On 21st February 2011, I gave a presentation to the Maths, Statistics and Operational Research (MSOR) Network, which is one of the 24 Subject Centres supported by the Higher Education Academy. It was on how to make mathematics online accessible to disabled students. This blog post summarizes the issues presented. The presentation and the blog post draws on experiences over the last 5 years or so at the Open University in seeking to address this challenge and I acknowledge with thanks my colleagues Tim Lowe and Jonathan Fine in helping me to compile those.
What is different about maths?
In written English it is the linear order of letters that conveys meaning. In Maths it is the 2 dimensional relative positioning of symbols, their relative sizes etc., that codes meaning. Maths is a symbolic language whose representation aids its manipulation. Examples of this are the way we readily cancel identical terms in algebraic equation, or the mantra I learnt at school for simple differentiation: “bring the power to the front and reduce the power by one” which soon becomes visualized around the symbolic representation.
This facilitation may or may not be persevered in alternative representations intended for disabled people; if not to what consequence? Because of this symbolic nature Maths raises additional issues when presented online in a learning context than an alphabetic language.
Maths issues across a process
How Maths is encoded is a web resource is only part of the challenge there are lots of interrelated issues from the facts that:
- The Maths needs to be authored by lecturers and different tools are available for this
- As well as the standard encoding in “main resource” in a VLE or other Web resource transformation to alternative formats will be required to meet the needs of some disabled students
- How the Maths is presented to the student depends on browser renderings (which vary) and client-side transforms e.g. speech synthesizer with refreshable Braille display
- Students need to be able to interact with the Maths not just passively read it; they need to copy it into documents, manipulate it and then communicate it with their tutors
- This student/tutor interaction may have to be facilitated by online communication in the symbolic language of Maths
- The challenges of Math need to be address in formative and summative assessments too
Issues of Encoding
Which way of encoding maths in a web page is most accessible? There is no one simple answer to this question! There are two major options:
- Images with alt-text descriptions
- Specialised maths mark-up – MathML
Encoding as images
With Maths encoded as images (e.g. generated from LaTeX) it is possible to implement the technology so that these images can be enlarged and colours changed; key access techniques for some visually impaired people and some with dyslexia. For those who can not see sufficiently Alt-Texts to such images are a possible solution but for simple maths only. Alt-Texts can be transformed to speech or Braille but this can be problematic and creating suitable Alt-Texts is not easy for complex expressions.
Encoding as MathML
MathML is an XML based mark-up language. There are two forms of MathML: Presentation Mark-up (how the mathematics should look) and Content Mark-up (which describes the semantics). The standard allows these to be used individually or in combination. Some of the accessibility advances of MathML derive from Presentation Mark-up some from Content Mark-up. However Presentation Mark-up alone is most commonly used and this restricts the potential accessibility advantages
Issues of Presentation
Where someone is not able to access the normal Maths presentation there are two possible tactics:
- Transform the visual representation into a form that can be accessed, or
- Provide an alternative means of accessing the underlying semantics (meaning)
Presentation to the student (or any user) is dependent on: the underlying coding of the Maths in the web resource; transformations made server-side (at the University) and how the browser interprets that code (inc. plug-ins). Transformations may also be made client-side (by the students’ computer and/or assistive technology).
Note on Maths & Braille
Braille is important to some visually impaired learners but <15% UK blind people (all ages) are competent Braille users. Some blind mathematicians extensively use maths Braille although a small percentage of blind people ever learn this. There are numerous variations in the way maths is encoded in the Braille schemes of different countries. Firstly English as represented in the Braille codes of the UK and the USA, for example, differ considerably; then UK Maths Braille differs from Nemeth Code commonly used in the USA and Marburg used in Germanic countries. Alt-texts of Maths expressions rendered as Braille by a screenreader and refreshable Braille display are not expressions in Maths Braille but Braille equivalents of the English descriptions of the Maths. A University’s response to the needs of Maths Braille users If a students preferred way of interaction with maths is through Maths Braille all reasonable steps should be made by the educational establishment to accommodate this. The Open University uses specialist external transcription agencies for this for course texts. However online presentation can be more challenging; e.g. in some formative assessments mathematical expressions are parameterised differently on each visit by the student. It can be difficult to accommodate the needs of Maths Braille users in such circumstances depending on implementation.
