Brokk Toggerson – UMass Amherst

Memorization in Physics

I just finished my unit on circuits in Physics 132 and, along the way, discovered a useful tool for helping biology students grasp the importance of completely understanding and memorizing a mechanism.

In physics, we often consider memorization to be a “dirty word.” We pride ourselves on being the discipline that doesn’t require much, if any, memorization. In fact, many physics instructors I know will say, “I don’t want them to memorize.” We provide equation sheets and other memory aids in many physics exams. Usually, this aversion to memorization comes from a reasonable place: I think the aversion to memorization ultimately comes from the idea that we don’t want students’ inability to recall certain facts to get in the way of the problem-solving skills we actually care about.

However, I’ve come to the conclusion over the last couple of years that this disciplinary cultural aversion to memorization has perhaps gone a bit too far. There are certain facts that you do just need to know in order to solve problems. Many points in the literature emphasize the importance of teaching and mastering conceptual understanding upstream of the problem-solving process. This is the entire motivation behind Eric Mazur’s introductory physics textbook and the main takeaway from Paul and Webb’s paper, which advocates the same approach.

If we therefore accept that conceptual understanding is foundational to problem-solving success in physics, then it follows that students must actually remember certain fundamental physical facts. This is relevant in my circuits unit, where I continue to use a series of questions I developed 15 years ago involving the physical processes involved in charging capacitors: consider the voltage drops along wires (you can’t consider wires to be ideal, resistance-less conductors for this exercise), how those voltage changes can also be viewed as electric fields, and how those electric fields exert forces on the charges already present in the metal thereby charges the capacitor.

While teaching this sequence this past semester, I had a sudden inspiration in class, which I acted on. I told the students, after we had completed the sequence, that this series of questions and the underlying logic therein was effectively the “Krebs cycle for capacitors,” and that they really needed to know these steps.

Using the phrase “Krebs cycle” truly seemed to resonate with the students. I saw many nods of understanding that I had not seen before, nods indicating that they understood the importance of memorizing the sequence. Moreover, there was a slight giggle in the room, so I asked, “Y’all just surprised that a physics instructor knows the Krebs cycle?” Several of them said yes. I think that this reference to a fundamental biological mechanism served multiple purposes in promoting authenticity. I used the language of biology to emphasize that we were talking about a mechanistic process similar to the ones with which they are familiar and have experience memorizing. Moreover, the Krebs cycle is foundational, and so calling the series of physics steps that underpin capacitor charging a “Krebs cycle” showed the students, in a biologically authentic way, the importance of what we had just discussed.

Now, of course, I don’t yet know the effects of this reference, but I’ll be watching in office hours over the coming weeks to see the number of questions coming in about the capacitor-charging process. Unfortunately, I don’t have a lot of notes with which to compare from prior years, but often this process results in a lot of questions during office hours. If most students now seem to have grasped the process, I will consider it a beneficial step. Even if there’s no change, the use of a biologically authentic phrase such as “Krebs cycle” is, I think, a useful tool when teaching introductory physics for life sciences.

A New (to Me!) Way of Using Graduate Students in an Apprenticeship Model

Within our department, there are graduate students who are interested in enhancing their teaching credentials either because they believe that such enhanced credentials will give them a leg up on the traditional academic job market, or because they see themselves ultimately pursuing a teaching focused career. Moreover, due to sabbaticals etc., our department sometimes needs graduate students to serve as the instructor of record for courses both during the standard fall and spring academic semesters, as well as during our summer and winter online sessions. While the 691G course I created for incoming for graduate students provides some introduction to the principles of active learning via the physics education research literature, there is no mechanism currently in place at UMass for such students to get additional formal training in teaching. To help meet this need, I shifted my TA usage, from primarily serving as a student resource in class and during office hours, to more of an apprenticeship model giving GTAs both an under-the-hood look at running a large-enrollment introductory course and experience in front of such a classroom. I specifically want GTAs to get experience in this particular environment as such courses are both generally part of the workload for instructional faculty and an experience that most early-career research-focused faculty lack. In this model, the GTA still serves as an in-class assistant, but instead of out-of-class office hours, they meet with me for two hours after each class to help with the logistics of running such a course and planning the next day’s lesson.

