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Accessible maths

From retrofitting to inclusive design?

Emma Cliffe

Mathematics and Statistics Resource Centre University of Bath

Universal design

  • Meet the naturally varying needs of a diverse student population
  • Recommends provision of multiple means of engagement, representation and action
  • Creating inclusive learning environments by design is generally more effective than trying to retrofit access when students present with specific requirements

But what about in the mathematics department?

Health warning: This is a huge topic. I was asked to cover: LaTeX, not Word; notes and boards; how can equations and graphs be universally accessible? Universal curriculum design would need more but we all have to start somewhere.

Diverse student population

Naturally varying needs

Why? The Legal

"A person has a disability [...] if he or she has a physical or mental impairment and the impairment has a substantial and long-term adverse effect on his or her ability to carry out normal day-to-day activities."

  • Ensure disabled students are not unjustly disadvantaged or unfavourably treated due to their disability.
  • In a proactive manner, make anticipatory reasonable adjustments to resolve barriers to access.
  • In addition to anticipating barriers staff should make reasonable additional adjustments if barriers remain.

Example anticipatory adjustment

"A university recognises that making an adjustment to provide handouts in advance in electronic format is a common anticipatory need for disabled students, for example students who lip-read, students with dyslexia and students with visual impairments. The university makes this adjustment and agrees timescales to ensure all staff have teaching notes available in this way. This is an example of an anticipatory adjustment."

From the Equality Act (2010) guidance

Example additional adjustment

"It may be appropriate for a university to install a hearing loop in all its lecture theatres to anticipate deaf students’ needs, but it may not be reasonable for it to have a British Sign Language (BSL) interpreter on its payroll prior to any deaf students being admitted to the university."

From the Equality Act (2010) guidance

Why? The reality

In the UK HE, disability disclosure rates have increased from:

  • 5.4% (119,545 of 2,200,175) in 2003/4 to
  • 11.3% (256,995 of 2,280,830) in 2015/16
(Equality Challenge Unit, 2017)

Why? The mathematical

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

Why? The practical

  • Adventurous young people break thumbs, hands, wrists, arms, collarbones, coccyges...
  • Students come with smartphones pre-installed: They want and expect resources which work well on these devices
  • Mature students lead busy lives and, also, might be juggling that smartphone with reading glasses and caring responsibilities
  • Life happens to students too, sometimes Gran dies or they get stuck in Denmark or their girlfriend gives birth or they are quarantined due to a measles outbreak...

Visible and authentic recognition of diverse needs can lead to a positive learning environment

Multiple means

Of engagement, representation and action

Quality Assurance Agency for HE (2015)

Learners benefit from seeing arguments developed [...] in 'real time' [...] Traditional board-based lectures continue to be widely used, often augmented by more interactive teaching approaches.

Equality and Human Rights commission (2011)

A common anticipatory adjustment of providing resources in advance in electronic formats.

What we want...

For all students to follow the lecture and to engage with the concepts and arguments!

We don't want other tasks e.g. careful copying to take precedence.

A blurry photo of a blackboard containing mathematics standard LaTeX print notes
  • "[I am] struggling to make accurate notes during the lecture."
  • "Without the lecture notes there is no point in being there"
  • "The notes our lecturer uploads [...] are in hand-written format which I find extremely difficult to read"
  • "notes in text [...] would significantly facilitate my learning"
  • "My eyes don't especially like the font and it is all a bit close together."
  • "I often find my eye wanders around the page with some of the fonts that are used making it really difficult to follow what is being said/asked"
  • "I wondered if I could get some editable ones as theres lots of gaps and font size changes on the PDFs online which make it really hard when I'm trying to read them."
  • "Speech doesn’t work..."

Mind the gap!

  • Computers rely on structural integrity to process maths:
    • PDF, print, PowerPoint, handwriting and E-books using images of maths cannot be processed (DEMO)
    • They are inaccessible and inflexible on, for instance, small screen devices. They are lossy formats for maths!
    • Word and HTML based formats have structural integrity and are accessible to many assistive technologies
  • Using a computer and/or assistive technology to take mathematical notes is a specialist skill!
  • Using assistive technology effectively for maths requires authors to produce accessible materials

But why might a student be using technology to do maths?


