Daryl Deford is a fourth year graduate student in the department of Mathematics. He received his B.S. in Theoretical Mathematics Summa Cum Laude from Washington State University. Students in the math department are required to teach their own classes as well as serve as teaching assistants before graduation. Daryl has taught two classes in calculus and has received evaluations that are near perfect.
It is not only the exceptional evaluations from his students, who noted his patience and engaging demeanor, that indicate Daryl’s high level of competence in this field. Daryl has also consistently gone above and beyond the teaching requirements of his program by identifying and addressing learning opportunities at Dartmouth and beyond.
To help mathematics graduate students pass their qualifying exams during the summer of their first year, Daryl and another graduate student wrote a 240-page book of sample questions from previous exams and developed seminar sessions around solving the problems. Daryl also took it upon himself to adapt the materials taught in the first year ethics courses for suitable application to students in the mathematics program. He has also coached local student teams who have placed first in statewide mathematics contests and taught courses at the John Hopkins University Center for Talented Youth.
In addition to his initiative and excellence in teaching, Daryl has also authored and coauthored 6 papers and 5 preprints for his work with his advisor Dan Rockmore and has twice received an honorable mention for the NSF Graduate Research Fellowship.
We asked Daryl to give us some insight into his approach to teaching, what inspires him to inspire others, and advice he has for graduate student teachers.
Tell us about your program and research interests:
I am a 4th year Ph.D. student in the Mathematics Department. My research is centered on the mathematics of data analysis and complex systems. The recent explosion of ``Big Data'' and related fields motivates many interesting questions in pure and applied mathematics. I use tools from Algebra and Combinatorics to study the underlying mathematical properties of these systems.
One of my main focuses is the study of multiplex networks, which are mathematical representations of the many different types of connections and interactions that might be shared between two objects. In particular, I am interested in the global dynamics of these systems, such as how information is transmitted differently between people in person instead of over the internet or how different commodities are traded between pairs of countries.
What brought you to Dartmouth?
My first exposure to the Dartmouth Mathematics Department was meeting recent graduates during my last two years of college. I attended several conferences to present my research and continually encountered successful Dartmouth students everywhere. They really impressed me, not only because they were doing great research but compared to graduates from other schools, they seemed to all have developed a wide range of professional and pedagogical skills that demonstrated their readiness to be effective faculty members.
The graduates that I met encouraged me to apply to Dartmouth and when I visited the department I encountered more students who were obviously great educators in addition to being excellent researchers. That experience made it easy for me to choose Dartmouth, as graduates from the Mathematics program are prepared to succeed in all facets of life as a professional mathematician.
My personal experiences at Dartmouth have only further confirmed these initial impressions. The Mathematics Department makes a significant, concerted effort to allow its students to develop all of their skills. The support that I have received from the Mathematics Department has allowed me to become an effective researcher and educator without feeling like I was choosing one over the other. As a student here I have had an enormous number of opportunities to follow my interests and pursue goals in both Mathematics and teaching that I could not have accomplished anywhere else.
How do you effectively translate your passion for your work/research into your teaching?
The most obvious way is that I love doing math, and my enthusiasm and excitement for solving problems comes through naturally in my lecturing style and in interactions with students. I tend to prefer giving informal, interactive lessons where I can model mathematical reasoning and demonstrate my approaches to problem organically.
Additionally, working in data analysis means that it is easy for me to work in examples from my research in to classes. Some recent examples include social networks, stock market models, electrocardiograms, and real-time Fitbit accelerator data. These examples help provide a real life context for the mathematics that we are studying and are some of the most memorable moments for the students in my classes. At the beginning of each term I survey my class to determine what sorts of data will be closest to my students interests. Tailoring the applications to the students' majors always leads to lively discussions and increased student engagement.
Finally, my viewpoint as a mathematician affects my philosophy of education and the learning objectives that I emphasize. In particular, I view mathematics as the perfect setting to discuss formal logical analysis and develop critical thinking skills. Through assessments and discussion I encourage students to move beyond a computational/repetitive mindset towards a deeper engagement with the topics and abstract reasoning about mathematical objects.
What are the highlights your teaching experience?
For me, the most rewarding teaching moments are "light bulb moments'' when you can tell that a student has understood a concept that was puzzling them before. Watching students improve throughout a quarter due to their sustained, consisted efforts is also very rewarding. My most memorable moment from this past term was constructing a 3-d Styrofoam surface with perpendicular planes cut out to motivate the definition of partial derivatives. This was a topic the class had really been struggling with and playing around with the surface really helped the students develop the right intuition. Seeing that intuition develop into fuller understanding was very rewarding.
What skills did you learn as a teacher that you might not otherwise have had access to?
A big benefit of teaching lecture courses is that you get a lot of experience presenting material and answering questions on the spot. Practicing explaining concepts to students with varied backgrounds and having to explore fundamental concepts from many different angles is also invaluable. My presentation and organizational skills have greatly improved due to my teaching experiences.
What have you learned from your students?
Teaching mathematics frequently requires the use of metaphors to connect abstract mathematical concepts to ideas that students already understand. Giving lectures, talking to students, and answering questions has vastly expanded my collection of metaphors that students seem to find helpful. An example that a student suggested for the different types of discontinuities was ``it is like the difference between rolling out of bed and falling in a well.''
Do you have any advice for others who are starting to take on teaching assignments?
Take time for thoughtful preparation. The best thing you can do for your students is to remember to prepare the lessons with their perspectives in mind. Your students won't have the same background and familiarity with the material that you do so taking some time to think about what the topics are like when seen for the first time is very helpful.