I have always been a teacher. From high school to graduate school my fellow students would approach me with questions or confusions, knowing that I am a capable, uncondescending explainer who can typically figure out what facets of the topic they do not grasp and explain the same idea in a variety of different ways. I also have a knack for making connections or comparisons to other disciplines and for pointing out how some new idea relates to something familiar. I believe that all sorts of subjects and knowledge can be connected to great gain.
I am approachable. Throughout graduate school students who I only peripherally knew from substitute lecturing or departmental events would come to my office to ask me conceptual questions, for technical clarifications, or alternate intuitive explanations. I always enthusiastically made time to talk with them and work through their misunderstandings and sticking points.
I love to learn. Having had exciting, engaging, passionate, and illuminating teachers, I know that the quality of a professor’s teaching skills can make or break a class. I always aim to make a learning environment one that I myself would enjoy as a student: whether discussing physics one-on-one, in a small group, or with a room full of people, I try to put myself in the shoes of others so as to ensure I cover the important or difficult points. Achieving enjoyable and productive learning has great consequences.
Interesting subjects can be ruined by disorganized or muddled trains of thought. It is important to start at the beginning, on familiar, common ground, and to expand from there in a sensible order. However, watching a professor copy notes onto the blackboard is extremely boring. Moreover, following algebra does not translate into good physical intuition. As an undergraduate I valued demonstrations and found that discussion of the demos with sketches of how the math works out (as opposed to step-by-step derivations) allowed me to learn very easily. For example, I thoroughly enjoyed my experience in Waves and Vibrations, and truly learned a great deal about physical phenomena even though (or perhaps because) the class was designed to maximize “physics per unit math”. I aspire to be an adept teacher, and strongly believe that well-designed and well-placed demos are extremely valuable in this regard.
Nonetheless, there are times where derivations or working out an example in detail can be important. Writing out notes helps me lay out the ideas and arguments so that they’re presented in as clear a manner as possible, allows me to find pitfalls, insert jokes, mnemonics, or anecdotes, and draw connections with familiar ideas. I try to write notes that will keep me from making any algebra mistakes and that will remind me to hit certain points, but that are not a script that must be followed precisely.
If possible (for example, in the context of a regularly-scheduled classroom session), I try to prepare extensively. During my graduate school career I enthusiastically volunteered to substitute-teach my advisor’s lectures whenever he was traveling. Over the course of four years, I delivered quantum mechanics lectures five times and electromagnetism lectures twice. Each time, I prepared detailed notes. For example, for a two hour lecture on Bloch’s theorem, crystals, and phonons, I wrote twelve pages of notes that included questions to pose to the classroom. Writing and polishing these notes took around twelve hours, but going through such effort ensured that I was deeply familiar with that day’s topic and could field questions. Then, after delivering the lecture I went and edited those notes for what worked, what needed clarification, and what generated student questions. I recognize that six hours of prep per hour of class time will be unrealistic and unsustainable. However, I expect that prep will be easier for simpler material and (even for difficult material) as I accumulate a set of well-considered notes.
Of course, many students have great difficulty learning from lecture, and research demonstrates the value of other approaches to physics education. I have also taught classes which required interactive, on-the-fly, or hands-off teaching styles. During my first year of graduate school, I was a teaching assistant for three classes: introductory classes for biologists and pre-med students, for engineers, and for elementary educators. Each exposed me to a different classroom style and equipped me to handle different kinds of settings.
The class for engineers was taught in a traditional lecture-based fashion, and section was focused on problem solving and techniques. I wrote up and distributed solutions that worked through the problems in some detail but omitted most of the intermediate algebra. I always offered the students the option of spending half an hour discussing that week’s quiz. For the remainder of the section, however, I encouraged students to bring questions about that week’s lectures or questions from the textbook that were similar to the questions assigned for homework that we could work through in depth together on the board. Before diving into algebra, we would discuss the problem, their intuition, and a number of ways to check if their answers made sense. We would consider extreme cases, simpler problems, dimensional analysis, and any symmetry we might expect the answer to have. This felt very much akin to how I make sense of and solve problems.