When graduate students have served as primary instructors for our department in the past, they often do excellently in front of the classroom. Their lectures are well thought out, the figures well designed, the problems carefully considered, and the exams fair and well built. Some of our graduate students have even explored some active learning and alternative grading techniques in their own courses. I believe this expertise comes from their many years both as a student and as serving as in class GTAs for courses at UMass Amherst.

However, almost all our graduate students serving as primary instructors have also stumbled with what I call under-the-hood management of such horses. For example, one postdoctoral scholar serving as a primary instructor a few years ago scheduled his night exams 4/6 PM to 8:00 PM. His rationale for this time slot was that the more common 7:00 to 9:00 PM was a bit late; he said he would not have liked to take an exam that late at night, and so it seems unreasonable to ask his students to do so as well. While I fundamentally agree with this reasoning, such a choice greatly increased the difficulty that this postdoctoral scholar had to deal with regards to exam administration. At UMass Amherst, the 7:00 to 9:00 PM slot is reserved for night exams. Consequently, exams scheduled during this time slot take precedence over most other university activities classes labs etcetera. In contrast, exams scheduled outside of this window have a lower priority than other university activities requiring the instructor who scheduled such an exam to give the makeup. While giving makeup exams in a small class of approximately 20 or so is not a significant challenge, the logistical complexity increases dramatically with class sizes of several hundred. If this postdoctoral scholar had engaged in some sort of deeper, more formal training with regards to teaching, then he would have known about this rule and could have made at least a more informed decision.

Another challenge many of our graduate students in teaching roles have come across, and one that I myself came across as a new instructor, is familiarity with the slew of active learning techniques that can be employed in a classroom of several hundred. While I discuss the importance of active learning in 691G, and demonstrate some techniques, many instructors, both new and experienced, are more reluctant to attempt such techniques in a large classroom format due to logistical concerns. Moreover, novice instructors who do attempt active learning techniques in the large lecture setting often give up after negative experiences. My own experience as an instructor shows that these negative experiences are often the result of issues with either: implementation, choice of activity, or trying to “shoehorn” an activity or technique with inadequate consideration of the instructional context. By observing class, GTAs learn the techniques of each technique. Through our two-hour after-class meetings, they are encouraged to ask questions about what they have observed to be better prepared to implement them in their own classrooms in the future.

To add further complexity, many, though certainly not all, active learning techniques in a large classroom environment require some application of technology. Flipped classrooms require an online homework system to help students be prepared and some sort of classroom response system for quizzing. Moreover, many aspects of running a large-enrollment class are much smoother with technology: effective LMS usage helps students navigate the course, asynchronous communication platforms help build community, and tools like 3-D printing can help create an equitable learning environment.

The apprenticeship model I have developed over the past year provides an excellent opportunity for GTAs to gain a deeper familiarity with these tools. GTAs in this new approach complete tasks such as writing quizzes in the Edfinity online homework system, managing LMS content, creating and facilitating teams in CATME, using the VEVOX audience response system, using mail merges to provide feedback to students, as well as using Excel to facilitate communication between these tools. While I do not expect my GTAs to ultimately use all these technologies in their future classes, at least not at first, I do hope that exposure to them all will give them confidence to address pedagogical challenges in their future courses with technology.

In addition to these technical details of active learning implementation and technological familiarity, I strive to teach the GTAs in this apprenticeship model the fundamentals of instructional design: both at the micro class level and at the macro course level. With regards to individual classes, my role as a member of the executive board of the MSP (our faculty union), requires me to miss a few classes a semester. After observing several weeks of class, the apprentice GTAs are in a great position to gain experience in front of a class covering for me. I work very closely with the GTAs in helping them prepare for their sessions. Not only do I work with them to prepare their slides and notes, but we also do a “dress rehearsal” in the room to ensure that they are comfortable both operating the room’s technology, and demonstrations, and to ensure that they are comfortable with the performance aspect. After their lecture, I ask the GTA to review the recording of class and use a protocol from Harvard (https://cepr.harvard.edu/files/cepr/files/l1a_teacher_video_selfie.pdf) to reflect on their performance and how they will improve in the future. I also provide feedback on their instruction based on the video recording.

