses and explore topics in greater detail.

Criteria for Participation and Recruitment

The study was approved by the Institutional Review Boards at the University of South Carolina Upstate and Georgia State University. A purposive sampling strategy was used to select “a sample from which the most can be learned” (Merriam & Tisdell, 2016, p. 96). U.S. students in grades 6–12 who had been using braille in STEM courses for at least 6 years were eligible to participate. The study was advertised to parents and guardians through multiple social media posts (Facebook) and email lists such as AERNet, Principals of Schools for the Blind-STEM electronic discussion group, and several state electronic discussion groups. Parents and guardians nominated study participants by providing informed consent and completing a brief online demographic form. Eighteen students were invited to participate in a focus group.

Data Collection

In February and March 2021 three focus groups were conducted using Zoom, a web conferencing tool. Students provided verbal assent in advance of their participation. At the beginning of each focus group, participants introduced themselves, and the researchers explained the purpose of the study. Students seemed comfortable interacting with each other and were eager to share about their experiences with similar-aged peers who are blind. The researcher employed a member check prior to data analysis. A member check is a data validity technique wherein participants review transcripts from an interview or focus group and confirm the content accurately conveys their intent (Birt et al., 2016; Merriam, 2009). The students were asked via email to review the transcript for accuracy and to reply with edits, corrections, and additions. Two students responded with suggestions for minor edits for their group's transcript. After the member check was completed, participants were assigned a pseudonym.

Data Analysis

The three focus groups were recorded and audio files were transcribed by a third party. Both researchers read the transcripts multiple times and used open-coding methods to create codes without predetermined ideas or hypotheses. This process is based upon the methodology of Glaser as described by Merriam (2009) as well as Walker and Myrick (2006). The codes were then refined by the two researchers until emergent categories arose to describe the data across the transcripts. Afterward, the categories were “fleshed out and made more robust by searching through the data for more and better units of relevant information” (Merriam, 2009, p. 182). Using this method of data coding does not result in a theory, only a description of the data.

Results

Participants

The 11 students were from eight geographically diverse states and ranged in age from 13 to 17 years. Students reported using a variety of mainstream and assistive technologies. The most frequently mentioned technologies were laptops or computers (n = 9), JAWS (n = 8), and BrailleNote Touch or BrailleNote Touch Plus (n = 8). Interestingly, all of the students in seventh and eighth grades reported using a Perkins braillewriter in math class, while none of the students in grades nineth through twelveth grades reported using this tool. See Table 1 for additional student information.

Table 1.
Information About the Participants.

Pseudonym Grade Current science, Technology, Engineering, and Mathematics (STEM) Class(es) Mainstream Technologies Specialized Technologies

Emily 7 Pre-algebra (8th grade math) and Life Science (8th grade) Computer/laptop, Microsoft Word JAWS®, BrailleSense Polaris, tool similar to Draftsman, Perkins braillewriter

Jin 7 Algebra I and 7th grade science Desmos, computer/laptop, math editor in Microsoft Word, Google Drive Audio Trace (feature in Desmos), BrailleNote Touch, JAWS®, braille display, home swell paper machine, Perkins braillewriter

Sharda 7 8th grade math, Physics/Chemistry Desmos, computer/laptop Braille display, Perkins braillewriter

Walter 7 Accelerated 7th grade math and Advanced Life Science computer/laptop, MobyMax (online education program) Braille Note Touch, NVDA, JAWS®, Perkins braillewriter

Susan 8 Algebra I (gifted) and Physical Science (gifted) Computer/laptop, Microsoft Word, Google Drive, Teams Duxbury Translation Software, BrailleSense Polaris, Perkins braillewriter, braille display, JAWS®

Tia 9 Geometry and Biology Desmos on phone, computer/laptop JAWS®, BrailleNote Touch

Beth 10 Laptop BrailleNote Touch Plus, JAWS®, Mantis™ Q40

Hallie 10 Honors Algebra with Trigonometry and Honors Chemistry Laptop BrailleNote Touch Plus, Orion TI84 talking graphing calculator, JAWS®

Pat 11 Precalculus and Physics Laptop BrailleNote Touch, JAWS®, braille display

Scott 11 Physics (dropped midyear) and Engineering Iphone, ipad BrailleNote Touch

Marnie 12 Geometry and Chemistry BrailleNote Touch, BrailleSense Polaris, Orion TI84 talking graphing calculator

The student could not recall the name of the device nor were they able to provide sufficient detail to identify the specific device.

