Experiences of Teachers of Students With Visual Impairments in Learning and Teaching a New Braille Code for Mathematics and Science

Abstract

Introduction: In 2016, the United States transitioned to two new braille codes for science, technology, engineering, and mathematics (STEM). Little is known about the experiences of teachers of students with visual impairments in learning and supporting their students in learning these new braille codes: Nemeth Code within Unified English Braille (UEB) Contexts and UEB Technical. Methods: Thirteen certified teachers of students with visual impairments participated in one of three focus groups during the spring of 2020. The audio files were transcribed and then analyzed. Results: Some participants reported that they were still in the process of transitioning to Nemeth Code within UEB Contexts or UEB Technical. The majority of participants learned a new code through self-study and were introducing the symbols incrementally to their students. The participants reported that their students had been successful in learning Nemeth Code within UEB Contexts or UEB Technical, but there were challenges, including inadequate lead time, in supporting their students in STEM classes. Discussion: Affordable training and professional development for learning a new code were needed. Additional resources, including grade-level charts and curricula for K-12 students, should be created for both codes. Implications for Practitioners: Teachers of students with visual impairments are an essential part of the STEM educational team for students who read braille. Supporting student learning requires specialized knowledge of the braille codes used in STEM courses and technologies for producing tactile materials. Sharing of instructional materials, existing resources, and teacher expertise throughout mentorship would benefit the field of visual impairment.

Keywords

braille literacy braille code Unified English Braille Nemeth Code tactile graphics STEM education

Teachers of students with visual impairments must ensure students who are visually impaired and tactual learners become proficient in the braille code or codes necessary to access all content areas, including science, technology, engineering, and mathematics (STEM). These teachers are often responsible for adapting instructional materials into braille as well as providing guidance to paraeducators who prepare materials or support students who are visually impaired and tactual learners (Spungin et al., 2017). In addition, they are tasked with ensuring their students develop the skills necessary to systematically scan and interpret increasingly complex tactile graphics (Spungin et al., 2017; Smith, 2017).

The Nemeth Code for Mathematics and Science Notation (hereafter, Nemeth Code) was adopted by the Braille Authority of North America (BANA) in 1972. Nemeth Code was the standard code for STEM materials until 2016, when the United States officially transitioned to Unified English Braille (UEB). The BANA board could not reach consensus on a single braille code for technical materials (BANA, 2015). Instead, two codes were recognized: Nemeth Code within UEB Contexts and UEB Technical (BANA, 2015). According to BANA (2018), “When Nemeth Code is to be used for mathematics and science, the actual math and technical notation is presented in Nemeth Code or the Nemeth-based Chemistry Code, as applicable, while the surrounding text is presented in UEB” (p. 1). However, sometimes the original Nemeth Code, where the surrounding text was presented in English Braille American Edition, has sometimes not been replaced. See Figure 1 for an illustration of differences in how instructional materials would be transcribed in the three braille codes. Resources such as Guidance for the Transcription Using Nemeth Code within UEB Contexts (BANA, 2018) and UEB Guidelines for Technical Material (International Council on English Braille, 2014) have been developed to assist individuals who read braille, including teachers of students with visual impairments, in learning the new codes. Additional resources are currently under development by BANA, including a codebook for Nemeth Code within UEB Contexts.

Figure 1.
Sample Geometry Word Problem in Different Braille Codes.

Although BANA selected January 4, 2016, as the date to formally implement UEB, states, and organizations established their own timelines and goals for transitioning to Nemeth Code within UEB Contexts or UEB Technical or both. Transition plans varied greatly, and some entities required several years to complete the transition process (BANA, n.d.). Some teachers of students with visual impairments were uncertain about the updated codes and reported a lack of resources to learn and teach the newly adopted codes (Herzberg & Rosenblum, 2022; Hong et al., 2017).

