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Challenges for Deaf Students in Mathematics Graduate School

Gerardo R. Chacón
Christopher Hayes

There are several recent studies on how underrepresented groups are starting to overcome barriers to participate in the field of mathematics. Barriers such as racial/ethnic underrepresentation Fig15, a self-perception of incompetence in mathematics and sciences BW12, the social context of the graduate program Fig15, or even the cultural practices and expectations of the mathematics community Her023 have been identified. In this article, we discuss these and other barriers that have a specific impact on some deaf and hard of hearing students who want to pursue graduate studies in mathematics.

Individuals who are deaf, hard of hearing, or otherwise have hearing difficulties, form a group that is diverse in communication modes and abilities. Here, we focus on the subset of people who use sign language (such as American Sign Language, hereafter ASL) or signing systems (such as Signed Exact English) as part of their communication in educational and professional settings. The members of this subset also have significant variation in hearing levels, technology use, fluency in sign, and communication preferences. For this article, we refer to members of this subset as “Deaf” with a capital D, with the note that in most other contexts the definition of Deaf is slightly different and refers to individuals who identify with Deaf culture. Individuals who have typical hearing levels will be referred to with the adjective “hearing”.

Statistics about deaf and hard of hearing people in the United States are difficult to obtain due to educational and medical privacy rights and the fact that the set is not universally well-defined—how much hearing loss “counts”? Who will self-identify as deaf or hard of hearing? Are we interested in including those with hearing loss due to age or noise exposure after their developmental and educational years? Nevertheless, it seems clear that their representation in mathematics is very low. In a white paper by a group of mostly Deaf scientists SBK12, the claim is made that in the 2007 to 2008 school year, 27.4% of hearing students in 4-year programs are STEM majors and that 24.4% of deaf and hard of hearing students are STEM majors, but that only 0.13 to 0.19% of these students obtain a doctorate, in comparison to 11.0 to 15.3% of such hearing students. The same paper states that during the years 2006 to 2010, only 13 doctoral degrees in mathematics were granted to students that self-identified as deaf or hard of hearing. There is a claim that roughly 5% of a country’s population has deafness or significant hearing loss WRC07. Applying this estimate to the 1,960 mathematical doctorates awarded in the United States that were reported to the American Mathematical Society from 2017 to 2018 Gla05, we would expect that a representative number of deaf or hard of hearing graduates would be roughly 392 over four years, which is nowhere close to the rate of 13 over four years. Anecdotally, in the case of Deaf students who sign, one author is a recent 2022 PhD graduate who is Deaf (Christopher Hayes, PhD from the University of Connecticut) and is only aware of one other recent mathematics PhD in the US who is also Deaf (Jason Quinones, 2020 from the University of Arizona). The Deaf community is small enough and connected enough for us to both comfortably claim that we are likely to be the only ones in the past five years, and almost definitely, there are no more than five in the past five years. Of course, the above rough analysis is using varying definitions of “deaf and hard of hearing” and is looking at different time periods, but underrepresentation is still obvious.

Mathematics as a language

One way of defining mathematics is as “the explicit communication of implicit relationships” CK106. As such, the language in which such communication is made determines the understanding of mathematical concepts. It is therefore apparent that there is a close connection between language and mathematics CK106.

In a world dominated by oral languages and their written forms, an evident barrier for Deaf students is the reduction or lack of language access. Most Deaf students, when pursuing graduate studies, are forced to acquire new concepts through the use of a sign language interpreter, and through written texts in a language that is not fundamentally accessible to them (typically English). A distortion in mathematical language and vocabulary can have a great impact on the mathematical levels of Deaf students CK106.

It is a common but incorrect belief that sign languages are essentially modified or simplified versions of spoken languages. In fact, sign languages such as ASL are distinct languages with their own grammatical structures and vocabularies, even if there is overlap due to the fact that Deaf people live within societies that use various spoken languages and are exposed, at bare minimum, to them through writing. For example, question words in ASL are typically placed at the end of a sentence; moreover, as is the case for any pair of different languages, there exist many ASL signs that do not have a perfect correspondence to some English word and vice versa. Within mathematics, some English-language structures, such as conditionals, comparatives, negatives, inferentials, abbreviations, and words with different meanings in mathematics and everyday life, have been identified as causing special difficulty for Deaf learners KBK15.

