By Alex Luna

After about two and a half years of graduate school, my perspective about many things has changed. The way that I interpret studying and general learning is one example, but an unexpected item is communication. Professional interaction is an area that I put a lot of thought into, as it is something that occurs frequently in my day-to-day life. Within just my own institution, I am constantly in contact with undergraduate students, other graduate students, my professors, and my advisor. With these characters in mind, I find that there are three main, not necessarily disjoint, categories of people that I interact with regularly:

• Mentors: This includes my advisor, any other research mentors, and the professors of my courses

• Peers: This set contains other graduate students, but an important subset is those that are in a common classes, or do similar research

• Mentees: Members here include the students in my discussion sessions, students in my reading courses, and other undergraduates seeking advice

With respect to communication in each category, I have identified common hurdles that I, but possibly others, have faced, and reflected on how to overcome them. While these tips are useful locally, they have also been helpful while attending conferences and talking with guest speakers outside of my institution, and also to global life, outside of math.

For me, most anxiety linked to communicating with faculty members, especially my own advisor, has come from the insecurity of simply not feeling smart enough. To be more specific, the main situation is lacking confidence while talking with a mentor about something they are more experienced in. For example, even though I may prepare thoroughly for a research meeting, or an office hour appointment, beforehand, I sometimes feel more lost in the meeting, rather than when I was thinking about things on my own. After some reflection, my main takeaway was that my mentor and I probably do not share the same intuition about the subject matter. As a consequence, the lack of fluidity in my mathematical questions or explanations are highlighted while talking to the expert. With this perspective in mind, the solution is hidden within the observation. The course of action is to become comfortable with this uncomfortability of not being fluent in the subject. After all, every expert was once also inexperienced. To help ease the uncomfortability, I often think about where I was mathematically about six years ago, when I had just started college, and compare it to where I am now. After reflecting on where six years of work has taken me, I imagine where my advisor and professors, who have decades of experience over me, may lie. This thought process allows me to be okay with making mistakes in front of mentors of this caliber, and to be patient with the learning process.

With this perspective handy, it also transitions into communicating with my peers. Since everyone comes from a different background, there are other students that have different strengths. From the outside, they may seem to be much more knowledgeable, better teachers, or better at their respective research, than me. Out of fear of, again, not sounding mathematically confident, the communication challenge that I face in these situations is avoidance. Unlike having to meet with my advisor weekly, or needing to meet with a professor to help further a homework assignment, it is not a requirement to talk to my peers. However, when I do interact with other students, it is easy to choose the trajectory of the conversation in such a way that it avoids any type of serious academic discussions. To overcome this behavior, I try to keep the same perspective regarding experience imbalance  in mind, but I also force myself to have these mathematical and academic conversations regardless. Eventually, these conversations become easier with practice, but at the same time, if I feel that someone is a stronger student than me, I identify in what sense, and then try to learn about their thought process in such a domain. Essentially, I do my best to see each interaction as a possible learning experience, and this makes socializing in this category less daunting.

One significant difference that separates my graduate professional life, and my undergraduate one, is the existence of the third category above. A common communication battle here lies in the process of gaining the confidence of my mentees. In other words, I always strive to communicate with a mentee in such a way that they trust in my mathematical ability, but more importantly to prove that I do have their best learning interest at heart. My main approach is to treat my students the same way I would like to be treated by my teachers. This tip may be overused, but certainly not overrated. What one looks for in a mentor is unique to each individual, but for me, I constantly remind my students that it is okay to struggle. When they do have mathematical struggles, I actively try to figure out their thought process, and try to look back at my own history. If common ground is found in this procedure, I very openly share my experiences and personal advice. Again, while the actual process might look different for everyone, being a graduate student gives a unique opportunity to be a mentor and mentee simultaneously, and these two positions complement each other very well.

While these are just some tips from me, I’m constantly learning and trying to improve my professional communication skills. Some of these hurdles may be unique to only me, but I hope that others that may relate, find my process helpful. 

Alex Luna is a third year graduate student in the mathematics department at University of California, Irvine.