Today, people often place mathematical notation on the web in the form of an image. As explained elsewhere, such notation is not accessible, in the real sense, to anyone although it can be viewed by people with graphical browsers.
Let us consider the following expression:
a3+b3=(a+b)(a2-ab+b2)
Imagine it is not text on the page but appears as an image inserted into the text. Imagine there is an alt tag for the image and maybe a long description of what it contains. The alt tag, or long description, might say one or more of the following,
But there will most probably still be difficulties for some users.
MathML (from W3C at http://www.w3.org/Math/) is an XML mark-up language for mathematical notation. Users can write mathematics in a compliant editor and view the symbolic representations on the web. MathML has been written with universal accessibility as a priority. MathML offers two formats for representing an equation: presentational tags and semantic/content tags.
Today this often means using a mathematics editor, such as Amaya, or mathematics software - see the list of MathML compliant browsers and the list of MathML compliant mathematical software below.
It is worth visiting http://www.mathmlconference.org/Talks/rudisill/ to see about using mathematics notation in WebCT. The authors in that case wrote the mathematics notation in Word using the Equation Editor and then translated it into MathML using WebEQ generator - a shareware translator - and users viewed the notation with their graphical browsers augmented with the WebEQ plug-in (free).
This simple example of MathML gives you an idea of how it works. The equation in question is:
x2 + 4x + 4 =0
and below are two ways that this can be represented, first using presentational tags, then using semantic tags. The presentational tags generally start with "m" and then use "o" for operator "i" for identifier "n" for number, and so on. The "mrow" tags indicate organization into horizontal groups.
<mrow>
<mrow>
<msup> <mi>x</mi> <mn>2</mn> </msup> <mo>+</mo>
<mrow>
<mn>4</mn>
<mo>⁢</mo>
<mi>x</mi>
</mrow>
<mo>+</mo>
<mn>4</mn>
</mrow>
<mo>=</mo>
<mn>0</mn>
</mrow>
The semantic tags take into account such concepts as "times", "power of" and so on:
<apply>
<plus/>
<apply>
<power/>
<ci>x</ci>
<cn>2</cn>
</apply>
<apply>
<times/>
<cn>4</cn>
<ci>x</ci>
</apply>
<cn>4</cn>
</apply>
MathML encoding can be used on pages encoded in XHTML. See how to put MathML into a web page that is written in XHTML. The pages can be viewed using most graphical browsers with a plug-in or directly with browsers such as Amaya, etc. See more information on browsing possibilities at
Back in 1998, Dave Raggett and his colleagues and HP worked on something called EzMaths - it was very promising. See http://www.w3.org/People/Raggett/EzMath/ (local version)
Use the validating MathML test suites at http://www.w3.org/Math/testsuite and the validator at http://www.w3.org/Math/validator.
From http://www.w3.org/Math/#Software
Note received 18/7/2001:
Hello Liddy,
Most of Maple 7's functionality is accessible to visually impaired users who utilize either speech- or Braille-synthesizing screen readers, such as the JAWS screen reader. According to Dr. Peter Torpey, a blind physicist at Xerox who uses JAWS at work, Maple's interface is quite legible to screen readers, with only a few exceptions. There are some user-interface features that have not yet been optimized for accessibility to screen readers, but we will be addressing these in our next product release sometime in 2002. I will be happy to provide you with more details if you like.
Maple software does not generate any sound outputs, so hearing impaired users will have the same accessibility as users with normal hearing.
Please let me know if I can be of further assistance in your preparation of specifications for students with special needs.
Best regards,
Jason Schattman, Ph.D.
Manager, Applications Marketing
Waterloo Maple Inc.
57 Erb St. West
Waterloo, Ontario N2L 6C2
(519) 747-1278 x 351
http://www.mapleapps.com
.
An older but perhaps useful approach for short term work is to use the EzMath editor - free and downloadable for Windows 95/NT from http://www.w3.org/People/Raggett/ezmath1_1.zip
As the authors, Dave Raggett (dsr@w3.org), Davy Batsalle (batsalle@email.enst.fr) say (see http://www.w3.org/People/Raggett/EzMath/):
"W3C's MathML provides two sets of tags, one concerned primarily with presentation, and the other with the meaning of mathematical expressions. MathML aims to provide a low level format for machine to machine communication. It is much more verbose than EzMath, and is not intended for direct editing.
The EzMath editor also provides support for marking up expressions in MathML's content tags. To do this, you simply change the clipboard format to MathML."
The advantage of using EzMath is that you can make editable maths for use on the broewser screen. the disadvantages include that it is an incomplete set of maths expressions that can be handled, for instance sometrigonometric expressions may not be possible, nor are a number of other expressions. Writing EzMath is something that can be done fairly easily by specifying how the expression is understood in a form that makes it fairly easy to author.
Some examples are offered:
ax^2+bx+c=0
integral from 0 to pi of sin ax wrt x
limit as x tends to infinity of function f(x)
matrix M = matrix (1,2;2,1)
and
a^m over a^n = either a^{m-n} when m > n or 1 when m = n or 1 over a^{n-m} when m < n
which, when displayed using EzMath, appears as:
It is possible that EzMath is suitable for screen readers.
Last updated: 8 March 2002