In GBR20, several individuals qualified to discuss mathematics in ASL show a lack of consistency in vocabulary even for basic pre-college concepts like the slope of a line. From personal experience, the authors, who teach mathematics majors at Gallaudet University, an institution where all undergraduate courses are taught in ASL, lack uniformity in many signs owing to different backgrounds in how and where they learned ASL. Even when there is consensus at Gallaudet (such as the sign for “derivative”), the other university in the United States with the largest Deaf student population, Rochester Institute of Technology, is known to have an entirely different sign for derivative. This lack of consistency persists in interpreters, who may use various signs in a graduate mathematics course, many of which a student may be unfamiliar with.

As another example, when teaching some basic concepts of set theory, it is common for students to confuse the symbols and . This confusion gets emphasized when both symbols are signed in the same way. After noticing this issue, some mathematics professors at Gallaudet, decided to use different strategies such as keeping the “in” sign for and finger spelling the word “subset” when referring to . Another professor simply says “under-set” for subset.

A similar example comes from the words equality and equivalence. Both concepts use the same sign, but their mathematical meaning is different. This makes it confusing to discuss equivalence relations. Again, a solution such as using the sign for “quotation marks” before the sign for “equal to” when referring to an equivalence, or replacing it with a substitute sign such as “similar” depends on the instructor’s knowledge of sign language and mathematics.

The diversity of strategies to address the lack of standardized signs for many mathematical concepts is as rich as the diversity of teachers and interpreters, this could also cause confusion for students when building their knowledge Pag06. As a consequence, when a Deaf student begins to attend a graduate school program, she needs to deal with new interpreters and new styles of signing and communication while also facing all of the same challenges as the other graduate students.

Furthermore, interpreters themselves rarely know mathematics to a high level. This means that interpreters are attempting to interpret content they do not understand. In practice, this effectively means interpreters are doing what is referred to as “coding” which means they are mouthing and signing English words as they hear them, instead of genuinely translating into ASL. For Deaf students who who are used to ASL, this can be difficult and mentally taxing to parse, and could affect their performance.

Visual accessibility

When talking about visuals in the teaching-learning process, one may think of explanatory graphs or neat presentations. In the world of Deaf students this has a much broader meaning, starting, for example, with the way classrooms are set up. A typical classroom is optimized first for audio communication and then for visual communication, without giving much consideration to the lines of sight for deaf students and interpreters KLP03. For comparison, the seats in classrooms at Gallaudet are almost always arranged in a U shape, so that every student can see every other student.

A blocked line of sight affects Deaf students when interacting with other students and instructors in the classroom, as they are unable to see those who are speaking, making it challenging to follow the conversation. This is also the case if instructors expect to gain the attention of students just by starting to speak. Deaf students might miss important information by switching their attention to the instructor a few seconds later.

Following an advanced class is more demanding for Deaf students since they are not only trying to understand mathematical concepts but also multiple visuals. “The student has to monitor all visuals within their peripheral vision and decide which one to focus on, and to ignore the others. This visual attention management process occurs simultaneously with the student’s learning process. As a result, many deaf and hard of hearing students can become mentally fatigued” KLP03.

On a related note, the comments in MH08 and PSB03 about the results of an attention test administered to Deaf college students in 2003 are important. The results suggest that Deaf individuals are more prone to inattention than their hearing counterparts when presented with stimuli in their central field of vision. The authors link this phenomenon with the evidence of a reorganization in the visual attention system in Deaf individuals, giving a heightened sensitivity to the occurrence of events in the visual periphery. Without auditory input, the visual systems become the primary source of alerting and processing language, and it has been observed that the visual systems of deaf people enhance peripheral attention and reduce central attention relative to that of hearing people. One implication for the classroom is that peripheral distractors would probably have a greater effect on Deaf students.

