Author: Brokk Toggerson

The Structure of Scientific Revolutions – Review and Application to 13X

I have been reading The Structure of Scientific Revolutions1, and, while dated, I found it quite interesting. I would love to hear the thoughts of a colleague from psychology or sociology. I feel that many of his thoughts and conclusions suffered from, essentially, selection bias as a former practicing physicist: many of his examples are drawn from the history of physics and the adjacent sciences of chemistry and astronomy with few from biology and even fewer from further afield.

However, I did find one thought potentially relevant for my interdisciplinary work with 131 and 132: the question of “Is helium a molecule?” In the text, the author asserts that physicists and chemists gave different answers to this question. A chemist says yes because it behaves like a molecule on the kinetic theory of gases. A physicist, on the other hand, may not say that it is a molecule because it does not possess the interatomic bonds necessary for molecular Construction. This is a cool example and citation for our discussion on different ways of knowing between the different Sciences.

  1. T. S. Kuhn and I. Hacking, The Structure of Scientific Revolutions: 50th Anniversary Edition (University of Chicago Press, Chicago ; London, 2012). ↩︎

Alternative Assessment in Upper-Division Quantum Mechanics

Replacing Midterm Exams with Multi-Attempt Quizzes

This past semester forced me to implement two changes to my Quantum Mechanics II class that I had debating implementing back in January, but decided against to minimize the number of changes. However, midway through the semester, some UMass international students at began to have their visas and statuses revoked. The first student to fall victim to this abuse of government power was a physics undergraduate. This information broke on a Wednesday, and my sole midterm examination was scheduled for the following Tuesday.

I felt that going ahead with the midterm under such circumstances was neither fair nor appropriate without a conversation with the students. Moreover, I felt that I could not delay the midterm by another week because of holidays and snow days had already resulted in the midterm being later than I would have liked. After a discussion with the 12 students in the class, one of the students, who had taken a class from Bill Leonard in our engineering department, proposed the very “mastery model” that I had already considered implementing semester.

The implementation I ultimately decided upon was one similar to one Jennifer Ross, now at Syracuse University, had implemented in her 500-level Optics course here at UMass Amherst several years ago: students have the opportunity to take multiple assessments on every given topic in the form of short two-or-three question quizzes. After seeing their results, students can then elect to take another quiz on the same topic. Only the highest score is kept. Due to the complexities of creating quizzes for QM II, I was forced to restrict the number of attempts to three on each set of topics:

  1. Fundamentals of Angular Momentum (Review from QM I).
  2. Group Theory.
  3. Parity and Translations.
  4. Angular Momentum Addition and Rotation Theory.
  5. Identical Particles and the Periodic Table.

We ended with perturbation theory at the end of the semester and, given the newness of this entire procedure and the limited time for retakes, I did not offer a quiz on this topic.

End-of-Semester Presentations

In addition to replacing the midterm exams with quizzes, I also replaced the end-of-semester final exam with a presentation. For those who may not be familiar, the textbook, Griffiths and Schroeter’s Quantum Mechanics 3rd Edition, follows a format where concepts such as parity are introduced and then applied to interesting physical systems such as crystals. For this final assignment, students worked in pairs and had 25 minutes to present one of these application topics. To make sure that everyone was prepared, and that the topic could be covered in such a small amount of time, there were reading expectations in advance. Students were also expected to ask questions during other students’ presentations. In addition, all teams were told to expect two questions from me that they must be able to answer.

Review

The changes represented a good first attempt. Unfortunately, few students completed the end-of-semester evaluation so I got little feedback from them. My summary of the pros and cons can be found in the table below:

ProsThings to change next time
1. Students have both the opportunity to learn from their mistakes and the incentive to do so.

2. Makeups are not an issue.

3. The end-of-semester presentations are AI proof: students are allowed to use it in preparation though told that AI sometimes gets this level material quite wrong. Moreover, as an instructor I can clearly identify when students rely on AI as they are unable to answer questions. 		1. Many students waited too long to complete the quizzes and thus did not have time to retake, after additional studying, as many times as they otherwise would have.