After we worked out an answer, we would go through and examine it using the criteria we developed. To enable these kinds of checks, I would also insist upon not plugging in numbers until the last step—continually typing numbers into a calculator is a good way for a student to distract themselves and lose track of what it is they were trying to do; it is harder to reason about how answers depend on the various parameters of the problem without an algebraic form.
The introductory class for biologists and pre-med students was led by the University of Maryland Physics Education Research Group. The class was lectures, hands-on labs, and tutorials in which each section was divided into groups of a few students each. The tutorials were organized around work sheets (sometimes accompanied by a small experiment) that guided discussion amongst the groups. In this setting, another teaching assistant and I would float from table to table, checking in on progress and asking the group to explain their shared understanding and disagreements. By asking probing questions, I could often help them resolve their differences, help them realize their differently-phrased ideas were ultimately the same, or encourage them to refine their thinking. Both my students and I got a lot out of this style of interaction—they would formulate and criticize ideas themselves (the surest way to learn something) and I could see where they were struggling and what the tricky points were. I certainly witnessed the greatest number of “Aha!” moments where concepts clicked in this setting. However, it required a great deal of manpower (two teaching assistants for 24 students) to create such effective learning conditions.
The lab portion of that class was a weekly two-hour period, but it differed from many undergraduate labs (especially at the introductory level), in that the lab guide was not akin to a cookbook with clear directions on what to do and how. Instead, the labs were structured to mimic actual research. For example, the lab guide, which was to be read before coming to class, contained a discussion of the concepts and questions the students were expected to investigate. In class, the groups were expected to design their own experiments, decide how to collect, refine, explain, interpret, and present their data to their peers, and to turn in a report as they left. Implementing the labs in this way encouraged creative and critical thinking, enabled the discussion of experimental technique, statistical and systematic error, how the real world differs from the simplified world without, for example, friction. The students impressed me by not only adapting quickly to this unique approach to labs, but also by the varied and creative experimental designs they used. While these labs did not often demonstrate idealized theory, they provide an engaging way of discussing those idealizations and when their underlying assumptions break down. This, too, felt like a valuable and authentic approach to science.
The class for future elementary school teachers was entirely lab-based, and very interactive. As the students were, by and large, not naturally inclined to study science, this course provided a very different teaching experience. The semester was broken into three stand-alone units—circuits, heat, and motion—in which each group of students followed more direct and prescriptive lab manuals. The professor and I visited each group, ensuring nobody was getting stuck or having technical difficulties, discussing the ideas behind the experiment, and asking probing questions. Each experiment was relatively simple but was built upon understanding developed in previous experiments, so that the students gained a coherent picture of the subject. Homework consisted of essay and short answer questions. Grading these assignments was very different from the kinds of grading I was used to, and I quickly adjusted my rubric to award points to a consistently-argued (though possibly wrong) explanation or conclusion and to deduct points for answers which were self-contradictory. Helping the students learn to argue lucidly and rationally became paramount, and the relatively simple in-class subject matter facilitated this well. Though they may never again study physics, this class also aimed to sharpen their long-term writing and critical thinking skills. While I was initially skeptical, the design of this course created a welcoming invitation to science for reluctant and hesitant students.
My other formative teaching experience is as a professional SCUBA instructor, teaching teenagers the classroom and in-the-water skills required for hobbyist certification. The difference in subject matter and course structure makes me reluctant to directly equate this kind of teaching to the teaching of physics. However, some subjects are common between the two—the ideal gas law, for example, explains why it is dangerous to hold your breath while diving: if you ascend, the air in your lungs can expand, popping them and causing a dangerous pneumothorax. I would often embellish one training dive with a demonstration of this dramatic volume change at depth with balloons (one inflated at the surface, the other inflated at depth). This and other demonstrations allowed me to follow a fixed curriculum while adding my personal touch and fun, informative illustrations of serious technical material. Teaching diving helped me learn how to integrate demonstrations, classroom instruction, and practical instruction to great effect. Moreover, it was extremely rewarding to share my passion with my students, and the tremendous pleasure of teaching in this capacity is partially responsible for my decision to pursue a career in academia.
I believe these varied teaching experiences and my computational physics background have forged me into a well-qualified candidate for a position with important and substantial teaching duties and I am excited to pursue such an opportunity and to create a welcoming, diverse, learning environment.