Issues of Interaction
Maths presented online is not to be just passively read. Students need to interact with and manipulate the Maths. They may need to:
- Copy it into documents
- Import it into maths engines (Mathematica, Maple, etc.)
- Exchange maths expressions with tutors and peers in forums, e-mails, etc,
Issues of Pedagogy
Mathematics is used differently in different contexts. For example compare level 3 Maths course with the basic calculations in an introduction to social-science course. What learning path are we a seeking to take the student through over their period of study? For the disabled student this might include a transition in the way they interact with mathematics. There is a long asked question here: how do people learn. In this case the question is made more complex by the secondary question: how do different presentations of Maths affect the learning? Don’t forget assessment! Techniques students use in their learning must be available in their assessments both summative and formative.
Current Practice at the OU
The Maths department normally writes courses in TeX; however other departments/faculties vary and includes the use the Equation Editor for Word. For long texts PDFs are produced with figure descriptions. Audio descriptions maybe recorded e.g. as for MU123 (pre-calculus basic level maths) ~ 3,500 students / year. The VLE program (2005-2008) produced a MathML filter – if MathML there it can be displayed. Graphics presentation or access to MathML is selected as a user option.
Browser Issues – Issues of Support for the OU
[This section updated following personal communication from Paul Topping, President and CEO, Design Science, Inc.]
There can be problems for a student setting up for MathML (different browser issues). IE requires a plug-in from Design Science called MathPlayer (they are currently developing the plug-in for I.E. 9.0). Firefox does not support MathML in HTML but does support it in XHTML. Chrome, Safari and Opera web browsers support MathML natively (however there are some version and consistency of display issues). This presents an IT support challenge so for this reason the OU-VLE defaults to displaying images.
MathML in the OU-VLE
User’s can select if Images or MathML presented; if the former the VLE converts MathML to an image. We are trying to improve image quality resulting from this process. VLE user settings cover size and colour contrast preferences. However these approaches still not used a great deal but students – but also not been widely promoted. There has only been 1 presentation of introductory course MU123 so far. We don’t really know how helpful these approaches are being to disabled students. Some non-disabled people using image enlargement (picked up from forums) others have discovered that TeX within $$ $$ is rendered by Moodle (this is a Moodle feature not turned off – but not advertised).
What the OU is seeking to move towards
We want to get things on VLE in more interactive fashion and to more easily manage student choices of what presentations best suit them. There are usability issues we want to address; e.g. when in a quiz radio buttons are displayed next to a MathML rendered expression it is easy to click on expression which produces and enlargement instead of selecting the radio button, this is due to Design Science plug-in feature. We also want to overcome current problem some delay when loading multiple images.
What format should be specified as the base format maths should be stored in before transformation to other formats as required? – Some argue for MathML others TeX What are the best authoring tools to offer academics that need to write courses containing Maths? MathML only currently only used on a few courses so we have had limited experience with it. We don’t know enough about the users! – This is a planned subject for future research. A new course M347 Mathematical statistics will be making substantial use of MathML. It is the first upper level Maths course to be presented on VLE only – first presentation due Feb 2012. It will be a crucial course for institutional learning – we will know a lot more in 1-2 years!
There are issues of how to meet disabled students needs without reducing quality for the rest. E.g. where MathML used > 95% of students not receiving benefits of MathML – and receive arguably poorer visual rendering of the maths but no complaints about this have been received. There is the possibility of supplementing MathML with an images supplied from original TeX.
There are curriculum issues, of “graduateness”:
Shouldn’t all maths graduates be able to produce nicely formatted printed Maths, therefore should we teach TeX/LaTeX)? Further should mathematical notation itself be part of the curriculum? – E.g. tree structures, order of operations, etc.
Making mathematics fully accessible to a diversity of people in online learning is not a solved problem. Nor are the options for presenting maths online generally optimally resolved. However it is clear that one solution will not suit all users and contexts and thus flexibility is key!