17 Accessibility and Inclusive design
17.1 Introduction
17.1.1 Why accessibility should matter to you
(Cliffe 2023) of Bath University’s mathematics accessibility working group answers as so:
Mathematics at university level is
…characterised by the need for a high degree of conceptual and abstract thinking within the learning process… — (Mathematics Subject Benchmark)
We want students to have the processing capacity to engage with concepts and abstract thinking!
Students with a print disability, with difficulties with taking notes, memory and concentration may spend substantial processing capacity on entirely different tasks.
Accessibility is then part of a wider goal to communicate clearly. However, accessibility is distinguished from more general clear communication by a focus on avoiding marginalisisation1 of mathematicians with disabilities. Though the intended target of an accessibility change benefits the most, often the quality-of-life improvements are felt by a much larger population (see curb cut effect). This is why it’s best to view accessibility as an active process in good design, asking how the product can be better for everyone in the audience.
The approach above recommends active thinking about accessibility during the design process — an approach sometimes called “born-accessible” design. The intended contrast is with “retrofitted” accessibility, often present in a mindset that views accessibility as an arcane compliance checkbox to be satisfied after the main work is done. This lazy approach can go wrong in almost every conceivable way: not only does it often lead to an unsatisfactoy solution to disabled people, but it also leads to technical debt that makes the material unpleasant (and expensive) to work with. See (Lazar et al. 2026) for a review.
This document intends to make the core principles of accessibility less arcane, so that mathematics communicators may communicate accessibility almost effortlessly.
- Equality Act 2010 requires organisations to make ‘reasonable adjustments’ towards web accessibility.
- The Public Sector Bodies (Websites and Mobile Applications) Accessibility Regulations 2018 requires public bodies (such as universities) to make their online material to conform to the latest WCAG guidelines, grade AA. Not doing so is treated as a failure to make a reasonable adjustment under the Equality Act. (Department for Work and Pensions, n.d.)
17.2 Theory of disability
This section introduces some modern concepts and observation relating to accessibility. As technology, culture, and the medical establishment changes, specific accessibility guidelines may be obsoleted and superceded every decade. What will change less so is the theory of what accessibility aims to achieve, and how to think about the effects of an accessibility intervention.
17.3 Practical guide to accessibility
17.3.2 List of Resources
- WCAG 2.x overview, web-content accessibility guidelines.
- See also WCAG 3 overview (WCAG 3 is in draft phase as of 2026). WCAG 3.0 intends to cover more types of web interaction, and provide more accessibility guidelines for cognitive disabilities.
- CAST UDL Guidelines, a set of suggestions on how to satisfy the UDL framework.
- London Mathematical Society’s page on accessibility
17.3.3 Accessible diagrams, figures, longform text layout, and other design
idk, this has to go somewhere. Topics include: contrast, logical representation of information, possibly UDL’s “multiple means of representation”. Some select WCAG guidelines which apply outside the web. Basically, very basic design skills which won’t be covered by UDL or technology.
17.3.3.1 Colour contrast
17.3.4 Inclusive design in mathematical communication today
Rapid pace of advancements in technology is increasing the possibilities of what can be done to increase inclusivity of mathematical communication. Given the right opportunity, learners — especially disabled learners and learners from disadvantaged socioeconomic backgrounds — can heavily benefit from technology:
- output accessibility:
- text, audio, video, interactive, VR/XR modalities
- easy physical access to information and content using the internet
- screen readers for vocalisation or braille conversion
- adjustable rendering
- alternative navigation controls
- graph sonification
- refreshable Braille displays
- content digestion, personalisation, and conversion using GenAI
- physical models and demonstrations
- cheaply-available scientific tools
- VR/XR modalities
- input accessibility
- mouse-only, keyboard-only interaction
- mobile-friendly
- reduced motor requirements using predictive AI
- speech input and navigation
- braille input
- electromyography input
- computer vision input
While these tools have great potential to improve mathematical communication, they become inferior or even useless if the communicator does not put in effort to be accessible to these technologies.
