How a physicist is healing from trauma caused by math teaching
I remember a couple experiences that shaped my interaction with physics/math that I would like to let go of now. The first involved an undergraduate course on electricity and magnetism with Prof. Koushiappas who I knew as a hard core theoretical physicist. My entire experience in his class was quite discouraging, but a few instances stick out. One day while struggling through a problem, I harnessed the courage to finally speak up in his office hours. Usually, I would attend and take notes on the “good” questions posed by other students so that it would help me through my own problem solving. This time, I decided to give myself a chance.
I was standing so close to the doorway of his office that I was practically invisible when I raised my hand and he called on me to contemplate my question. Other students nodded that this part of the problem I raised had caused them trouble as well. Prof. Koushiappas firmly stated that what I had brought up was in fact not an appropriate question because it was a math question and this was a physics course. He then went on to clarify that it was his job only to teach us physics, not mathematics and that we should not approach him with questions that were not physics questions. This was traumatic for me because I was ashamed for having made that mistake, and I was also angry that my question would still not be answered. He would not answer my question because I had not asked a “good” question. So from that moment on, I spent most of my time trying to make sure I could see the distinction between what is physics and what is not. I had a panic attack at the final exam and failed the course.
I had to take the same course again with Prof. K and kept my questions to myself while I endured his disconnected teaching methods. I passed the course this second time, but only after he crushed my excitement about the subject a few more times. Both semesters were traumatic experiences for me and it had nothing to do with the content of the course. I could not avoid Prof. K so all I could do was lower my head and keep quiet any time I interacted with him while on campus.
A second defining encounter came from within an actual mathematics course. And I have worked extremely hard to forget most of the details of this so forgive me for the foggy description. In partial differential equations, the professor who had never given a lecture that I found the least bit informative declared that the final exam would be an oral exam. He gave us no more information so in order to prepare, I decided to talk out and write out my conceptual understanding of many things we went over in class. When I arrived at the so called oral exam, he pointed out all the problems on previous exams that I had not demonstrated my ability to solve. Instead of me talking as I expected in an oral exam, he requested that I solve a problem on the board while he watched. This made me freeze. And I panicked and began talking through the problem as I do when I solve problems. He immediately with frustration firmly stated that I should just do the problem on the board.
At this moment I found myself frozen again but this time, it was paralyzing because I did not know how to respond to his frustration with my style of problem solving. This is the moment where things get blurry for me as I don’t remember exactly what happened. All I remember is accepting my inadequacy and pleading for at least a passing grade (this was my last math requirement) so that I would never have to see him again. I passed that course and avoided this man for the rest of my time on campus.
Relevant context to these two encounters is that I am a black female and these professors are white males. I am sure they know very little about what it feels like to be a black girl in a space surrounded by white men. There is no equivalent experience that would illustrate the power dynamic involved in white male gatekeepers of mathematical knowledge checking the black girl at the door. Not only was I probably one of the only black females they have taught and interacted with, I had the audacity to ask questions and demonstrate an alternative problem solving style. No wonder they seemed so frustrated with my presence. And no wonder I learned quickly to say little and keep my head down when in the classroom or the hallways of the engineering building. It is actually quite illogical that I decided to continue in an environment that would ask this of me.
This past week, I have been reading Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching by Jo Boaler which has convinced me that I can begin to move forward from the painful learning experiences still haunting me and causing me anxiety today. A few things I have learned from this book…
1. The actual evolving community of physicists is not the same as the physics classroom full of blocks sliding down ramps
Math (and physics) is treated differently than all other subjects in terms of how it is taught and how it is socially constructed and accepted as something some can and others cannot do. Math (and physics) classrooms tend to have an important void where students don’t appreciate the beauty of mathematics, ask deep questions, explore connections or learn about its applicability. Mathematics is about knowledge creation through our understanding of patterns. This is directly contradictory of the way math is taught in classrooms as just a set of rules that you memorize and master or not. “The powerful thinkers are those who make connections, think logically, and use space, data and numbers creatively.” This statement from the book underlines the difference between what mathematics is and what is taught in mathematics classrooms.
Similarly, physics is dependent on mathematics. We force students to sit in classrooms and solve isolated problems in a timely manner as if this is what it looks like to be a physicist in society. I met physicists who spend years solving a problem of interest, dissecting it from every angle available in the three dimensional universe. Yet, if you cannot solve the wave equation in less than 10 minutes, you may be filtered out of the running to become a physicist.
The way physics is socially constructed and taught in classrooms has not evolved with society. With the popularization of computers and technology, we need people with intuition used to make connections and design much more than we need people who can carry out understood calculations. This is not reflected in the way physics is taught currently. What if we implemented methods of teaching and developed a growth mindset (a term defined in the book) about physics to transform the current void into the actual beautiful mathematical realm of possibilities and inclusion? Maybe people would interact differently with physics and maybe as a whole, Americans would do better in STEM.
