STEM Solving for X-essability: Equation Challenges

Mary Alvarez and Cherise King

Why are we considering equation accessibility?

Who benefits from accessible equations?

Students who are completely or partially blind
Students who can see, but have focusing problems or dyslexia
Students who want the equation to be a bit bigger
Students listening to content while they drive, do dishes, change diapers, etc.

What is the Goal?

The goal for equations can be a bit complicated. Most of us really want to please accessibility checkers. We also want to ensure that equations look the way they are expected to look. It would also be wonderful if all students could access the content without the assistance of someone else.

In some cases, it's pretty easy to meet all three goals. If you need a simple equation like 3 + 5 = 8, then that's it. Just type it in and you're done. It looks like it should look, it doesn't get flagged by accessibility checkers, and it will be read nicely by screen readers.

In other cases, it's not so easy to meet all three goals. For example, I may need to use the statement $LaTeX: A=\left\lbrace x\in\mathbb{R}\mid x>0\right\rbrace$ . I've added this equation using the equation editor in Canvas. It looks the way I expect it to look and it doesn't get flagged by the Canvas Accessibility Checker. However, it does get flagged by the DesignPLUS accessibility checker and the Immersive reader reads the bar that should be read "such that" as "vertical bar". The statement is not read perfectly, but at least students hear all of the elements of the statement. I also know that the DesignPLUS accessibility checker is asking me to add alt text to the equation, but that alt text will never be heard. So, I don't quite meet all three expectations, but what I have is pretty useful for learners.

A Venn diagram with three circles Accessibility checkers met: Checks the boxes in the accessibility checker being used. Is accessible: Helps students with accessibility needs to actually engage with the content. Looks familiar: Looks as you and most students expect it to. A star is placed in the overlapping section between Is accessible and Looks familiar.

Which of the following options for equations are accessible?

Text

(1 foot)(12 in/foot)(2.54 cm/inch) = 30.48 cm

5x + 2y = 3

½(2x + 3) = 15

All of these are accessible. Some of them, like the first one, don't look very pretty and you may not want to use them, but all of them are accessible. These are written using normal text in Canvas.

Table


1 foot	12 inches	2.54 cm	=	30.48 cm
	1 foot	1 inch

This table looks a lot like the picket fence method used in unit conversion. However, it is not friendly for screen reader users and it definitely will not meet the demands of accessibility checkers.

Image

Conversion set up with one horizontal line running through each conversion , and a vertical line running in between each conversion factor to represent multiplication

Although this is an image of an equation, it includes helpful alt text: "Conversion set up with one horizontal line running through each conversion , and a vertical line running in between each conversion factor to represent multiplication". Screen reader users cannot navigate the equation like they can using an equation editor, but they still have all of the needed information.

Equation Editor

$LaTeX: \frac{1.6\text{ atm}\times 27.0\text{ Liters}}{3.5\text{ moles}\times0.0821\frac{\text{Liters}\times \text{ atm}}{\text{mol}\times \text{K}}}=150.3\ K$

This equation is accessible. It does not need alt text because the code includes what is needed to translate what is written for a screen reader user.

Using Equation Editors

Canvas

To open the Equation Editor in Canvas:

Place your cursor where you want the equation to be inserted.
Select "Insert Math Equation" ( $LaTeX: \sqrt{x}$ ) from the toolbar.
In the Equation Editor dialog box, use the buttons to insert your equation or switch to the LaTeX editor to add LaTeX.
When you are finished adding your equation to the Equation Editor, select "Done".
Resize the equation if needed.

