We are taking our home garden a bit more seriously this year. The pandemic, and poor health practices by shoppers at the local grocery store, have made it more important to offset time spent in the aisles by planting at home. If C-day was the day Texas’ leadership abandoned its people, unarmed, to a new viral enemy, then this would be the resurrection of the small victory garden.
For me, this started back early in the lockdown in March. I had already been told to remain away from my university campus starting March 6; I had just returned from CERN and my university had, earlier that week, banned all international travel. This gave me a small head-start on thinking ahead about what we might need during a longer lockdown, which came a couple of week’s later in Texas. At the time, I experimented with growing potatoes indoors. Two of those potato plants took off like weeds. The others I spent too long before planting, and they’re never sprouted actual plants.
The leafy greens took off fast outdoors. The potatoes indoors should be ready to harvest soon. I’ll keep some of the potatoes for new seed and replant the plants if they are still viable. We’ll have a small portion of food to eat and a little more freedom from spending too much time in the presence of average Texans who cannot be neighborly, nor show the empathy for a fellow person that is the hallmark of simple mask-wearing.
When I arrived at SMU in 2009, I was not a teacher. I was a researcher. Unfortunately, it has been common in our field to leave people unprepared for the teaching environment. When I was in graduate school, there either were no classes in, or no one advised me to take classes in, how to teach physics. While it is somewhat regular now that universities offer graduate students (or, in some cases, require) a course in teaching physics, it’s less common than it needs to be.
So how did I learn to teach? Well, there was the standard “here are my notes, teach off of these,” offerings of colleagues. That didn’t work. First, there is deciphering someone else’s notes. Then there is deciding whether or not this is how you want to present the subject. You wind up teaching yourself anyway. What I came to learn was that there is no lack of material to teach … but there is a fantastic dearth of material for faculty on how to be a teacher. Those are two very different things.
All physicists beyond a Bachelors Degree know what to teach: introductory mechanics, relativity, electricity and magnetism, advanced mechanics, quantum mechanics, and statistical physics. That’s the core, handed down since it was effectively developed in the 1800s and early 1900s. Then there are the specializations: atomic physics, solid state physics, plasma physics, particle physics, astrophysics, etc. We all know what to teach.
But how did our professors prepare for class? How much in advance did they set up written or demonstration material? Did they have help? Did they practice before coming to class? How did they unwind after class? (I am usually pretty worked up after class period) How did they take on a new class, one they’d never taught before? How did they decide on course structure? What systems worked behind the scenes to enforce that structure? (a spreadsheet, a notebook, something else?) How much of a course is dictated to them (e.g. by curriculum) and where do they have a free hand?
When I started teaching at SMU, I began as I had been taught: chalkboard lecture. I hated it. It wasn’t that I couldn’t do it. I just hated the fact that I had to focus hard on board layout, on controlling the size of my handwriting, on controlling the quality of my handwriting. I remembered the things that frustrated me as a student: a professor’s notation deviating from the book in some subtle way (e.g. the way they draw a Greek letter), or when material starts on a board and continues, not on the next one, but a far-removed section of the board. I made those mistakes, too. I hated it.
After my third-year review, I vowed to overhaul my teaching. Inspired by some of my local colleagues who preached the gospel of data-driven physics education research, I flipped my classroom. Instead of lecturing at the students for 50 or 80 minutes in-class, I used class time to work with the students. Lectures moved online. Reading and lecture video had to be watched before coming to class. This was checked with a brief quiz. Class was spent learning to grapple with concepts and apply them to solve problems.
I’ve written about that before. What I’ve written less about is the concept of the Grand Challenge Problem that became a living part of my classes. I’ve deployed it with increasing frequency since I started using them in about every one of my classes. I have never been disappointed.
The Grand Challenge Problem appeared in my classes for the first time in Spring 2015. If you compare my Fall 2014 electricity and magnetism course for life-science majors, and the equivalent one in Spring 2015, it’s night-and-day. My Fall 2014 course is a standard lecture course. My Spring 2015 course is the first time I flipped the classroom. As I wrote about it in the syllabus for my class that spring:
A culminating event of this semester will be the completion of a Grand Challenge problem. This is a physics problem with no textbook solution. Rather, you will draw upon your own creativity, informed by the principles of physics you learned in PHYS 1307 and are learning in PHYS 1308, to address the question in as detailed a manner as possible … This is not purely a storytelling exercise; rather, you will engage in a mathematical and physical exercise where the math speaks, and you will describe what it says.