At the macro course level, we discuss the basic principles of course design such as backward design and essential questions. The goal of the backward design discussion is to help GTAs see the utility of this approach and to convince them that one of the first tasks is to write exams. The literature is very clear on the effectiveness of this approach. However, many novice instructors, and even some experienced ones, approach course development from slides: the first thing they do after writing a syllabus is begin writing slides. While this is an understandable approach, going into the semester with a few weeks ready to go definitely provides a sense of relief, almost any instructor will, at some point in the semester, catch up to what they had developed prior to the semester’s start. The subsequent writing as one goes is generally sustainable unless there are other significant instructional tasks to complete, such as writing and administering exams. This argument provides a practical reason to backward design supplementing the best-practices argument.

Ultimately, I have been very pleased with this change in GTA usage from student-resource to apprentice. Not only does the apprentice model help our graduate students become better instructors in the future, but it also is more engaging. The student-resource model, by contrast, has always yielded mixed results: some GTAs are highly committed to the role, while others feel pulled towards other obligations. This model also has a benefit for the department of requiring fewer graduate TAs, a benefit particularly salient in the current funding situation. If GTAs are the primary source of office hours etc., then many GTAs are required. The apprenticeship model, by contrast, uses a single GTA per section with the student-resource aspect of office hours etc. served, often more effectively, by cheaper undergraduate TAs. In short, I definitely plan to continue using this approach I the future.

Some random thoughts on 131: a new way to look at math

While I am not currently in the rotation to teach 131, and probably will not be for some time, I still sometimes think about it. Frankly, it is nice to be able to just think without the pressure of having to teach it as the lack of pressure allows my mind to wander on the big-picture parts of courses in fun and surprising ways.

Last night my mind was wandering on 131 and I realized that there is another theme running through the course that I had not really made explicit to myself before: a new way to look at math. As you can see from the description of 131, the course braids several different threads. One of these is my general interest in the difference between math-in-physics and math-in-math (see the right column of the poster!). Another is the integration of computation. The insight from last night is that these, along with graphical analysis, are all aspects of the same goal: learning to use math differently than students are accustomed from their math classes.

Writing equations corresponding to models of nature.
Reading an equation to predict how systems will behave with changes of variables.
Using equations (particularly differential equations) as “stepping rules.”
Graphs as a mathematical representation.

While this is a neat insight, I am now concerned if there is too much in the class.

These are thoughts to keep pondering!

Perceptions of interdisciplinary critical thinking among biology and physics undergraduates – Review and thoughts

This is a collection of my thoughts from reading:

A. B. Heim, G. Lawrence, R. Agarwal, M. K. Smith, and N. G. Holmes, Perceptions of interdisciplinary critical thinking among biology and physics undergraduates, Phys. Rev. Phys. Educ. Res. 21, 010138 (2025).

The paper is available on the PaperCast at https://open.spotify.com/episode/394yVw46zKSA8gPYLKLaGh?si=7bb3c2173d9545aa

Structure

This post is a series of thoughts on different topics that arose as I read the paper.

Tasks as the basis of research as well as curricular design and sharing

Listening to this paper on interdisciplinary curricular design, one justification they mention for focusing on learning tasks is that tasks are a manageable level for curricular design research. Tasks are simpler than entire courses, and once designed, they can be sequenced into a full course. An additional argument is that approaching a course holistically is simply too complex. While I agree that designing a course by first defining overarching goals and objectives, then breaking those down by unit, and only then developing tasks to meet the established goals, is more complex, I believe it produces a much stronger result. My initial experience designing 131 is an example wherein I designed tasks first and then strung them together did not produce an effective course. Thus, while I recognize the value of research on tasks and understand why they serve as a convenient focal point for curricular design research, I struggle with the idea that tasks should be the starting point. This perspective connects with ideas I’ve been developing for my new graduate TA training system. Graduate TAs often focus on designing lectures and other tasks, but I want to encourage a more holistic perspective—thinking critically about course goals and objectives first. In summary, while I agree that tasks are a critical part of curricular design and a convenient unit of research, I do not believe they are an appropriate starting point. That approach feels backward to me. It’s like designing the perfect brick before knowing what you’re going to build. If you’re building a house, that brick might be useful. But if you’re building a boat, that perfect brick may not help—and trying to use it could result in a boat made of bricks, which is ineffective at best.