Equation Examples

$LaTeX: x\times y=10$

$LaTeX: x\cdot y=10$

$LaTeX: \left(x-3\right)\left(x+5\right)=15$

$LaTeX: \frac{3}{7x-1}=24$

$LaTeX: \frac{51}{\frac{3}{5}}$

$LaTeX: \sqrt{49}=7$

$LaTeX: 3.2\cdot10^8$

$LaTeX: \sin^2\theta+\cos^2\theta=1$

$LaTeX: \frac{d}{dx}(x^3+2x)=3x^2+2$

$LaTeX: \sum_{i=1}^ni=\frac{n\left(n+1\right)}{2}$

$LaTeX: \frac{\partial z}{\partial x}$

$LaTeX: \sum_{n=0}^{\infty} r^n = \frac{1}{1 - r} \quad \text{for } |r| < 1$

$LaTeX: \vec{v} = \langle 3, -1, 2 \rangle$

$LaTeX: P(A\cup B)=P(A)+P(B)-P(A\cap B)$

$LaTeX: \mu = \frac{1}{n}\sum_{i=1}^{n} x_i$

$LaTeX: \sigma^2 = \frac{1}{n}\sum_{i=1}^{n} (x_i - \mu)^2$

$LaTeX: A=\{x\in\mathbb{R}\mid x>0\}$

$LaTeX: \mathrm{CH_4}+2\mathrm{O_2}\rightarrow\mathrm{CO_2}+2\mathrm{H_2O}$

$LaTeX: m \ddot{x} + c \dot{x} + kx = F(t)$

$LaTeX: m\frac{{d^{2}x}}{dt^{2}}+c\frac{dx}{dt}+kx=F(t)$

Word and PowerPoint

To open the Equation Editor in Word or PowerPoint:

Place your cursor where you want the equation to be inserted.
Select alt/cmd + = on your keyboard or select the Insert tab -> In the Symbols section select Equation -> from the dropdown menu, select Insert new equation
Use the Equation tab to insert symbols and structures or type in the LaTeX code.
1. After inserting LaTeX code, you may need to use the Conversions section of the Equation tab to convert your LaTeX to Professional math.

LaTeX Tips and Tricks

Simplify mathematical expressions if possible: Simplify complex math expressions to improve clarity and reduce cognitive load for screen reader users.
Use Descriptive Text Alternatives to supplement LaTeX: Pair complex equations or chemical reactions or symbols with plain-language descriptions to convey scientific meaning effectively.
- Instead of (or in addition to) $LaTeX: \frac{d}{dx}\big(\frac{ax^2+bx+c}{\sqrt{x}}\big)$ write "the derivative of (ax²+bx+c) divided by the square root of x".
Logical Equation Structure: Screen readers struggle to convey nested fractions and radicals due to their layered verbal complexity. Structure equations so they unfold logically when read aloud by assistive technologies.
Text Elements in Math Mode: Using \text{} ensures non-mathematical words are read as text, improving screen reader interpretation.
- $LaTeX: 8.1 \text{ m}/\text{s}$ is written as: 8.1 \text{ m}/\text{s}
Proper Units Formatting: Using \mathrm{} distinguishes units from variables, preventing misinterpretation by screen readers.
Spacing for Clarity: Strategic spacing commands like \, and \quad create pauses that improve auditory clarity and comprehension.
- $LaTeX: \sum_{n=0}^{\infty}r^n=\frac{1}{1-r}\quad \text{for }|r|<1$ is written as \sum_{n=0}^{\infty}r^n=\frac{1}{1-r}\quad \text{for }|r|<1
Use Copilot to help: If getting started seems daunting, or if you have a particularly complicated equation, use Copilot to help write an equation.
1. Take a screenshot of the equation you want to use
2. Paste the screenshot into Copilot
3. Ask Copilot to write LaTeX code for the equation
4. Copy and paste that LaTeX code into the equation editor

What will students hear?

Before listening to what students hear when there is an equation entered using an equation editor, it's important to pause and discuss the different ways students may choose to listen to their materials.

Screen Readers vs Text-to-Speech

You have likely heard both of these terms. Some people use the terms interchangeably, but there are some differences to be aware of as you build and test your content.

Screen Readers

Who:

Typically students who are blind or partially blind
Often also have an official accommodation

Examples:

JAWS
NVDA
Voiceover
Narrator

What they do:

Read everything
Use HTML code
Can read hidden code

Text-to-Speech

Who:

Students who listen while driving, doing dishes, etc.
May not have an accommodation

Examples:

Immersive Reader
Read Aloud (Microsoft Word)
Read&Write
Speechify

What they do:

Read text (sometimes more)
Essentially copy and paste and read what comes over
Unlikely to read hidden code

Text-to-Speech software

Immersive Reader

The Immersive Reader is readily available for students on Canvas Pages and Assignments. You can test it on your own.

Open a saved Canvas page
Select “Immersive Reader” (near Student View)
Highlight what you want to hear
Select Play

Note: The Immersive Reader is only available on Pages and Assignments. It won’t appear on Discussions, Quizzes, or Announcements.

