Universal Design for Math Learning:
Bridging the Technology and Policy Divide
Steve Noble, Director of Accessibility Policy Design Science, Inc.
ABSTRACT
This paper attempts to make fundamental connections between
the technological capabilities now available for creating universally designed
math, and the body of public policy which demands that educational offerings be
made accessible to students with disabilities. The premise to be examined is
that making math accessible is as much a public policy issue as it is a
technological one. The concept of what is required under law (public policy)
continues to expand as the technological issues of effective access are
resolved. Now that the technological issues of accessible math have been
resolved, it is essential that disability advocates and educators push for
better public policy to support the availability of accessible math in the
classroom.
CONNECTING MATH
PERFORMANCE AND ACCESSIBILITY
The attainment of good math skills has been identified as
one of the major goals of the American educational system. However, according
to data from the National Assessment of Educational Progress (NAEP), there is
great disparity between the levels of math literacy for students with
disabilities when compared to the results for students without disabilities. Research
compiled by the National Science Foundation further shows that students with
disabilities exit high school with significantly fewer course credits in
mathematics and science subjects than students without disabilities. Overall,
students with disabilities are much less likely to graduate from high school
and enroll in postsecondary educationand among those students with
disabilities who do graduate, they generally take fewer science and math
courses, had lower grades, and had lower achievement scores than their peers
without disabilities (National Science Foundation, 2003).
There are undoubtedly many factors at work which have a
connection to the poor math performance of students with disabilities. A
fundamental contributing factor is that virtually all mainstream math
instructional content is not designed to be utilized with the assistive
technology products that many students with disabilities use, and is thus not
accessible. This is especially true of print classroom textbooks, which are
commonly used to determine the instructional math program for students in most
school settings. 75% to 90% of all classroom instruction is based on textbooks,
and, in most cases, those books define the scope and sequence of the material
being taught (Tyson & Woodward, 1989). This is also the case with math
instruction, where 80% to 90% percent of grades 4  12 math and science
classrooms use textbooks (Hudson & McMahon, 2002).
Of late, many in the education community have turned to the
use of digital texts which can be transformed with assistive technologies into
an audible version of the textbook using synthetic speech on a computer. Such
conversions to digital formats have been a boon to providing equitable
instructional access for students with disabilities who use these technologies.
"Technology allows print textbooks to be made accessible to students with disabilities
through conversion to digital form. The same material in digital form offers many
options for students with disabilities. It can, for instance, be read aloud by
a computer or screen reader, or printed on a Braille printer. The power of
future curriculum will be in these alternative digital formats." (Stahl
and Aronica, 2002)
The use of digital texts, however, has been largely focused
on providing access to standard literary materials, rather than to math
content. Higher level math access with assistive technologies is particularly
problematic, due to the fact that common scanning and optical character
recognition (OCR) technologies used to convert print materials to digital form
cannot process complex math symbols, and publisher created digital resources
commonly use inaccessible graphical images of math equations.
Unfortunately, this lack of
available accessible digital content in areas of math instruction is perhaps
even more problematic for students whose disabilities affect reading
comprehension. This is because of the additional mental processing that is
required to interpret math expressions compared to literary content. Such an understanding
may be supported by the fact that more than 60% of students with learning
disabilities which affect reading comprehension, for example, have been shown
to possess significant disabilities in mathematics (Light & DeFries, 1995).
A number of studies have found that students with learning disabilities
experience more significant difficulties in acquiring math skills than do their
peers without disabilities (Miller & Mercer, 1997).
Research has also shown that
students with language deficits react to math problems on the page as signals
to do something, rather than as meaningful sentences that need to be read for
understanding (Garnett, 1998). In particular, this research points out that
many students with learning disabilities have a tendency to avoid verbalizing
in math activities. Such findings tend to reinforce the concept that LD
students with math deficits are seemingly unable to selfverbalize math
equations. Computerized reading of math equations could therefore aid students
by both reinforcing selfverbalization skills as well as providing access to
content for students whose disabilities prevent effective selfverbalization of
math equations.
