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Beyond mainstreaming.

Jane, a pretty brunette with an easy laugh, always had her sippy cup mounted on the side of her wheelchair and a bag of notebooks hanging off the back. When I did mathematics research with Jane, we spread our notes out over a big table, created conjectures, and shot them down until we found one that survived, which we then tried to prove. A chain of proofs led to a theorem and a math paper accepted at a refereed undergraduate math journal; a good experience and outcome for both of us.

Jane and I were a team for the summer of 2008, before Jane's junior year of college. Jane has Friedreich's ataxia, a degenerative condition that has complicated her education. Our story belongs in this issue of the CUR Quarterly, dedicated to at-risk students, for several reasons. Disabled students often have hefty medical costs that strain their finances. Their disabilities also drain their time since literally everything takes longer than planned. For students whose conditions worsen over time, worries about mortality run in the background of any discussions about the next academic year. In spite of all this, however, disabled students can make excellent research partners.

In many ways, disabled college students resemble a random slice of the undergraduate population. The breakdown among their majors, career goals, and finances shows little difference from those of other students. For instance, math has the same "popularity" among disabled students as it has among students without disabilities. When we look at the graduate part of academia, we find few disabled researchers in STEM disciplines. According to a massive 2007 NSF report, in 2004, 25,991 science and engineering doctorates were conferred in the United States. Of those, 88 were awarded to people with physical disabilities.

Jane was a top student in my calculus classes at Aquinas College. Her classmates deferred to her, not out of pity, but because she was always right. Jane worked hard at all her subjects. As she says, "I couldn't just do what my peers expect. I have to exceed expectations. I don't want to be seen as if I'm barely keeping up. My drive motivates people and that makes me happy."

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Aquinas has an endowment that allows the awarding of the Mohler/Thompson Summer Research Grants for faculty and students. When I received a grant, I made Jane a priority in my research plans, and I had no trouble getting her to apply to do summer research with me. This choice, however, led to some interesting discussions amongst Mohler professors. The Mohler/ Thompson guidelines urge professors to work with students aiming for graduate school, a common long-term goal of such programs. My desire to work with the best student possible, however, won out over worries about Jane's likelihood of going to graduate school.

The choice proved most fortunate, partly because of Jane's intelligence but also because of a coping strategy she had developed. As her fine motor skills deteriorated, Jane would take fewer notes by condensing the ideas before writing things down. So in calculus, for example, she would perform as many steps in her head as she could. Now faculty members have all seen the mistakes students make when a lazy pencil combines with a stumbling mind. Jane's drive would not allow such sloppiness, however. She became quite good at watching a blackboard fill with math and then writing down a condensed version. She could fit a thorough summary into a complicated, but brief, picture. She could also perform the reverse, teasing the most information out of a figure or equation.

Our area of summer research was knot theory. I introduced her to some difficult, open questions that researchers had left behind as the frontiers of knot theory expanded. We began chipping away at relevant examples, small parts of much bigger problems. Jane repeatedly amazed me with her ability to study a tangled Medusa's head of pieces of curves and sketch the simplified version far faster than I could. Once, when faced with a drawing in which the strands were interlaced in way I thought was, in a sense, maximally interlaced, Jane drew a simplification with very few crossings of strands remaining. I took it home and worked on it for 90 minutes. Jane was right! When I asked how she had seen it, Jane said that she had combed it with her fingers, mentally. I had a research partner skilled at our most annoying task!

Neither of us will never forget a summer day at the library when we were counting how many ways certain sorts of diagrams could occur and found a sequence beginning 1, 1. Then I went to the restroom, and Jane computed her assigned cases, getting a 2 and a 3. Next, it was Jane's turn to take a break while I worked on my cases without seeing hers, getting a 5 and an 8. When we put our calculations together, we recognized a "celebrity" in the world of mathematics. The Fibonacci numbers, that sequence beginning 1,1,2,3,5,8,13. the start of The Da Vinci Code, those integers were in the problem! Our satisfaction was complete when we were able to prove that the objects we were counting did indeed occur in these famous amounts. When I accompanied Jane to her home on my bicycle, our wheels barely touched the ground.

Our result can be interpreted visually. Imagine a round room with people along the perimeter, backs to the wall. Each person may link arms with the person to the left or the right or neither. We were considering all possible cases, with particular attention to the cases where at least one person was isolated. Eventually, we used the Fibonacci numbers to establish that the ratio of cases with isolated people to the total number of possibilities approaches one as the number of people increases. In other words, if a large number of people link arms at random, almost certainly at least one person stands alone. (Of course, our math figures were not people. Interested readers will find our paper, "Fibonacci numbers when counting chord diagrams," in the Pi Mu Epsilon Journal.)