In a recent survey of 225 teachers of students with visual impairments in 41 states, approximately one-fourth (n = 60) responded they did not know either Nemeth Code within UEB Contexts or UEB Technical (Herzberg & Rosenblum, 2022). Teachers of students with visual impairments who reported knowing one or both of the newly adopted braille codes were asked to rate their skills as beginning, intermediate, or advanced. Slightly more than 50% of the participants rated their reading and writing skills as beginning (Herzberg & Rosenblum, 2022). Herzberg and Rosenblum's (2022) findings indicate that some teachers of students with visual impairments may lack the skills necessary to instruct students in Nemeth Code within UEB Contexts or UEB Technical or both.

Adequate lead time to prepare braille materials, including tactile graphics, has been a concern documented in the literature for the last three decades (McBride & Diamond, 2020; Rapp & Rapp, 1992; Rosenblum & Amato, 2004; Rosenblum & Herzberg, 2011). In the study by Rosenblum and Herzberg (2011), 50% of teachers of students with visual impairments reported that they were given only 1–2 days to prepare STEM materials. Some of the study participants indicated that the lack of lead time prevented them from proofreading their materials (Rosenblum & Herzberg, 2011). Likewise, in a study by McBride and Diamond (2020), 5 of 16 teachers of students with visual impairments reported that they could not always provide mathematics materials in a timely manner either because the mathematics teacher did not provide the print materials in a timely manner or a vendor did not produce the materials in a timely manner. Teachers of students with visual impairments have also emphasized how time-consuming it is to create graphics and teach students how to read and interpret graphics (Sheppard & Aldrich, 2001; Zebehazy & Wilton, 2014). Although BANA provides guidelines for preparing tactile graphics (BANA, 2010), there are currently no guidelines on how to teach tactile graphics literacy (Rosenblum et al., 2018).

The purpose of this study was to explore the experiences of teachers of students with visual impairments as the United States transitioned to Nemeth Code within UEB Contexts and UEB Technical. The research questions were:
How did the participants learn Nemeth Code within UEB Contexts and UEB Technical?

How did the participants support their students who are visually impaired and tactual learners in transitioning to Nemeth Code within UEB Contexts and UEB Technical?

What are the processes the participants use for preparing STEM braille materials, including tactile graphics?

Were there challenges? If so, identify these challenges.

Methods

Question Development and Procedures

Focus groups were utilized to obtain a better understanding of the teachers’ experiences and beliefs. This methodology is commonly used in educational research and allows participants who do not know each other to interact, discuss topics, react to responses of other focus group members, and make additional comments beyond their initial response (Flores & Alonso, 1995; Krueger & Casey, 2015; Merriam, 2009). The researchers developed a semistructured 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. Their feedback was used to refine the final question set. During the focus groups, participants were asked follow-up questions to clarify responses and explore topics in more detail. At the end of the focus group session, the participants were given the opportunity to share their thoughts about other related topics.

Criteria for Participation and Recruitment

This study was approved by the Institutional Review Boards of the University of South Carolina Upstate and Georgia State University. Participants provided consent though an online form in advance of their participation in a focus group. A purposive sampling strategy was used to select “a sample from which the most can be learned” (Merriam, 2009, p. 77). Teachers of students with visual impairments with a minimum of six years of experience who routinely teach and/or support braille readers in grades K-12 in STEM subjects were invited to participate in the study. Participants were recruited through multiple social media (Facebook) posts and email lists such as AERNet, Principals of Schools for the Blind-STEM electronic discussion group, and several state electronic discussion groups especially for teachers of students with visual impairments.

Data Collection

Three focus groups were conducted in April 2020, each with three to five participants. One of the focus groups consisted primarily of STEM teachers who were also teachers of students with visual impairments while the other two included teachers of students with visual impairments who provided more general support. The focus groups were conducted virtually using Zoom, a web conferencing tool. Each focus group was moderated by one or two researchers with an additional researcher observing and taking notes. Focus groups lasted from 90 to 120 min. The order in which participants answered a question first was rotated to reduce the risk of bias. The focus group sessions were recorded, and audio files were sent to a third party for transcription. The second author proofread each transcript, assigned pseudonyms, and divided the transcripts into topical sections.

