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What are the technology issues involved in making math accessible?

Learning Points:

  • Although some educators have ignored the importance of accessible math in the past, these attitudes are now changing due to the availability of new technologies.
  • By using universally designed math technologies like MathML to create accessible math equations, the resulting content will also provide for alternative access to meet a student's special access needs.
  • Most math equations currently used in digital environments like the Web are simply static bitmaps (digital drawings) of equation images, and are inherently inaccessible.
  • Using MathML provides a number of accessibility benefits and produces math equations that can be both rendered visually on the screen and also available through alternative access means.
  • Turning math expressions into audio form can be a very effective form of alternative access for people who have visual or learning disabilities. Images of equations do not by themselves supply information to support any form of audio rendering, but coherent and consistent audio rendering of math expressions is available when using MathML.
  • Since there are many users who can see but who have some form of visual impairment, the need to enlarge mathematical equations on a computer screen is very common. Using MathML provides for user flexibility to change visual aspects such as the size and color of the font as well as the background of the display.
  • Synchronous highlighting of math equations with audio can be beneficial for students with learning disabilities or attention deficit disorders, as well as for students with low vision. Math equations which have been encoded in MathML can permit a range of highlighting reinforcement options.
  • The ability to provide math access through refreshable braille displays and hard copy braille output is important for both blind and deaf-blind users. Math images cannot be accessed by braille, but braille access to math encoded in MathML can be provided.
  • The ability to better comprehend longer or more complex mathematical equations in audio form is aided by user navigation within a math equation. This is not feasible with prerecorded audio files or text equivalents, but can be made possible when using math content encoded in MathML.

Changing attitudes through new technologies

In the past, it is sad to say that math accessibility was not considered a viable concern among many educators. It was not unusual to hear people express the opinion that math was not a primary subject needing much focus, that providing access to math content was too difficult, or that most students with disabilities would simply find math too complex anyway and therefore not worth the trouble. At Design Science, we reject these notions as regressive and insulting to people with disabilities. Such old attitudes are now changing, and greater levels of effective access to mathematical information has been made available thanks to continuing improvements in math accessibility. Although there are many technical issues involved in making math accessible, Design Science wants you to know that we have found solutions for many of these issues, and are actively involved in research projects with an aim to design even better math accessibility technologies in the near future.

Providing for alternative access

For users with special needs, having access to math information in something other than just ink on paper is essential. In educational settings many students with print disabilities must rely upon alternative format materials in place of standard print in order to access textbooks, tests, classroom hand-outs or other types of instructional content. Having math displayed on a computer screen begins to remedy some accessibility issues by providing an environment where the content can be enlarged for people with low vision, or by allowing someone with no use of their hands to virtually "turn pages." But the common current practice of using graphical images to represent mathematical equations in computer applications, such as using GIF or JPG image files to display math in Web pages, does nothing to make those equations accessible to many people with disabilities who depend upon assistive technologies like synthetic speech or refreshable braille displays.

By using MathML to create universally designed accessible math equations, the resulting content can be translated into any other imaginable output format needed, which ensures that alternative formats that meet a student's access needs will be available for use with their assistive technology. Math with accessible equations can be rendered with synthetic speech, can be utilized with synchronized highlighting, and can be also converted into braille math code for blind students. Synchronized highlighting of math equations on a computer screen with synthetic speech helps those with low vision, and can be a significant aid to students with learning disabilities.

Accessible equations, unlike images, will format and display correctly on PDAs and on high-resolution output devices not yet invented. They can use larger fonts and match a user's preferred color schemes. Accessible equations will form the basis of universally designed math instructional content, as well as fully accessible math assessments for use by all students. By having accessible math content available in instructional software, e-books, and assessments, all students will have equal access to the same content and the same learning supports, regardless of whether or not they have a disability. This eliminates the need to have a totally separate process to create an alternative format at a later date, and virtually guarantees that students with disabilities will be able to access the same content at the same time as students without disabilities.

The problem of math images

Most of the math equations one currently finds in digital environments like the Web are simply static bitmaps (digital drawings) of equation images in GIF, PNG, or JPEG formats. These images can be seen with the human eye, but they are devoid of non-visual information that can be utilized by assistive technologies. Such image formats are, by themselves, inherently inaccessible. They do not provide for alternative output modalities, such as braille or synthetic speech and cannot be easily altered for people with low vision (for example, font enlargement or color and contrast changes). Furthermore, such image formats are plagued by other usability and aesthetic problems such as ease of alignment, sizing, and color conformity with the text, require the author to spend much more editing time to make visually appealing web content, and require authors to keep a large inventory of static equation images which are not easily editable, requiring the author to redraw images when even small changes are made. Finally, images take up relatively large amounts of bandwidth, which is a hindrance for low-speed Internet connections.

The typical method of providing accessibility to common images in digital environments is by including a written description of the graphic referred to as a "text equivalent," generally either an "alt" tag or a "long description." For most images this will be sufficient to comply to minimum accessibility standards, such as those required under Federal Section 508 Electronic and Information Technology Accessibility Standards or the W3C's Web Content Accessibility Guidelines. However, providing alt tags to graphical images of math equations can only provide a very limited form of accessibility for the simplest types of equations.

