Guru meets Yogi in math class
by Prof. Steven Bell
One of the pleasures that has come with getting old and gray in our Math Department is that I get to mentor young faculty about their teaching. This past semester, I sat in on Golomb Assistant Professor Veronica Quitalo's differential equations for engineers class (MA 303) to watch her in action and maybe give her some pointers about how to improve her teaching.
I expected the session to go well because I often talked with Veronica about her teaching and I knew she was serious about it, but I did not expect the role reversal that was about to occur.
MA 303 is a second course on Differential Equations for Science and Engineering majors. On the day I visited, Veronica was teaching a rather difficult section on the phase plane and solutions to first order linear systems. She made clever and efficient use of the blackboard, using multi-colored chalk, and started by giving a gentle introduction to the subject that made the class "discover" the standard interpretation of the phase plane. She interspersed her lecture with questions to the class and waited patiently for students to respond, so the class was truly interactive. She described the way trajectories follow the direction field in the phase plane by comparing the field to a 2D field for fluid flow and solving initial value problems like dropping a "little boat" in the "lake" and letting it follow the flow. I had the feeling that the students had a very vivid and tactile understanding of the concept after Veronica's presentation.
The atmosphere was relaxed and pleasant. The students were all attentive, taking notes. It was clear that they liked Veronica and were comfortable to speak up in class.
Up to this point, Veronica was merely a polished and skillful instructor, but then she did something that surprised me. She said, "Ok, now you work this problem while I erase the board." The whole class dove into their notebooks and began working on the problem, making it clear to me that this was part of their daily routine in this class.
She kept saying how much fun the problems were and I think the students really believed her.
"How is she doing this?" I asked myself. Something seemed fishy!
Then she did something I had never seen before. She paused to give the class a short break. I had a feeling something unusual was about to happen because the class didn't start pulling out cell phones or talking to each other. They straightened their backs and closed their eyes! Veronica then led the class in a five minute, very professional, meditation, breathing, relaxation exercise. I wish I had a video of the whole thing. All the students participated and it was clear that they were highly refreshed, smiling, and eager to learn afterward.
After class, I told Veronica my reaction to what I had just seen and asked her how it has affected her teaching evaluations. They have gone through the roof! I asked if I could read the evaluation comments from students and found uniform high praise for the meditation break feature of Veronica's teaching. In particular, students who complained about having had math anxiety and of having performed poorly in math classes find this exercise most beneficial. Some students called Veronica a ray of sunshine or a beacon of positive energy. Many called her their favorite math teacher of all time. Many claim that her teaching and positivity made attending her class a pleasure, and consequently, they did better than they had ever done before in a math class. Students also felt that Veronica cared about their well-being, not just about their mathematical advancement.
I sensed that Veronica held particular sway over the young women in the class. She was clearly a fantastic and very supportive role model for them.
Veronica has a secret math teaching weapon and she knows how to use it very effectively. She exhibits in her classroom a sophisticated teaching philosophy that calls for active learning and constant mastery and reinforcement, with support and encouragement at a very deep level.
That day, the master became the pupil!