Teaching Statement

Teaching is truly my passion. I love working with students to build their confidence in mathematics and helping them to feel like they belong in math, no matter their background. I have developed this philosophy through my varied teaching experiences: At Illinois I have been a TA for seven semesters, teaching the full Calculus sequence from Preparation for Calculus to Multivariable Calculus, which prepared me this past summer to be the instructor of record for an 8-week calculus course. I have been on the List of Teachers Ranked as Excellent by their Students (top 10% of teachers on campus) many times, including every class I taught online during the pandemic. I have experience teaching underrepresented students in the Merit program at the U of I, a program dedicated to providing students from non-traditional backgrounds with extra resources and excellent teachers, as well as small class sizes and more individualized attention. To have more experience with a diverse group of students, I also tutored and led Algebra workshops at the Danville Correctional Center with the U of I Education Justice Project and have organized extracurricular math activities for middle and high school girls with the AWM. I am excited about the opportunity to bring these experiences to a variety of courses, including higher-level courses.

In my opinion, the most important thing we can teach our students as mathematics educators is confidence in communicating math to others, and therefore giving them the opportunity to feel like they belong in the world of mathematics. So many students arrive to college with insecurity about doing math, and a pervasive fear of failure. The myth about the existence of “math people” perpetuates the stereotype that math just isn’t for some people. Anyone can do mathematics.

Building confidence starts, somewhat counter-intuitively, with embracing failure and desirable confusion. Mistakes will happen – it’s how students react to making them that matters the most. Students who struggle often see the situation as hopeless, whereas students that often understand can shut down over minor mistakes. If a student gets something wrong, I latch on to what they do understand correctly and build off their own understanding. One of my students from my Fall 2020 discussion section wrote in evaluations that “[They] looked at things from our perspective which I think allowed [them] to help us in the ways we most needed it.” During active learning, I encourage students to share their work without being afraid of making mistakes, because mistakes should be seen as a learning opportunity. If one student does something wrong a certain way, it’s useful to know how to unpack that and analyze why that method didn’t work the way they wanted it to. One student from my Fall 2017 discussion wrote me after to say “I’m thankful you helped me draw a distinction between the feeling of being hopelessly bad at math and the feeling of being uncomfortable because I’m learning something new.”

For fostering students’ success in mathematics, as well as confidence with the material, I like to focus on concepts and problem-solving skills rather than rote memorization. Whether in a math major or future work, students will never be accosted by someone in an alley and asked what the cosecant of pi/6 is. They will instead need to know how to apply the tools they have learned in the context of solving problems. In the calculus class I taught over the summer, I implemented hybrid exams that included open-book open-note take home exams. This is how students will need to apply their skills – they will need to know how to use their resources and how to approach novel problems, without an arbitrary imposed time limit. I also focus on building intuition about the topics they are learning, rather than memorization. When they think about derivatives after their calculus class is over, I want them to remember “a derivative is an instantaneous rate of change” rather than just “the derivative of x^2 is 2x.” The first might help them in knowing when they should take a derivative, and the second will only help them if someone asks them what the derivative of x^2 is. This focus on problem solving helps them in learning how to communicate mathematics to others, an invaluable skill in all their future endeavors. As a professor, I hope to incorporate project-based learning into my classes, because it shifts the focus from getting the right answer to being able to communicate your process and justify your solution. Presentations are also great tools, not only for students being able to communicate mathematics but for building students’ confidence as well, as they feel like they are an expert in what they are presenting.

Another essential for building student success is listening to and caring about your students. Students cannot learn the skills we want to teach them if they feel like they aren’t heard, or if they are struggling with no one to go to. I make myself available to my students no matter what questions they have, and work with them to help them learn in a way that is conducive to them. I have had several students come talk to me about an overloaded schedule, test anxiety, and serious mental health problems (I then referred them to the appropriate campus resources). One of my students from Fall 2020 said it well: "Dana was most likely the best TA I have had the privilege of working with this semester. They were fair and had a very open-door policy for questions or concerns regarding the course, and they were always willing to offer a listening ear if you happened to have any other concerns as well. While Calc 1 itself certainly wasn't my strongpoint this semester Dana was exceptional."

Lastly, belonging in mathematics is not always something that comes naturally, but is something that we as educators need to consciously foster in our students. Even for talented students, if they do not see themselves in math, they will not feel they belong. As an out non-binary person, I have been that direct role model to queer students of mine as well as younger graduate students in the department, who have felt comfortable being out partly because I did it first. I have also been a huge supporter of traditionally underrepresented genders in mathematics (women and non-binary students) through my outreach work with the Association for Women in Mathematics (AWM), of which I was Outreach Chair for two years, organizing extracurricular programs primarily for middle and high school girls.

However, it is extremely important to also support students who are minoritized in ways that we are privileged. With the racial injustice still ongoing in our country, it is important as a White person for me to assess how Whiteness and Eurocentrism permeate not only the way we teach mathematics, but the very foundations of the mathematics we teach. In the fall of 2018, I took a fantastic class with Rochelle Gutierrez about Sociopolitical Perspectives in Mathematics and Science Education. I learned about how many different “ways of knowing” are just as valid as the ones we are taught in school, and how focusing on one White, Northern cultural way of knowing can leave out students of different races from seeing themselves in mathematics. I have worked with diverse students at the Danville Correctional Center, who not only are majority minoritized races, but who have often not taken a formal math class in many, many years. They often have a hard time feeling like they belong anywhere, much less mathematics. We need to decolonize our math education and teach mathematics in a way that includes everyone.

As an educator in graduate school, I have had great success with teaching students from different backgrounds and helping them to build confidence and feel like they belong. I listen to them, and have helped them embrace failure, communicate mathematics, and learn problem-solving strategies and the skills they need to apply the tools they learn in class. I not only want my students to succeed in my classes, but I want them to feel confident in their abilities and understand that anyone can do mathematics, even them.