Since these technologies are constantly in flux, communicators should focus on these areas at first:
- know the guidelines to make hand-crafted materials accessible
- Know how to make resources maximally accessible with the least effort using software
- Focus on adaptability and future-readiness
Communicators wishing to improve the standards of accessibility should work with institutions and special interest groups.
17.3.5 Accessibility in mathematics
17.3.6 UDL
17.3.7 Barriers to Learning
17.3.8 Materials for Learning
17.3.8.1 Visualisation
17.3.9 Note on AI
17.3.10 Resources
- https://www.lms.ac.uk/policy/mathematics-and-accessibility
- https://www.lms.ac.uk/publications/accessiblemaths
- https://webaim.org/articles/cognitive/cognitive_too_little/
↩︎A spatial metaphor for a process of social exclusion in which individuals or groups are relegated to the fringes of a society, being denied economic, political, and/or symbolic power and pushed towards being ‘outsiders’. (Oxford Reference, n.d.)
Some things are not even covered by the most general definition of “health”.
- A student does not have perfect attendance, does not pay attention in lessons, or otherwise fails to grasp the content of a lesson, for any reason that is not health. An inclusive lesson plan would allow the student to reconstruct the content of the previous lesson(s) without extraordinary effort from the student, and so the student does not fall behind.
- A student is in a situation where silence is mandatory. If they wish to watch a lecture recording or educational video, they must rely on subtitles instead of audio.
- A student’s digital device has broken audio. They are in perfect health, but their equipment isn’t.
At the time of writing (2026), use of AI in education is still controversial. See section on AI for why accessible access by agents is a good thing. TODO fix link↩︎
These notes are written in Quarto, which is built on top of Pandoc. Quarto automatically handles both web design and web accessibility for us; we only need to maintain good semantic metadata.↩︎
17.2.1 Social Model of Disability
Nearing the end of the 20th century, models of disability can be roughly classified into two extremes: the medical model of disability, and the social model of disability:
The long prevalence of the medical model led to the gradual popularisation of the remediative social model in the Anglophone world in the ’80s and ’90s (Wasserman and Aas 2026; Oliver 2013). The social model explicitly focuses on social barriers and their “disabling” impact on people with “impairments”. By slightly reframing disability, the social model recognises that disability is caused by society, and hence society has the power and responsibility to eliminate disability — a goal that is unclear without dichotomising disability and impairment.
17.2.1.1 Inclusive design
Anything property, physical or mental, which can cause disability by the social environment is a useful case when thinking about accessibility. Not everything fitting that criterea automatically qualifies it under the socially-accepted definition of “disability” or into the disability community; alcohol intoxication is not a disability, but public transport design infrastructure with that in mind. Likewise, there are many health conditions2 we wish to be aware and inclusive of.
Here is a non-exhaustive list of conditions you may wish to mindful of:
We often do not even know the audience well enough to know what specific disabilities we should accommodate. Even in a fairly close-knit environment like a classroom, it is easy to miss the presence of certain “impairments”, either because they are undisclosed, undiagnosed, or the effect is indirect (e.g. a sleep disorder). Plus, by making a material fully accessible, it will be ready for new audiences in the future.
17.2.1.2 Curb cut effect
The Curb cut effect is named after the observation that a curb cut, initially intended as an accessibility provision for wheelchairs, started being heavily used by others:
One should not make the fallacy of thinking that only a narrow part of the population benefits from an accessibility intervention. When facing a barrier, some people can get by, some cannot, and others don’t consider crossing until the barrier is brought down.
What curb-cuts can be seen in mathematics communication?
17.2.1.3 Universal Design
A related notion to the curb cut effect is universal design, another term that comes from civil engineering. Universal design us a set of principles intended to allow anyone to use a product or space without difficulty. For example, the Department for Education (Accessibility Manual, n.d.) promotes the following set of principles (see link for their explanation):