Geometry Telephone: Designing a Math Course with Inclusive Education Principles

By Melinda Lanius, Assistant Professor, Auburn University

Melinda Lanius

How do you effectively teach visual geometry asynchronously online to a student with a visual impairment? How do you effectively relay mathematics via one-way telephone? While this question might be an interesting thought experiment for most educators, it was a very real and intimidating question posed to me last spring because I was about to attempt just that: effectively teaching visual geometry to a student with visual impairment. In this blog post, I will reflect on my journey and the lessons that I learned about course design that I plan to use moving forward in all classes and for all students.

To provide context, in Summer 2021, I was given the unique opportunity to propose and develop the materials for an asynchronous online introduction to linear algebra course at the University of Arizona. With the excellent support (and cheerleading) of the math department’s online education expert Michelle Woodward and academic technology expert Cheryl Ekstrom, I was quickly designing interactive and highly visual videos following the Quality Matters rubric for online course design [1]. My flavor of linear algebra grounds every concept in a geometric question before building algebraic machinery to compute. For example, solving a system of linear equations is first posed as understanding the intersection of a set of planes in 3-space. I somewhat had accessibility in mind as I worked. For example, I researched which color combinations to avoid and which ones to use in case a student was color blind (coincidently, the UArizona red and blue make a very colorblind-friendly palette).

Three planes in UArizona colors intersecting at a point.

When I learned I had the opportunity to guide a student with visual impairment through a more geometric linear algebra, I honestly was afraid. Every student deserves quality and I didn’t know if I was capable of delivering. If the class had met in person, I imagined 3D printing models for the students to manipulate and being able to clarify topics in real time. How would this possibly work asynchronously and online? Quickly, the Disabilities Resource Center on campus reviewed my materials and gave me candid feedback on their accessibility. I will briefly walk through those recommendations and how implementing them taught me valuable universal design lessons to incorporate into all of my future courses.

Recommendation 1: Create notes suitable for a text-to-speech reader.

Coincidentally, the text-to-speech screen reader we used is called JAWS and that summarizes how I felt the first time feeding in my hand typed notes and hearing the output. The system is extremely literal and announces all punctuation. For example, R_2 (my convention for labeling the rows of a matrix) became “R underline 2” to JAWS. JAWS had no idea what to make of matrices. I learned to type “begin matrix 1 0 bar 1 next row 0 1 bar 3 end matrix” for a two by three augmented matrix. Through trial and error, I came up with conventions that were understandable when converted to speech for all of the standard linear algebra notations. The key was to type verbatim what I would regularly say during a lecture, rather than what I wrote on the board.

Universal Design Lesson 1: Provide written words to caption any symbols used.

There is a large discrepancy between the symbols we write during lecture and the words we speak. For a student who is only seeing this mathematical notation for the first time, it is very easy to get lost. For example, I might write bold R squared but say 2-space. Moving forward, I will train myself to caption any symbols with the words that those symbols are meant to convey. For example, I would map the words I say to their corresponding written symbols for span in the following way:

Recommendation 2: Provide descriptive captions for images.

My first attempts at providing alt text (i.e. the written copy that appears in place of an image on the web in the event that the image cannot be displayed or seen) were awful. For example, I provided details on each and every color used. This is saying way too much, while also not explaining why I even included the image in the lecture in the first place. The key to useful alt text is to keep it brief and to convey why the image is there. What is the student supposed to understand after having viewed this graphic?

Universal Design Lesson 2: Briefly describe what students should focus on in an image.

A picture may be worth 1,000 words if you know what you’re looking for. Captions help all students because they indicate what they should be focusing on and why. Moving forward, I will train myself to describe the important artifacts of an image and what the image is meant to convey.

Finally, I also want to offer two process tips in providing effective accommodations and building a more inclusive course design.

Tip 1. Be kind to yourself, take in feedback, and keep working at it.

Feedback isn’t a personal criticism; it's just feedback. I stumbled over the speech-to-text software. At one point my student used speech-to-text software to email me: “Is the class listed Math 313 dash 101?” I was so confused. I thought maybe there was a dashboard where students register for classes? How do students even sign up for classes at the University of Arizona? Only after emailing back and forth several times did it occur to me that the student was asking to verify my course section number: Math 313-101.

I also had instances of poor choice of phrase in the middle of recording a lecture video that were mortifying. For example, I once said, “Don’t just blindly follow this algorithm.” How insulting! Instead of saying what I meant—don’t use an algorithm without considering the consequences—I conflated blindness with thoughtlessness. I deleted the recording and started over.

Tip 2. Communicate with students.

Most campuses provide a letter describing the requested accommodations for a student. Note that these are usually a bare minimum to meet a legal requirement. To fully support students, I think we should push beyond what the letter asks for. While being mindful of privacy (NEVER ask a student to explain a disability), you can inquire if a particular accommodation is working effectively for the student’s learning process. This is especially important as accommodation letters are generally several years behind technology innovations. When uncertain about how to support your student, don't guess, just ask!

My work to ensure accessibility for my student and then understand how that accommodation benefits all students, not just the one who requested it, is an example of inclusive education principles. (See [2] for a discussion of this movement and its current role in higher education.) Inclusive education is the belief that we should strive to build education that allows ALL students to actively and fully participate. This mindset celebrates differences and sees accessibility accommodations as a way to improve the current system to benefit everyone. Accommodations are not a headache, but rather present a valuable opportunity to improve a system that continually marginalizes folks with disabilities.

References:

[1] https://www.qualitymatters.org/qa-resources/rubric-standards

[2] Anabel Moriña (2017) Inclusive education in higher education: challenges and opportunities, European Journal of Special Needs Education, 32:1, 3-17, DOI: 10.1080/08856257.2016.1254964

Melinda is an assistant professor of math discipline based education research at Auburn University. In her spare time, she enjoys outdoor adventures with her dog Johnny, long distance running, jigsaw puzzles, and podcasts.