Math, computer and the Internet: better employment opportunities for persons with disabilities.

In our current job market, math skills and familiarity with computers and Internet resources are becoming more and more important. For adults with disabilities, the presence or absence of these skills and competencies will greatly determine vocational choices. Assessment of math, computer and Internet skills may be very important in individual vocational planning, but people with disabilities are not using computers and the Internet as extensively as the general population. Many consumers in the vocational rehabilitation (VR) system are poorly prepared in math and computers skills. Several new tools will help individuals with disabilities, their teachers and their counselors in improving skills needd for the current job market. This article explains the need for math skills, identifies barriers to math and science education for people with disabilities and provides examples of some of the tools designed to help people use computers and the Internet to build math skills.

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Mathematical Literacy: Important in Today's Job Market

Access to information is rapidly changing the way we do things. In the global information environment it is nearly impossible to predict what knowledge will be required for productivity and leadership in the future. Knowing how to manage and evaluate information is certainly critical to our sustained success as a nation; and knowledge of math is essential to decision making as we go about selecting and applying information to the many complex problems we face as individuals and as a society.

Educational trends, reflected in the Goals 2000: Educate America Act, the Improving America's Schools Act and the reauthorization of the Individuals with Disabilities Education Act, call for high educational standards for all students. All children are to have access to the same knowledge and the opportunity to acquire the skills they need to succeed in the high-tech workplace of the 21st century. (1) The 5-year plan of the Federal Coordinating Council for Science, Engineering and Technology suggests that mathematics education needs to be reformed so that all students can participate in a rich and challenging mathematics curriculum. Of particular importance is the full participation of groups underrepresented in high levels of math proficiency. But many adults who did not have this opportunity do not have the math skills they need for today's jobs.

Becoming a participant in this age of rapid technological change requires adults and children alike to develop numeracy (mathematical literacy), which involves more than basic arithmetic. The National Institute for Literacy has helped identify seven themes, which serve as the foundation for adult numeracy standards (Curry et al., 1996). This foundation of knowledge enables students to:

* find relevance or make connections between mathematics and other disciplines;

* use math to solve problems, reason and make decisions;

* communicate mathematical ideas;

* have a conceptual understanding of numbers;

* interpret data;

* understand sense and measurement (geometry); and

* recognize patterns and relationships (algebra).

These competencies allow individuals to approach problems thoughtfully and make informed decisions; they are necessary for many jobs. Understanding the relevance of math literacy to everyday life helps to make the lessons meaningful, especially for adult learners.

Barriers to Math for Students With Disabilities

Dr. Devva Kasnitz, research director of a Research and Training Center at the World Institute on Disability, describes her experience with math barriers: "As a child, I had disability-related manual dexterity difficulties and was not able to pursue the subject past high school. It is hard to learn math when you can't read your own handwritten figures! Though I am happy with my career in anthropology, I often wonder if my problems with math kept me off an equally productive path through the "hard" physical or life science fields" (Kasnitz, 1996).

If students with disabilities in grades K-12 receive limited or poor instruction in science and math, they are not prepared to pursue educational opportunities in technical and scientific disciplines, limiting their chances to pursue employment in these areas. Common barriers to math education include limited access to certain tools needed to learn math and a lack of teaching about how people with disabilities, and others, use math on the job and in their daily lives.

Many children with physical disabilities perform at grade level or better until their math lessons become too difficult or abstract to complete "in their heads." Normally, children accomplish more difficult lessons using pencil and paper, an option that is commonly not available to certain children with physical disabilities. As math becomes more difficult, around the 5th grade, students cannot compete with others in the classroom. While computers may help by providing a calculator function, the computer keyboard needs to be accessible, and the software needs to support the understanding of math calculations, not just show the answers. A child who falls behind in math or becomes frustrated with math may be unable to participate successfully in other math-dependent studies such as the sciences, economics, engineering, and many computer-oriented disciplines.

