Math Accessibility

Why Accessible Math?

STEM Equity

Significant barriers exist in education and employment for disabled people in science and engineering, with 65% of STEM workers with disabilities holding less than a bachelor’s degree education (NCSES, 2023). While 11% of doctoral degrees awarded in 2021 went to people with disabilities, social sciences had the highest rate (13%) and engineering had the lowest rate (8%) (NCSES, 2023). Scientists and engineers with disabilities have a higher unemployment rate than both peers without disabilities and the general U.S. populations (Bernard, 2021).

In spite of significant research and our own lived experience demonstrating the strengths and creativity that disabled people bring the STEM fields, multiple barriers exist to disability inclusion. Faculty mentors who identify as disabled are important as role models, but all faculty can be instrumental in supporting students with disabilities, the science and engineering fields, and ultimately society as a whole.

Information Conveyed by Equations

We know that mathematics is an integral part of engineering content, but have you ever considered the information conveyed in an equation? Glancing at an equation or formula conveys visual information such as the length, hierarchy, complexity, use of parentheses, fractions, exponents, and often the context of the equation. Without the visual representation for support, the cognitive load of forming that same mental picture is much higher. Consider the following versions of this simple equation and the information gained from the spoken and visual representations.

Auditory Version of Equation (click to reveal)

Audio Reading of Equation (Microsoft, 2022)

Transcript of Equation (click to reveal)

Heading level 1 Math equation example 1. Heading level 2 solve for x colon.

Equation two plus three over four, times x, equals x minus, three over four.

Left side constant and term. 2 plus, three over four, times x

Left side constant. 2

Left side term. Plus, three over four, times x

Middle comparison. Equals

Right side term and constant. x minus, three over four.

Right side term. X

Right side constant. minus three over four

Visual of the Equation (click to reveal)

$LaTeX: 2 + \frac{3}{4}x = x - \frac{3}{4}$

LaTeX input into Canvas Equation Editor: 2 + \frac{3}{4}x = x – \frac{3}{4}

Video Demonstration of Alt Text and Screen Reader (click to reveal)

This YouTube video was a keynote address from mathematician Zach Lattin, who shares his passion for mathematics and accessibility in STEM (Lattin, 2022).

Beginning at timestamp 21:30, Zach provides sample alt text for an image and unintentionally illustrates the difficulty of creating a mental picture while unable to see the image.
Zach shares compelling reasons to create accessible math content so that blind mathematicians like him can share the pain of wrestling with complex equations like their sighted colleagues.
He shares the text and symbolic versions of a definition to illustrate the differences between representations favored by various audiences.
He demonstrates the use of a screen reader to navigate through the hyperbolic tangent definition using an equation built with MathType using MathML.
Finally, in his closing thoughts, Zach share how accessibility efforts in STEM fields can be compared to the limit definition of a derivative.

What is Math ML?

MathML (Mathematical Markup Language) is an international open standard for encoding math content. While similar, HTML does not have a standard way to mark up mathematical expressions. MathML uses a Extensible Markup Language (XML) tags to mark up both the presentation and mathematical semantics of equations, which provides access to both the visual representation and meaning of equations for assistive technology. MathML has a number of benefits such as changing font size, translation into native languages and allowing allow users of screen readers to take a deeper dive into the structure of equations using aural (audio) navigation.

MathML provides the highest level of accessibility to math in a digital format, While images with alternative text are considered an acceptable alternative for simple math content that can be accurately described using alternative text (alt text). For more complex equations, however, images with alt text do not provide true comparable access to the information found in equations built with MathML (DO-IT, 2023; Lattin, 2022).

Math Rendering Tools

MathType

MathType is a plugin for creating accessible MathML equations
MathType is a convenient authoring tool with its menu of mathematical symbols and templates, keyboard shortcuts, and LaTeX input capabilities
You can also enter LaTeX directly into Word documents and use MathType to render equations
MathPlayer, from the same company as MathType, is an plugin needed to visually render formulas and equations and to convey the structure and content to screen readers for audible rendering.

EquatIO

EquatIO includes several ways to create math content including typing the equations, using voice dictations, writing equations by hand, and taking screenshots of existing equations.
Output from EquatIO can be an image of the equations or formulas with alt text that would be read aloud by assistive technology such as a screen reader.
Output can also be MathML or LaTeX code that can be used to edit the equation or paste into other applications such as Canvas equation editor.

Canvas

The Canvas Equation Editor can be used to create equations using a simple menu or for more complex equations. You can also create or import LaTeX code to create accessible equations directly on a Canvas page.