Alt tags are limited to a narrative description of math equations, and must be laboriously hand coded by someone who can fully understand the context of the expression and unambiguously describe it with complete consistency. Even if this could be guaranteed, there would still be no way to intelligently navigate though a math equation, and still doesn't fix some of the previously mentioned issues like support for brailled math output. So although the use of properly authored alt tags may supply minimum access to math content, it is still a far cry from the maxim that individuals with disabilities should "have access to and use of information and data that is comparable to that provided to the public who are not individuals with disabilities" as mandated by the provisions of the 1998 Amendment to Section 508 of the Rehabilitation Act.

Benefits of MathML

As we just discussed, math images (with or without a text equivalent) cannot provide a level of access that is comparable to, or as effective as, the level of access that individuals without disabilities are being provided. Instead, the preferred (and vastly more effective) technique is to use a standardized markup language that can be accessed by the assistive technologies that people with disabilities use. Using such a technique means that the author has to encode information only once because there is no need to go back through a second time and add an alternative (alt tag) description. The same coding supplies, at the same time, the needs of both those who use and those who do not use assistive technologies, and hence is a much more effective authoring method.

MathML (Mathematical Markup Language) has been adopted by the W3C as the standard way of expressing math on the Web, and provides the basis for math equations that can be both rendered visually on the screen and also available through alternative access means. MathML contains sufficient information and structure to provide support for both visual display and alternative access means such as synthetic speech and braille. Equations which are encoded in MathML will increase in size as users change font size to increase readability, unlike images. When using synthetic speech, MathML will allow the user to set different verbosity levels and can automatically adjust for the user's native language. For braille users, using MathML will allow for the choice of various braille math formats, depending upon braille translation software support.

Audio rendering of math equations

Turning math expressions into audio form can be a very effective form of alternative access for people who have visual or learning disabilities. Images of equations do not by themselves supply information to support any form of audio rendering, although text equivalents can be audibly rendered by synthetic speech applications as mentioned previously. Producers of alternative format materials can also provide previously recorded audio files (either from human readers or synthetic speech used at the producer end) that can supply an audio rendering of math equations in digital environments even without the presence of a screen or text reader on the end user system, as is commonly done in currently available Digital Talking Books. This approach does provide access for users with visual or learning disabilities, but would be of no benefit for deaf-blind users. Just as in the case of text equivalents, this type of audio rendering can only supply a very limited level of accessibility and only for the most simple equations.

However, much more coherent and consistent audio rendering of math expressions is available when using MathML. Synthetic speech engines used by students who are blind, such as JAWS, Window-Eyes, HAL, Supernova, MAGic, and Serotek System Access, and text readers used by students who have learning disabilities, like TextHelp's Read & Write Gold and BrowseAloud, can already seamlessly interface the reading of MathML math expressions by using MathPlayer. Further development of math speech technologies will allow user customization of speech generation rules and control of prosodic cues such as the pitch and rhythm of the math speech, which will help to increase the comprehension rate of users for both the structure the content of the expression.

Enlarged font display

Since, in comparison to the number of people who are blind, there are many more users who can see but who have some form of visual impairment (commonly referred to as having "low vision") the need to enlarge mathematical equations on a computer screen is much more common. Such users may also need to change the color of the font as well as the background of the display. Math images (graphical formats) do not enlarge well, and cannot be enlarged by simply changing browser settings. There is also no simple user defined method available to change image colors. When math equations are encoded in MathML, however, visual definition does not degrade with size increase, and users have control over the size, color, and contrast of math font display just as they do for literary text. MathML also provides for consistent linebreaking when math equations are enlarged, which is important for all users but particularly important for people with low vision.

Synchronous highlighting of math display with audio

Most of the text reader applications currently on the market make use of synchronized highlighting of literary text as the words are being spoken. This technique is also available with Digital Talking Books when they are used with visual display environments. Synchronous highlighting is beneficial for students with learning disabilities or attention deficit disorders, as well as for students with low vision. Although significant research has been conducted demonstrating the value of synchronous highlighting toward increasing reading comprehension of literary materials, the fact that synchronous highlighting of math has only recently become possible has limited the availability of research supporting increased comprehension of math expressions through synchronous highlighting to this point. However, the implication that synchronous highlighting of math expressions as they are spoken increases comprehension seems very likely.

Math equations which have been encoded in MathML can permit a range of highlighting reinforcement options. Equations can be broken down into various subcomponent sections as they are being spoken depending upon the flexibility provided within the reading application. The degree of highlighting granularity desired will likely depend upon the individual student's instructional need or user preference.

Braille rendering of math equations

The ability to provide math access through refreshable braille displays and hard copy braille output is important for both blind and deaf-blind users. Most good braille readers find audio-only access to mathematics considerably inferior to braille or combined braille and audio access. Math images cannot be accessed by braille, but braille access to math encoded in MathML can be provided. However, there are a number of competing math braille codes in use around the world, which complicates the ability to support braille output for MathML. A relatively new type of two dimensional math braille called DotsPlus is simple to produce with MathML content. Support for other commonly used math braille, like Nemeth code, is dependent upon MathML support by makers of braille translation software.

Navigation within a math expression

The ability to better comprehend longer or more complex mathematical equations in audio form is aided by user navigation within the equation to hear different expression elements separately. This is not feasible with prerecorded audio files or text equivalents, but can be made possible when using math content encoded in MathML.

Allowing navigation of math expressions using keyboard commands will allow the user to explore the structure of an equation at the user's own pace. Although it may be difficult to comprehend especially long equations through audio access only, the ability to audibly walk through an unambiguous vocalization of the expression and subdivide lengthy equations at natural "chunking" spots greatly enhances intelligibility of accessible math expressions.

Further Information and Resources

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