Data Coding and Analysis

Glasser's (1965) method of constant comparative analysis was utilized. A table with three columns was made for each section of the three transcripts. In each row of the table, the first column contained a quote from a participant, the second column was used for coding by the researchers, and the third column was reserved for notes from the researchers. The researchers coded inductively at first but progressively assembled a code book to use for subsequent focus groups and tables. The authors collaborated in all coding and resolved any conflicts through discussion. The authors tallied codes across questions to elicit themes and selected quotes from participants to represent emergent themes. This method has been used in previous research with students with visual impairments (Hilson et al., 2016; Wild et al., 2013) and teachers of students with visual impairments (Wild et al., 2022).

Results

Participants

Thirteen certified teachers of students with visual impairments from eight geographically diverse states participated in the focus groups. All but one of the teachers were female. Several of the participants held additional certifications, including orientation and mobility (n = 3), mathematics (n = 3), and science (n = 1). See Table 1 for additional information.

Table 1.
Type of Employment and New Code(s) Utilized.

Pseudonym Role New Codes utilized

Doris Itinerant Nemeth within UEB contexts

Patric Residential Nemeth within UEB contexts

Sherry Resource room UEB Technical

Tonya Itinerant Nemeth within UEB contexts

Megan Itinerant Nemeth within UEB Contexts

Sondra Itinerant Nemeth within UEB Contexts

Alice Itinerant Nemeth within UEB contexts

Jordan Itinerant Nemeth within UEB contexts

Tracy State-wide organization Nemeth within UEB contexts

Carla Itinerant Nemeth within UEB contexts

June Residential Both

Ruth Residential UEB Technical

Barbara Residential Nemeth within UEB contexts

Teachers Learning New Codes

Teachers’ proficiency in the updated codes varied. Ten teachers reported that they have learned (n = 7) or were in the process of learning (n = 3) Nemeth Code within UEB Contexts. For example, Sondra shared, “We're in a state where we do Nemeth [within UEB Contexts] so when it comes to the switches and the changes, I always have to look to see what I have to do.”

Two teachers had learned UEB Technical, and one teacher had learned both codes. The participants learned the new codes in a variety of ways, but the most common method was self-study. Other methods included collaborating with colleagues to learn the code (n = 3), attending professional development training sessions (n = 2), taking face-to-face or online courses (n = 3), and creating reference materials for themselves (n = 1). Almost half (n = 6) of the participants reported there was very limited training to assist them in learning the new codes.

Transitioning Students to New Codes

Participants were asked about how they transitioned their students to Nemeth Code within UEB Contexts or UEB Technical or both. Seven participants (63.6%) reported that they taught new braille symbols within mathematical contexts. For example, one of Tonya's students “came from a state that was using UEB [Technical] and did not know Nemeth. So we spent probably a couple of weeks working on Nemeth getting started. And then the rest of it has been at least the day before he's going to see it in class.” Sherry shared that learning the new symbols in mathematical contexts has worked well for her student, “I make sure I teach them the symbols, like at the beginning of the unit, so that when they go to their mathematics class, they know what those symbols are already.”

Five participants described using an individualized approach to teaching their student. June explained that she has a diverse caseload, and “every student is different. I can have a student that just lost their vision and they're just learning [braille]. And then I'll have another high school or middle school student that has been using braille their whole life. So it's a variety of situations that I'm involved with, depending on the individual student. I just find the best way for them to learn.” Carla shared about her experiences teaching an 11th-grade multilingual student who was new to her. Although her student primarily used Nemeth Code within UEB Contexts in her Algebra II class, she also used UEB Technical at times. Carla reported that sometimes her student “takes notes using one of her devices in UEB Technical just because it works better for her that way. She's an English language learner. Research shows in your brain you've got some cognitive flexibility when you're working in two languages. So I don't know if that makes it easier for her to split between the two, but she's just like, ‘Oh, I use them both. It's no problem.’”