2. While I did have a rubric, it was clear that many students were unclear on exactly what was expected.

3. Having only a single presentation meant that the opportunity to learn and improve did not exist.

Things to do differently next time

  1. Do it from the beginning!
  2. Have two rounds of presentation: one about midway through and the other at the end so that students can improve their presentation skills too.
  3. Have a timeline for the quizzes so that students cannot get too far behind.
  4. Consult with Bill Leonard, Jennifer Ross, and other experts more deeply for a more considered approach.

A First Crack at Introductory Lab for Physics and Astronomy Majors (Physics 181 Lab)

This past semester saw my first attempt at teaching introductory lab for physics majors (Physics 181 Lab at UMass Amherst). I worked with Chris Ertl, leveraging his expertise in developing labs for Physics 131 inspired by Course-based Undergraduate Research Experiences (CUREs) common in biology1. In CURE lab courses, students explore authentic scientific questions and share their results with the broader scientific community. Development of such curricula is comparatively simple in biology as almost any soil sample will include microorganisms unknown to the literature.

While true CUREs are difficult to construct in physics, as most authentic physics research questions are beyond the reach of introductory students, we strove to incorporate the ideals of this approach as well as synthesize it with both the AAPT’s Recommendations for the Undergraduate Physics Laboratory Curriculum2 and the thoughts expressed in Introductory Labs: We can do Better3 article from Physics Today’s January 2018 edition. We also owe a lot to the prior instructor, Scott Hertel. The resulting course focused on the following goals with the aim to make the experience as close to that students will see in future lab work:

  1. Physics-identity promotion and acculturation: The literature is very clear on the importance of the development of physics-identity, particularly with regards to students whose identities are not traditionally associated with physics4,5. We explore different careers physicists purse from the traditional academic/lab roles to comic-strip authors. Within the research sphere, we discuss the different modalities of theoretical, phenomenological, computational, and experimental along with a bit on what the day-to-day lab work is like for each group. Finally, we discuss some practical aspects of being a physics student including the concept of REUs, getting involved in research and TAing including the financial aspects (that you get paid for REUs and graduate school for example). This last point particularly important for first-generation and international students who may be less familiar with the structure of physics education at the university level in the U.S.
  2. Scientific philosophy and values: Students received explicit instruction into some of the fundamentals of scientific philosophy, such as the logical impossibility of proving things true and the differences between inductive and deductive reasoning. Moreover, helping students understand and appreciate that experiments almost never work the first time was baked into the course from the foundations. Students also engage with the fundamentals of modeling: what variables are important, what can be ignored, etc. as they build their own models from their data.
  3. No “cookie-cutter” labs: All the labs had minimal instructions with regards to procedure forcing students to design the procedures themselves.
  4. Construction of their own apparatus: Instructors of more advanced labs had commented that students in these courses were not comfortable with using equipment as basic as C-clamps. My hypothesis was that this discomfort arose from the structure of prior lab courses: historically, students have entered the lab to find the setup already established by the lab instructional team. Instead, we had, the more authentic, shelf of materials which students could use to construct their own apparatuses.
  5. Understanding uncertainties: Students were explicitly taught the difference between statistical and systematic uncertainties in an explicitly frequentist framework. Moreover, students were expected, by the end of the laboratory, to
  6. Refinement of Procedures: Dovetailing with goals 2-5 above, and inline with the recommendations for CUREs, students are always given time to refine their procedures and try again. Of course, refinement takes time. As a consequence, we only did five labs over thirteen weeks with each lab taking two or three weeks to complete.
  7. No “black boxes”: In order for students to achieve goals 4-6, students must fully understand and be able to calibrate their measurement tools. As such, only the most basic experimental tools are used: rulers, scales, protractors, timers, etc. This is in distinct contrast to prior iterations which used a lot of electronic measuring tools. My issue with these tools is that students can neither innovate nor really understand the uncertainties involved.
  8. Exposure to different subfields of physics: As described in Exploring subfield interest development in undergraduate physics students through social cognitive career theory6, many students are unfamiliar with most physics subfields beyond the “popular” upon entering higher education. Thus, we strove to include labs from multiple subfields including astronomy and granular materials etc. to both expose students to new fields and/or excite those who may already have such an interest.
  9. Exposure to python as a data analysis tool: This course is not designed to be an introduction to programming course – we have one of those which comes later. The programming goals of 181 Lab are simply to expose students to a python programming environment and to begin to get comfortable with manipulating data through text commands. I use the pandas python data analysis library due to is superficial similarities to spreadsheets which most students have at least opened and used in a superficial way.

