Today in intro physics, after introducing the new unit, we did test review using “sometimes, always, never,” which I learned from Frank Noschese.  We have covered projectile motion, Newton’s 2nd Law, and Uniform Circular Motion.

Here were our statements:

1. Constant speed means zero acceleration.
2. Normal force points in the opposite direction of weight.
3. When an object is on a ramp, the acceleration is always down the ramp.
4. When a projectile hits a surface, it’s final velocity is zero.
5. For an object in free-fall, its speed at maximum height is zero.
6. In projectile motion,the horizontal component of acceleration is 9.8 m/s/s.
7. For uniform circular motion, velocity and acceleration are 90 degrees apart.
8. Given two velocity components, the speed is found by simply adding them together.

The rules are students must draw / describe two examples, no matter whether they think it’s always, sometimes, never.

In QM, by far the most common thing that students said for what was helpful was clicker questions. Below are upper division students’ responses to why clicker questions are helpful.

Students’ responses touched upon important themes about learning such as active processing (i.e. force me to think), self-assessment (test our understanding), meta-cognition (i.e., see what I know), and proximal feedback (wrong understanding gets corrected in the moment).

“It gives us some time to process what we’ve learned rather than just write it down and hope we understand our notes later.”

” I feel like it helps sink things in we’ve talked about.”

“They usually contain questions that really test our understading of the material. They are also a good tool for us to identify our weak areas and what we need to work on.”

“It is nice to see what I know and/or can deduce from what we are going over in class.

“They tend to be helpful in checking my understanding conceptually of what is going on.”

“Knowing that they’re going to happen forces me to come to class prepared to think, which helps me focus more intently while you are lecturing. Also, having to explain our reasoning has forced me to think deeply”

“Are very helpful because it forces us to take a breather and actually process what you just told us/ what we just wrote down. “

“They are very helpful in that they give me time to stop and make sure I truly understand what I’ve been watching be presented. The class leaves me feeling challenged and engaged. “

“I find it helpful since it forces a question/problem that makes you actually think and apply the material instead of just going into a note taking mode. It also helps if your understanding is wrong, because at that moment it’s corrected. “

In addition to clicker questions students’ mentioned other things that were helpful, that touch upon important educational themes such as “making connections to prior knowledge”, “relational vs instrumental knowledge”, and “multiple representations”, “multiple encounters”.

Students brought up things like:

– Making connections / analogies to things we already know.

“In class, if we relate a new topic to an old one with which we are more familiar (like between the Schrodinger Equation and N2L) it helps my understanding of what we are doing.”

– Focusing on what is physically / conceptually going on (not just mathematically)

“I am greatly appreciative that you do your best to give us conceptual understandings for the material.   Having that conceptual knowledge to start from, it gives me a basis to understand the rest of the material.  “

– Emphasizing visualization.

“I find the visual representations very useful for learning (even though its not easy to do for quantum mechanics).”

– Articulating Learning (Goals)

“It does not always happen, but some days you tell us to write down something new that we learned. I have gotten into the habit of doing this at the end of each class, as well as a question or two that I may still have. This has proven to be beneficial.”

“I like that we start the class with a quick summary of the day’s material that will be covered. ”

Feedback is for Me and for Students

Part of why I ask for feedback is to actually get feedback from students’, and to make adjustments. This semester with my QM students I am making adjustments to homework grading, how I articulate to students’ the reasons why we are doing a particular example problem, and how often and when I pause to give them time to write down thoughts from a discussion, among other things.

But asking for feedback, gets them to articulate things about their own learning. It is always the case that students’ (collectively) responses touch upon sooooo many important things about teaching/learning. When people ask me how to get students to “buy-in” to active learning,  my responses is always, “give them an opportunity to articulate things about learning” and help them to see how your class to organized to do those very things.

This week we started look at time evolution in quantum mechanics. Since this is a spins-first approach, that we means we first take a look at the spin-1/2 particle in a uniform magnetic field.

Here are clicker questions from our day looking at this:

1. This first question was asked after setting up the problem, but before getting into QM. Take in a moment to make sure we understand the classical perspective.

2. This question was asked after having worked through the time evolution, and have an expression for the state as a function of time. Good time to re-emphasize the significance of an overall phase change and the idea of energy eigenstates as being stationary.

3. This question was asked after changing the initial state to be a superposition of energy eigenstates. In talking through this question, we both “cranked out the calculations”, but spent a fair amount of time sense-making about precession in the x-y plane.

This last question, brought us back to physically sense making and to take in the big picture, rather than sense-making about a particular mathematical expression or result.

