Today, I’m reflecting on vision and mathematics. That’s largely because as I write this, I’m also simultaneously evaluating whether a new computer I received as an early Christmas present is going to be a good fit for me or if I’ll need to return it in favor of one that I find more accessible given a specific set of eye muscle problems I have. Those eye muscle problems cause images to double, switch back and forth, or even twist in a way that can best be described as appearing to be melted.

Even as a kid, I thought “wandering eyes” and “lazy eye” were pretty mild descriptors for what I was experiencing: wonky eyes that mostly seemed to operate out of their own accord and without consulting one another. For instance, sometimes I just couldn’t keep one eye from turning in towards my nose. So, for a good chunk of the day, I would be trying to learn or play while also getting constant and disruptive views of my nose. Without being able to do anything to change the images I was receiving. Talk about distracting and frustrating. Often, glasses on or glasses off, I couldn’t see very well.

Somehow – I’m still not 100% certain how – I thrived academically, though I was never given the option of receiving academic accommodations for my vision issues until I reached college. Even then, my vision issues greatly impacted my education and the quality of life I experienced while I was in school. I had to work incredibly hard to master concepts that I knew wouldn’t be so challenging if I wasn’t visually impaired. I graduated, triumphant but burned out from having to push myself so hard to excel despite my visual disability, and uncertain that I wanted to attend graduate school, despite my deep love of math.

Things are better now. After I was told at age 24 that my only option for ameliorating my double-vision was for me to wear an eye patch at all times for the rest of my life, I got fed up and pursued a direction that is still controversial in the medical community: vision therapy. Specifically, mine is a combination of exercises and a virtual reality program in which I play games designed to help my eyes work together more effectively. Two years into therapy, things are better now, but I still have a long way to go on my journey to better vision.

Reflecting on all of this, I don’t think we talk enough about mathematics and vision, or about how vision problems can affect mathematical education. As a student, when I was struggling because of vision issues, sometimes I felt lost about how to begin discussions with professors about the medical challenges I was facing and I often wasn’t aware of the options that might have been available to help me in different ways.

Below is a short list of pieces related to the topic of mathematics and vision problems.

“Math Adaptations”

On this post for the “Teaching Students with Visual Impairments” blog, Carmen Willings provides links to resources related to teaching different math concepts to students, from numbers and counting to geometry and spatial sense.

“Guidelines for Collegiate Faculty to Teach Mathematics to Blind or Visually Impaired Students”

Al Maneki, senior STEAM advisor for the National Federation of the Blind Jernigan Institute and retired mathematician, wrote this document. Maneki is blind. “The news that a sighted mathematics faculty member in a two- or four-year college program will have a blind student enrolled in a course at any level is all too often greeted with disbelief, panic or resentment. The common assumption is that it is impossible for a blind student to learn or comprehend any mathematical material, given the supposedly highly-visual nature of this subject. This initial reaction immediately places a barrier to the effective teaching of mathematics to a blind student by a sighted faculty member. It is important for us to overcome the difficulties that these negative stereotypes place in the effective teaching and learning of mathematical subjects,” he wrote, adding “In this document, our aim is to provide a set of guidelines to assist two- and four-year college faculty members to provide meaningful mathematics instruction to blind and visually- impaired students.”

“Teaching Math to Students Who are Blind or Visually Impaired”

In this webcast, presenter Susan Osterhaus begins by describing her early experience with teaching at the Texas School for the Blind (now the Texas School for the Blind and Visually Impaired). When she began there in 1978, she had never taught blind or visually impaired students and didn’t know the Nemeth code – the Braille code used for math and science. She went on to teach herself – and fellow staff – that code.

Here’s a poignant excerpt:

“I knew, you know, virtually nothing about teaching the blind and visually impaired. And, in fact, in those days, unbeknownst to me, a lot of people really didn’t feel that a blind person could go on into higher mathematics.

Let me put it this way, the average person. We have our geniuses, you know, that just happen to be blind and so forth. But the average student who was blind was thought to, you know, not really have any hope of going into higher mathematics and so forth, that it was such a difficult subject. Well, anyway, I didn’t know that and so I just jumped in.

And bottom line, when I started in 1978, the highest level of mathematics taught at our school, at least, was a kind of a two-year, I’d say equivalent to pre-algebra nowadays. And now we have students taking calculus, scoring fives — five, that’s the highest you can score on an AP calculus exam. So we proved them wrong, those other people.”

Osterhaus also discusses tactile graphics and other accessible math materials, applying a multi-sensory approach to and universal design to math instruction for all students, issues and challenges with standardized testing for students with blindness or visual impairment and more.

“Math blind”

In this post for the Backreaction blog, Sabine Hossenfelder, author of “Lost in Math: How Beauty Leads Physics Astray,” reflects on Andrew Hacker, her daughter’s vision (one of Hossenfelder’s daughters doesn’t have stereo vision) and what she calls “being math blind.”

“You can lead a pleasant life without mathematics because it’s possible to fill in the lack of knowledge with heuristics and anecdotes. And yet, without math, you’ll never see reality for what it is – you’ll lead your life in the fudgy realm of maybe-truths,” she wrote.

Also, if you haven’t seen it before, don’t forget to check out Allyn Jackson’s 2002 article “The World of Blind Mathematicians” for Notices of the AMS.