The result of our collaboration was, I must say, one of the most successful first attempts at a course I have had in a long time. While there are, of course, things to change in the next iteration, I am excited to see how this course develops. Once it is more mature, I will create a dedicated page.

  1. Atreyee Bhattacharya, Pamela Harvey, and Perri Longley, CURE | Course-Based Undergraduate Research Experience (CURE) | University of Colorado Boulder, https://www.colorado.edu/research/cure/home. ↩︎
  2. D. MacIsaac, Report: AAPT Recommendations for the Undergraduate Physics Laboratory Curriculum, The Physics Teacher 53, 253 (2015). http://scitation.aip.org/content/aapt/journal/tpt/53/4/10.1119/1.4914580?ver=pdfcov. ↩︎
  3. N. G. Holmes and C. E. Wieman, Introductory physics labs: We can do better, Physics Today 71, 38 (2018). https://physicstoday.scitation.org/doi/10.1063/PT.3.3816. ↩︎
  4. E. W. Close, J. Conn, and H. G. Close, Becoming physics people: Development of integrated physics identity through the Learning Assistant experience, Phys. Rev. Phys. Educ. Res. 12, 010109 (2016). ↩︎
  5. S. Hyater-Adams, C. Fracchiolla, N. Finkelstein, and K. Hinko, Critical look at physics identity: An operationalized framework for examining race and physics identity, Phys. Rev. Phys. Educ. Res. 14, 010132 (2018). ↩︎
  6. D. Zohrabi Alaee and B. M. Zwickl, Exploring subfield interest development in undergraduate physics students through social cognitive career theory, Phys. Rev. Phys. Educ. Res. 21, 020109 (2025). ↩︎

Using Discussions in Upper Level Courses

As I go into my third round of teaching the second semester of advanced quantum mechanics I’ve been giving some thought into what to do with the discussion sections. These are standard part of many upper level courses at University of Massachusetts Amherst, but there seems to be no consistent way of using them. The most recent paper that I read on student challenges in learning degenerate perturbation theory, really helped me see the parallels between teaching Quantum Mechanics for second and third year majors compared to teaching of introductory physics to students in their first year. As mentioned in my last post, in both of these cases students lack what we would call quote correct unquote? Intuition about the subject. In the case of introductory physics the alternative conceptions of motion and forces are well documented. In the case of quantum mechanics, on the other hand, students is lack of Prior intuition is completely understandable given the removal of the subject from their everyday experience and the famously non-intuitive nature of quantum mechanics as a subject.

This parallel between introductory physics and advanced quantum mechanics presented in the paper suggests a way in which to use these discussion sections: use them for students to complete tutorials. As detailed in the paper described in my last post, there are now several different tutorials for quantum mechanics such as the quilts. Thus, the discussion could be a good time for students to work through some of these tutorials in the company of both myself and a graduate ta. This would serve an additional function in helping graduate TAs learn how to apply active learning pedagogies to more advanced courses.

Teaching Quantum Mechanics: Active Learning and Parallels to Teaching Introductory Physics

I just finished reading Challenges in sensemaking and reasoning in the context of degenerate perturbation theory in quantum mechanics1 (could not be a paper cast as there is far too much mathematics for that format!). Not only did the paper give some good insights into the active teaching of time independent degenerate perturbation theory, but I also gained an improved appreciation of the parallels between teaching quantum mechanics at the 3rd/4th-year level and introductory physics at the first year level.