Several factors, including textbook adoptions and standardized testing, appeared to influence the transition process and timeline for teaching a new braille code. Ruth, a secondary mathematics teacher at a residential school for the blind, shared, “We officially switched over… This year, the testing is going to come in UEB [Technical]. So we went back and taught all of our students who’ve been doing Nemeth, we taught them UEB [Technical].” Barbara's students are still in the transition process. She said,
Our books are adopted in 10-year cycles. So all of the books that we last adopted are in Nemeth Code. … If I get tests made by our transcribers at our school, they will make them be UEB plus Nemeth Code, and the kids seem to do fine with that. But all of my students grew up with Nemeth Code, and we're still using it. They just write down whatever makes sense to them. It's when we get stuff from the transcriber that will be UEB plus Nemeth that they've got to be able to read. And usually they can do that without any problem.

Production of Materials

The participants described how STEM materials are prepared for their students who are visually impaired and tactual learners. All participants were responsible for preparing some or all of the tactile materials. The majority had support from a paraeducator (n = 6), braillist (n = 4), transcriber (n = 1), outside transcription service (n = 1), or a combination of these options. The level of expertise of the support personnel seemed to vary. For example, Sherry shared that she prepares mathematics materials up through Algebra I and sends more advanced materials or materials with many graphics to the transcriber. On the other hand, Sondra worked with a paraeducator who produced materials with errors, so she either had to proofread or prepare the materials herself.

Participants used a variety of technologies (often multiple, linked technologies), to produce STEM materials. Seven teachers created materials using Scientific Notebook, MathType, or Microsoft Word and then imported the material into Duxbury braille translation software or sent the files directly to students’ electronic braille notetakers. Tonya shared, “I use Duxbury, and the [STEM] teachers are sending me their work … through Google Docs.” A couple of teachers mentioned creating graphics in Microsoft Word and then producing the graphics with a Tiger Embosser or Pictures in a Flash (PIAF). Sherry indicated flexibility, with different strategies for different situations: “For graphics, if I do them, I'll use QuickTac and import them into Duxbury. And then occasionally, I'll use the PIAF if I need to, or sometimes I use Picturemaker. If I'm in class with [students] … I make something in Draftsman.”

Two participants seemed frustrated with technology issues they had encountered when creating tactile materials. They resorted to manually entering braille into Duxbury and using verbal descriptions for graphics. Both of these teachers seemed interested in learning more about the processes and technologies used by other participants in the focus group.

Nine of the participants shared strategies they use when transcribing materials. Three teachers asked colleagues questions, and another teacher created reference sheets for her own use. The teachers also used reference materials and books when transcribing materials into Nemeth Code within UEB Contexts or Nemeth Code, including the Nemeth Code for Mathematics & Science Notation, 1972 Revision (Nemeth, 1972; n = 2; 15.4%); Nemeth at a Glance: A Math Resource, Grade-Level Chart, and Evaluation Tool (Cleveland et al., 2017; n = 2; 15.4%); Learning the Nemeth Braille Code: A Manual for Teachers and Students (Craig, 1987; n = 2; 15.4%); Nemeth Code Reference Sheet for Basic Mathematics available from American Printing House for the Blind (APH; n.d.; n = 2; 15.4%); and Nemeth Tutorial (APH, n.d.; n = 1; 7.7%). When asked what additional resources are needed, three participants indicated that an updated codebook was needed for Nemeth Code within UEB Contexts. Similarly, teachers used a variety of reference materials and books when transcribing materials into UEB Technical, including the UEB Math Tutorial available from APH (n.d.; n = 1; 7.7%) and UEB Guidelines for Technical Material (n.d.; n = 1; 7.7%).

