[Spoiler alert: This post is, in part, a reflection on the show “In & Of Itself“, written and performed by Derek DelGaudio. If you are near New York City, I strongly encourage you to see this show before it ends on 8/19/18 and before reading below.]
This summer, I have helped lead a professional development workshop for mathematics educators on student-centered pedagogy. One session of the workshop  is organized around a paper by María Trigueros and Sally Jacobs entitled “On Developing a Rich Conception of Variable”. Trigueros and Jacobs argue that the concept of “variable”, which seems unified from an expert perspective, is multifaceted. Moreover, they point out the ways that this multiplicity is challenging for students and that there are structural issues with our curricula that fail to support the development of a rich conception of variables in most students. Faculty can easily take a deficit perspective on students whose conceptions are unlike our expert perspectives, and this concept in particular is at the root of a lot of the blame we lay on students when they think differently than we expected.
At the workshop, we use this image of an old parable about scholars and an elephant. The elephant represents the concept of variable, and the scholars each describe an important facet of the concept: as unknowns, general numbers, parameters, co-varying quantities, or something else. The point is that student conceptions of variables are reasonable attempts to make sense of the contexts in which we have placed them and judging them for not having integrated those contexts into a unifying concept feeds into some of the structural issues with our educational system.
In his show “In & Of Itself”, Derek DelGaudio also engages the parable of the elephant and the scholars. But in his search to read every version of this story, he noticed that none of the stories ever tell the experience of the elephant. What would it be like to have scholars prod at pieces of you and then have a creepy argument in which they try to define you? And what if you really were a magical creature with a snake, spears, and fans on your front, a rope on you back, walls on your sides, and four tree trunks below? How long would it take for you to start feeling like an elephant rather than a magical creature if scholars always insisted you were an elephant?
DelGaudio suggests that this might be why we don’t see magical creatures in the world anymore. His larger point is that identity is an illusion, both internally and externally; in his framing this illusion becomes true identity when the external and internal illusions agree. But these illusions are built on partial and incomplete observations; we are defined more by what isn’t seen than what is seen. And the illusions have the power to influence the observations and the truth. In the context of our students, we never see all of their conceptions, and we certainly don’t see their whole humanity or identity. Any interaction can modify the illusion; in fact any interaction does contribute to the illusions, internal and external, especially given the power we have as educators. No interaction is neutral, so we need to be better and see the violence we are doing when we impose on students external identity-illusions. Perhaps this is why we see so few mathematicians in the wild, among our students.
On an even more personal level, the last decade has been very hard for me. People see parts of me, and they get to impose a narrative. Perhaps I was a sphinx, but the world got to set the narrative that I had to be a lion because sphinxes don’t exist, a snake because chimera don’t exist, a crow because I can’t be a phoenix. I’m not sure I remember. But I do remember the pain and the anger that bleeds and persists through the illusions. Over the years, I’ve used every tool at my disposal, including some attempts at therapy; I’ve gotten stronger in resisting the unwanted illusions, slowing down the violence, and I’ve made some big changes recently, including taking a leave to learn from and with students at a high school in Manhattan next year. But I was starting to give up hope about actually healing. DelGaudio’s Elephant gave me hope again. I am a multitude, both seen and unseen. I can be what I seem in the world without being defined by or beholden to that seeming. I don’t have to forgive or forget to move on; I can simply rewrite the story to allow for magical creatures again, including me.
PS: DelGaudio’s framing of identity is interesting and fruitful for me, but I haven’t had the time to sit with it and discover any implicit issues. Please forgive me if this framing of identity is flawed or oversimplified in ways that could hurt you.
 This workshop is funded by the NSF grant PRODUCT, and this session was designed collaboratively by Jess Ellis Hagman, Jane Cushman, Amy Ksir, Elizabeth Thoren, Nina White, and myself.