From the Editor: Because many people learn mathematics visually, blind students are often urged to study other disciplines, and, if they find it hard to grasp a concept, they are quickly assured that their lack of vision is to blame. Couple this with the tendency of Americans to shy away from math and other hard sciences, and it is not surprising that the number of blind mathematicians is quite small. With creativity and motivation blindness need not come between bright people and the key to engineering, physics, chemistry, and the other sciences that bring us inventions both to lengthen our lives and enhance their quality. Here is the account of one blind student as she prepares to master geometry and to take her place in determining the shape of the future. It is reprinted from the Old Dominion University website. It appeared April 11, 2011.
"We have congruent angles and proportional sides. If I can get a couple of these measurements, I can extrapolate." Suzanne Doviak, senior lecturer in mathematics, makes a point about geometry to her math 302 class in Old Dominion University's Constant Hall. It's a large lecture hall, and the fifty or so students dutifully take notes. The final examination is coming up soon, and there's no time to waste.
Meanwhile, two students in the second row hold a quiet conversation. Jeff Abbott takes a piece of modeling clay and folds it into the shape that Doviak is drawing on the board. Mary Carlisle runs her fingers gently over the clay. The whispered conversation continues as Abbott tells, as well as shows, Carlisle what he sees.
Born extremely prematurely, Carlisle suffered severe damage to both retinas in the days after she was born from receiving too much oxygen in an incubator. Her entire life she's had zero vision in her right eye and can see only shapes and colors with her left. But she's on track to graduate in the fall with a degree in education--and getting an A in Doviak's highly visual geometry course, thanks to a system she and Abbott developed after randomly sitting next to each other the first day of class. Carlisle hopes to become a teacher herself.
"It was purely by accident. I was sitting in class, and Mary came in and sat down next to me. We just started casually talking," said Abbott, a retired Navy air traffic controller, who is at ODU on the GI Bill, majoring in special education. "By the end of the class she said she was going to have to go to disability services to get assistance for the class, and I thought, `What can we do together here?'"
The next day Abbott brought pipe cleaners into class. As Doviak drew diagrams, Abbott would shape the pipe cleaners into physical objects Carlisle could touch, replicating the shapes on the board. As the problems became more complex, he switched to modeling clay. Now, after three months in class together, "we've got it down pat," he said.
Doviak was worried when informed by Kate Broderick, ODU's director of educational accessibility, that Carlisle was enrolling in the class. But that worry has turned to wonder as she has watched Carlisle and Abbott work out their system to help her learn geometry. "I really worried about how she was going to keep all those little pieces of information in her head. But having a tactile model is just another way of seeing. It's been phenomenal," Doviak said. "Jeff and Mary worked this out together, and I'm just pleased as punch. They're also both incredibly strong students." Doviak said she barely changes the way she conducts her lectures in class. She doesn't need to.
"She's stopped us in class a couple of times and asked us if we're OK. I looked at her one time and said, 'We're ahead of you,'" Abbott said.
Carlisle had her own concerns about taking the class, despite having tackled physics and statistics previously. She said she's "extraordinarily appreciative" of the help she's received from Abbott. "I've had some tough classes, but I had been dreading this class. I knew that the entire class was visual," she said. "But when Jeff makes the clay, I can feel it tactilely and it just makes sense of what she's saying. Honestly, I probably would be failing if it wasn't for him."
Abbott said he is also benefitting from the process and not just because it's an ideal workshop for a future special education teacher. "It honestly helps me in the class," he said. "As an air traffic controller for twenty years in the Navy, I had to function in a two-dimensional world, but see things in three dimensions. By using the clay, we create that three-dimensional world for Mary. It helps me gain a greater understanding of the problems."
The duo talk quietly through classes, as Abbott makes sure Carlisle is grasping the concepts. Occasionally he will joke with her to break the tension. Doviak said the rest of the class doesn't even notice. "Like me, they're just so proud of these two, and they have so much admiration for everything they've been able to do. It's like taking a course in a foreign language and not being able to hear, but managing to get an A at the end of the course.”