Mathematics presents unique obstacles in designing accessible course materials due to the notation and communication styles used. This page aims to introduce practical tips, tools, and technologies that instructors of math (or other subjects with similar notation, including science and engineering) can incorporate in their materials. A specific focus on alternative formats and accessibility for users of assistive technologies is present throughout.
What are alternative formats?
The Accessibility for Ontarians with Disabilities Act (AODA) describes Accessible Formats and alternative formats as materials provided so that persons with disabilities can have equal access to information. While this is commonly used to refer to materials for persons with visual disabilities, others may also benefit from alternative formats, including (but not limited to) persons with learning or physical disabilities. Some features that users might require include: magnification, compatibility with screen readers/text-to-speech software, transcripts or recordings, and many more. Each person accessing these materials will have unique needs.
Practical tips
The following table showcases actions, both small and large, that instructors can take when designing or delivering course materials. These will either directly help students to be able to access content, or help streamline alternative format production for applicable cases. While some tips are more math-specific than others, all of them aim to address typical instruction and assessment styles present in math courses.
When reviewing the tips below, focus on incremental change: consider what steps you are already taking and any additional steps you can easily incorporate into your approach to instruction and content development.
| Tip | Explanation and examples | Rationale | Further consideration |
|---|---|---|---|
| Use headings and other built-in formatting | Built-in formatting for documents and webpages (for headings, lists, images, tables, etc.) should be used instead of simply bolding a title or using dashes for a list. | This structure provides anchor points for navigating effectively with a screen reader or similar technology, and is helpful for all students in locating information more easily. | For digital accessibility more generally, check out Waterloo’s Digital Accessibility and the Accessible Digital Documents & Websites page from the Council of Ontario Universities |
| Keep your source files | If you typically provide students with PDFs, be sure to also save the underlying Microsoft Word document, TeX file, etc. | Different formats and file types are compatible with different types of assistive technology. Providing more options enables more people with diverse needs to access content and allows for easier conversions between formats. | When appropriate, you may also consider making these files available to all students alongside the PDF output (particularly for students in earlier years to be exposed to LaTeX formatting). |
| Give context for complex graphics |
In the content surrounding an image, clarify its general trends or key takeaways. If you would like students to reflect for themselves first, have this appear on a subsequent page/slide. An example follows in the dropdown below. |
Helps to identify why an image is being used and what about it is most important | To understand the challenge and techniques of describing complex images, see Making sense of complex images from Alistair McNaught and other accessibility professionals |
| Prioritize accessibility when choosing textbooks/resources | Avoid poor quality scans or photocopies that are not compatible with assistive technology. Is the textbook available in multiple formats (print and accessible e-text)? | Many e-texts are already well-formatted with accessibility in mind, reducing the delay for students to get the materials they need. | When choosing resources, check if the provider/publisher addresses accessibility on their site (as an example, this Commitment to Accessibility page from Macmillan Learning). |
| In-person instruction: describe and provide alternatives |
Try to avoid overreliance on one medium. Consider recording lectures or posting lecture notes. Make an effort to provide oral descriptions of visual content. One way to think about this: imagine if your lecture was a podcast. Would listeners be able to follow along? |
In line with the UDL principle of representation, multiple means of engaging with in-class content allows people to engage on their own time and in their own way. | The Council of Ontario Universities has resources specifically for Teaching Students with Visual Disabilities, as well as a collection of Teaching Tips addressing many disabilities. |
Example: Giving context to complex graphics
Note: this example was created for this site and is not representative of real-world data.
Providing context
Depending on the reason for using this graph, a student may need to know the general trend of the data, or they may need to know the value of each individual point (in which case a table of values might be a more appropriate alternative format rather than a paragraph description).
To give context, the surrounding content might say something like "An effect of the Earth's axial tilt" or "Is the signed area between the line of Helsinki and the x-axis positive or negative? Ignore all other cities.". You could also highlight or circle areas that you plan to reference specifically, e.g., the trend of one country.
Any of these things helps to guide students when reading or reviewing, as well as helping to guide someone writing image descriptions to ensure that they provide necessary context to engage with the material while not being overwhelming.
Providing alternative text
The alternative text given for the image on this web page says "A line graph showing the average temperatures across 12 months of 5 cities with various climates.". It is written in this way because that is all that is relevant to its purpose on this page.
