On Being Imperfect

By Gizem Karaali, Pomona College

I have a secret: For the last year or so, my nine-year-old daughter and I have been trying to develop a meditation practice. This guy, Andy, who leads us daily through meditation sessions facilitated by a phone app, has become a familiar name between my daughter and me. (Even my five-year-old occasionally mentions Andy when going to bed at night; sleepy-time Andy tells us to lie on our backs and close our eyes and start by saying good night to our toes.) One day my daughter posed me a question. We had just completed our ten-minute session for the day. She was not willing to move on yet, it seemed, so I waited. She finally formulated her question and asked, very carefully, “Mom, is Andy perfect?”

This is a profound question even though it has an easy answer: “No”. If Andy is human, he is not perfect. Yet none of his flaws are really my business, because he is effectively teaching us to be better. He is consistently, with kindness, in good humor, and with no sign of condescension, telling us how we can do better.  In every session, or let me be honest, in most sessions, we learn from him.

Aren’t there always those we look up to who exemplify ideals we wish to uphold or those who represent the type of character that leaves us in awe? Reading Art Duval’s post on kindness in this very blog, listening to Francis Su’s talk on mathematics for human flourishing, digging into clear critiques of our community fearlessly dispensed by mathematicians such as Piper Harron and Izabella Laba, some of us might wistfully say: but I am not good enough. I am not as capable. I am not as kind. I am not as forgiving. I am not as insightful. I am not as brave.

Now let me rephrase that for you so as to be clear. All of the above are ways of saying the same thing: “I am not ready to be vulnerable.” All these amazing people are amazing partially because they are willing to put themselves out there, trying to live up to their own ideals. (And for some, an alternative may not even exist.) Do they ever falter? Maybe they do. It is not my story to tell. Again, like Andy, any of their possible faltering is none of my business. What is my business is what I learn from them.

Now some might be concerned that I am potentially giving some people free pass to be terrible human beings as long as they try to uphold certain ideals. Slippery slope and such, and where do you stand with respect to Thomas Jefferson and Bertrand Russell and Roman Polanski and Bill Cosby and <pick your favorite fallen idol here>? I could of course share my opinions about those particularly imperfect men here, or I could simply affirm that certain people seem to be allowed more imperfections than others. But that is not my point here.

My point is that those of us who see teaching as our vocation are probably not all perfect, and many of us will never be perfect. But we should allow ourselves this imperfection as we continue to try to teach as well as we possibly can. Ours is a profession in flux: we grow every day we go into the classroom, we have opportunities to learn with every mistake we make, with every new topic we get into, and with every new pedagogical tool we adopt or leave behind. And we are not going to be perfect every day; for many of us, it is actually a rare day that ends without any major snafus. But we are human and we continue to grow and make mistakes and strive to improve till we die. When we can accept this as a fact of life and stop beating ourselves up about our imperfections, we have that breathing room to grow, and perhaps even ironically, to get closer to our own ideals.

As teachers, we owe it to ourselves and to our students to try and be decent human beings. There are simple rules after all: Respect your students, respect the fact that there is a power differential in the classroom and in any teacher-student relationship, and respect the needs and life constraints of your students. Once we are agreed upon these basic rules, however, the test is no longer about perfection. We need to allow ourselves to embrace our humanity and our own “under construction” status.

This, I hope, is a liberating point. As a teacher you are probably not perfect. You are probably not doing everything right. But if you have your heart in the right place (in terms of the three respect-related rules above) and if you are striving to be a better teacher, occasional failures or imperfections are expected and should not stop you from trying and trying again. Francis Su explains this in exquisite language in his talk on the lesson of grace in teaching, and I cannot claim to be able to say it better: “Your accomplishments are NOT what make you a worthy human being.” Here is the friendly amendment summarizing this post: Your imperfections are part of what makes you a worthy human being. Do not reject or hate them. Instead accept them, learn from them, and grow with them.

Next comes the question of transparency. Ok, even if we come to terms with our own humanity and the necessarily associated imperfection, how much of this can we reveal to our students and colleagues? Do we share with students our pedagogical flaws or mathematical troubles? Do we discuss our shortcomings with colleagues?