“The highest-scoring students in the world are those who approach mathematics looking at and thinking about big ideas and the connections between them.” This line from the book really stood out to me. Because essentially, my brain works in this way — seek out big ideas, connect them to lay out a roadmap, now solve detailed problems associated with this. But in math and physics, my experience has been to be discouraged from doing this in the classroom.
It has even caused me great self-doubt when thinking about my research and feeling ashamed and nervous that someone will look at what I am doing and declare that it is not in fact physics at all because it looks nothing like what I do in the classroom. This disconnect affirms much of my imposter syndrome by illuminating the fact that maybe I am only good at research because it is really not physics at all. Now, I am thinking maybe the way physics is constructed in the classroom is the problem. Maybe if it was presented as an opportunity to explore the world around us instead of a list of rules discovered hundreds of years ago then physics would not be (like mathematics) in risk of being ‘dead’. And maybe if it was presented this way then we would value more perspectives and make room to allow for different pathways and methodologies in our curriculum.
2. Including various teaching methods opens up the field to the marginalized
Chapter 6 of the book is titled “Mathematics and the Path to Equity”. At the center of inequity problems is “the elitist construction of math” that the book describes as being used as a performance subject whose role is to separate students into “those with the math gene and those without”. We have to be willing to embrace the reality that holding this elitist view of mathematics produces the culture of mathematics we currently have today which excludes large groups of people.
Admittedly, it is an ego boost to continue to think of math and physics in this way because if you are able to jump through the hoops then you find yourself a part of an elite group of few. But this payoff comes at the cost of pushing many people down for a few people to look taller. And while, many of us have enjoyed the benefits of being a part of such an elite group and been patted on the back for succeeding, it is time to acknowledge that our contributions to the field are hindered by this. And most importantly, it is time to admit once and for all that there is nothing objective about constraining teaching methodologies and restricting accessibility so that only a select few thrive.
This is why I find this book so powerful even as someone who is not a teacher of mathematics. The findings of this research confirm that 1. Thinking differently about mathematics and 2. Using better teaching/parenting techniques for mathematics can transform the number of people who perform well in mathematics. Nothing about this has to do with the supposedly objective subject content in itself. Which undercuts the narrative that those of us who have mastered mathematics in its current curricular state are not necessarily smarter than those who could not but have been able to jump through the hoops of academia much better. And research on the brain has now revealed that it is possible to grow and shrink different parts of the brain throughout our lifetimes. “But we have a great deal of evidence that although people are born with brain differences, such differences are eclipsed by the experiences people have during their lives as every second presents opportunities for incredible brain growth”.
“Many people recognize that mathematics inequality comes from stereotyped ideas about who can achieve in mathematics and they work to combat them on a daily basis. Unfortunately there are others who work hard, whether consciously or not, to promote the inequities that pervade the mathematics education landscape.” This hits on something that I have stressed throughout my own exploration of inequality in STEM fields at large — the role of intent. Every way I turn, someone disagrees with the inequity prevalent in STEM not because of the data but because of the guilt associated with the implication that people are actively promoting inequity. But this can be conscious or unconscious and does not need to be made personal (about whether or not the department chair or the individual teacher is a good or bad person). It is just the reality that the current climate of STEM is to promote inequity and in order to promote equity, we have to do some things differently or dare I say we have to change the way we think about the subjects at large.
3. The elite nature of the field damages us even when we are seeking to be affirmed by it
My last experience in the physics department will not define me even though it tried. When I sat down after pouring out my truth in my commencement address, I picked up the program for our department ceremony and eagerly searched for my name. Of course they spelled Africana wrong when they listed my second concentration. My heart sank as I realized that every single student who had fulfilled the requirements to complete a bachelor of science in the department of physics had gotten honors except for, you guessed it, me. After giving me an award for best undergraduate thesis in physics and for declaring their diversity and inclusion plans based on activism I had sparked, I was too tired for this.
Now, it may seem extremely petty and elitist to focus in on getting honors as disheartening (and it is) until you understand the façade that is the process of qualifying for honors in physics at Brown. It is extremely subjective. And in our department, there was an unspoken assumption that if you do a thesis and get the science bachelors, you will get honors. I watched less than mediocre thesis presentations in the department that should have brought shame to advisors or at the very least humor, and those students got honors. But I also watched amazing presentations that deserved the recognition gained very much. So it did not seem worthy or a battle I could win. After being punished over and over and over again for having an atypical learning style and not being male and not being white, this felt like the ultimate attempt to steal my joy. But in the name of recovering from traumatic undergraduate experiences, I am deciding to let go of toxic experiences that I taught me so much about the field of physics and about myself while accepting that the physics community would deny all of it.
As I learn more about better teaching strategies and better ways to frame mathematics, it allows me to start to believe that my encounters in classrooms and offices during undergrad do not have to define the way I think about physics and mathematics moving forward in my career. I do not have to keep living with the anxiety that maybe what I am doing is not really physics but something else. I do not have to keep punishing myself for needing to process information externally by talking or visualizing concepts as I work through problems. I can move forward and I must move forward in order to contribute to knowledge production in my field.
P.S. show some love with a clap, recommend, share and follow me @JamelleWD