Exceptional variation in neurocognitive processes

Graph of a spiky profile
  • Noticeable and unexpected weaknesses when compared with verbal and/or visual abilities for a given individual
  • Tasks of learning, remembering, time management, social interaction, attention span, fine/gross motor movements


Dyslexia mainly affects the development of literacy and language related skills. It is characterised by difficulties with:

  • Phonological processing
  • Rapid naming
  • Working memory
  • Speed of visual processing

This can result in difficulties with reading, writing, spelling, sequencing and memory. Areas of relative strength might include, for example, verbal comprehension, visual reasoning, and holistic, rather than sequential, processing.

Areas of difficulty in maths

  • Overload of working memory, focus, worse if anxious
  • Processing visual content within a time constraint
  • Retaining mathematical associations between symbol and concept throughout a text
  • Reading errors: May use text to speech to support literacy
    • Layout, font and style of "traditional" mathematics texts can add to processing difficulties
    • Working memory may be overloaded when processing conceptually abstract or multi-step material
  • Copying errors from line to line and between media, symbol confusion/reversals, word/symbol substitution
  • Combining multiple aspects and sequencing in procedures, arguments or proofs


Dyspraxia affects the planning of what you do and how you do it. It is associated with problems of perception, language and thought and is characterised by difficulties with:

  • Motor coordination, including handwriting, drawing etc.
  • Speed of visual processing
  • Visual reasoning
  • Working memory

This can result in difficulties with organisation, attention, spatial awareness, managing time and space, sequencing, memory and written expression. Areas of relative strength might include, for instance, verbal comprehension, verbal reasoning and 'out of the box' thinking.

Areas of difficulty in mathematics

  • May have similar difficulties with processing speed and working memory as experienced by students with dyslexia but reading/spelling not specifically weak
  • Spatial issues and weaker visual reasoning can have specific impacts e.g. geometry, concrete questions in 2D or 3D, seeing symmetry and structure
  • Notetaking/solutions may be very difficult to read back, inaccurate and incomplete
  • Drawings of figures etc. may be hard to follow
  • May produce non-standard solutions

Autism Spectrum Condition

Autism spectrum conditions are characterised by difficulties with:

  • communication
  • flexibility of thought
  • the social environment
  • sensory stimuli

This can result in difficulties with processing information, change, seeing another's point of view, concentration in presence of sensory stimuli and communication with peers. Areas of relative strength might include, for instance, a high level of focus on mathematics of interest, logical thinking, appreciation for detail and complexity of arguments.

Example difficulties

  • Concentration and focus in lecture and other busy learning environments
  • Processing information, deciding on what is important, notetaking and summarising
  • Adapting to a new way of learning mathematics, flexibly transferring mathematical knowledge
  • Seeing connections and the 'big picture'
  • Adapting to less deterministic outcomes - e.g. that answer may no longer be simply right or wrong
  • Motivation in areas of mathematics which are not of personal interest

Mental health issues and other conditions

Students with mental health issues, conditions which cause pain, fatigue or restricted movement and students with sensory impairments may experience difficulties with:

  • With concentration, memory, motivation and organisation
  • Reading standard print effectively, following real time exposition and taking notes simultaneously
  • Using handwriting to take personal notes or to complete rough work
  • Producing legible handwritten mathematics
  • Using a standard computer or using their assistive technology to communicate mathematically and to access mathematical resources and software

In the maths department

A 15 year journey...

from retrofitting to(wards) inclusive design


The journeyman years, or, tilting at windmills

Seriously though, LaTeX is Turing Complete. You can program in it. Which means non-trivial properties of the behaviour of 'documents' written in LaTeX are undecidable. To know what output a 'document' produces you have to be TeX.