Student access issues further
accumulate with increasingly difficult mathematics as students attempt to
understand the meaning and syntax of mathematical expressions that occur in the
study of higher math subjects such as algebra and calculus. Such mathematical
disciplines incorporate a distinct symbolic language which students must learn
to recognize and decode as an essential task to developing math literacy
skills. The capability to hear math equations properly decoded and verbalized
could therefore be an important accessibility component for students with
learning disabilities. Similarly, for students who are blind, the ability to
have math equations unambiguously spoken by computer technology, or able to be
used with refreshable braille displays, can be a vital accessibility technique.
THE NEED FOR
UNIVERSAL DESIGN FOR MATH LEARNING
Standard print textbooks and other types of commonly used
instructional materials are inaccessible to a large percentage of students with
disabilities and usually require transformation into alternative formats, such
as recordings, braille or accessible digital formats to provide access to
students with various print disabilities (Stahl, 2004). Math textbooks and
other instructional materials will provide much greater accessibility for
students with visual or learning disabilities when they are made available in a
universally designed accessible digital format. Such a universally designed
digital format for math content can be achieved by using Mathematical Markup
Language (MathML).
MathML is an open industry
standard first adopted by the World Wide Web Consortium (W3C) in 1998. MathML
is an XMLbased application for describing mathematical notation and capturing
both its structure and content. Using MathML enables mathematics to be served,
received, and processed in digital environments such as the World Wide Web,
just as Hyper Text Markup Language (HTML) has enabled this functionality for
literary text. Most importantly for this discussion, using MathML provides for
a standard approach to content tagging and information structure which can make
mathematical information available to assistive technology in a way that is
comparable to standard access by students without disabilities.
MathML provides the technology foundation for accessible math—as
opposed to just graphical images that are the current norm. Using MathML will
allow assistive technologies to provide builtin alternate access avenues, such
as using synthetic speech to read math equations out loud, or providing for
seamless text enlargement, braille support, and providing a means for students
to navigate both visually and aurally through complex math formulas and
highlight expressions as they are read.
Until very recently, speech
synthesis technology has been unable to process complex math equations, and
virtually all digital math content has been produced using graphical images
which are inherently inaccessible to either text reader or screen reader
assistive technologies. Design Science, Inc., a developer of mainstream math
publishing technology, has been engaged in research and development efforts
since 2003 supported in part by the National Science Foundation (SBIR Grant No.
0340439) to make math expressions created with MathML seamlessly accessible to
people with visual or learning disabilities. One of the fundamental principles
of this work has been to provide integrated access to mathematical content
through users’ existing screen readers or other assistive technology. The
advantage of this approach to math accessibility is that it allows materials
containing math to be read with standard browsers and familiar assistive
technology devices instead of depending upon a standalone proprietary application.
MathPlayer, made by Design
Science, provides the stateoftheart in audio rendering of mathematical
expressions, navigation of mathematical expressions with audio feedback, and
audio rendering synchronized with highlighting of the expression being spoken. Commonly
used assistive technologies, such as JAWS, WindowEyes, HAL, MAGic,
Read&Write and BrowseAloud, can take advantage of MathPlayer's unambiguous
speech access in a transparent manner which works in concert with the user's
usual technology environment. For assistive technologies that support word highlighting,
MathPlayer also integrates math highlighting so that both the words and the
math expressions are highlighted as they are spoken. These accessibility
provisions, however, all depend upon the digital source math content being made
available in MathML.
CONNECTING MATHML
WITH NIMAS
Under the provisions of the
Federal Individuals with Disabilities Education Act (IDEA) of 2004 and its
implementing regulations, publishers are now providing textbook content using
the National Instructional Materials Accessibility Standard (NIMAS). NIMAScompliant
textbook files are sent by publishers to the National Instructional Material
Accessibility Center (NIMAC), which in turn provides these files to thirdparty
accessibility entities who distribute studentready versions to students with
print disabilities. These provisions can contribute greatly to schools meeting
the No Child Left Behind (NCLB) requirements for Adequate Yearly Progress (AYP)
by providing curricular content in usable form at the same time that opportunity
to learn exists for all other students, which is a prerequisite for
participation in standardsbased reform and accountability (Elmore, R.F., 1995;
Guiton, G. & Oakes, J., 1995).