Active Learning of Perturbation Theory

As has been discussed elsewhere, I have been teaching a QM II class (Physics 564 at UMass Amherst) for the past two springs, and will be teaching it again this coming Spring 2025 semester. This course is based on chapters 5-7 in Griffiths and Schroeter’s excellent textbook2 with a much more lengthy discussion of symmetries through the lens of an introduction to group theory than is present in that text. Much of this group theory material is from Matthews and Walker’s Mathematical Methods of Physics3 as well as my own notes4.

As I have been iterating the course, I have been adding more and more active learning activities: an approach which I think works well in a more advanced class such as this. In the first pass, there were occasional activities as I refreshed myself on the material. Starting with the second pass, I began to incorporate some activities of my own devising starting with the opening sections of the course. However, I was unable to add them to all the topics in a single semester. In particular, the discussion of perturbation theory was still predominately based on a traditional style lecture.

This step-wise approach, however, led to an interesting, if expected-in-retrospect, result which reemphasized my commitment to active learning; students’ exam scores were noticeably lower on those topics which did not have as many active learning exercises. Thus, for the coming semester, I have committed to incorporate even more active-learning exercises in my discussion of perturbation theory. Moreover, the materials of Christof Keebaugh, Emily Marshman, and particularly Chandralekha Singh (the authors of the paper) seem to be a good starting point.

The parallels of teaching quantum mechanics compared to introductory physics

The main thrust of the paper, from my perspective was the parallels between the teaching of quantum mechanics and the teaching of introductory physics. In both cases, the students are novices to the subject. This novice identity applies to both the physics content, and the mathematical language which is used to describe the physics.

In introductory physics, many of the students are seeing the subject for the first time and the challenges students face in developing a Newtonian perspective are well documented in the literature. In addition, many of the students are simultaneously new to the mathematical practice of calculus: having just completed it or being co-enrolled at the same time as introductory physics.

Similar conditions apply to students first “real” exposure to quantum mechanics in their 3rd/4th year. Here I refer to courses based in linear algebra as opposed to the introduction that many students first get in a 2nd-year modern-physics class. Just as with introductory physics, many students do not enter with any sophisticated conceptual picture (quantum mechanics is famously non-intuitive after all!). Moreover, quantum mechanics, being based in linear algebra is mathematically fundamentally different than the basis in calculus and differential equations which characterizes prior courses such as classical mechanics and electricity+magnetism.

As a consequence of these parallels, students in introductory physics and quantum mechanics show several similar behaviors:

  1. Their conceptual schema are only locally, as opposed to globally, coherent. As a consequence, their answers to deeply related questions may not be internally consistent and may even be mutually contradictory.
  2. Students in both courses do not always check their results for reasonableness.
  3. In both courses, students can get stuck in “math mode” or “physics mode” when solving a particular problem, but struggle to integrate the two perspectives.
  4. Students in quantum mechanics exhibit some of the same novice problem solving strategies which they have “grown out of” in the context of classical/calculus-based physics including engaging in with Tuminaro and Redish call the “recursive plug-and-chug” epistemic game,5 as well as memorization and recourse to authority.

These are all facts to keep in mind as I move forward to preparing my course for spring 2025.

  1. Keebaugh, Christof, Emily Marshman, and Chandralekha Singh. “Challenges in Sensemaking and Reasoning in the Context of Degenerate Perturbation Theory in Quantum Mechanics.” Physical Review Physics Education Research 20, no. 2 (November 5, 2024): 020139. https://doi.org/10.1103/PhysRevPhysEducRes.20.020139. ↩︎
  2. Griffiths, David J., and Darrell F. Schroeter. Introduction to Quantum Mechanics. 3rd edition. Cambridge: Cambridge University Press, 2018. ↩︎
  3. Mathews, Jon, and R. L. Walker. Mathematical Methods of Physics. 2d ed. New York: W. A. Benjamin, 1970. ↩︎
  4. These are from courses I took with Prof. Jonathon Feng at University of California – Irvine as a Ph.D. student. ↩︎
  5. Tuminaro, Jonathan, and Edward F. Redish. “Elements of a Cognitive Model of Physics Problem Solving: Epistemic Games.” Physical Review Special Topics – Physics Education Research 3, no. 2 (July 6, 2007): 020101. https://doi.org/10.1103/PhysRevSTPER.3.020101.
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