Challenges to Supporting Students Who Are Visually Impaired and Tactual Learners

All participants identified lead time as a significant barrier to providing high-quality STEM braille materials to students. For example, Megan commented, “One of our biggest challenges is getting the materials enough in advance to be able to create all the graphics and create the materials.” Jordan echoed, “…[G]etting the materials, the content from the teachers is where we tend to struggle at this point in a timely fashion.” Sondra added,
I agree [with Jordan] with getting materials ahead of time is very difficult, if not impossible. I probably spent two or three months trying to reinforce the fact that I needed to do the braille for math because it is not the same as literary braille so you cannot send it [instructional math materials] to her [the student] in a Word document.
Sometimes teachers do not receive instructional materials to transcribe at all. As Sherry described, “I walk into a class, and teachers are like ‘Oh, we’re doing this.’” She reported that she quickly decides if a graphic or brailled material is warranted. If so, she prepares it using tools such as a Draftsman or Picture Maker.

When participants received materials without adequate lead time, options for braille transcription were reduced. Doris described the process used in her district:
I have to submit a Google form and wait three days [if the transcriber is going to prepare the materials]…and you guys know these [STEM] teachers don’t give you three days and you’ve walked into a class, a science class or a math class, like “Oh, we’re doing this today.” Or you find out the day before.
A lack of lead time also impacted the teachers’ ability to proofread the materials, which, in turn, affected the quality of the braille materials. Barbara reported, “Sometimes I have enough time to do that [proofread] and sometimes I don’t. And if I don’t, I just tell the students, ‘Hey, this is hot off the press and I haven’t proofread it.’”

Inadequate lead time also restricted the teachers’ opportunities to refresh their own knowledge of the subject and preview the materials. Jordan explained, “If I have more time, then that gives me more time to look up what I need to be able to look up and learn or relearn.” Lack of time also affects a teacher's ability to prepare a student who is visually impaired and a tactual learner for upcoming instruction. As June shared,
I try to encourage TVIs, when they can, to pre-teach those diagrams so that when those kids come in, they don’t spend the entire time the teacher's talking about it, just trying to figure out what they’re looking at. But time's always an issue…. That doesn’t always happen.
Jordan added that with adequate lead time, she is able to “pre-teach or preview whatever it might be with my students who then they are prepared going into the classroom.”

Eight participants reported challenges in preparing students who are visually impaired and tactual learners to take high-stakes tests. Of these, four did not have access to a Thermoform machine. For example, Tonya stated,
The graphics that come with state tests are all on Thermoform [paper], and I don’t have access to a Thermoform machine. So any graphics that I create are not really the same as what they’ll experience on their state tests.
To overcome this challenge, Tonya reported, “We also got released copies of our state test from last year and pulled out the math and looked over it just so [the student] was familiar [with graphics produced using a Thermoform machine].” Other challenges identified by participants included a lack of opportunities for students to listen to tactile graphic descriptions (n = 1); instructional materials used daily are in the older Nemeth Code, but the state tests only come available in Nemeth within UEB Contexts (n = 2); and the inability to enhance tactile graphics on national college entrance exams (n = 1).

Discussion

Even though the United States transitioned to Nemeth Code within UEB Contexts and UEB Technical in 2016, as of spring 2020, some participants were still in the process of learning the new code and transitioning their students who are visually impaired and tactual learners to a new code. Similar to the findings of Herzberg and Rosenblum (2022), the participants’ level of proficiency in the updated codes varied. Transitioning to Nemeth Code within UEB Contexts or UEB Technical may be challenging for teachers of students with visual impairments when formal training and professional development opportunities are limited. Learning symbols “just in time” may make the process of transitioning to a new code less daunting and more manageable. In addition, teachers of students with visual impairments who have mastered Nemeth Code within UEB Contexts and/or UEB Technical should be encouraged to share their resources, strategies, and expertise with colleagues who are still learning a new code.

Teachers of students with visual impairments should introduce braille symbols in tandem with grade-level standards (Smith, 2017). Teaching symbols in context mirrors how general education mathematics teachers introduce symbolic notation incrementally. Grade-level charts, assessments, and curricula should be available for both Nemeth Code within UEB Contexts and UEB Technical. Teachers who create high-quality instructional materials for teaching braille symbols should be encouraged to share what they create. A national repository would eliminate the need for individual teachers to create materials and allow for the pooling of resources.