Physics education, especially for biology students and even engineers, is at a point where curriculum reconsideration may not be absolutely necessary, but is certainly warranted. We need to ask: what are we teaching, and why? This line of thinking is influenced by the Hake paper¹, which emphasizes that active learning is where learning happens. However, active learning takes time. This means that designing a course requires hard decisions: what do you teach, and—more importantly—what do you drop? I would encourage others, as Redish² does in his reconsideration of introductory physics for biologists, to start by digging into what you want students to learn and why—then move on to the tasks.

The “Earthworm Problem” as a Level-2 Problem

This is referring to

Alice Churukian, David Smith, Colin Wallace, Duane Deardorff, Daniel Young, and Laurie McNeil, Living Physics Portal: PALS Breathing Worms, https://www.livingphysicsportal.org/details/d7a0eea7-e6a5-4fb9-a644-c276ee0968bf.

Later in the same paper, they discuss the Nexus Physics curriculum’s well-known earthworm problem. This involves comparing oxygen absorption through the skin with oxygen usage in the body—a scaling law problem. Surface area scales with R², and volume with R³. For cylinders, surface area scales linearly with radius, and volume (or cross-sectional area) scales with R². This relationship is relevant here.

While the problem is solid in concept, I still find it somewhat lacking. Perhaps not inauthentic, but not as engaging as it could be. The main issue is that students are told exactly what to do: create this equation, graph that one, identify where the lines intersect. While this applies physics problem-solving techniques to a biological context—which the paper classifies as “level two”—I don’t like that the path is laid out so explicitly.

In my IPLS course, I want students to figure out how to approach problems. They may need some guidance, but ultimately, I want them to be able to look at a biological or chemical situation and apply physics tools independently. The goal is for them to encounter something in a biology or chemistry course and think, “I’ve seen something like this before in physics. I know how to use physics to better understand this phenomenon.”

Importantly, I want them to apply this reasoning to new contexts—not just replicate what we’ve done in class. That’s why my exams use novel scenarios. If they can look at something like bird vs. bumblebee flight and think about the role of Reynolds number, or apply physics when studying blood flow in chemistry or biology, then they’re doing what I hope they’ll do. If an instructor mentions the electrical properties of blood, they should be able to draw on physics problem-solving to deepen their understanding—not just memorize the concept.

So, while the earthworm problem has value, I believe it would be stronger as a more open-ended task. For example: “Why do earthworms have limited cross-sectional area per unit length?” Something that invites critical thinking, not just procedural execution.

Presumed Uniformity of Introductory Biology Curricula

I also want to mention another critique of the paper: its assumption about the universality of biology curricula. In adapting Nexus materials at UMass Amherst, I’ve found that our students arrive in IPLS with different backgrounds than those at the University of Maryland. This makes me wonder whether biology curricula vary more than physics curricula across the country.

My conversations with biology colleagues suggest that variation exists even within UMass. For example, Laura Francis emphasizes a mechanistic and quantitative approach, while Caleb Rounds focuses on data literacy and graph interpretation. Others still follow a more traditional memorization-based approach. These differences suggest limitations in the universal applicability of the paper’s ideas.

For this reason, I believe authentic IPLS development requires close collaboration with local biology and chemistry faculty. These partnerships help align course design with the actual experiences of students. A good example is how my focus on HOMO-LUMO transitions in organic chemistry—used to motivate quantum mechanics—emerged from conversations with Laura. Using shared language and figures, and teaching this content simultaneously in chemistry and physics, reinforces its authenticity for students.

In short, one must be cautious when trying to generalize IPLS implementations from one institution to another. Biology prerequisites and emphasis vary, and effective course design must reflect this.