Depending on a student's disability, one or more types of accommodation might be necessary to ensure math learning. For students with physical disabilities, special software may help by simulating paper and pencil. Students with disabilities that affect memory may have difficulties recalling formulas and number facts even though they may know how to apply the information to problem solving. Some students have learning disabilities that affect the ability to organize information or sequence the steps to solve a problem. Some may not be able to organize a problem until they hear it: They need auditory support. Low vision or visual perception is also a factor that affects learning mathematics since math relies heavily on visual skills such as number and operation sign recognition. Students with visual perception difficulties need to have visual distractions removed so that they can focus on one task or problem at a time.

Solutions to access barriers are not enough to ensure math achievement. The motivation to study math, and to learn, comes from understanding the relevance of math to everyday life and using math skills to solve problems at work and at home. For students with disabilities, there is also the importance of learning about other people with disabilities who are succeeding in math and science careers and applying math and science in their lives.

Levels of Math and Reading for VR Clients

The Longitudinal Study of the Vocational Rehabilitation Services Program, provides information on the levels of reading and math education for consumers of vocational rehabilitation in the State-Federal Vocational Rehabilitation Services Program (see Tables 1 and 2) (Hayward and Smith, 1999). Many people that apply to VR have low levels of math proficiency. And, not surprisingly, those with higherlevels of math performance are placed into higher-paying jobs. Tables 1 and 2 were prepared from data from the study; the individuals who applied for VR services were included in the data. (2)

In the VR population, the mean math grade level is 7.7 years, compared to 8.5 years for reading grade level. The median shows an even broader gap, in both men and women. Half the VR population reads at grade 9 or above, while for math, half reads above grade 7.

Overall, 27.8 percent of people who use VR had math levels less than sixth grade, and 26.2 percent had reading levels less than sixth grade. Over half of the population had math levels less than high school level, and only 4.7 percent had levels above 12th grade. Of these with some college-level math, two-thirds are male, one-third are female (See Table 2). Obviously, as the Longitudinal Study demonstrates, the educational level of these VR participants will affect the range of job choices available. People with higher competencies in reading and math will have more job choice.

MathPad [TM]: Reducing barriers to math education for students with disabilities

MathPad [TM] is a software tool developed to provide a means for learners with physical disabilities to access the mainstream mathematics curriculum. MathPad [TM] provides students with physical disabilities a way to work out arithmetic problems without need for pencil and paper. MathPad [TM] contains accessibility features including built-in scanning, speech output, a variety of text size options, options for color and contrast, and automatic navigation to reduce keystrokes. The program makes use of other assistive technology such as an IntelliKeys and other alternative input devices. MathPad [TM] has been given a special needs software award by Technology and Learning magazine. (3)

MathPad [TM] modules supports learning addition, subtraction, multiplication, division, statistics, and fractions and provides appropriate manipulatives. Each software module is compatible with existing curricula and lessons. These tools are intended to:

* Remove barriers that students with physical disabilities encounter while interacting with mathematics curricula materials;

* Encourage students with physical disabilities to explore mathematical ideas using accessible electronic manipulatives which will enable them to link the concrete with the symbolic;

* Provide opportunities for practice and instructional feedback to accelerate mathematics achievement for disabled students;

* Improve the disposition of students with physical disabilities toward mathematics achievement;

* Increase access to, and use of, computer-based mathematics materials by students with physical disabilities; and

* Make the curriculum for learners with and without physical disabilities consistent by integrating problem sets from popular texts and published curricular materials.

MathPad [TM] is not a calculator. Students perform basic arithmetic problems directly on the computer. The students must decide when to borrow, carry, or show a remainder. The software has built in features that carry out these functions with a minimum number of keystrokes. MathPad [TM] is also useful for students who have difficulty organizing math problems, because there is a built-in structure for working on problems and showing work.

Many design features support accessibility. The software permits a student or teacher to tailor the environment to the individual needs of a student. The program provides audio feedback to students in a variety of ways. The speech function can be activated to speak the problem, to identify the row, the entry, and toolbar buttons, or other screen navigation icons. To facilitate scanning and other alternative input devices, all commands and dialog boxes have a keyboard equivalent. A student may elect to scan the toolbar buttons using either step or automatic scanning. The type size and colors on the page can be customized to meet individual needs such as high-contrast settings for students with impaired vision.

