Campbell Rutherford, left, and her Calculus III professor Tony Crossland show the quadric sections Crossland had 3D printed for Campbell, who is blind

Campbell Rutherford, left, and her Calculus III professor Tony Crossland show the quadric sections Crossland had 3D printed to help Campbell “see” the shapes that go with the equations in class. Rutherford is a Braille reader and cane user, having lived with a a rare genetic eye disorder her entire life.

Blind since birth, Campbell Rutherford of Dandridge is used to “seeing” the world a different way from her sighted peers. But as a dual enrollment student at Pellissippi State Community College since fall 2020, Rutherford has helped her professors “see” new ways of teaching. 

“Parts of calculus are inherently visual,” said Associate Professor Tony Crossland, who had Rutherford for Calculus III this spring. “I’ve taught this course for several years and gotten away with drawing shapes for the students, so I knew it would be a challenge with Campbell because she would need to ‘see’ the shapes.” 

Calculus III is the study of functions in two or more dimensions. This includes a focus on six quadric surfaces, which are 3D extensions of conic shapes such as ellipses, parabolas and hyperbolas. Students learn how to examine cross sections of these shapes to figure out what surface a given equation represents. 

“The main task of Calculus III is to learn the equations that equal these shapes,” Crossland explained. “Calculus III is about 60 percent visualization, so I was a little bit nervous because Campbell is the first blind student I’ve had in my classes.” 

Rutherford wasn’t intimidated, however, having lived with Leber congenital amaurosis, a rare genetic eye disorder commonly referred to as LCA, her entire life. The condition causes moderate to severe vision impairment to blindness and, as a Braille reader and a cane user, Rutherford describes herself as “much closer to the totally blind end of the spectrum.” 

“I have to access all my schoolwork through screen readers,” she added. 

Rutherford, now 19, has been homeschooled since fifth grade and wanted to take dual enrollment courses at Pellissippi State to gain experience in a classroom before attending college full time. She thought it would be helpful for her to practice requesting accommodations as well. 

“It has been much easier to get accommodations at Pellissippi State than in public school,” noted Rutherford, who has taken Spanish I and II, Calculus II and III, and General Biology I and II at Pellissippi State. “I have not had a problem getting anything I needed. Disability Services has always been there.” 

But when it came to Calculus III, Crossland went above and beyond her expectations, working with Associate Professor Lynn Klett, who teaches Mechanical Engineering Technology classes, to make 3D models of the six quadric surfaces. He then loaned those models, called quadric sections, to Rutherford for Calculus III. 

“I wanted her to get an idea of what kind of shape goes with what equation,” Crossland said of the shapes, which range between 7 and 8 inches tall and vary in thickness. “It helps that Campbell has an affinity for mathematics and that she enjoys the subject matter. It’s been a pleasure to work with her, and I’m fascinated by learning how she learns.” 

Close up of Campbell Rutherford's hands and the 3D printed quadric sections for Calculus III

Campbell Rutherford shows the quadric sections her Calculus III professor had 3D printed for her.

While Rutherford has been provided existing 3D models in science classes – representing molecules and DNA, for example – this was the first time a math instructor had 3D models made especially for her, she noted. And this was not an accommodation that she requested. 

“Having these quadric sections was extraordinarily helpful because the surfaces we were examining are composites of the different figures we have learned in Calculus I and II and even algebra,” Rutherford said. 

For the nonmathematically minded, Rutherford gave the example of a paraboloid, which she described as a U-shaped bowl instead of a U-shaped line on a graph. Calculus III students need to be able to examine its cross sections in order to reproduce the equations in two dimensions, she explained. 

“Think of an Easter egg,” Crossland added. “The shape is oval if you slice it horizontally, but round if you slice it vertically. Students need to know how to piece these surfaces together to get the right equations.” 

Rutherford finished Calculus III with an A and has already committed to Harvard University this fall, where she plans to major in applied mathematics as an undergraduate with a goal of pursuing either biostatistics/bioinformatics or cybersecurity in graduate school. 

“For homeschooled students especially, I would recommend taking dual enrollment classes to help prepare you for college,” she said. “In college you will have to be self-motivated because people won’t stay on top of you to turn in your assignments, and you’ll develop different study habits. 

“For students with disabilities, I would say, ‘Don’t be afraid to talk to Disability Services and ask them for what you need, but don’t go in demanding your rights with an attitude of entitlement,’” Rutherford added. “You’ll be surprised how far a civil conversation can go, and it will help you to build good relationships with college staff and your professors. They will be more willing to help you and not treat you like a burden.” 

Crossland balked at how Rutherford ever could be considered a burden to her teachers. 

“She has been so accommodating to us,” he stressed. “She’s such an eager and earnest learner, and her work is always immaculate. There are problems that require me to use scratch paper, and she already has the answer! It’s very impressive the way she can visualize and calculate in her beautiful brain.” 

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