Cliff's Column on Productive Failure: The Burden of Proof in Belonging

A second post by Cliff Bridges, CU Boulder

Alright, it’s time to get to the business at hand: what stories do I have of failure and how could they possibly soothe anyone else?

The failure which may resonate with the most students, in particular graduate students, is founded in my department’s introductory graduate exams. My department calls these “Preliminary Exams”, or prelims. These are written exams given in each of the first 5 semesters as a graduate student until you pass, and as the name suggests, is meant to test students in material which is requisite for their career as a mathematician. Most graduate math programs have an analogous exam, though names, timetables, and number of attempts may change. In any case, I have heard that failing these exams is the largest cause of attrition in math departments. And by now you may have guessed that I did not pass these exams at first.

Saying “at first” is something I’ve been conditioned to do; to soften the blow of failure and look forward to the future where the endless joy of success nullifies the sting of defeat. But describing endless joy is not the point of this column. The point of this column is to work through the sting. So, more earnestly, I did not just fail prelims at first, I failed at second, third, and fourth too. All of these attempts and failures affected my experience as a graduate student, so that is what I will focus on now.

Some of the more memorable parts of my prelim process were the comments I received, such as “Did you not study?” and “I passed, why didn’t you pass?” and “Maybe you shouldn’t be here. There are departments with lower standards than ours that you could think about joining.” In fairness to these department members, I sincerely don’t think their comments were ill-intentioned. I do, however, think their comments were callous and harmful. Despite this, I unnecessarily spent mental energy replaying their words and thinking about how to respond.

Initially, I took their comments as fairly innocuous. (Unless you are threatening my physical well-being, I usually don’t have much of an emotional response to words.) I thought, “Of course I studied, I studied a lot. That can’t be what you mean to ask.” But, there was no simple answer to the question “did you study?”, which was code for: “Do you really belong here?” Okay, I guess a simple answer was “yes, I belong”, but that felt pretty unconvincing after failing something so “introductory” it is called a prelim. For 3-6 months I had to sit with the unanswered question of my belonging until the next opportunity to provide evidence confirming my suspicions. Carrying a load like that weighed on me, and I think that this weight was the strongest force pushing me out of the department.

The comments of department members magnified this force urging me to leave, and this is why I say their words were harmful. But once I discovered this magnifying effect, I was very adamant that a scaling factor wasn’t going to be the thing that got me to leave. If I was going to leave, it would be on my own accord, based on my own feelings about belonging in this group. I would not be forced out by someone else’s emotional reaction towards my presence. I didn’t want anyone who would try to sabotage my career to have enough power in my life to carry out their plans.

Now, I still had to deal with the initial weight of the "do I belong" question. For me, there was no outside influence who could lighten this load, no support of a mentor or family member who could convince me of something I couldn’t convince myself of. So I had to figure out a way to prove to myself that I did belong, or I had to leave. However, for better or for worse, “prove” is a loaded word for a mathematician.

There was no formal way to prove that I belonged, and there is no formal way for anyone reading this to prove that they belong. Due to the implicit subjectivity of anything defined by society, belonging to a social structure is either trivial, completely subjective, or both. Because of this, there will always be people, a.k.a. gatekeepers, who want to exclude you from groups they think you shouldn’t belong to. I don’t know your struggle, and I won’t be able to help you prove to yourself that you belong. Honestly, I don’t even want to convince you of your belonging. I want to empower you to make this decision for yourself, despite what the gatekeepers are speaking in your ear, despite how much extra weight they are adding to the forces pushing you out, even despite the people who will talk you into belonging to a group you don’t like. I want you to be able to recognize that their words can make the decision heavier, but those words can’t determine whether or not you belong. Only you can do that.

Nowadays I intentionally make space to reflect on where my belonging has been questioned, and even where I have questioned someone else’s belonging. Practicing identifying those situations in my own life has shifted my mindset towards leaning into how failure can be productive. This has even helped me find words to encourage my students when they need another push. Overall, I can’t say that I see failure less, but I can say that I worry less when I see it.

Alright everyone, the bumpy journey through failure has begun. I hope you’re still hanging on looking forward to the next installment!

SY’s Editor’s Note Cliff hits many key issues in the critical period of time, when many students are considering staying vs. leaving graduate school. Thank you Cliff for sharing your story and for being your authentic self on a challenging topic.

One issue I would like to focus on is the role and responsibility of faculty. Speaking as faculty, I see my role as being a positive force for student. And this means mentoring students and being careful about how we speak and being attuned to the needs of students. Women and people of color are significantly underrepresented in Mathematics, and many carry extra burdens placed upon them by circumstances and society and have more obstacles to overcome. Many of these burdens and obstacles are not easily visible, and faculty can be quick to judge. I encourage all faculty from all backgrounds to consider how we can support students, especially when they are dealing with challenging circumstances, and to come into these situations from a position of generosity, compassion, and empathy.