Using MathPad [TM] modules, students can solve computational and word problems with whole numbers, fractions, decimals, and percents and strengthen their understanding of concepts using accessible on-screen fraction circles, fraction bars and decimal grids. Currently, these tools allow students to represent or solve problems in multiple ways using both numerical and visual models. Future modules will include algebra and geometry. By using MathPad [TM] on the computer, the student learns other computer skills which can be applied to other software and education experiences.

Using the Web for Learning About Math

Using the Internet to pursue educational opportunities has great potential for expanding the math skills of people with disabilities. There has been a dramatic increase in Web-based learning materials and distance education opportunities including virtual classrooms. For individuals with disabilities these resources are promising for increasing access to education and removing barriers, the least of which are transportation barriers. Now it is possible for students with disabilities to pursue education without leaving their homes or offices.

Only recently has the Internet developed as an effective tool for education, a powerful and flexible tool for delivering curriculum. Researchers and educators are continuing to experiment with the Web as a medium for delivering instruction and providing creative learning explorations.

The Internet empowers individuals to choose how they will acquire knowledge and information. For instance, one key to the success of the Internet for educational purposes is its ability to present information in a non-linear format. In contrast to reading a printed book, this non-linear approach may be very effective for adult learners who are more motivated to acquire knowledge appropriate to their own individual circumstances. Students who are encouraged to use the Web for mathematics learning will likely increase other crucial skills needed in the workplace such as reading skills, information skills and technology skills in the process.

For adult learners, math takes on greater meaning and understanding when it is directly applied in the workplace or in real-life situations. The Internet provides a wealth of resources for experiential and contextual mathematics learning. Furthermore, many disability organizations and memberships have Web sites. There is a wealth of information on disability rights, disability services and useful publications. Through the use of other assistive technologies, persons with disabilities can access these materials and pursue new opportunities. But some aspects of Web design limit the accessibility of a Web site for a person with a disability. Progress is being made to make this information accessible to individuals with disabilities through a variety of means. One of the organizations concerned with this effort is The Web Accessibility Initiative Working Group of the World Wide Web Consortium (http://www. w3.org/WAI/). As the Web becomes increasingly accessible, a computer hooked to the Internet will bring nearly unlimited information and communication resources as close as your home, public library or school.

Using the Internet effectively has the potential to increase the capacity of people with disabilities to engage more fully in academic and employment opportunities. However, in an age of such rapidly developing information and technology, individuals without appropriate skills and access are at significant risk of being left behind. According to a recent report from the National Institute on Disability and Rehabilitation Research, the computer revolution has left the vast majority of people with disabilities behind; only one-quarter of people with disabilities own computers, and only one-tenth ever make use of the Internet (Kaye, 2000).

PlaneMath [TM]

The National Aeronautics and Space Administration (NASA) has a commitment to advancing education in grades K-12 and has developed a number of grant programs designed to increase interest in aeronautics careers. PlaneMath [TM], an interactive Web site designed to teach math to students with disabilities, is a result of the NASA initiative. (4) Students use PlaneMath [TM] to solve math problems. They can also learn about role models, people with disabilities who use math and science in their jobs.

PlaneMath [TM] was designed to accomplish several objectives:

* To improve access to mathematics and aeronautics curricula materials for 4th-7th graders with physical disabilities;

* To improve mathematics proficiency outcomes among 4th-7th grade students with physical disabilities;

* To inspire and motivate students with physical disabilities to pursue aeronautics-related careers; and

* To increase access to, and innovative use of, digital communication and multimedia technology among students with physical disabilities.

The PlaneMath [TM] Web site includes 23 sets of activities which align to the National Council of Teachers of Mathematics standards (NCTM, 2000). The lessons are presented in meaningful aeronautics settings and organized into three groups: "PlaneMath Enterprises," "Pioneer Plane," and "Applying Flying." During each lesson a student uses mathematics knowledge gained earlier, while acquiring new knowledge. In addition, students are introduced to aeronautics concepts which emphasize the connections among science, technology and mathematics.

