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 education--and 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 self-verbalize math equations. Computerized reading of math equations could therefore aid students by both reinforcing self-verbalization skills as well as providing access to content for students whose disabilities prevent effective self-verbalization 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 XML-based 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 built-in 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 stand-alone proprietary application.

MathPlayer, made by Design Science, provides the state-of-the-art 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, Window-Eyes, 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). NIMAS-compliant textbook files are sent by publishers to the National Instructional Material Accessibility Center (NIMAC), which in turn provides these files to third-party accessibility entities who distribute student-ready 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 standards-based 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 non-literary 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 NIMAS-compliant 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 NIMAS-compliant 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 resolved--by virtue of MathML and its adoption within NIMAS--it 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. States--as well as school districts in states not having statewide textbook adoptions--have 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

DAISY Consortium Press Release: "Mathematics Now Added to the DAISY Standard". March 22, 2007. Accessed at: http://www.daisy.org/news/news_detail.asp?NewsId=296

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Garnett, Kate. (1998). "Math Learning Disabilities". Accessed at http://www.ldonline.org/article/5896

Guiton, G. & Oakes, J. (1995). "Opportunity to learn and conceptions of educational equality". Educational Evaluation and Policy Analysis, 17(3) 323-336

Hudson, S.B., McMahon, K.C. & Overstreet, C.M. (2002). "The 2000 National Survey of Science and Mathematics Education: Compendium of Tables Authors". Horizon Research.

Light, G. J., & DeFries, J. C. (1995). "Comorbidity for reading and mathematics disabilities: Genetic and environmental etiologies", Journal of Learning Disabilities, 28, 96-106

Miller, S., & Mercer, C. (1997). "Educational Aspects of Mathematics Disabilities". Journal of Learning Disabilities, 30 (1), 47-56.

National Science Foundation, Division of Science Resources Statistics (2003). "Women, Minorities, and Persons With Disabilities in Science and Engineering: 2002", NSF 03-312.

Rose, D., Testimony to NCLB Federal Commission August, 2, 2006, Aspen Institute in Washington, DC

Stahl, S & Aronica, M. (2002). "Digital Text in the Classroom". Journal of Special Education Technology, 17 (2), spring 2002 (accessed from http://jset.unlv.edu/17.2T/tasseds/rose.html)

Stahl, S. (2004). "The promise of accessible textbooks: increased achievement for all students". Wakefield, MA: National Center on Accessing the General Curriculum. Retrieved 05-26-06 (accessed from http://www.cast.org/publications/ncac/ncac_accessible.html)

Tyson, H., & Woodward, A. (1989). "Why students aren't learning very much from textbooks". Educational Leadership, 47 (3), 14-17.

US Department of Education. 34 CFR Part 300. Accessed at: http://nimas.cast.org/about/proposal/register-v1_1.html