PHYS 1308 Spring 2015 Syllabus
The Grand Challenge Problem evolved out of something that our new college dean, Thomas DiPiero, said during an early faculty meeting in the fall of 2014. He had just joined SMU in June of that year, and challenged the faculty to educate students in new ways. He encouraged the use of “Grand Challenge Problems” – problems with a significant and large-scale theme that drives people toward a big goal, but by encouraging them to move along threads of specific interest to them. For example, a grand challenge problem in modern physics might be to detect the constituents of dark matter. This is the umbrella problem, but with no simple or textbook recipe for solving it. Rather, people have to pursue, most often in teams, attempted solutions to the problem: axion detectors, particle detectors, new theoretical frameworks, etc. One or more of these might succeed – or all might fail. That is the beauty of the grand challenge problem: there is no predefined answer.
My first problem for my students that year was as follows:
A patient, bored before their MRI exam, rubs their feet aggressively on the shag carpet of the waiting room. Also a bit nervous, they unconsciously scratch at the small, dark blue, circular tattoo on their left arm. Soon after, they are placed in an MRI machine. Describe at least three interesting things that could happen to this patient when the MRI machine is turned on.
Grand Challenge Problem, Spring 2015, PHYS 1308
When I took over as the instructor for our new Honors Physics Class, a teaching assistant (Eric Godat) and I worked the Grand Challenge Problem into that class as well. We had already done a demonstrations of such a problem for the PHYS 1308 class, including a paper on a challenge we gave ourselves (“All the electrons in the Solar System are suddenly moved into the Sun; describe three things that happen next.”). I have not deployed the Grand Challenge problem in my introductory mechanics class, only because I am not sure how to handle grading papers or presentations from over a dozen teams. For Honors Physics or PHYS 1308, there were a manageable number of teams (not more than 10 teams of about 3 students each).
Which brings me to my first semester of my second decade: Fall 2019. For the first time since my first year at SMU, I got to teach the third-semester physics class. As an aside, I have been trapped by my department in teaching introductory physics classes for most of this decade, despite having asked to teach upper-level or graduate classes. To rebel, I teach the curriculum but the way I see fit. My goal is to make physicists out of these students, not just “teach physics.” I follow the best-practices of the field in doing so, of course, but I am intent on recreating in miniature the research environment inside the classroom. That isn’t quite the teaching philosophy inside my department, but with more young people in our department now than a few years ago there is clearly a shift afoot.
Since I last taught third-semester, or “Modern,” physics in Spring 2010, I had to radically alter the course compared to how I taught it a decade ago. First of all, it was time to flip the classroom. I generated a playlist of modern physics lecture videos . It’s not technically complete, and some videos need edits after mistakes in the first round, but it’s a good foundation. In concert with that, I reflected on what students really needed to learn in this class to be ready for the next steps.
The next steps are mathematical methods and advanced mechanics. So it will be some time before they see the Schroedinger Wave Equation again, although relativity will likely (depending on who’s teaching the class) be reinforced again in advanced mechanics. It was clear I needed to emphasize a few key things:
Special relativity and its implications, as well as experimental evidence for it.
Thermodynamics, up to but not including the laws of Thermodynamics, since it’s not taught in introductory physics and is a key foundation for quantum physics.
The particulate nature of electromagnetic radiation under certain conditions.
The wave nature of matter.
That’s it. All the rest is exercise and application. If one groks these basics, one is prepared for deeper study of all of them in future mechanics, electromagnetism, and quantum mechanics classes; as well as in elective applications of this in specializations like atomic or plasma physics. I looked to other universities to see how far they typically go in a 1-semester modern physics class. For classes like ours at SMU, using the same book as we do (Harris, 2nd edition), those classes are broken into 2 semesters: the first semester completes chapters 1-6 of Harris (special relativity, photoelectric effect and blackbody radiation, wave nature of matter, and the Schroedinger Wave Equation with 1-dimensional applications). They save all the specializations (hydrogen atom, atomic physics, solid state physics, nuclear, and particle physics) for the second semester, which we do not offer.