Limitations

This study had several limitations. First, it was an initial investigation of a phenomenon; and additional research is needed. Second, the results may be limited by the small sample size. Third, teachers of students with visual impairments volunteered to participate, and their views may not be representative of the population. Volunteers participating may have been more interested in the topic of STEM education than the larger population of teachers of students with visual impairments. Fourth, the proportion of STEM professionals in the sample is greater than in the general population of teachers of students with visual impairments; almost half of the participants specialized in STEM education. Fifth, one of the questions used during the focus group sessions may have assumed there were challenges. In future research, this type of question should be asked differently.

Future Research

This study provides insight into the experiences of teachers of students with visual impairments with more than six years of teaching experience. Additional research is needed to explore how less experienced, newly qualified teachers are supporting their students who read braille for STEM classes. It may also be helpful to explore how teachers with weak braille or mathematics skills support their students who are visually impaired in STEM learning. Future research should examine the experiences of students who have transitioned to Nemeth Code within UEB Contexts or UEB Technical, including multilingual learners and students with additional disabilities. The readability of embossed graphics should also be investigated, especially since many textbooks and high-stakes tests now routinely include embossed graphics.

Implications for Practitioners

The study participants reported they served in a variety of roles that required extensive professional knowledge and flexibility consistent with Spungin et al. (2017). Teachers of students with visual impairments must build a unified educational team that works together to meet the unique needs of students who read braille. It is often incumbent on teachers of students with visual impairments to foster relationships with STEM teachers, implement a system for sharing electronic files and hard copy print materials, and assist educational team members in overcoming any challenges that may arise with the student fully participating in all aspects of STEM education. As recommended by Spungin et al. (2017), teachers must provide training, support, and supervision to paraeducators and braillists who are often hired with limited or no experience in producing braille materials. Teachers of students with visual impairments may need to work with administrators to ensure these individuals have the technology and supplies necessary to efficiently produce braille materials and tactile graphics. Teachers should also work closely with students to ensure they have the necessary compensatory and technology skills to succeed in STEM classes (Spungin et al., 2017), which includes students not only having knowledge of Nemeth Code within UEB Contexts or UEB Technical but also how to organize their materials, interpret increasingly complex tactile graphics, and use technology to access class materials and complete assignments.

A specialized set of skills is required to produce high-quality STEM instructional materials in braille (Herzberg & Rosenblum, 2014; Smith, 2017). Just knowing Nemeth Code within UEB Contexts, UEB Technical, or both is not adequate. Individuals who prepare braille materials, including tactile graphics, may benefit from having strong technology skills. Study participants who were proficient in using and integrating braille translation software, specialized software for mathematics notation, and embossers reported they were more efficient in creating STEM braille materials than participants who did not have these skills. Teachers who are able to efficiently produce tactile materials may have more time to proofread materials and preteach concepts and symbols. There should be multiple, affordable opportunities for individuals to learn Nemeth Code within UEB Contexts and UEB Technical and build their technology skills. Teachers of students with visual impairments who produce high-quality materials should consider mentoring colleagues entering the field and supporting them if they have gaps in their knowledge and skills.

Study participants reported that the lack of lead time to prepare and preview materials was a persistent barrier to supporting students in their STEM learning. Inadequate lead time has repeatedly been identified as a problem in the literature (McBride & Diamond, 2020; Rapp & Rapp, 1992; Rosenblum & Amato, 2004; Rosenblum & Herzberg, 2011). The efforts of individual teachers of students with visual impairments, advances in technology to easily share materials electronically, and advances in software used to prepare STEM braille materials have not been sufficient to overcome the challenge of inadequate lead time. As Rapp and Rapp admonished in 1992, “efforts to remedy the difficulties being faced must be far more aggressive than are currently being made” (p. 117). Establishing a timely workflow is even more important considering the recent movement away from traditional textbooks to online platforms, apps, and remote learning which are often not accessible (Rosenblum et al., 2020). Teachers of students with visual impairments must continue efforts to collaborate and educate STEM teachers and administrators who may be unaware of the time required to prepare high-quality instructional materials in braille, preteach concepts, and ensure that students who are visually impaired and tactual learners can successfully use the materials in the STEM classroom. In addition, when teachers of students with visual impairments routinely do not receive instructional materials in a timely manner, there must be a system of accountability and administrative support so that the situation is rectified and materials are received with enough lead time that accurate, high-quality braille can be provided to the student alongside their print reading peers.

