High Anxiety

“I’m not just teaching you math, I’m teaching you how to think.”

That was Katherine Heller’s (MS Mathematics ’06, PhD Mathematics ’10) “light-bulb moment,” when her high-school calculus teacher explained to a skeptical student why what may have seemed like an esoteric course would be worthwhile for their lives. From that point on, Heller began to consider devoting her life to mathematics.

In her fifth year of pursuing a Ph.D. in operator theory in the College and Graduate School of Arts & Sciences, Heller has known she would teach since she “fell in love with teaching” as an undergraduate teaching assistant at the University of South Carolina.  

The U.Va. Mathematics Department has quietly achieved renown for the teachers it produces. For three consecutive years, the winners of the University’s Teaching Resource Center All-University Graduate Assistant Teaching Award in the sciences, which includes engineering and nursing, have been mathematics graduate students. Heller is this year’s nominee. 

Mathematics graduate students, who do two to three years of coursework before their thesis research, typically also work as teaching assistants. “We have a few people who are supported purely on research fellowships, but most of our students are T.A.s,” says Mathematics Professor Barbara MacCluer, who is the department’s director of graduate studies and Heller’s thesis advisor. Unlike departments of mathematics at many universities, where graduate students teach discussion sections of large lecture classes taught by professors, U.Va. mathematics grad students are responsible for their own courses, usually (but not exclusively) introductory calculus classes; two versions are offered, for math and non-math majors, and typically they have about 40 students, typically first years.  

“The two various calculus classes have their own challenges and their own rewards,” says Heller, a South Carolina native. “The math and science majors share that inner math nerd for what we’re actually doing. I’ve had several come by and say, ‘I think I’m going to be a math major.’” 

She also greatly enjoys the nonmajors. “The applied calc students usually have very little interest in the material itself. I want to help them find value and excitement in the course. I try to encourage them and win them over throughout the semester.” 

“The students are phenomenal, I love working with them, they’re so much fun,” she says.

Calculus students all take the same examinations, but otherwise, the graduate-student instructors are given freedom in how they run their classes, says Heller. “We can decide if we’re going to use online homework or paper homework or projects, and I think that inspires the grad students to want to do a really great job—to try different things. We spend a lot of time sitting around our office and even when we’re out to dinner and socializing, we’re talking about our teaching and brainstorming about what works and what doesn’t work.

“Everybody has their own personality and their own teaching style. We steal notes from each other and are happy to let others borrow them. It’s a really open environment for a lot of that dialog and I think it inspires really great teaching.” 

MacCluer helped Heller pull together her dossier for this year’s teaching award competition. “I’ve looked at lots of evaluations, but I’ve never seen any quite so outstanding as Katherine’s,” she says. “She’s a very caring teacher, she manages to connect well with all of her students, whether they’re naturally talented in mathematics or whether they’re at the opposite extreme.” 

The department’s graduate program is funded in part by a Graduate Assistance in Areas of National Need grant from the U.S. Department of Education. “They are interested in supporting excellence in a variety of ways, including excellence in teaching, so as part of our GAANN grant we certainly pay attention to developing our students as good teachers,” says MacCluer. 

All first-year graduate T.A.s take a teaching seminar that focuses not only on the courses they are teaching but on broader pedagogical issues. A faculty member observes their teaching in the classroom as well. “When they finish here, they have extensive documentation of their teaching ability, and they usually have had a wide variety of teaching experiences that serve them well, especially if they’re going on the academic job market.” Says MacCluer.

Heller takes her passion for teaching, mathematics and young people outside the classroom, too. With Associate Professor Irina Mitrea, she has volunteered for Girls and Mathematics, a weeklong summer program sponsored by the College and Graduate School of Arts & Sciences and the Department of Mathematics for middle-school girls in Charlottesville that exposes them to mathematics’ joys as well as its challenges (which are often the same). 

U.Va.’s Mathematics Department has an unusually high number of women graduate students. According to figures published in the August 2004 issue of the Notices of the American Mathematical Society, between 1996 and 2003, 37 percent of U.Va. math Ph.D.s were women, compared with 22 percent at its peer Group I public schools, and 19 percent at Group I private schools. The University tied with the University of Oregon for the top percentage among Group I public schools, and was in the top 20 mathematics graduate programs in the country in terms of sheer numbers of women Ph.D. recipients—ahead of programs many times the size of this relatively small program. “The successes of previous women students in our program and the large cohort of current women students serve to encourage others to apply and matriculate here,” says MacCluer. 

Heller has also been active in the Teaching Resource Center with Deandra Little, an assistant professor and faculty consultant there. “She and other members of the TRC staff have helped me grow as an instructor,” says Heller. “I work with other grad students, from Italian, psychology, history— very different fields from the one that I’m in, but it’s been amazing to dialogue with those instructors, and the challenge is to analyze why and whether or not they’re being successful in the classroom. It’s been a wonderful experience.”

For Heller, it’s the non-math majors who have provided her most rewarding experiences as a teacher. “They come in with math anxiety, work hard, come by during office hours a couple times a week and at the end of the semester, they’ve worked so hard and are so proud to get their Bs or Cs. They have a look of confidence and ‘I did it’ on their faces, and my hope is that they’ll take that memory and that confidence and apply it to other aspects of their lives as well—take that challenge, look back on calculus class and see that they were able to overcome their fears.” 

She may just be giving her students their own light-bulb moments, moments that will not only ignite in them a passion for the subject matter but ignite a sense of strength and confidence that will serve them throughout their lives.