In "PlaneMath Enterprises," students solve problems designed to help them learn many of the math concepts used in aeronautics design. In "Pioneer Plane," lessons and activities are based on the experiences of flight pioneers Amelia Earhart and Jimmy Doolittle. In "Applying Flying," exercises challenge students to find the shortest path between two cities, to learn how planes lift off, to build a kite, to calculate airplane capacity, and to perform other related activities. For each activity, the student is invited to "meet" a person with a disability who is using aeronautics and math in his or her career, including:

* Ken Iliff, Chief Scientist, NASA Dryden Flight Research Center, who has degrees in aerospace engineering, mechanical engineering, electrical engineering, and business engineering. Ken uses a wheelchair; he got polio when he was 9 years old. He was completely paralyzed at first, and now has some use of his hands and arms. Ken's job at NASA as a research engineer is to analyze how aircraft perform. Ken says "If you are trained and properly qualified in the kinds of math and aeronautics careers we have been talking about, I think you will find that your handicap is a non-issue as far as the job is concerned."

* Julie Pollitt, NASA Mechanical Engineer, who works in the wind tunnels helping researchers design and build their test apparatus. Julie uses a wheelchair. She would definitely encourage young people to attempt careers in aeronautics, saying, "The biggest challenge I've dealt with in my career--to do with my disability--has been other people telling me what I couldn't do and me having to prove them wrong ... I would encourage young kids to follow careers in math. Math provides the basis for most technical careers."

* Eric Sheppard, assistant professor of aerospace science engineering at Tuskegee University, who wears an elbow-elbow prosthesis which he helped design. Eric says "The key thing is to be able to understand what's happening in the world through math. You might not have to use all that you learned every day, but if you have a firm understanding of math it will help you understand how the real world works ..."

* Other people that students can learn about include Neal Loving, who is a pilot and engineer. NeaI, an African American, is the first double amputee who is a licenced racing pilot. Mike Smith, president of Aero Haven Flight School, also a pilot, uses a wheelchair. Mike teaches people with disabilities how to fly.

Cathy Platano, a special education teacher at Sterling Morton Elementary School (Mentor, Ohio), wrote to the PlaneMath team about her classroom experience and the importance of the role models. Her student Jimmy had a severe physical disability; he had a tumor removed from his brain and now has only partial use of his right side. He prefers using his left arm for activities. Cathy introduced him to PlaneMath [TM] and the "Applying Flying" activity where he could meet engineers who use math in their work. She wrote, "I wish you could have seen Jimmy's face when he realized that there were successful adults with physical limitations such as his ... or worse. You would have cried! We have done much of the program together ..." (Platano, 1999).

PlaneMath [TM] has received a number of awards and recommendations, including. ED's A-OK Award from ED's Oasis; a selected resource of The Scout Report; one of the Web Crawler Select; a "Blue Web'N" from Pacific Bell Knowledge Network; and is an Education World reviewed site. Over 800 classrooms, with over 1,000 students with disabilities, have registered with the PlaneMath [TM] site. Because of the importance of context and relevance for adult learners, PlaneMath [TM] is also useful for adult remedial math practice and for career exploration.

Conclusion

The Internet is becoming an essential communication, education and job search tool for people in the labor force. The Internet has the potential for reducing many barriers to information and communication including geographic barriers and is a resource for finding work opportunities. The inability to speak, hear, see, or move is not a limitation in electronic communication. The Internet has the potential to provide access to information and foster communication. It is particularly relevant to individuals with disabilities and other groups who may have been underrepresented in or underserved by traditional information, communication and educational systems.

This article has described examples of new computer and Internet tools and resources for improving the math readiness of people with disabilities. More tools will emerge as our technology improves and as the use of computers and the Internet continues to expand. Vocational counselors and educators should encourage students with disabilities to use these tools to increase their math knowledge and to develop math and computer skills needed for jobs in the current work force.

Table 1
Reading and Math Levels of Consumers in the State-Federal
VR Services Program, by Gender

                      Reading         Math
                     Grade Level   Grade Level
Overall    Mean          8.5           7.7
           Median        9.0           7.0
           Minimum       1.0           1.0
           Maximum      16.9           16.9

Males      Mean          8.3            7.7
           Median        8.3            7.0
           Minimum       1.0            1.0
           Maximum      16.9           16.1

Females    Mean          8.7            7.8
           Median        9.1            7.2
           Minimum       1.0            1.0
           Maximum      16.9           16.9