The Importance of Language in Problem Authorship

Another interesting example from the paper involves two different prompts for protein unfolding. The first is essentially a physics problem imposed on a biological context—no more authentic than a cheetah chasing an antelope. While it might be fun, it doesn’t feel authentic to many students, and in my experience, some even resent such forced pairings.

The second prompt, involving the energy landscape, feels much more authentic. In addition to structural differences, a key factor is the use of biologically native language. This aligns with ideas from my mutual mentoring work: authenticity is enhanced when you speak the language of the students.

This is something that I find missing in many IPLS discussions. Language and conventions matter. For example, I used to describe HOMO-LUMO transitions as “excitation from ground to first excited state”—the physicist’s language. Calling it a HOMO-LUMO transition, though, immediately felt more authentic to students. I don’t have hard data to support this, but my classroom experience strongly suggests it helps.

The Value of Level-One Tasks

One final point: what the paper calls “level one” tasks can actually be counterproductive. Many students are perceptive. They recognize when a problem is a forced attempt to make physics seem relevant. When it feels fake, they may conclude that physics has nothing to offer biology. In fact, the paper eventually makes this same point.

What I’ve found effective are tasks where students can draw relevant biological, chemical, or medical conclusions. For example, calculating eyeglass prescriptions based on eyeball size, predicting absorption lines of organic molecules, or solving for a 70 mV membrane potential. These are meaningful, relevant facts, but students often don’t know their origins. When they see physics helping them understand such concepts, engagement increases.

R. R. Hake, Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses, American Journal of Physics 66, 64 (1998). ↩︎
E. F. Redish et al., NEXUS/Physics: An interdisciplinary repurposing of physics for biologists, American Journal of Physics 82, 368 (2014). ↩︎

Structuring groups for gender equitable equipment usage in labs – Review

These are my thoughts on

M. Dew, E. M. Stump, and N. G. Holmes, Structuring groups for gender equitable equipment usage in labs, Phys. Rev. Phys. Educ. Res. 21, 010162 (2025).

Listenable on the PaperCast at https://open.spotify.com/episode/6ZG4lZH9dXpUHODtij31Bo?si=bbb689ca533640f4

I would like to examine some of the citations within the introduction. Also, the paper does not discuss the alternative educational goal for a first-semester mechanics lab: cohort formation, which is why we rotate groups. I would be curious to see the impact of semester-long groups on this cohort formation process. However, I am already starting to think that, first, forming our own groups as we currently do is the best approach, and second, that some sort of final exam at the end is almost certainly beneficial. The authors indicate that even in some other studies with group formation that resulted in equitable equipment usage, there was still inequitable computer usage. This phenomenon of inequitable computer usage is definitely something I have observed in the Physics 181 lab. Therefore, some sort of lab practical involving computer usage along with other basic skills seems helpful in establishing equitable use.

Following up, I think there is value in asking students to list people with whom they would like to work, as well as those with whom they would prefer not to be partnered. Finally, I do like the question of whether they would prefer to be in a majority-woman group, a majority-man group, or have no preference. The self-described category will be difficult to manage because of the numbers. We will need to think about an effective way to address that.

The paper seems to suggest that rotating groups is generally detrimental to equitable equipment usage. However, they cite a prior paper by the same author that shows this effect can be mitigated by using partner agreements in conjunction with a lab practical exam. I have already considered implementing a lab practical exam for the 181 lab this coming semester. I also see some value, particularly in the first semester, in rotating groups to facilitate cohort cohesion. Moreover, my groups remain the same for three weeks, as opposed to the two-week duration used in this study. It seems to me that the most optimal system for my particular course and goals would be to rotate groups every experiment—that is, every three weeks—and to include some time at the beginning for a partner agreement. Teaching students how to create and use partner agreements also has value beyond the 181 lab. These students will be working in pairs and groups throughout their undergraduate curriculum, so teaching them how to facilitate those interactions is, in itself, a valuable skill.

In short, I believe the best solution is fixed groups, which I was already planning to implement, combined with partner agreements. I should look up that earlier paper and see exactly how those partner agreements were structured, along with incorporating the lab practical I was already considering.