Learning a New Braille Code

All participants (n = 11) began their braille education learning the Nemeth Braille Code for Mathematics and Science Notation. Subsequently, 10 participants learned Nemeth Code within UEB Contexts and Scott learned UEB Math/Science. The high school students reported learning a new code in fourth grade (n = 1), sixth grade (n = 2), in 2016 (n = 1), gradually “picked it up” (n = 1), or did not mention a specific year or grade level (n = 1). The middle school students reported learning a new code in second grade (n = 2) or did not provide a specific grade or year (n = 3). Eight students commented on the ease or difficulty of learning a new braille code. Six students indicated learning a new code was “easy” or “not that difficult”. In contrast, Susan said, “It was kind of hard for me to learn UEB because when UEB came out, I was in 2nd grade, and so I had learned a fair amount of the old code.”

Beth, Emily, Raveena, Scott, and Tia reported that their textbooks or statewide assessments or both were in Nemeth Code even though they had learned and preferred Nemeth Code within UEB Contexts or UEB Math/Science. At times, using materials in a different braille code affected the students’ learning or caused them to answer questions incorrectly. Tia shared that her
state tests are in old Nemeth Code and it's been a couple years since I've switched to using [Nemeth Code within] UEB [Contexts] more often so it's a little confusing to go back, especially taking such a difficult test, and also trying to remember all those symbols.
Similarly, Scott commented,
Most of them [textbooks] are still in Nemeth, which is somewhat frustrating for me because I'm used to reading and writing in UEB Math/Science. But I think sometimes, mostly on tests, I occasionally choose the wrong answer simply because I don't entirely remember what the Nemeth Code was.
Hallie, on the other hand, received materials in Nemeth Code within UEB Contexts, but sometimes used Nemeth Code for her own work, as a matter of preference. She shared,
Actually, I still switch between Nemeth within UEB Contexts and the original Nemeth Code. … I'm more familiar with the old code because I've been learning it for a while. And if I'm in a hurry, I will default back to the old code, but most of the time I will use Nemeth within UEB Contexts.

Lack of Access to Timely and High-Quality Materials

Eight students described multiple instances when they did not receive their STEM braille materials in a timely manner. They reported that their teachers of students with visual impairments or paraeducators or both often did not receive instructional materials from the general education teachers with sufficient lead time. Beth, for example, commented that she did not always receive her history, math, and science materials when she needed them, “Well, usually she [Beth's paraeducator] gets what she can done and then I start on that in class and then she gradually gets me the rest, or an alternative, or whatever the case may be.” Jin was conflicted because he understood why it might be helpful for some general education teachers to create just-in-time materials in order to be responsive to student needs. Jin shared, “Last year, pretty much all the math was on the fly, which is really good for students, like the actual learning math concepts, but it was hard to adapt in time.”

Nine students shared that their learning had been affected by delays or errors in their braille instructional materials. The extent of the impact varied. Abigail elaborated,
It depends on what we're working on and if it involves a lot of graphics and how good my teacher is at giving lectures and explaining without referring to what is on the screen. I think it impacts my learning sometimes.
Elizabeth explained that she sometimes did not have graphics and noted when they were discussed in class,
If I don't have a graphic, I'll ask a teacher to describe it to me the best they can and I'll usually tell my TVI [teacher of students with visual impairment] if it's something I need…. There has been a lot of times in math where I don't have the notes on time, so I write down as much as I can from the lectures.
However, errors were problematic at times for Beth. She shared,
I've had errors in the math books to the point where it would have caused me to get the answer wrong. We just have to muddle through with it. I get very stressed out about grades and everything, especially when I don't know the materials. I may ask, “Well, what is this supposed to say again? Because I'm not getting the right answer. There might be an error here. I don't understand.” So I may have more questions than the others.
For Scott, the consequences of delays in receiving instructional materials were even more substantial.
The worst case was this year when I was in a physics course and all of my [general education] teacher's documents, there were so many of them, that my vision teacher did not have time to complete them because I also had other classes that needed to be converted [transcribed]. And so I wasn't doing the work on time. I eventually had a very bad grade in that class and dropped that course because I felt that [it] was too much. It was too frustrating and too stressful for me.