Pseudonym	Role	New Codes utilized
Doris	Itinerant	Nemeth within UEB contexts
Patric	Residential	Nemeth within UEB contexts
Sherry	Resource room	UEB Technical
Tonya	Itinerant	Nemeth within UEB contexts
Megan	Itinerant	Nemeth within UEB Contexts
Sondra	Itinerant	Nemeth within UEB Contexts
Alice	Itinerant	Nemeth within UEB contexts
Jordan	Itinerant	Nemeth within UEB contexts
Tracy	State-wide organization	Nemeth within UEB contexts
Carla	Itinerant	Nemeth within UEB contexts
June	Residential	Both
Ruth	Residential	UEB Technical
Barbara	Residential	Nemeth within UEB contexts

Footnotes

Authors’ Note

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

References

American Printing House for the Blind. (n.d.). Nemeth code reference sheet for basic mathematics.

American Printing House for the Blind. (n.d.). Nemeth tutorial. https://nemeth.aphtech.org

American Printing House for the Blind. (n.d.). UEB math tutorial. https://uebmath.aphtech.org

Braille Authority of North America. (2010). Guidelines and standards for tactile graphics. http://www.brailleauthority.org/tg/web-manual/index.html

Braille Authority of North America. (2015). BANA takes action at fall meeting in Crystal Lake, IL [Press release]. http://www.brailleauthority.org/pressreleases/pr-2015-11-18.html

Braille Authority of North America. (2018). Guidance for transcription using the Nemeth Code within UEB Contexts. http://www.brailleauthority.org/ueb/nemeth-guidance/Nemeth%20Guidance%20Final.pdf

Braille Authority of North America. (n.d.). Planning the implementation of UEB. http://www.brailleauthority.org/ueb.html#plans

Cleveland

Bean

Bird

Kelley

O’Brien, Osterhaus

S. A.

Sewell

Torrence

(2017). Nemeth at a glance: A math resource, grade-level chart, and evaluation tool. Texas School for the Blind and Visually Impaired.

Craig

(1987). Learning the Nemeth Braille Code: A manual for teachers and students. American Printing House for the Blind.

10.

Flores

Alonso

C. G.

(1995). Using focus groups in educational research: Exploring teachers’ perspectives on educational change. Evaluation Review, 19(1), 84–101. https://doi.org/10.1177/0193841X9501900104

11.

Glasser

(1965). The constant comparative methods of qualitative analysis. Social Problems, 12(4), 436–445. https://doi.org/10.2307/798843

12.

Herzberg

T. S.

Rosenblum

L. P.

(2014). Print to braille: Preparation and accuracy of K-12 mathematics materials. Journal of Visual Impairment & Blindness, 108(5), 355–367. https://doi.org/10.1177/0145482X1410800502

13.

Herzberg

T. S.

Rosenblum

L. P.

(2022). Information gathered to assist in designing STEM braille training materials: Survey results. Journal of Blindness Innovation and Research, 12(1). https://doi.org/10.5241/12-234

14.

Hilson

Hobson

Wild

(2016). Conceptual understandings of students with visual impairments about biodiversity across ecosystems. Journal of Blindness Innovation and Research, 6(2). https://nfb.org/images/nfb/publications/jbir/jbir16/jbir0602tc.html https://doi.org/10.5241/6-102

15.