Francis Su talks about some of this in the context of grace, but my daughter has already noted that Andy does not admit to many flaws in his recordings. In my case, I have noticed that as I got older and became a part of the furniture in my department, my teaching persona has grown more and more comfortable with her faults in front of her students. I have found also that as long as I do not pretend to be perfect, my students are able to show me the compassion I sometimes seem to withhold from myself. Opening myself up in this way and receiving such compassion even if occasionally helped my teaching persona become a much more fluid and connected part of my overall identity.

Some of my transparency about my mathematical shortcomings has even helped me connect with students. In calculus for example, the first time I shared with my students that epsilon-delta proofs had been awfully confusing to me as I was learning them, I noticed some optimism appear in several students’ strained faces. This revelation is now a routine part of our discussion when we get to that topic. In other contexts, too, I often share with my students that it took me a while to understand some of the connections we are making together.  I occasionally share with them several of the treasured but simple-minded tools and mnemonics I use to differentiate between basic ideas or pairs of words (for example a capital “H” has a horizontal line through it and that is how I, a non-native speaker of English, can tell apart the words “horizontal” and “vertical”).

A not-so-trivial question raises its head here: Is the ability to show vulnerability to students or to colleagues a sign of privilege? I do not have proof for this, but my tentative answer has to be yes here. I have been lucky throughout my teaching career to have only rarely faced authority-undermining behavior from students (and most of that happened when I was pregnant). But if you dig into that luck, you will find several layers of privilege. My skin color, my glasses, and my weird accent seem to have protected me for years against student doubt about my mathematical competence. Furthermore my relentlessly growing age has basically immunized me against youth-based stereotypes. In my present context then, it is, I surmise, both personally rewarding and professionally productive for me to not hide my imperfections.

However, many do not feel like they have that kind of freedom. And if you are not tenured or on the tenure track, if you are an adjunct, if you do not have a PhD, if you are not white, if you are not cis-gendered, if you are not able-bodied, if you work at an institution where students consistently challenge instructors’ authority, you might be correct in assuming that your students and even sometimes your colleagues may not always be compassionate about your humanity. People are not always nice and they are not even always good. If people are indifferent, inconsiderate, or just plain deplorable about my imperfections, as occasionally they are bound to be, I try to interpret this as a sign telling me something about them and not about me; it might even be their burnt coffee that morning. But hostility is not the norm in my professional environment today. When there is at least a modicum of mutual respect in a professional context, I’d say that giving people the benefit of the doubt goes a long way.

If on the other hand your professional context is hostile or dehumanizing or if your academic position is vulnerable, then I certainly do not advise displaying imperfections. In fact many people in such situations end up extending the no-defecation-in-your-place-of-employment rule to the level of no-show-of-humanity-in-your-place-of-employment. Such defensive positions are about self-preservation, which comes above all else. I know; I myself have lived in that mode for several years. So I will not suggest that people in such positions do anything that will make them feel more vulnerable. People know their contexts best.

As some of our colleagues find themselves forced to take up defensive positions, the rest of us with various sorts and levels of privilege have the duty to work to make our spaces less dehumanizing. Part of this rehumanization is going to be about accepting our own imperfections and living with them openly. Not giving credence to the genius worship cult, not paying lip service to the mathematical celebrity culture, not acting the part of the perfect professor are some of the follow-up steps. (If you are ambitious enough, let us rehumanize mathematics from its roots!) But showing our humanity and emphasizing to students, to colleagues, and to ourselves that imperfection is part of the human package is a good start.

End Note

For those readers who were disappointed that this post did not turn out to be about contemplation in the mathematics classroom, here are a few leads to pursue: If you are totally new to the topic, I would suggest starting with Tobin Hart’s article on mindfulness in the classroom. Luke Wolcott’s article on contemplation in mathematics brings things much closer to home. On a related note, some might find this article I wrote about metacognition in the mathematics classroom of interest, too. After all, being reflective about our pedagogical practice and encouraging students to be reflective of their own learning go hand in hand and naturally round out a coherent view of contemplative pedagogy.