Melanie Dennis joined the Dartmouth math department after being encouraged by Emily Proctor while at Middlebury College. Proctor, a Dartmouth alumna from the math department, instilled in Melanie an abiding love of learning, and inspired her to apply to pursue a PhD at Dartmouth.
Since joining, Melanie’s easy-going yet dedicated approach to teaching has impressed many of her peers and advisors, and also made a significant contribution to broadening access and participation for students. In her diversity statement, Melanie acknowledges that she is a student with a disability and that this has driven her to shape an approach to teaching that eliminates barriers, many of which she herself experienced as a student.
As a result, Melanie creates content and learning opportunities that open mathematics to audiences that might otherwise struggle. She strives to develop equal access for women and minority students, and frequently goes above and beyond to tailor her teaching to the needs of her students.
The consequence is a deep understanding of how to harness the strengths of her students and develop them until they feel at ease with the material and can rise to new challenges as independent learners. And as a result of her approach, Melanie’s teaching evaluations are outstanding, consistently scoring well above departmental averages.
Melanie possesses a true understanding of what it takes to be a good teacher, and insightfully adjusts her pedagogy with a nimbleness that even some more seasoned mentors would struggle with. And she doesn’t stop learning and honing her skills. For this, she has been recognized by two Outstanding Graduate Teacher Awards from DCAL, and acted as co-organizer for the annual Sonia Kovalevsky Day at Dartmouth.
Beyond campus, Melanie has also contributed to many community events for local schools and has served as a Governor’s Institute of Vermont Instructor. She served as Chapter President of the DREAM Program whose goal is to enhance educational aspirations among low income youth, and has worked directly with students in subsidized housing. Without doubt, Melanie Davis is a most worthy recipient of the Teaching Award. Congratulations.
We asked Melanie to share some insight from her experiences at Dartmouth.
"My primary research interests lie in enumerative combinatorics, with secondary interests in networks and knot theory. My research uses bijections to create combinatorial proofs to linear algebraic identities. My recent projects apply the Matrix Tree Theorem to linear algebraic identities, turn them into spanning forest identities, and prove these identities using graph theoretic bijections. Using this method, I created and proved spanning forest identities for the Lewis Carroll Identity and the Dodgson/Muir Identity, two determinantal identities involving matrix minors. My research creates a bridge between algebraic identities and graph theoretic identities."
Why did you choose your program at Dartmouth?
The math department at Dartmouth has a wonderful teaching seminar that takes place over the summer after your second year. It is an intensive course with over 100 contact hours that works through different pedagogical techniques and practical skills, such as how to create assessments and lesson plans, how to project your voice, and how to work with students with a diverse set of needs. I could not find any other PhD program with such extensive teaching training, and as a result, the math department at Dartmouth was my first choice.
How do you effectively translate your passion for your work/research into your teaching?
I do work in combinatorics, which is an accessible field with relatively little background machinery to get started on real projects. As a result, it is a great field to introduce undergraduates to unsolved pure mathematics projects.
What were the highlights or a memorable moment in your teaching experience?
A memorable moment  occurred with two students in my abstract algebra class. They began the term at the bottom of the class, and hardly ever volunteered to ask or answer questions. Never having seen proofs before, they were extremely intimidated by tackling a much more abstract form of math than they had ever encountered, and simultaneously learning to write proofs rigorously. Then, partway through term, I grouped them together, walked them through many correct proofs, and had them work together to critique each other's proofs. As a result, they decided to do their group project together on Polya enumeration, becoming experts in the class on it as the only students studying that topic. Each time they explained new discoveries to me or their classmates, they grew more confident, and even began answering questions in class without prompting. At the end of the term, they gave one of the best presentations of the class, and their final papers had complete and rigorous proofs. One of them told me that, although he had not thought he would do well in the class, he thoroughly enjoyed it and was excited to continue taking more math classes.
What skills did you learn as a teacher that you might not otherwise have had access to?
As a teacher, I have learned how universal design can make learning easier for students of all backgrounds. In particular, I have learned to make slight adjustments to course design in order to help my students with disabilities succeed. My students should not have to be marked as different in order to make it through class with a disability. When students come to me with accommodations, I try to normalize their requests as much as possible. For example, one of my students needed access to my lesson plans the day before each class. I did not want other students seeing him with the lesson plans and asking him how and why he was able to get them, making him explain his disability. Instead, I turned my lesson plans into organized review sheets and posted them on the course website the day before every class. Since everyone had access, instead of his disability marking him out, he got the help he needed while still being a regular member of the class. These practices ensure equal access to class content no matter students' learning conditions.
What did you learn from your students?
I work hard to get to know my students personally. I require students to come by my office hours in the first week so that they know where my office is and feel comfortable there. I always ask how they are doing outside of class, and many students end up staying to chat about how their term is starting up. A student's performance in class is often intimately related to what is going on in the context of the rest of their life, and knowing what some of that context is helps me tailor the class to best teach each student. Many of my students come from diverse backgrounds that come with challenges that I have not personally experienced. Asking about students' lives outside of class helps me understand their difficulties the best that I can. I have talked with many students about how family emergencies, difficult classes, current events, mental illnesses, and bullying have all impacted how they are able to manage their time and emotions. By individualizing my responses to my students based on their needs, I aim to support all of my students, including women, minority students, and students with disabilities, and encourage greater confidence and participation in math. My goal is that students feel welcome and supported to seek help, whether math-related or not, outside of class. My students have taught me how to listen to the challenges of others in order to learn from them what help they need.
Do you have any advice for others who are starting to take on teaching assignments?
Successful learning outcomes have reaffirmed to me the value of active participation, independent learning, and fostering a welcoming environment in the classroom. I hope that new teachers will apply this model for teaching to empower students to take their education into their own hands.