Hong

Rosenblum

L. P.

Campbell

A. F.

(2017). Implementation of UEB by teachers of students with visual impairments in the United States. Journal of Visual Impairment & Blindness, 111(6), 543–555. https://doi.org/10.1177/0145482X1711100605

16.

International Council on English Braille. (2014). UEB guidelines for technical material. https://iceb.org/guidelines_for_technical_material_2014.pdf

17.

Krueger

R. A.

Casey

M. A.

(2015). Focus groups: A practical guide for applied research (5^th ed). Sage.

18.

McBride

C. R.

Diamond

(2020). Critical issues in education for students with visual impairments: Access to mathematics and the impact of the Covid-19 pandemic [Doctoral dissertation, University of Georgia]. ProQuest Dissertations & Theses.

19.

Merriam

S. B.

(2009). Qualitative research: A guide to design and implementation. Jossey-Bass.

20.

Nemeth

(1972). The Nemeth Braille code for mathematics and science notation. American Printing House for the Blind.

21.

Rapp

D. W.

Rapp

A. J.

(1992). A survey of the current status of visually impaired students in secondary mathematics. Journal of Visual Impairment & Blindness, 86(2), 115–117. https://doi.org/10.1177/0145482X9208600205

22.

Rosenblum

L. P.

Amato

(2004). Preparation in and use of the Nemeth braille code for mathematics by teachers of students with visual impairments. Journal of Visual Impairment & Blindness, 98(8), 484–495. https://doi.org/10.1177/0145482X0409800804

23.

Rosenblum

L. P.

Cheng

Beal

C. R.

(2018). Teachers of students with visual impairments share experiences and advice for supporting students in understanding graphics. Journal of Visual Impairment & Blindness, 112(5), 475–487. https://doi.org/10.1177/0145482X1811200505

24.

Rosenblum

L. P.

Herzberg

(2011). Accuracy and techniques in the preparation of mathematics worksheets for tactile learners. Journal of Visual Impairment & Blindness, 105(7), 402–413. https://doi.org/10.1177/0145482X1110500703

25.

Rosenblum

L. P.

Herzberg

T. S.

Wild

Botsford

K. D.

Fast

Kaiser

J. T.

Cook

L. K.

Hicks

DeGrant

J. N.

McBride

C. R.

(2020). Access and engagement: Examining the impact of COVID-19 on students birth-21 with visual impairments, their families, and professionals in the United States and Canada. American Foundation for the Blind.

26.

Sheppard

Aldrich

F. K.

(2001). Tactile graphics in school education: Perspectives from teachers. British Journal of Visual Impairment, 19(2), 69–73. https://doi.org/10.1177/026461960101900303

27.

Smith

(2017). Mathematics. In Holbrook

M. C.

McCarthy

,, & Kamei-Hannan

(Eds.), Foundations of education: History and theory of teaching children and youths with visual impairments (pp. 479–509). AFB Press.

28.

Spungin

S. J.

Ferrell

K. A.

Monson

(2017). The role and function of the teacher of students with visual impairments [Position paper]. Division of Visual Impairments and Deafblindness, Council for Exceptional Children. https://dvidb.exceptionalchildren.org/dvidb-publications/position-papers

29.

Wild

T. A.

Herzberg

T. S.

Hicks

(2022). An examination of early intervention services during the COVID-19 pandemic. Journal of Visual Impairment & Blindness, 116(6), 764–773. https://doi.org/10.1177/0145482X221144043

30.

Wild

T. A.

Hilson

Farrand

(2013). Conceptual understanding of geological concepts by students with visual impairments. Journal of Geoscience Education, 61(2), 222–230. https://doi.org/10.5408/12-379.1

31.

Zebehazy

K. T.

Wilton

A. P.

(2014). Quality, importance, and instruction: The perspectives of teachers of students with visual impairments on graphics use by students. Journal of Visual Impairment & Blindness, 108(1), 5–16. https://doi.org/10.1177/0145482X1410800102