The students were expected to use a variety of instructional materials and online textbooks, some of which contained images without alternative text or description. For instance, Tia explained that her online geometry textbook was “just basically a website filled with images … and my JAWS will not read [it] at all.” Other students reported that the accessibility of PDF documents varied. Scott shared he sometimes needed to convert PDFs to “a [Google] Doc or Microsoft Word file to read it. And when that happens [in math], basically all of the mathematical symbols that are in the questions are erased.” The students offered strategies they used when instructional materials were not accessible. Some students used a hardcopy braille textbook while others requested that their teacher of student with visual impairments or paraeducator adapt the materials.

Advice for New Teachers

At the end of each focus group session, students were asked for advice they would offer a new teacher of students with visual impairments. Six students mentioned the importance of obtaining instructional materials in advance from the STEM general education teachers. Tia commented:
It happens in pretty much all of my classes but it affects me more in the STEM classes. This year it's more physics because communication isn't always the best between my TVI and the teacher…. If I don't have materials in advance, I can just listen to them read it out loud or just have someone else read it out loud to me. But since there are so many symbols and graphics and charts that I need to understand or read, I have to have those in advance or just the whole lesson becomes pointless.
Similarly, Marnie shared,
Mostly it's math and science because my other classes it's more text than graphics, so some [general education] teachers just do it on their own. I'm lucky this year because I have [STEM] teachers that try their best to communicate with my TVI [teacher of students with visual impairments] and send stuff in a timely manner.

Three of the students indicated that teachers of students with visual impairments should not offer too much help. Hallie stated,
There's such a thing as [being] too involved—where they [teachers] are doing things that you might not necessarily want them to do without consulting me. I know what I want, so discuss it with me instead of just jumping into it.
Abigail added that teachers of students with visual impairments should avoid “doing too much to the point where it's almost like you're doing the work for me.”

Several students provided advice related to tactile graphics and descriptions. Five students recommended detailed, yet concise, descriptions without subjective commentary. Jin said, “I've had a couple [of] explanations with subjective stuff in it, that isn't actually part of the image, it's like an interpretation. So that might be best to avoid.” Three students reported they would inform a new teacher of students with visual impairments about their preference for tactile graphics, audio descriptions, or both. Jin expressed, “I think tactile graphics would be good, especially for complex stuff.” Scott explained, “I would let my vision teacher and my other main teachers know that I do usually process information audibly, so they know to describe things properly to me.” On the other hand, Susan preferred access to both tactile graphics and descriptions: “I would tell my new teacher that I would like to have the graphic adapted, but I also like to have a little description or maybe some labels.”

Discussion

The 11 students who participated in this study used a variety of technologies in their STEM classes, similar to Tuttle and Carter (2022). The students learned Nemeth Code and, at some point, transitioned to either Nemeth Code within UEB Contexts or UEB Math/Science. The students had been introduced to one of the new codes incrementally. In contrast to the teachers who participated in the Herzberg and McBride (2023) study, learning a new code did not seem stressful for the middle and high school students. However, the students reported their learning and performance on assessments were sometimes negatively affected when materials were provided in different codes, contained errors, or were unavailable when needed. These findings build on previous research (Bell & Silverman, 2019; Herzberg & McBride, 2023; Herzberg & Rosenblum, 2014) by connecting delays and errors in braille materials to their effect on students’ ability to learn.

The students showed a deep knowledge about themselves and their STEM learning, and it was apparent that they had developed self-determination skills (Wolffe et al., 2014). They articulated their preferences, strengths, and needs. During the focus groups, students shared a variety of strategies they used when instructional materials were not available in an accessible format. Most of the students seemed comfortable and confident in advocating for themselves. Their comments revealed maturity, self-awareness, strong self-determination skills, and a keen understanding of the complex demands of teaching STEM subjects to a diverse student population. Participants recognized that their general education STEM teachers sometimes needed to improvise or change lesson plans in response to overall student learning.