The style of a mathematics lecture in spoken language also presents subtle difficulties for Deaf students using sign language interpreters. Lecturers often will use words and phrases like “this,” “that,” “this guy,” “the integral on the left,” “the formula down here,” and so on. Understanding these requires awareness of where the lecturer is standing, or pointing, or gesturing. A Deaf student who is focused on the interpreter will miss out on this information. Furthermore, the interpreter themself is typically looking at the student, away from the board, and will not know what the lecturer is referring to, impacting the quality of interpretation. A Deaf student will typically try to circumvent this by studying the board and watching the lecturer’s gestures, but then they miss out on what is being said.

Social interactions

The role of social interactions in the success of students in graduate school has been established by several authors. Typically, graduate school environments in mathematics require not only intellectual integration and sharing values with the mathematical community, but also social integration with other students and faculty Her023.

Student-faculty interactions influence students’ behavior in academy and might have consequences in students’ success. Such interactions are diverse; for example, a faculty member could be a role model demonstrating appropriate behaviors in the academic environment, a faculty member could be a student’s advocate and provide useful information and resources, or they could be a bridge providing opportunities for students to interact with the academic community Fig15.

The lack of, or difficulty in, such social interactions will have an impact on a student’s integration into the academic community. Some authors argue that students who don’t feel integrated are more likely to voluntarily withdraw from a graduate program Her023. Additionally, students may belong to several different communities such as family, religious groups, and social groups, and there may be expectations from these communities that could inhibit or promote a student’s integration in the academic community Her023.

For Deaf students, the difficulties of communication with peers could hinder their integration into the academic community. Moreover, there are almost no Deaf faculty role models that could help them better understand the social interactions in graduate school. Additionally, most Deaf are part of the Deaf community and find comfort in interacting with peers who use American Sign Language in everyday life. Leaving the comfort zone of the Deaf community to enter an academic community dominated by hearing peers could result in feelings of guilt and of not belonging that could ultimately lead to isolation.

Lastly, an important part of doing mathematics is discussing math with other mathematicians, including other graduate students. This often happens informally—in an office, tea room, or hallway at a conference; after a seminar; in a study group or homework group; et cetera. Students with hearing loss have difficulty participating in these discussions, especially when there are multiple people in the conversation.

Best practices

In this section, we would like to make a few recommendations for those faculty members who have Deaf students in their graduate programs.

We begin by pointing out the somewhat evident fact that communication is a crucial component of effective instruction ES06. It is understandable that there will be communication barriers between hearing faculty and Deaf students, and it is important to keep this in mind in order to minimize the consequences. For example, it is important to remember that having an interpreter in class usually does not mean there will be full communication. There are always misunderstandings since interpreters typically have limited familiarity with mathematical concepts and symbols.

To address such limitations in communication, we suggest that faculty use as many visualization tools as possible. For example, the use of visual organizers such as concept maps, spider graphs, tables, and flowcharts showing information and the relationship between concepts so that students may see rather than hear about them, are helpful for content-area acquisition for Deaf students ES06. Furthermore, faculty should write important comments on the board instead of only stating them aloud, even if not directly relevant to the other material on the board. This is especially true for comments of a more big-picture or philosophical nature, since these give good insight and are rarely written down.

Furthermore, it is recommended in MH08 that in order to prevent distractions due to the increased peripheral attention of Deaf students, it is best to provide a consistent arrangement of seats and seating positions, which will make the environment more predictable. This will assist Deaf students in becoming accustomed to the environment.

Regarding social interactions, the lack of access to informal mathematical chatter is a huge hurdle for Deaf graduate students. Faculty and fellow students alike should be proactive in ensuring that a Deaf student is included. This could mean a strong online text-based community or ensuring interpreters are present at department social events, or in graduate student offices a few times a week, or at study groups. When planning an event, organizers should arrange for interpreters to be there instead of expecting the Deaf student to do it. This can usually be done through a university’s office for students with disabilities.