Even though mathematicians usually don't care about movie stars, we lose it in the presence of famous mathematical entities! Jane's and my euphoria had a small setback when we found that the objects we were counting were just a little different-looking from a long-known example of Fibonacci numbers, but we were still quite happy that the sequence had occurred unexpectedly within the context of knot theory. Jane has presented our work at Michigan State University, Grand Valley State University, and Aquinas College. The publication and talks certainly provided a happy ending to our tale for Jane and me.

Other professors should ask themselves if they have similarly kept their disabled students in mind when they're prodding students to apply for undergraduate research programs. The Americans with Disabilities Act prohibits discrimination in programs that receive assistance from the U.S. Department of Education. Professors should consider disabled candidates, regardless of their funding sources, however. This is not to imply that any professor would discriminate against any reasonable candidate for a research experience. Yet disabled students are underrepresented in the sciences, and certainly as this article indicates, inconveniences for students and faculty can arise during the research process.

Jane takes hours to write, long-hand, what amounts to a page of type. This is not writer's block. Using a computer tires her eyes. She can barely hear over a cell phone, making quick revisions impossible. Put these all factors together, and it is clear that writing a paper with Jane takes a long time. A professor who works with a disabled student thus should commit to flexibility of methods and scheduling, as well as other accommodations that may not be predicted before the project starts.

Jane's story illustrates, though, the good things that can happen when unusual candidates receive consideration. Some students don't seriously ponder undergraduate research for various reasons, and disabled and other at-risk students might automatically think, "Here is another opportunity that is not for me." I believe that any professor who can make a connection for a good candidate has a duty to do so, though, regardless of physical or financial contingencies.

Jill Straub, program specialist for student support services at Aquinas, acknowledges that disabled students might hesitate to apply for a research experience for several reasons. Sometimes their summer begins with lots of prescribed rest; the last thing they want after a year of college is eight weeks of math. Many disabled students avoid using their difficulties as an excuse, and they might see the unknown activity of summer research as a situation in which their physical limitations would become a central issue. Jane competes hard for success partly because she does not want her difficulties to receive any notice, except to inspire other students to work.

Straub also notes that people often expect disabled students to be activists for better facilities and access, but they do not expect them to pursue additional purely academic work, such as research.

A student's disability complicates many actions every day. Straub maintains her workload and does graduate work while dealing with a spinal cord injury, noting "You try not to let the disability control you. But in many ways the disability is the first priority."

When I asked Jane for her favorite parts of doing research, she placed productivity first. She also admits that getting her mind off her condition helps her cope, although she says this is secondary to getting good results!

I never discussed the physical hurdles with Jane during our summer research. We literally talked math all the time, even during lunch breaks. I did learn diligence from Jane. She inspired me to work hard because on days when we did not meet, I knew she would produce pages of broken conjectures and attempted proofs to show me the next time I saw her?so I could do no less. I appreciated her skill and respected her intelligence. I did not, however, until the research was finished fully see her bravery or appreciate my good fortune and the many ways in which math provided research opportunities. I took it for granted that Jane would love research and that we would find good things in knots.

Research turned out to be a good fit for Jane, however. "Talk about thinking outside the box!" she says. The progression of "Friedreich's ataxia requires adaptability. I have to figure out a new way to do something I've always done," Jane notes. Similarly, finding new ways around obstacles summarizes much math research. Although many at-risk students might hesitate to apply to do research, they may have--as Jane's diligence and persistence demonstrate--very beneficial skills or attitudes.

When a topic meshes with a student's skill set, great things can happen. Thinking about such a match is worth some forethought by faculty members. Jane liked being a motivator and speculates, "If a professor has three researchers and one, like me, creatively adapts to life's problems, the other two gain experience from working with that one unusual student."

Michael McDaniel

Aquinas College

1607 Robinson Road SE

Grand Rapids, MI 49506

mcdanmic@aquinas.edu

McDaniel has been a CUR Councilor in math for three years. His time at CUR coincides with his journey into undergraduate research. Knot theory and geometry have given his summer researchers new results each year, with a paper for each summer, two accepted for publication in refereed undergraduate journals. These successes blur into his course preparation, where entry-level students explore knots and geometry beyond their texts, creating projects that fill display cases and decorate the department. He has taught in the US Virgin Islands, New Jersey, Maryland and Michigan.
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Title Annotation:CUR Focus
Author:McDaniel, Michael
Publication:Council on Undergraduate Research Quarterly
Article Type:Essay
Geographic Code:1USA
Date:Mar 22, 2011
Words:1960
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