LaTex code:

\frac{d\left(\frac fg\right)}{dx}(x)=\frac{g(x)\frac{df}{dx}(x)-f(x)\frac{dg}{dx}(x)}{g^2(x)}

Results from Canvas Equation Editor:

$LaTeX: \frac{d\left(\frac fg\right)}{dx}(x)=\frac{g(x)\frac{df}{dx}(x)-f(x)\frac{dg}{dx}(x)}{g^2(x)}$

Microsoft OneNote and Immersive Reader

Microsoft OneNote and Word feature an immersive reader to read aloud math expressions.
In OneNote, you can use the drawing feature to handwrite math expressions, select the drawing using the marquee tool, and convert the handwriting to text using the Math button. You can see the steps involved to solve the equation, and insert both the equation and solution steps into OneNote.
Solving Math Equations with Math Assistant in OneNote

MathML and Browser Compatibility

Mozilla Firefox directly supports the use of MathML
Microsoft Internet Explorer requires the MathPlayer plugin

EquatIO Resources:

MathType Resources:

Accessible Math Equations with NVDA and MathPlayer Demonstration (YouTube Video)

Accessible Math Webinar

This video hosted by blind mathematician Stacy Scott dives into the complex subject of accessible math. A panel of accessible math content creators demonstrates a possible workflow beginning with an inaccessible image-based document to an accessible math expression experience on a web page. Along the way they demonstrate tools and techniques to manipulate equations in a variety of languages and formats and how screen readers handle different formats.

The presentation slides and transcript are located at the DAISY Creating and Reading Accessible Math (W) webinar page.

References (click to reveal)

Bellman, S., Burgstahler, S., & Chandler, E. H. (2018). Broadening participation by including more individuals with disabilities in STEM: Promising practices from an engineering research center. American Behavioral Scientist, 62(5). https://doi.org/10.1177/0002764218768864
Bernard, M. A. (2021, July 21). Advancing disability inclusion in the scientific workforce. National Institutes for Health. https://diversity.nih.gov/blog/2021-07-21-advancing-disability-inclusion-scientific-workforce
DAISY Consortium. (2021, October 20). Creating and reading accessible math. Digital Accessible Information System (DAISY). https://daisy.org/news-events/articles/creating-reading-accessible-math-w/
DAISY Consortium. (2021, October 26). Creating and reading accessible math. YouTube. https://youtu.be/wufqq72hhcM
Disabilities, Opportunities, Internetworking and Technology (DO-IT). (2021, April 9). What is MathML? University of Washington. https://www.washington.edu/doit/what-mathml
DO-IT. (2017). Using a screen reader. University of Washington. https://www.washington.edu/doit/videos/index.php?vid=81
Lattin, Z. (2022, February 15). Arbitrarily close to access in STEM [Video]. YouTube. https://youtu.be/VMnZuvTcnkc
National Center for Science and Engineering Statistics (NCSES). (2023, January 30). Diversity and STEM: Women, minorities, and persons with disabilities. National Science Foundation. https://ncses.nsf.gov/pubs/nsf23315/report/
National Center on Accessible Education Materials. (2023). Creating accessible STEM materials. CAST. https://aem.cast.org/create/accessible-stem-materials#1
Tanase, I. (2022, August 11). Making math accessible. Microsoft. https://blogs.microsoft.com/accessibility/making-mathematics-accessible/

Math Tool Comparison Table (click to reveal)

This table provides an overview of the types of documents you may encounter, the accessibility of the built-in equation editor in each application, and accessibility of content created with LaTeX, EquatIO, and MathType.

Location	Is the Built-In Equation Editor Accessible?	LaTeX	EquatIO	MathType
Canvas	Yes The Canvas equation editor is LaTeX based	Yes You can directly input LaTeX into the Canvas equation editor or copy and paste from other math tools such as EquatIO or MathType.	Yes You can copy LaTeX from EquatIO and insert into Canvas editor You can copy MathML and insert into HTML code for the Canvas page and the equation will be rendered correctly on the page	Yes You can copy the MathML from MathType and insert into HTML editor for the Canvas page
PowerPoint	No	No Content created using PPT Equation Editor is NOT correctly read by assistive technology. Often parts of the equation are ignored leaving the spoken math equations meaningless to the listener.	Yes EquatIO inserts images with alt text in PPT files Alt text must be verified by subject matter expert to check for accuracy of spoken text. Math ‘punctuation’ must be specified including hierarchy such as fractions and parentheses or brackets. To edit the equation image, you need to take another screenshot to open the equation in EquatIO	Yes But only if you provide the PowerPoint file (not a PDF version of the PPT file) Equations may appear VISUALLY incorrect in the PPT file when viewed in various browsers, including in Canvas. Brackets, matrices, and vectors are common issues. The equations should be read aloud correctly by the screen reader.
Word	Yes But only if you provide the file as a Word doc, which is LaTeX based	Yes The MS Word editor is LaTeX compatible	Yes EquatIO can insert equations as images with alt text. Alt text must be verified for accuracy. You can also copy LaTeX from EquatIO to insert into Word equation editor	Yes But only if you provide the file as a Word doc, which is LaTeX based
PDF	N/A	No	Yes Images with alt text	No
Output	N/A	LaTeX code which could be used in other applications such as Canvas, EquatIO or MathType	EquatIO Output Options Image with alt text LaTeX MathML	MathType Output Options MathML LaTeX Image which would need to have alt text added

Note: All equations regardless of program or tool used must be verified for accuracy, including the visual display and alt text of images.