Read&Write with Equatio

Read&Write and Equation are free Chrome extensions. They are easy to learn how to use and will read more than Immersive Reader does. They work on all webpages. Read&Write can be used on its own, but it does not read equations without the Equatio extension added to Chrome.

In Google Chrome, install the Read&Write Extension and the Equatio Extension
Open a saved Canvas page
Open the Read&Write Extension
Highlight what you want to hear
Select Play

Note: Read&Write only reads equations if you have also added the Equatio extension. Equatio doesn’t need to be open, it just needs to be an extension.

Screen Readers

It is likely that you have a screen reader available on your computer (Narrator for Windows machines and Voiceover for Macs). However, screen readers have a steep learning curve. They are not easy to open and just start using. However, they are extremely useful for some students with disabilities. A screen reader reads everything on the page (and sometimes features not on the page). For example, on every Canvas page there is a hidden "Skip to Main Content" button that allows screen reader users (and keyboard users) to quickly skip the navigation buttons always available in Canvas. This button is built in and crucial for students to have a comparable experience to sighted users. Otherwise, they always have to listen to and tab through all of the navigation buttons.

In the following demos, I used the screen reader JAWS. JAWS is the industry standard. NVDA, Voiceover, and Narrator are all free and have their perks, but it is likely that your students are using JAWS if they need a screen reader.

Word

Notice that the screen reader announces when fractions begin, when they end, include "over" to let me know when I'm moving to the denominator, automatically interpreted units, read subscripts and superscripts correctly, and simplified the way it said the fraction "1 over 12". This is about as good as it gets.

PowerPoint

Notice that the equation began repeating before finishing the first equation. It was not prompted to do so. What you don't see and hear is the difficulty with which the PowerPoint is navigated. I had to select "esc" several times to get out of the first equation. Then I have to use tab to get to the second equation. To get the screen reader to even tell me it's "math content" I have to know to select enter on my keyboard. In short, the math reads correctly, but it's difficult to navigate using a screen reader in PowerPoint.

PDF

Notice that division was never mentioned, the times symbols were read as "x", the prime on omega was skipped, the square root sign was skipped, squared terms were just read as "two", and it is generally difficult to understand what is going on if you close your eyes.

Canvas

Notice that, like Word, it is easy to tell when a fraction starts and ends, where you are in the fraction, what units are used, and that superscripts are exponents. It's beautiful for screen reader users.

Additional Features

Equations built using equation editors in Canvas and Word have an additional benefit of a Math Viewer for screen reader users.

Canvas also includes the added benefit of zoom, highlight, and other features for equations built using equation editors. You can try these out right now by right clicking on the equation below and trying various options in the menu. See if you can make the equation twice as large as it is now.

$LaTeX: \frac{145\text{ lb}}{1}\times\frac{453.59\text{ g}}{1\text{ lb}}\times\frac{1\text{ kg}}{1000\text{ g}}=65.8\text{ kg}$

How a screen reader sounds—Copilot

Do you want to know how your equation sounds when read by a screen reader, but you don't have screen reader skills? Use Copilot to figure it out.

View 1

In a saved Canvas page, right click on the equation.
Hover over Copy to Clipboard and select MathML Code.
Go to Copilot.
Ask, “How will a screen reader read this code? [paste in code]”

View 2

In a saved Canvas page, right click on the equation.
Hover over Show Math As and select MathML Code. Select all of the code and copy it.
Go to Copilot.
Ask, “How will a screen reader read this code? [paste in code]”

What we learned from listening and accessible features

After listening to how equations are read in various applications, it becomes pretty clear that not all formats are created the same. Some are much more accessible than others. Here's our recommendation:

If you can build what you need in Canvas, build it there. Canvas includes excellent screen reading capabilities, but also excellent additional features for all learners.
If you need a document to pass out, build it in Word. Word includes many of the same accessibility features as Canvas and it's fairly easy for screen reader users to navigate.
If you have to have a presentation, you can use PowerPoint. Technically, screen readers can access equations and hear them the same way they are read in Word. However, keep in mind that PowerPoints are difficult for screen reader users to navigate and they are more difficult to make accessible. Consider building your presentations in Canvas and presenting from there. Or creating an accessible Word document first and then building a PowerPoint based on that. You can circulate the Word document and keep the PowerPoint just for yourself during the presentation.
Try your very hardest not to use PDF. PDF does not include an equation editor. The best you can do is add alt text to every equation in your document. If you absolutely must use a PDF, provide an accessible Word document for learners as well. If all of your documents have been created using a LaTeX editor, consider using a service like GrindEQ LaTeX to Word to create accessible versions of your documents. There are other options that will convert LaTeX to html for free and you can use that in Canvas.