Teaching QM has certainly made me think back on my own experience being in upper division courses. Specifically, I’ve been wondering recently what were the conditions that contributed to a handful of lectures I watched as an undergrad staying in my brain ever since. Like so much so that I clearly remember that feeling of being in that class, I can see writing on the board, the writing in my notebook, and forever have been able to recreate these particular derivations with little trouble.

Two of them are

1.  The method for deriving the results of gaussian integrals (from a Calc III class)
2.  How to derive the Green’s functions for damped SHM, and in the process applying the Residue Theorem as an integration technique (from a Classical mechanics course).

I think part of my answer for why I remember them is that I was so intrigued by both of the methods at the time, that I pondered them over and over and over, and recreated them again and again. The initial condition was certainly whatever it was that made me so intrigued at that moment, but the process of crystalizing that knowledge was not the lecture itself, but the acts of non-stop thinking about them over a long period of time.

This also reminders me in high school, I was obsessed with calculating the moment of inertia of three dimensional objects, under various geometries and mass distributions. I loved setting up the integrals and working them out, especially in spherical coordinates. I would work these out again and again again every time I was sitting in some other boring HS class. This was also something that was just “lectured” to me, but again my learning was immensely active and sustained over a long period of time.

It makes me think that a lot of the reason I did fairly well with math and physics throughout high school and college was that thinking about physics and math was not really school work, but an obsession. Re-deriving interesting things or playing with the math was like doodling, something I did constantly, all the time, anytime a piece of paper was at hand.

But this was also one of the reasons why I was not a “great” student in college. I didn’t do my HW all the time, because I’d be spending my time “doodling” what was interesting to me, rather than what the teacher wanted me to do at that time. While there was significant overlap between my doodles and the course work, this overlap was not so great as to make me a top student. [I am just remember know how much I loved solving normal modes problems].

Anyway, that’s been on my mind.

This question was good one from today. After introducing the raising and lowering operators, we had some “practice” reasoning about which matrix elements would be zero (and thus saving the work of cranking out each calculation).

I don’t spend a crazy amount of time deriving everything little thing in QM class, but I do work through some of our text’s derivations at the board. I try to chose those that I feel either give us an opportunity to grapple with important ideas, emphasize certain techniques, or those that help us keep a coherent narrative through our course of study.

I’ve been trying to use clicker questions at key points during the derivations to keep students engaged and hold them accountable for reasoning. Today we were working through ideas about how commuting operators have simultaneous eigenvalues, and how this leads to fact that QM states must exist with both definite values of angular momentum (magnitude) and one component of angular momentum (but not more than one).

Here are two examples of places where we paused to think about what we can and can’t conclude.

I’m not sure if doing these is optimal, but so far it’s not been awful either.

As usual, I give a early semester feedback survey to students. I have for years now been reporting students results, so here they are. No surprises here.

What do we do in class that is helpful for your learning? Why?

Summary: Students like a variety of things, including discussion, group work, whiteboard problems, seeing examples, hearing and explain thinking. Students reasoning touch upon a lot of important notions, such as active engagement, self-assessment, coaching, peer learning, self-explanation, etc. A few students mention ideas that are more focused on test prep.

My Response: Help them to see that there are a variety of things that people like. It is useful for them to know that their opinion is not necessarily “the opinion of the class”. If I have time, I might tell them about a few educational things.

It’s helpful that you provide visual examples and explain what is happening and why it is happening. It helps put into perspective.

Whiteboard problems are helpful. It allows me to think for myself and how to solve the problem.

Clicker questions and whiteboard problems. Help me to think on my own and discuss with my group why and how I got my answer. Whiteboards because it makes it easier to know if I really understand it or not.

The interactive stuff like the position vs time graphing with the motion detector, and the small group stuff.

Whiteboard problems and examples

When we do whiteboard problems, it allows me to practice while helping others or get the help from others that I need.

Making us explain concepts to each other. I tend to grasp concepts better when I am explaining it, like with the clicker questions.

When you walk through a problem step-by-step and have us immediately solve a similar problem. This allows us to understand what we are looking for without just giving us the answers.

I like the group work, I feel like I understand better from […] especially.

Being able to see a problem being done (or even just set up), and then working problems together in our groups, because I can see where I need to work on.

Practice problems on the whiteboards. Questions and discussions as a group.

Examples, because it let’s me see what kind of problems to expect on a test.

Clicker questions, because we discuss we each other. Sample problems and then letting us practice on our own.