The advent of the National
Instructional Materials Accessibility Standard offers students with print
disabilities significant newfound opportunity for access to the general
curriculum and learning by the flexibility of use of digital content. In his recent testimony to the NCLB Commission,
Dr. David Rose, CEO of the Center for Applied Special Technology (CAST), stated
“An important first step in ensuring this flexibility
has recently been signed into federal law—the National Instructional Materials
Accessibility Standard (NIMAS). This
standard requires that publishers of print materials, e.g. textbooks, must
provide flexible alternatives—digital versions—for students with “print
disabilities.” These alternatives
provide alternate paths to the same high standards for students who cannot see
or successfully decode traditional textbooks”. (Rose, 2006)
The NIMAS specification is essentially a subset of a larger
industry standard created for the production of digital talking books, called
the Digital Accessible Information System (DAISY). The federal regulations
defining NIMAS identifies which DAISY tags are mandatory, and which are
optional (US Department of Education, 34 CFR Part 300). Although the original DAISY specification upon which the
2006 NIMAS was based did not specify a way to integrate MathML into digital
publisher files, this problem has now been solved. The DAISY specification does
define how Modular Extensions can be added to the standard to deal with
nonliterary materials, and therefore the DAISY Consortium has recently
developed a solution for including mathematics using a modular MathML
extension, enabling full support for accessible mathematics in the DAISY/NISO
Standard. The publication of the Mathematics Modular Extension is thus crucial
to integrating accessible mathematics via MathML into DAISY and NIMAScompliant
books. Chuck Hitchcock, Director of the NIMAS Technical Assistance Center at the
Center for Applied Special Technology (CAST) indicates that the publication of
the DAISY Modular Extension for math is an important advance toward the
universal design of math instructional content. "Now that DAISY has
integrated a MathML vocabulary into its specification, publishers creating
NIMAScompliant files as part of federal IDEA requirements will soon be able to
support a much greater level of accessibility and educational efficacy for
elementary and secondary math textbooks" (DAISY, 2007).
CONCLUSION: BRIDGING
THE TECHNOLOGY AND POLICY DIVIDE
In conclusion, we should return to our original premise,
that making math accessible is as much a public policy issue as it is a
technological one, and that the concept of what is required under law (public
policy) continues to expand as the technological issues of effective access are
resolved. Now that the technological issues of accessible math have been
resolvedby virtue of MathML and its adoption within NIMASit is essential
that disability advocates and educators push for better public policy to
support the availability of accessible math in the classroom.
There are a number of policy vehicles available to push this
forward:
1) Updating of Federal NIMAS specifications
As previously mentioned the current NIMAS specification is
tied to DAISY, but does not have an explicit reference to the new DAISY MathML
modular extension. Without such an explicit linkage, one can only assume that
the MathML extension will be left as an optional requirement, leaving the
actual enforcement of the requirement to state by state interpretations. The
NIMAS Development Center at CAST is tasked under Federal regulations to update
the NIMAS specification, so this will be an important mandate for CAST to
propel through the regulatory change process as soon as possible.
2) State Implementation of NIMAS and MathML
States are the primary implementing entities under the
Federal NIMAS requirements. Statesas well as school districts in states not
having statewide textbook adoptionshave the autonomy to enforce publisher
requirements on their own, even without a specific Federal mandate. States
should use this ability to push their accessibility agenda forward and require
that publishers utilize MathML when preparing math textbooks for submission to
the NIMAC.
3) State and District purchasing requirements
States and school districts have federal obligations under
Section 504, the Americans with Disabilities Act, and the IDEA to make their
instructional content accessible to students with disabilities. Since the
advent of MathML has made accessible math a reality, educational entities must
move forward to ensure that math instructional content created with MathML will
be available to their students who use assistive technologies. Beyond placing
MathML requirements in textbook adoptions and contracts, states should also put
these requirements in Requests for Proposals (RFPs) for statewide assessment,
so that students can utilize accessible math in online assessments as well.
Furthermore, when states and districts negotiate major site license
relationships with assistive technology vendors, they should ensure that these
contracts require the vendor to support MathML technology. Including MathML
requirements in procurement policies for instructional software is yet another
vehicle for furthering the availability of accessible math technologies for all
students.
These are some of the most direct methods for securing
effective public policy to support accessible math. Such actions will help to ensure
that educational content in MathML will become available to students as quickly
as possible, and as broadly as feasible. Together, we can move forward toward an
inclusive universal design for learning environment for the study of math.
REFERENCES
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