But, we had no other plan

  • 2005/6: A blind student, specially produced notes
  • 2006/7: Partially sighted student, specially produced notes; other disabled students offered these notes
  • 2007-present: Only one academic year in which we had no maths student with visual impairment
  • 2007/8: Student offers LaTeX; secure web delivery
  • 2009/10: Admin support starts
  • 2010/11: Interpretation of "anticipatory measures"
  • 2011/12: HESTEM, fragile single master & conversions
  • 2012: Student declares visual impairment during term 1
  • 2015/16: Substantial changes to technology; produced single master more robust to conversion
  • 2016/17: Supported academics who wished to in updating single master; conversions available on a central server
  • 2017-present: Continued rolling boulder up hill

Who gets the notes?

Department of Mathematical Sciences. Lecture notes and audio recording. I accept that the material included in the lecture, notes and any recording made of the lecture is protected by copyright and may be used only for my own personal study. I will not make or distribute copies nor allow any other person to have access to or use the notes or any recording. I acknowledge that the lecture or the notes may contain accidental inaccuracies and that it is intended to be used in conjunction with other materials or sources and my own self study activities. I understand that the future supply of notes/permission to record lectures is dependent on my keeping to this condition.
clearly printed LaTeX print notes web format notes with equation enlarged
  • "The combination of notes I have prior to lectures and the narrative that lecturer add, enables me to determine words and equations written on the board."
  • "I have been finding them [clear print notes] much easier to read compared to other resources from lecturers"
  • "My plan is to print the [clear print] PDFs into OneNote which should enable me to annotate them during lectures"
  • "[It helps to] have notes and handouts laid out electronically, well-spaced out and so I can search within them using my computer"
  • "The clear print notes are incredibly useful."
  • "I would just like to say thank you. This service has been a great help over the last few years. Thank you very much for organising it and for providing quick help when it was needed."

We can also help staff out...

"in the case of [course materials the university] shall retain the right at any time to use, reproduce and adapt such materials freely for legitimate purposes."

2005-2019: We produced, preserved, maintained, updated, fixed and recovered LaTeX, returning it to staff as needed.

The future? Our main LaTeXer says "establishing a common standard for producing notes is the best way to not only produce accessible notes but to ensure easy transition between lecturers for a course"

  • "Currently we don't have a set of typed lecture notes. I was wondering if by any chance you had a large printed version of notes from previous years and if I could use the tex-file. It would save me an enormous amount of time"
  • "Here is the latex file for the notes, which [...] I am not able to compile" ... "Thank you - I was able to compile them!"
  • "This is tremendously helpful and saves me hours of work."
  • "If you have the LaTeX versions and would be able to send them to me that would be very helpful"
  • "We recovered the source via optical character recognition and human checking and correcting for a student last year and I attach this." ... "Many, many thanks"
  • "I am colour-blind [so] am unable to read [it]" ... "That's really helpful. I'd assumed there was nothing I could do about it."

Inclusive design?

It has been proved that we cannot convert LaTeX into formats needed. We have unlimited freedom and extensibility, which most of us do not use nearly all of the time. Either way we will need to give up some of this freedom, we each have a choice about what that looks like.

Hobson's choice

  • Use LaTeX and old school ways of producing graphs, try to keep, without guidance, to transformable subsets. Use tools which may or may not work and that cannot tell you, in general why something doesn't work.
  • Use R Markdown, incorporating LaTeX for equations and a simple markup language for the rest of the document. Learn to use emerging tools for creating accessible graphs. You will be confined to transformable subsets but you will be in control and will retain a quick compile loop. It is still extensible, just more reasonably so.


So, why not decide now to try it for new student facing documents?

The worst that will happen is you might have to quiz some statisticians on how to get R Studio working and use an hour or two to decide whether this will work for you. It will be much faster than trying to roll the boulder up the hill.

And we still get to keep the full power and glory of LaTeX for wondrous adventures in extreme typesetting in the rest of our working lives, when the boulder problem belongs to the publisher.

Next steps

Questions and discussion

These slides are available at:

My email address is:

Mathematics and Statistics Resource Centre University of Bath