I am a big “less is more” fan when it comes to teaching physics, and with my key foundations in mind I aimed to cover Harris chapters 1-6 plus inserted material on thermodynamics. This worked well, and allowed me to spend a full month on relativity and a full month on solving the Schroedinger Wave Equation. It was glorious. When you do that, there is no need to rush to cover all those later chapters: they naturally work themselves into the fold of problem solving in 1-dimension. I showed the students how to model the nucleus with an nearly infinite square well married to the Coulomb potential, and how to build a 1-D “solid” out of just 10 atoms, where all the basic properties (e.g. electron energy bands and band gaps) emerge naturally and readily. I did nuclear and solid state physics without naming it – it just felt natural, as part of solving the wave equation.
I also employed the Grand Challenge Problem in this venue for the first time, as a means to enforce synthesis learning and to allow students to explore those later specializations on their own. There is no need for me to cover them in class if the students are motivated to explore them on their own. I intentionally kept the question vague:
You cannot open it up to see what is going on inside, but everything depends on you being able to see what is inside.
Grand Challenge Problem, Modern Physics, Fall 2019
Students were arranged into teams, four in total. Two teams elected to explore stars and their deaths (after all, you cannot pick apart a star and see what is going on inside – you need physics to help do that dissection), one team looked at the aftermath of Chernobyl (inspired by the recent TV series), and the last team looked at harnessing lightning strikes as a mean to obtain stored electric energy (seeing what’s going on inside a storm, or a lightning bolt, or a capacitor designed to store a lightning bolt). I couldn’t have invented those assignments – the students self-directed toward interesting scenarios and then ran with them. In the process:
One team member re-discovered the “Beryllium bottleneck” that occurs in stars that are burning Helium (which begins when the star enters its death throes). They didn’t do a lot of a academic research on what was already known about stellar fusion, which is actually okay … because what they did instead was to set a goal and see how to meet it. They knew from academic research that helium-burning stars exist in that phase for hundreds of thousands of years. They used our model of the nucleus and quantum tunneling to predict the fusion rate of helium into carbon (actually, they predicted the rate at which helium pairs fuse and tried to calculate how long it would take to use up all pairs). They used kinetic theory to predict the collision rate between helium nuclei. They determined that a star of sufficient mass (e.g. 17 solar masses) would use up the Helium in its core in about 1/1000th of a year … which flies in the face of observational evidence. This is awesome. Turns out that helium pairs fuse to Beryllium-8, which is highly unstable. Unless it fuses with another helium nucleus within about a billionth of a billionth of a second, the Beryllium nucleus splits back to helium nuclei and the process has to start all over again. This is what stretches helium burning out for hundreds of thousands of years: improbability.
One team wrote an interface to standard stellar information databases, learned to sift stars from galaxies in these catalogs, and wrote software to convert data to predictions about the lifetimes of stars in the catalog. This went way above-and-beyond any kind of technical expectations I laid out for this project, and was entirely a product of enthusiasm and expertise from the students involved.
One team explored whether tunneling across a dielectric in a capacitor could be a significant source of loss of stored energy. That same team delved deep into how doppler radar actually works and how to see inside a lightning bolt using just emitted light spectra.
One team member inadvertently rediscovered that special relativity breaks down in certain regimes, one of which is when the acceleration due to gravity becomes very strong – at the Schwarzchild radius of a black hole, for instance. This is, in part, why Einstein needed General Relativity to fully understand spacetime.
I am excited for what lengths students went to in order to address scenarios of their own choosing, all motivated by a vague problem statement. This is more akin to real research, where the problems are ill-stated (thanks, Nature) and the answers are never guaranteed. In fact, failure is often the most important lesson to communicate: the failure to predict the burn-time of Helium in a dying star led to a discovery for that student, in a more dramatic way than reading it in a book ever could convey. That is what I want from my classes: a foundation of physics seamlessly linked to a structure for personal discovery.
After all, isn’t that what we spend our whole lives in physics actually doing?