In contrast, the alternative text written for this image in a lecture may say: "A line graph. The y-axis is labeled “Average Temperature (°C)”, ranging from -10 to 35 in increments of 5. The x-axis is labeled with the months of the year. Five lines are graphed: Helsinki Finland, Muscat Oman, Quito Ecuador, Windhoek Namibia, and Wellington New Zealand. Helsinki and Muscat both have their highest temperatures in July-August and coldest in January-February, though Muscat is consistently much warmer (20–34 degrees, as compared to Helsinki’s -5–13 degrees). Windhoek and Wellington show the opposite pattern: they are warmest in December and January, and coldest in July. Quito has very consistent temperatures of approximately 11 degrees all year."
Tools and technology
Depending on how the content is presented, some of these tools may be more practical than others (or a combination of many of them). Each tool has benefits and limitations for both the creator and the end user. Tools may also be more time-intensive to learn and adopt, so they may be more useful as a course is being (re)written so that they can be integrated during the course development process.
Some work has been done to examine the accessibility of LaTeX and the ease of conversion to other, more accessible formats. Internally, this was done through the Faculty of Mathematics Equity Office. Other universities have explored this as well: a helpful starting point is the University of York’s Creating accessible formats from LaTeX guide and template.
Preliminary exploration into these tools was largely focused on their ability to produce equations that can be read clearly by screen readers and text-to-speech software. Further exploration should be done to assess which tools can best support the needs of the most students.
Equations in Microsoft Word
Out of the technologies presented here, this is probably the most approachable as most people tend to be familiar with Microsoft Word. Documents with equations work particularly well in Microsoft Word because they display cleanly and as expected while also integrating well with Microsoft’s own Read Aloud feature, found under the "Review" tab. This feature functions as a text-to-speech software for these documents. In some cases, this format may eliminate the need for outside support or intervention, and if not, it is a useful format for AccessAbility Services staff in developing alternative formats.
There are many input methods, including LaTeX as well as a fairly comprehensive menu of symbols, and the ability to save your own presets for commonly used equations.
Read Aloud example
This equation was originally written in a Microsoft Word document and was read by Read Aloud as “Integral of numerator 1 plus x end numerator over square root of 1 minus x squared end square root dx end integral”.
Math on web pages with MathJax
MathJax allows users to input math notation in LaTeX, MathML, and more. It is then displayed on web pages in a clean and consistent way that is searchable and interacts well with assistive technology (particularly screen readers).
To see what this can look like: it is used to display equations in some places on CEMC’s website (particularly Problem of the Week, ex. Points on an Ellipse). Right click on any equation to see a menu with accessibility settings and the input that was used. It is verbalized by screen readers similarly to the Microsoft Read Aloud example above.
Handwritten math recognition with MathPix
MathPix allows users to upload or take pictures of handwritten content, which it will recognize and convert. While other similar tools exist for handwriting, MathPix’s specific focus on math allows it to recognize complex notation that is more common at the university level.
They currently operate on a subscription-based model, but as of December 2024 they offer a limited “Free & Educational” version to try and see if it might be useful.
Resources and further consideration
One resource for further exploration is the Accessible Maths page from the University of York. This page shares further practical and technical tips for improving accessibility in math courses, as well as a section on User Stories, showcasing the perspectives of instructors and students.
For example, the Accessible Maths Journey article shares stories of a blind student who studied math at York and a tutor, transcriber, and learning technologist who worked with her throughout her degree. Stories like these highlight the challenges students may face when engaging with math using assistive technologies, but they also show a team of people who came together to recognize and support the needs of a student who went on to succeed in her program.
There are many people who want to and are capable of studying math at a high level, and can succeed provided that the necessary supports are in place so that they can fully engage with their studies. As Tim Nolan, former director of Student Accessibility Services at McMaster, said: “If you build it, they CAN come. By creating a more accessible campus, students of all abilities can attend and thrive” (McMaster News).
Empathy for the end user is key for making meaningful change towards accessibility. Be open to learning about other’s strengths, needs, and experiences. A willingness to learn will help advance accessibility within mathematics education and research.
This web page was developed by Marshall Cowie, an undergraduate student in the Faculty of Mathematics and co-op student with the Campus Accessibility team. If you have any comments or suggestions, please contact aoda@uwaterloo.ca.