Practice problems. The extra lecturing on learning strategies and techniques help with problem solving as well. Having students engage and interact in activities (like the one with the graphs). The quizzes keep me up to date on the reading.

I love the group work. I love having to figure out of problem in groups. I love the whiteboard work in groups.

Going over and practicing many different types of problems.

Solving problems on whiteboards in groups.

Whiteboard problems, because we work together to answer questions.

You breaking down everything is helpful, even though it is annoying.

Going over and working problems that are similar to exam problems. It helps because many times reading the lectures is confusing, so going over it in class helps to clarify.

Individual discussion among tables for explanation can be helpful for cementing a concept and help retain it,

I really like the example problems we do in class.

Practicing questions together.

Whiteboard problems together, because we can ask what we did wrong when we are in class.

The whiteboard problems help because writing it out and working on them with other people helps me when I make a mistake.

I like the quizzes. I find it helpful to focus my reading. And going over problems.

The practice questions that we work out in class is very helpful, because it helps me see the process, step-by-step.

Working with groups. It helps because if I get confused, I can ask my group for help.

When other students explain how they got their choices to the whole class. Even though you explain things well, some professor just don’t.

When the instructor does a problem and give us a problem that is similar. We team up to do it and on own, and it this helps me learn the material more effectively.

Summary: Reading quizzes are stressful as is the idea of changing group.

My response: I will re-explain the purposes that the quizzes serve (getting students on time and them reading means we can “make the most” of our time together). I will change the grading so that showing up for the reading quizzes gets you 5/10, the five questions will be worth the remaining 5 points. For group stress, students will be able to request one person to work with and one person not to work with. When we change groups I will also structure an activity where they reflect and and discuss what worked and didn’t work well with their last group, and get them to form a plan/ norms for working well together.

Nothing.

I like group work, but sometimes it is more helpful to do things on your own.

Spending time on problems, when I feel like most of the class gets it.

The quizzes stress me out, and even though I’ve done well on them, I feel that they haven’t been as helpful to my learning as they are supposed to be.

Changing groups won’t be helpful, because now I have to relearn people and become comfortable with them, when I could just stay with my group and focus on learning, and how the awkwardness of meeting new people.

The reading quizzes don’t help me because I read the reading and study and still can’t seem to do well.

I’m sometimes confused about lab… [they are not unhelpful] they don’t always make sense, especially the questions in the back of the lab.

Doing practices that are not going to be on the test.

Nothing. The class is eclectic in all its phases.

The limited ability to go beyond the current situation, whether the lab or the topic.

Nothing is unhelpful, but working on whiteboards is the least helpful. I still think it is valuable.

Nothing.

(Blank)

I don’t have any complaints.

Switching groups. I connected with my group on the first day, which is very unusual. No one is looking down on anyone base on whatever question they had. Every single one of us literally have something to offer to the rest of the group.

Nothing, this lab is very helpful and is much more interesting than I thought it would be.

I don’t find the reading quizzes helpful. They add anxiety and stress towards coming to class. and they take away from the excitement of being here.

Can’t think of anything.

Nothing is unhelpful. It might not help me, but it doesn’t hurt.

Everything we do so far seems to have a purpose.

Everything seems helpful, but the least helpful is making us explain our answers to each other when sometimes we all have the same answer at our group.

Nothing.

Too many whiteboard problems, maybe try doing some individually. That way we actually test if we can do it ourselves, and not just one person in the group.

Nothing.

Can’t think of anything.

Nothing.

Most things seem optimized to help us learn as well as we can.

——–

What else do you want to tell me?

Summary: Students want more problems to practice problems.

My Response: I will guide / remind them in how to effectively work out problems at home. Give class time at end of the day to “deciding with their group” what problems they might like to try before next time, and making a plan for when you get stuck (email/call a friend, sign up for office hours, go to tutoring, etc).

(Blank)

I would like more test review. On the test, I had a hard time reading the questions and understanding them. There are so many different ways they can be worded.

I just wanted to say thank you. I was really nervous about this class, but you have made us feel comfortable and make it easy to ask questions.

(Blank)

More practice questions.

Labs are fun, but I wish we had more time to work on labs

Please don’t make us change groups. I am actually comfortable with my group.

I know its early in the semester, but when doing practice problems, everyone once and a while I’d like be given a problem that really makes everyone think outside the box.

It’s too bad Gene Wilder passed away. Really enjoyed his career even thought he hasn’t bee in a  film for quite some time.

I just wish we had more problems to work. Maybe do a practice exam in class that is timed?

I know reading quizzes are helpful, but quizzes everyday are a drag.