Should I use an equation editor every time?

The answer is maybe. You've seen that equation editors can duplicate almost anything you need to present to students. Remember our Venn diagram?

Because of the added benefit of being able to navigate an equation using a screen reader (in Canvas and Word) we highly recommend using equation editors. However, if you try your best to use an equation editor and you still can't get the equation to look like you need it to (ex. picket fence), then use an image with useful alt text. In such an instance, you may want to include extra context around the image to ensure students understand what is going on. For example, the excerpt below is from a lecture on Dimensional Analysis. Equations are used until the picket fences. This way, students using screen readers can explore the equations until they reach the picket fence. In reality, the look of a picket fence isn't that useful for students who cannot see it. It's far more useful for them to have the equation example before the picket fence. The formatting of this content allows sighted and unsighted students to get the best of both worlds.

Dimensional Analysis

What if I want to know how many centimeters there are in 2.5 feet? Well, we do not have a nice handy formulaic conversion for centimeters to feet. But we do have several conversions which are useful. We know that:

1 foot = 12 inches and 1 inch = 2.54 cm.

That gives us four conversion factors:

$LaTeX: \frac{12\text{ in}}{1\text{ foot}}$

$LaTeX: \frac{1\operatorname{foot}}{12\operatorname{in}}$

$LaTeX: \frac{1\operatorname{inch}}{2.54\operatorname{cm}}$

$LaTeX: \frac{2.54\operatorname{cm}}{1\operatorname{inch}}$

Our job now is to figure out how to put together these conversion factors so we can convert from 2.5 feet to centimeters. We start with the number of feet we are given, put in the conversion factors to cancel out the undesired dimensions, and we get our answer:

$LaTeX: \frac{2.5\text{ feet}}{}\times\frac{12\text{ in}}{1\text{ foot}}\times\frac{2.54\text{ cm}}{1\text{ inch}} = 76.2\text{ cm}$

Sometimes this expression is shown as follows where every vertical line indicates multiplication. Both ways are appropriate but you should be sure to understand each!

Conversion using dimensional analysis. Vertical lines separate individual conversion factors and denote multiplication.

Please confirm that we used two conversion factors which are both equal to 1, so we have not changed the original value. The original 2.5 feet is the same as 76.2 cm, or in other words: 2.5 feet = 76.2 cm. I am not saying 2.5 = 76.2 in some kind of bogus math scheme. You should all recognize that 2.5 feet is the same length as 76.2 cm, and so long as we all understand what units are being used, they both refer to the same length value.

Something else I want to bring to your attention: I started out with five length values on the left hand side: 1 foot, 12 inches, 1 foot, 2.54 cm, and 1 inch. I ended up with only one length value on the right: 30.48 cm. Where did they all go?

I did math with the numerical values (2.5*12*2.54) = 76.2, that is clear. But I also did math with the unit values. This was easier: we started out with (feet * inches*cm)/(foot*inch). All together foot/foot = 1: that cancels out. Inches/inches = 1, that cancels out. So I am left with cm. I keep track of that by canceling out the dimensions as I go so I am sure I end up with the right units. Here I have used strikethrough to show how they cancel.

A dimensional analysis problem, shown with units that have canceled each other out in strikethrough text.

If I cancel out the dimensions as I go, I can watch for when I get the right units at the end. In this respect, I keep using conversion factors until I get the units requested. When I get the right units, I know I have the right mathematical value.

Other useful tools

MathType—Started only using images with alt text. Misses the exploration tools available from Canvas and Word.
Equatio—Cool tool. Turns handwriting and images into images. Even allows you to do speech to text.
Mathpix—Worth a try, but may be just as efficient to use Copilot.
GrindEQ—Converts LaTeX documents to Word for you!

Resources

Public Digital Accessibility Course STEM Module
ADS—Can help you know what screen reader users may hear and help troubleshoot difficult circumstances.