I’ve been thinking more and more about using Desmos in algebra-based physics for getting students involved in writing simulations.
You can get students up and running pretty quickly. Here are three lines of code to simulate an accelerating object.
- 1st line defines the equation of motion, y as a function of time
- 2nd line plots the point.
- 3rd line defines time as variable that you can “play”
Of course, you get quickly get more sophisticated:
Here is a simulation for dropping stones at 1 second intervals…
Or a simulation for a vertical toss that blends with other representations
And lots of other stuff you can add… like adding images, getting rid of graphing look
Or blend with motion diagrams…
What I also like about it is that if my students just type in an equation exactly the way it is in the book… like this
It will prompt them to add sliders, which is what is needed to get the simulation up and running. You click “all”, and you are almost there. You just need to plot a point…. and press play.
Lots of cool things, like here in our lab where were trying to predict how far up a ramp a cart would go, we had a range of data for acceleration and initial velocity. So we could run the simulation for multiple values by defining acceleration and velocity as a list
You get something like this…
I’m call this “Cranking Five Times”…. (high/high, high/low, low/low, low/high, avg/avg)
Anyway, starting to think more seriously about best way to really do this with students (rather than doing it haphazardly, but I’m pretty excited, because it seems totally doable for the algebra-based physics population.)
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:
- Constant speed means zero acceleration.
- Normal force points in the opposite direction of weight.
- When an object is on a ramp, the acceleration is always down the ramp.
- When a projectile hits a surface, it’s final velocity is zero.
- For an object in free-fall, its speed at maximum height is zero.
- In projectile motion,the horizontal component of acceleration is 9.8 m/s/s.
- For uniform circular motion, velocity and acceleration are 90 degrees apart.
- 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. “
Other helpful things
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:
- 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
- The method for deriving the results of gaussian integrals (from a Calc III class)
- 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).