The Takeaways, by Rachel Vale

One of my earliest memories of mathematics is the struggle I faced in second grade learning subtraction.  I understood the concept and what I was supposed to do but I continually struggled with speed tests and doing computations in front of my peers.  My parents had high expectations for me and would make me practice in the evenings, however, by no fault of their own, this practice quickly began to feel like punishment.  I even began having nightmares that kidnappers called “the Takeaways” were after me.

My struggles with math peaked again in fourth grade with long division.  I remember lying to my parents that I couldn’t see the board because I was not sure how to explain my inability to do well on division tests.  Around this time, my mother and several other adults in my life began to console me by sharing that they also were not good at math.  This was comforting to me because it validated my struggles and gave me an excuse to ignore this daunting subject.

For the next few years, I excelled in school, especially in science where I was deeply interested in biology.  I did fine in math classes, but my arithmetic skills were still quite weak, and I continued to rely on my self-identity as “not good at math.”

In my sophomore year of high school, I wanted to take honors science but, in order to do so, the schedule would require that I take honors math as well.  The honors math teacher, Mr. Burrill, was notoriously challenging and had high expectations for his students.  My first quarter in his course, I earned a C.  While I was ready to drop the course and go back to relying on my excuse of not having a “math brain”, Mr. Burrill would not let me quit.  In fact, he doubled down on helping me succeed.  He connected me with a tutor who worked with me on arithmetic and algebra facts.  He made explicit his requirements that every step be shown neatly and in detail and, as much as it felt like a chore to do, it helped me understand what I was doing.  In addition, he started giving me different homework problems from what he was giving the rest of the class.  Recognizing my strengths with logic, he would let me skip the traditional textbook problems if I could write a convincing proof of the quadratic formula, for example.  I began to enjoy math for the first time in my life and, better yet, I began to see myself as talented in math.  By the end of that course, I was earning high marks and I was excited by what I was learning.

For the rest of high school, I continued to enjoy studying mathematics and I even passed AP Calculus my senior year.  I remember reading Simon Singh’s book on Fermat’s Last Theorem that year and feeling awed that people do mathematics for a living.  Still, I harbored deep seated beliefs that my abilities in math were somehow weaker than that of my peers.  I decided that the only way I would know if I was good enough was to major in math in college.

I did well in my math courses in college and even engaged in summer enrichment programs in math as well as some math research.  Around this time, I became aware that I suffered from “imposter syndrome”, a psychological phenomenon where one believes, contrary to evidence, that they are not good enough to belong. I truly fell in love with mathematics in college, but I felt so sure that my classmates were all doing better than me, especially when I was often the only student coming to office hours or asking questions in class.  My senior year of college, I felt that I had barely scratched the surface of what mathematics was, and I envisioned graduate school as an opportunity to finally understand every aspect of mathematics thoroughly.  I also believed that earning a graduate degree in mathematics would give me the external validation to finally convince myself that I was good at math.

It turns out that my idea of graduate school was terribly naïve.  In place of deeply understanding all of mathematics, I began to deeply understand myself and my motivations.  Graduate school forced me to face my fears about not being smart enough.  The process of preparing for and taking qualifying exams is humbling for most students.  It was in this process that I was able to refine my ability to organize deep ideas in my mind and to recognize when and how to ask for help.  There were many times when imposter syndrome almost convinced me to give up, but I was blessed with a tight-knit community of faculty and classmates who supported me and encouraged me to keep going.  We would give each other practice qualifying exams and one of my classmates re-taught me Abstract Algebra from the ground up.  My program was extremely small and so there were no classes offered for certain topics such as Recursion Theory which would appear on my 4th area qualifying exam.  In these cases, I taught myself the material, making visual aids to remember proofs and find connections between topics.  I felt almost euphoric every time I was able to answer a question confidently and correctly in a qualifying exam.  I learned that I, just like my classmates, would sometimes struggle with a concept but that, in the end, it was just a matter of time, patience, and finding the right angle to look at the material.  I failed my Topology qualifying exam multiple times but, eventually, I was able to pass it. As I began working on my thesis research, certain topics and questions in math were intriguing enough that I didn’t mind admitting that I didn’t understand, and I was able to engage with the discomfort of uncertainty.  I continued to hone my ability to be brave in asking for help and, through conversations with my advisor and peers, I was able to solve an original problem in mathematics.  In the end, I completed my Ph.D. in mathematics and landed a tenure track job as a mathematics professor.

I still struggle at times with imposter syndrome, but I have learned to dampen my desire to compare myself to others or worry so much about making mistakes.  My fear of mathematics as a young child drives my love for teaching mathematics today.  I love working with students who identify as “not good at math” and helping all my students work through the discomfort of not immediately knowing how to solve a problem.  Mathematics is not about having the answer the fastest or always being right the first time; rather, it is the art of finding patterns and using logic and problem solving to discover why things work.  The biggest takeaway I try to impart to anyone who will listen is that there is no litmus test for determining who gets to be a mathematician.  A mathematician is anyone who does mathematics.

Rachel Vale obtained her bachelor’s degree in Mathematics from University of California San Diego and her master’s degree and Ph.D., also in Mathematics, from Dartmouth College. Currently, she is teaching mathematics at Portland State University.  She LOVES teaching math, especially to students who are uncertain about their own capabilities in math classes.  Rachel sees mathematics education and quantitative literacy as crucial aspects in improving racial, gender, and socio-economic equality in the U.S. As such, her recent focus is on empowering minority voices in student-centered classrooms.

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