I’m very appreciative of this class. Thank you.

This is my favorite class this semester.

I wish we did more whiteboard problems it really helps you prep.

I feel this class is working out well.

So far so good, the only thing is I took physics in high school, and its been boring and frustrating at times to have to go over material I already know.

For my first physics class at MTSU, I have no complaints. Keep Rocking!

I wish we worked more whiteboard problems.

We need more breaks, to help with transitioning between things.

Can we practice more problems?

I love class discussions.

So far this class has been better than my high school physics class.

I would like to do more problem-solving in class.

Just sharing my QM clicker questions… feel free to use. [Edit: I’ve added some commentary.]

Day 1: Magnetic Moments and Introduction to QM

Question 1.1: Classical Stern-Gerlach thought Experiment. I

I used this question before a mini-lecture on magnetic moments, the magnetic potential energy associated with dipoles in a magnetic field, and then derived the magnetic force from the gradient of the potential.

In hindsight, I wish I began with (or also discussed), clicker questions about charged particles moving through magnetic fields (because students are more familiar with this). On a HW problem, many students did not clearly understand that this magnetic force was the result of a neutral atom having a magnetic moment in a magnetic field gradient, rather than a charged particle experiencing a magnetic force due to its motion through a magnetic field.

Question 1.2:

After deriving the relation ship between, magnetic moment and force, I wanted them to think about how only the z-component matters for the deflection. After this, we talked explicitly about the SG experiment, and how the result is surprising because we only see two possible values, rather than a continuous distribution of values.

After the Stern-Gerlach experiment discussion, we returned to question of “Why do particles or atoms even have magnetic  moment? After deriving an expression that relates angular momentum and magnetic moment, I asked the following question

1.3:  Classical Magnetic Moments

I wish I had spent more time (or pushed to the HW), discussion about why with the silver atoms we are measuring the intrinsic magnetic moment of the electron.

Day 2: More SG Experiments.

Question 2.1:

This question was the warm-up, serving to remind them about the SG experiment, and also challenging them on their interpretations of the results.

Question C should be revised to say, “straight up or down”. The goal here is to make sure that students know that the device only measures the z-component. Answers D is an good “classical” interpretation for them to be at this point.This question gets returned to at the end of the day, after we discuss other SG experiments.

Question 2.2: Students were supposed to have read through these experiments. Instead of lecture through them, we did clicker questions. We did lots of “how are you making sense of this?” Lots of “classical” interpretations naturally arise, such as “randomizing”, “filtering”, … these aren’t bad ideas. Later we’ll want to push them toward QM ideas about incompatible measurements, uncertainty relationships, etc, but now is not the time. I need them to “sense-make” with the results.

After each experiment, I introduce the formalism of dirac notation and how we “encode” states and the experimental results using bra, kets, inner products, etc.

Next time, I want to introduce the “frequency vs angular momentum” graphs now rather than later. And informally “notice” things about those distributions.

Question 2.3:

After introducing the formalism, I want to give students a chance to practice.

Day 3 Clicker Questions:

Question Set 3.1:  Sense-making about Off-Axis Measurements

These questions are after a HW problem where students looked at QM spin states that are prepared “off-axis”. Good warm-up for the day.

Question Set 3.2: “Seeing” Uncertainty and Expectation Value

In previous week, we didn’t talk in class a lot about expectation value and uncertainty. Students had calculated them for the HW, but I wanted to help students understand what they were even calculating. These ranking tasks were great for the job.

The rest of the day was spent doing example problems and introducing rotation operators.

Day 4: Reviewing Trouble Spots and Representations of Operators

Question Set 4.1: Overall Phases vs. Relative Phases

Students struggled on a HW assignment about relative phases, and it was clear we needed to discuss it more. So we spent the beginning of the day hashing it out.

The second of these three questions is pretty challenging.

Question Set 4.2:  Rotation Operators and Phases

One kind of clicker question I try to use is “getting started”, “or checking for understanding” in derivations I do in class. I try not to lecture too much, but certain derivations are useful to go over in class. My way of engaging students is ask questions along the way, that force them to think about what we are doing.

These questions are doable if you understand what the operators are doing, what the notation means, and can visualize rotations in a right-handed coordinate system.

Question Set 4.3: Representations in Other Bases

The day ended with a review of representing bra/kets in column and row vectors. An upcoming HW problem asked students to do similar work, so I wanted to make sure we discussed it. Prior to this we had only explicitly represented states in the Sz-basis.

We spent the rest of the day introducing operator representations.