Some Thoughts on Teaching

I believe that physics education aims not to drill students in equations and formulas that we deem necessary. Instead, it should be directed to teach the students how to learn, develop their own understanding, and share that understanding with their peers. To that end, my teaching philosophy centers around helping students develop physical models that they can use as a lens to see their future work through. I came to my conclusion about physics education through my experiences as a student, teacher, and, most importantly, a physicist.

My instructor for Introductory Mechanics my first year of college was incredible. The way he taught was like he was peeling back the curtain of introductory mechanics and showing us the beautifully simple mechanisms behind it. I was shocked to find out how often intro mechanics is taught as an example problem after example problems, a pedagogical machine after pedagogical machine. The way he taught the class wasn’t to show us examples of all the different exam questions we might see; he taught us how to approach a new problem that we hadn’t seen before. To this day, that lesson has given me so much confidence in my abilities to tackle new problems. I strive to instill that same level of confidence in my students by focusing class time on how to approach something new. For example, I pose difficult questions in class for students to discuss in small groups. Working in a small group in class alleviates pressure to answer the question alone while simultaneously exposing students to each other’s thought processes for approaching novel problems. Another way I instill confidence is to challenge students to write their own homework- and exam-style problems. I find that doing so is like asking them to pull back that curtain and gaze at the machinery behind it themselves; to see that all the problems they might see in their physics career are linked and that they need not fear the unseen, since it turns on the same premises they already know.

When I took multivariable calculus, the professor teaching the course would draw large numbers of axes directly onto the transparencies. He demonstrated that the topics we discussed applied to the standard 3D problems and any other number of dimensions. This concept stuck with me that the math we were learning wasn’t just applicable to the problems we did but could be extended to other cases. His cartoons of plots with 12 axes were models that showed me how the extensions worked. Today, I find that thinking in cartoons and simple models is one of the most important skills I have. When I’m teaching, I try to go beyond that, though. I believe that students need to be given the leeway to build their own mental models. This belief goes hand-in-hand with fostering confidence, as I mentioned above. Students gain confidence by seeing and understanding the underlying structures of physics and developing mental models. Similarly, well-developed mental models improve students’ confidence to keep attempting new problems and keep learning new things. A great way to build mental models is through interaction and experimentation with complex topics. I like to give students challenging problems that they can explore the nuances of and attack from many directions. Of course, it can be difficult to present purposefully challenging material without discouraging students or causing undue stress. That’s not my goal at all, and to prevent it, I fall back on transparent teaching policies and low-stress grading practices.

I don’t think that a teacher should withhold any part of a class from a student, with the possible exception of exam questions (but even then, I’m not convinced). One of the most significant parts of that belief is that grades should not be surprising to students. Between clear expectations for graded assignments and feedback from me, my students should know what grade they are on track to earn at any time and exactly what they need to do to change tracks if they want. To this end, I prefer the specifications grading method focusing on eventual mastery. In this method, students are only graded on whether they have demonstrated mastery over specified learning objectives. If they don’t pass any given assessment, they receive feedback about exactly why they didn’t pass and how to improve. Then, they are allowed to try again until they succeed. This grading style shifts the focus from “learn X, Y, and Z by given deadlines” to “learn X, Y, and Z by the end of the course, at a pace that works for you.” Students have the freedom to approach challenging problems without fear of how their grades might be affected.

I want to walk you through a day in my (in-person) intro mechanics class as a student. You come into class and grab the two handouts at the front. One is a blank sheet for scratching down notes to yourself, and the other has two big boxes on it with a dashed line for your name. I start the class by asking if anyone has anything to ask about a previous session or the required reading. After addressing any of those, I start going over the short assignment that precedes each class. These are just quick check-ins submitted online to gauge which topics students get and which they don’t. I go over any points I think were broadly missed, and then I pose a question to the class. Today, we’re covering the conservation of energy. I ask you to determine where on a simple rollercoaster with a loop the kinetic and potential energy are highest and lowest. I give everyone a minute to think and write anything down, then ask someone to volunteer their thoughts. Now I pose the next part of the problem — I invite you to determine the coaster’s velocity at several points. You get more time for this, a few minutes before I ask you to turn to your nearest neighbor and check to see what they think. You get a couple of minutes to compare your thoughts and talk to each other before I again call for someone to volunteer their thinking.

Now comes the fun part, I say. I ask you to determine the conditions that must be met for the loop-de-loop to be successful. You, your partner, and the nearest other pair get to talk about this. I remind you about centripetal force, then turn you loose to discuss together. I walk around, stopping to chat with each group about their thoughts and answering questions. After about ten minutes, I ask each person to summarize what their team discussed and decided on half their boxed sheet. After a few more minutes, I call the class back together, and we debrief about the problem. We probably get through another example like this before I start prepping you for the readings you need to do before the next class. Just before our time is up, I ask you all to think about why we used conservation of energy for this problem instead of conservation of momentum like we did before. You write your thoughts down on the other half of the sheet. As you leave, you drop off your filled sheet with me.

There are two points in the above scenario that I want to draw attention to: the use of scaffolded in-class work to prepare students for challenging problems and formative assessments to give students feedback in real-time. The scaffolding and check-ins start even before class time with assigned pre-class work. The students are built up from simple concept checks to basic examples before coming to class. Quizzes due before class give me a chance to check for their understanding and shore up misconceptions during class time before moving on to more in-depth examples. With a layered approach of practice, assessments, and feedback, the students can approach and tackle complex topics with confidence in a low-stakes environment. By the time that stakes are higher (they’re never very high because of my policy on mastery eventually instead of mastery right now), they have the confidence, skills, and internal model to demonstrate subject proficiency. More importantly, they will meet critical course goals and be set up for success in future studies.

Last updated on 3 April 2021.