For all deaf and hard of hearing students, captioning is an option for access. At some institutions (such as the University of Connecticut) students have been offered both interpreting and real time captioning, giving Deaf students more options to follow a lecture. We remark that real-time captioning and its relatives are done by humans who are transcribing what is said, not by automatic captioning, although automatic captioning has made significant advances in recent years. That said, these still have the issue mentioned above about gesture and position of the lecturer being crucial for understanding “this” and “that” in reference to writing on the board. Furthermore, if the lecturer shares video recordings (of any kind), in order to avoid any subtle mistakes, the lecturer should ensure that the video has properly formatted captions, instead of unedited automatic captions.

It is important to note that these best practices are not comprehensive, but they can serve as a starting point for addressing the needs of Deaf students. Our hope is that as the mathematics community becomes more aware of and supportive of Deaf students, we will see an increase in college enrollment and PhD completion. This will impact the representation of the Deaf community in leadership positions and open paths for new generations of Deaf mathematicians. Furthermore, we hope this article will raise awareness about the experiences of Deaf students who require interpreters in classes, conferences, and beyond.

Acknowledgment

Part of this article was written during the first author’s visit to Purdue University. The first author would like to thank Dr. Mark Ward and the Data Mine team for their wonderful hospitality.

References

[BW12]
Viveka Borum and Erica Walker, What makes the difference? black women fs undergraduate and graduate experiences in mathematics, Journal of Negro Education 81 (2012), 366–378.
[CK106]
Pagliaro M. Claudia and Karen L. Kritzer, Learning to learn: An analysis of early learning behaviours demonstrated by young deaf/hard-of-hearing children with high/low mathematics ability, Deafness and Education International 12 (2010), 54–76.
[ES06]
Susan R Easterbrooks and Brenda Stephenson, An examination of twenty literacy, science, and mathematics practices used to educate students who are deaf or hard of hearing, American Annals of the Deaf 151 (2006), 385–397.
[Fig15]
T. Figueroa, Underrepresented racial/ethnic minority graduate students in science, technology, engineering, and math (STEM) disciplines: A cross institutional analysis of their experiences, PhD thesis, 2015.
[GBR20]
Paul Glaser, A study of perceptions of mathematics signs: implications for teaching, Master’s thesis 2005.
[Gla05]
Amanda L Golbeck, Thomas H Barr, and Colleen A Rose, Report on the 2017–2018 New Doctorate Recipients, Notices of the American Mathematical Society 67 (2020), no. 8 (en).
[Her023]
A. H. Herzig, Where have all the students gone? participation of doctoral students in authentic mathematical activity as a necessary condition for persistence toward the ph.d., Educational Studies in Mathematics 50 (2002), 177–212.
[KBK15]
Ronald R Kelly, Harry G Lang, and Claudia M Pagliaro, Mathematics word problem solving for deaf students: A survey of practices in grades 6–12, (2003).
[KLP03]
Raja Kushalnagar, Karen J Beiter, and Raja S Kushalnagar, Optimal classroom views for deaf students, RESNA Annual Conference 2015.
[MH08]
Marc Marschark and Peter C. Hauser, Deaf cognition: Foundations and outcomes, Oxford University Press, 9 2008.
[Pag06]
Claudia Pagliaro, Deaf learners, Gallaudet University Press, 2006.
[PSB03]
Ila Parasnis, Vincent J. Samar, and Gerald P. Berent, Deaf adults without attention deficit hyperactivity disorder display reduced perceptual sensitivity and elevated impulsivity on the test of variables of attention (T.O.V.A.), Journal of Speech, Language, and Hearing Research 46 (2003), 1166–1183.
[SBK12]
Caroline M. Solomon, Derek C. Braun, Raja S. Kushalnagar, Richard Ladner, Daniel Lundberg, Ronald Painter, and Regina Nuzzo, Workshop for Emerging Deaf and Hard of Hearing Scientists: A White Paper, May 2012.
[WRC07]
Kathryn Woodcock, Meg J. Rohan, and Linda Campbell, Equitable Representation of Deaf People in Mainstream Academia: Why Not?, Higher Education 53 (2007), no. 3, 359–379, Springer.

Credits

Photo of Gerardo R. Chacón is courtesy of Yinzu Nairouz.

Photo of Christopher Hayes is courtesy of Stephen DePetro.