At approximately 3:30pm on a Tuesday afternoon in mid-July, 2000, I was completely baffled. There I sat, dressed in khaki pants and a polo shirt, in a nice leather chair with my arms folded on a mahogany table in a meeting room at Lockheed Martin Naval Electronics & Surveillance Systems in Syracuse, NY. Surrounded by some of the most brilliant minds I had ever encountered, I winced in the middle of this discussion of a high-tech research and development project as I painfully listened to their futile attempts to communicate with each other. Individually, these engineers had some amazing ideas. Imagine what could be accomplished if only they had the ability to effectively share their ideas with each other, I thought. This phenomenon is by no means endemic to Lockheed Martin in Syracuse, NY. I experienced this same bewilderment in many other internships I have had over the past few summers and would venture that in most companies, especially in technical fields, this inability to communicate ideas runs rampant. As we venture into the twenty-first century, the need for mathematicians and computer scientists in industry and the government is growing. From computer scientists developing new technologies at IBM to mathematicians developing new cryptographic algorithms at NSA, in order to stay on the cutting edge it is crucial that the people working in these sectors have the ability to verbalize technical ideas in a way that others can understand.

As I barely heard a five minute conversation that should have taken ten seconds, my thoughts wandered to some of my mathematics and computer science classmates at Colgate University. While the liberal arts education had endowed most Colgate students with effective communication skills, they seemed to have eluded many of my math and C.S. colleagues. I could name many bright students who could breeze through a problem set or programming assignment but could not explain their work to someone else if their life depended on it. It kind of makes sense, I thought. Unlike most humanities or social science majors, math and computer science students do not have many chances to practice communicating their ideas to others. Why does this have to be the case? I decided at that moment that it doesn't.

Three years later, now a teaching assistant and graduate student in the math department here at the University of Pennsylvania, I have not forgotten that resolution. My guiding philosophy in my teaching stems from that moment: teach students to be teachers. Rather than stand up in front of them and lecture, which I know will oftentimes at 8:30am go in one ear and out the other, I regularly give the students problem sets that they first work on in small groups and then explain in front of the rest of the class. During their explanations, I encourage them to elaborate on certain points, trying to help foster their ability to communicate their ideas lucidly. Students are sometimes shy about this at first, but these interpersonal skills are so crucial, and it is extremely rewarding to see them progress in that regard over the course of a semester. Also, by getting these extra opportunities in which they really have to think deeply about the material in order to explain it to someone else, students gain a better grasp of the subject material themselves. Another benefit of conducting recitation in this fashion is that frequently two students will propose different ways of approaching a problem, both correct, so that students are more likely to be exposed to a method that makes sense to them than they would if they just saw my way. In my two years of being a teaching assistant here, I have observed that students really listen to each other when they get up in front of the classroom to speak, probably much more so than with a professor. Being able to not only teach students a subject that I love but also to help them develop their own ability to be teachers is an absolutely joy. I believe my pedagogical philosophy of teaching students in technical fields to be teachers themselves will help them become leaders in industry and maybe even open up their eyes to the option of being teachers in some venue themselves.