Limitations

This study had several limitations. There was a small sample size. The perspectives of the participants may not be representative of other middle and high school students who read braille. The students who participated in this study may have been more interested in STEM than other middle and high school students. Based on the math and science classes the students were taking, it appeared that they were on grade level or advanced. This academic experience may not be true of all students with visual impairments. The researchers did not gather data about the performance of students in STEM classes (e.g., grades earned in the last marking period) outside of what students shared. Also, the focus group protocol did not include a question about the visual condition or acuity of the participants, and the participants did not volunteer this information.

Future Research

This research provides insight into the experiences of secondary students with visual impairments who had been reading braille for 6 years or more. The readability of embossed graphics should be investigated, especially since many textbooks and high-stakes tests now routinely include embossed graphics. In addition, the effect of errors in braille materials on student performance should be explored. Future research should also explore the correlation between achievement in primary, middle, and high school math learning by students with visual impairments and college admission rates, participation in STEM majors, and employment in STEM fields. Although the students in this study were enrolled in grade level or more advanced STEM classes, students with visual impairments are a heterogenous group with varying interests and abilities. It may also be helpful to explore the experiences of students with visual impairments who are below grade level or struggle in their STEM learning or both. Future research should include students with visual impairments and additional disabilities, including students with math learning disabilities and students who are deafblind.

Implications for Practitioners

Students who read braille in STEM courses should have access to high-quality, timely braille instructional materials. Teachers of students with visual impairments should cultivate relationships with general education STEM teachers and other professionals, coordinate the workflow for adapting instructional materials, and teach their students problem-solving skills so that when challenges arise they can advocate for themselves and make meaningful progress in their STEM learning. General education STEM teachers should be encouraged to employ universal design for learning strategies (Burgstahler, 2001), provide instructional materials with sufficient lead time so that the materials are accessible to the braille reader and can be used alongside sighted peers, and consult with teachers of students with visual impairments when questions or concerns arise. Students should learn to verbalize what strategies and accommodations help them learn as well as how to advocate when they are not receiving accommodations or braille instructional materials or both in a timely manner.

Pseudonym	Grade	Current science, Technology, Engineering, and Mathematics (STEM) Class(es)	Mainstream Technologies	Specialized Technologies
Emily	7	Pre-algebra (8th grade math) and Life Science (8th grade)	Computer/laptop, Microsoft Word	JAWS®, BrailleSense Polaris, tool similar to Draftsman*, Perkins braillewriter
Jin	7	Algebra I and 7th grade science	Desmos, computer/laptop, math editor in Microsoft Word, Google Drive	Audio Trace (feature in Desmos), BrailleNote Touch, JAWS®, braille display, home swell paper machine, Perkins braillewriter
Sharda	7	8th grade math, Physics/Chemistry	Desmos, computer/laptop	Braille display, Perkins braillewriter
Walter	7	Accelerated 7th grade math and Advanced Life Science	computer/laptop, MobyMax (online education program)	Braille Note Touch, NVDA, JAWS®, Perkins braillewriter
Susan	8	Algebra I (gifted) and Physical Science (gifted)	Computer/laptop, Microsoft Word, Google Drive, Teams	Duxbury Translation Software, BrailleSense Polaris, Perkins braillewriter, braille display, JAWS®
Tia	9	Geometry and Biology	Desmos on phone, computer/laptop	JAWS®, BrailleNote Touch
Beth	10		Laptop	BrailleNote Touch Plus, JAWS®, Mantis™ Q40
Hallie	10	Honors Algebra with Trigonometry and Honors Chemistry	Laptop	BrailleNote Touch Plus, Orion TI84 talking graphing calculator, JAWS®
Pat	11	Precalculus and Physics	Laptop	BrailleNote Touch, JAWS®, braille display
Scott	11	Physics (dropped midyear) and Engineering	Iphone, ipad	BrailleNote Touch
Marnie	12	Geometry and Chemistry		BrailleNote Touch, BrailleSense Polaris, Orion TI84 talking graphing calculator

Footnotes

Acknowledgments

The author(s) wish to thank Dr. L. Penny Rosenblum, who assisted with the final edits of the manuscript.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the US Department of Education, Office of Special Education and Rehabilitative Services (grant number H235E190003). The views expressed are not necessarily those of the funding agency.

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