Weighted estimates. Source: Unpublished data from Longitudinal
Study of the Vocational Rehabilitation
Services Program, Research Triangle Institute, NC: 1999.
Table 2
Frequencies and Distribution of Reading and Math Levels of
Consumers in the State-Federal VR Services Program, by Gender

Frequencies            % Reading       % Reading
                      Male  Female   Total   Male  Female   Total

<= 5th - grade         28.4   23.7     26.2   29.2   26.3     27.8
   6th - 8th           19.6   18.9     19.3   29.1   31.5     30.2
   9th - 12th          41.4   48.8     44.9   36.0   38.7     37.3
       > 12th          10.6    8.6      9.7    5.8    3.5      4.7

Total                 100.0  100.0    100.0   100.0  100.0    100.0

Row Distribution

<= 5th grade           58.0   42.1     100.0   56.0  44.0     100.0
   6th - 8th           54.4   45.6     100.0   51.4  48.6     100.0
   9th - 12th          49.4   50.6     100.0   51.6  48.4     100.0
       > 12th          58.7   41.3     100.0   65.6  34.4     100.0

Total                  53.5   46.5     100.0   53.5  46.5     100.0

Weighted estimates. Source: Unpublished data from Longitudinal
Study of the Vocational Rehabilitation Services Program, Research
Triangle Institute, NC: 1999.

Notes

(1.) The Office of Special Education and Rehabilitative Services identified 5,541,166 children with disabilities, from ages 6 through 21, served under the Individuals with Disabilities Education Act (IDEA) and Chapter 1 of the Elementary and Secondary Education Act. Of these, 69,492 are identified as children with orthopedic disabilities that may include manual limitations, inability to manipulate paper and pencil for manual calculations, or inability to manipulate a hand-held calculator (U.S. Department of Education, 2000).

(2.) For this article, the vocational rehabilitation population is defined as individuals entering a state's vocational rehabilitation agency program. The data on math and reading levels for this population, provided to the author by Research Triangle Institute (RTI), are unpublished data from the Rehabilitation Services Administration's Longitudinal Study of the Vocational Rehabilitation Services Program, which is being conducted by RTI. In the Winter 1999-2000 issue of American Rehabilitation, RTI and RSA reported on findings regarding demographics and employment outcomes for those consumers who obtained competitive employment as a result of VR services during the study data collection period.

(3.) MathPad [TM] was developed by In-foUse with funding from the National Institute on Child Health and Human Development, National Institutes of Health. MathPad [TM] is distributed by Intellitools, Incorporated.

(4.) PlaneMath [TM] was developed by InfoUse with funding from the National Aeronautics and Space Administration (NASA). The PlaneMath [TM] Site is currently maintained by California State Polytechnic University, Pomona (www. Planemath.com).

Bibliography 

Curry, D., Schmitt, M.J., & Waldron, S. (1996, July). Adult Numeracy Network. A Framework for Adult Numeracy Standards: The Mathematics Skills and Abilities Adults Need to be Equipped for the Future.

Hayward, B.J., & Smith, Davis, H. (1999). A Longitudinal Study of the Vocational Rehabilitation Service Program: Fourth Interim Report. Research Triangle Park, NC: Research Triangle Institute.

Kaye, H.S, (2000, March). "Computer and Internet Use Among People with Disabilities," Disability Statistics Report #13, National Institute on Disability and Rehabilitation Research.

Kaznitz, D. (1996). Personal correspondence to InfoUse.

National Council of Teachers of Mathematics (NCTM): Principles and Standards for School Mathematics. (2000).

Platano, Cathy. (1999). Personal correspondence to InfoUse.

Principles and Standards for School Mathematics Standards. (2000). (http://standards.nctm.org/document/index.htm)

U.S. Department of Education. (2000). Twenty-Second Annual Report to Congress on the Implementation of the Individuals with Disabilities Education Act.

Dr. Stoddard is President of InfoUse, the developer of MathPad [TM ]software and the PlaneMath Web site. She has directed many rehabilitation, independent living and disability statistics projects and is especially interested in expanding the availability of math resources for students with disabilities. Ms. Nelson served as InfoUse' s project manager for the development of MathPad [TM] Fractions and Decimals software; she has a background in mathematics publishing and in software project management.