Productive Student Ideas in Class: Pendulum

Despite the worsening classroom culture, there are still good things going  on. Here are some student ideas to make sense of why pendulum depends on length but not amplitude:

Idea #1:

When you raise the amplitude, you increase the distance back and forth, but you also increase the potential energy, which as the pendulum bob falls, increases the kinetic energy, which increases the speed the bob has. With an increase in distance but also speed, it’s plausible they could take the same time.

Idea #2:

When you increase the length, you have put the mass farther away, which we’ve seen makes things harder to turn (Note: we had played around with lead bricks near the center of rotation vs. the edge of rotation). Therefore, with more of the mass farther out from the rotation, the slower it will turn around the pivot point, making the time increase to get around and back again.

Idea #3:

When you increase the length (and keep amplitude fixed), you change the total distance the ball swings back and forth, but you don’t change the speed it has, because it still falls through same change in height. [Note: We had to check and verify that this seemed plausible–that the change in heigh is same. We were using the Phet Simulation, shined onto the whiteboard, so we could easily mark and see that this was the case… ] With more distance, but same speed, it must take less more time.

What I liked about these ideas was that they involved reaching back to concepts we had learned early. They were bringing up both results from observation we’ve seen before (the lead bricks), and ideas about energy.

It’s all too common for students to see physics as sets of unrelated ideas. We learned about energy, then we learned about moment of inertia, and now we are learning about pendulums. Here, in this moment at least, we were seeing energy, moments of inertia, and pendulum as inter-related, and seeing energy and moment of inertia ideas as tools for making sense of the pendulum phenomena.

The decline of productive classroom culture this semester…

My intro physics class has been experiencing a gradual deterioration of productive classroom culture:

  • There is a growing attitude of “let’s just get out of here as quickly as possible”
  • There is growing attitude of, “please just teach us what we need to know for the test”
  • Fewer groups work in ways that help to make sure everyone’s contributing and learning
  • There are more and more absences, and people who decide to leave after the quiz (if we don’t have a lab)
  • There are more and more students who are disengaging from trying and just waiting for someone to show them

I’m not sure exactly what the culprit is, but I will speculate about some of the influences:

Standards-based assessment has made me a bit more skill-focused, I think at the expense of nurturing wonder and curiosity. As the skills have become more difficult throughout the semester, the focus on skills has ramped up even more.

I have been less clear about my expectations for group work, and less consistent about monitoring and intervening. Last semester I was obsessively monitoring groups. This semester, I still do monitor, but I am less consistent and vigilant.

Last semester when students were absent (which was rare), I typically emailed them, or at least mentioned their absence the next time. There are too many absences this semester to make that easy. A big difference is having a Friday afternoon class this semester, where last semester was midday Tuesday and Thursday. Students both want to get out on Friday as early as possible to start the weekend, but they are also just more likely to miss class entirely, for traveling, or just because. This, in turn, creates a tacit culture of, “people miss class all the time,” which leads people to miss class more.

I teach a long day on Wednesdays, and physics is my last class of the day. I am exhausted by the time I get around to them, which is part of why I may be less attentive to productive group dynamics, fostering healthy learning culture, etc.

Before and after class last semester was time where I got to know students. Now its a time for reassessment. I used to also use the time before class to show or talk about cool stuff on the internet. We watched a few Derek Muller Videos. We watched a Vi-hart video. We watched Dan Meyer’s Ted Talk. I showed some blog posts from Rhett Allain when they were relevant to what we were learning. We watched a video on Carol Dweck’s Mindset research. Those videos often led to conversations about how to learn physics, about the culture of school, and how physics is related to the real world and to being in a community of people who like to talk about physics. Now, we talk about reassessment.

What do you all think?


Circular Impetus around the Coathanger Spin

Several weeks ago in physics, we were discussing circular motion. At one point during the day, the class was discussing what the path of an object should be immediately after the forces causing the circular motion cease (e.g., after a string breaks). The answer that students were supposed to settle on was that the object moves in a straight path tangent to the circle–an answer that is consistent with Newton’s 1st Law. One student, however, wasn’t buying it. He thought that if you spin something fast enough you should be make it keep curving around, even after the forces have lost contact. I said, “I’m with you man. Science is all about skepticism and gathering compelling evidence and arguments. You have skepticism, now go find some compelling evidence and convince me”

Weeks later that student comes back with a coat hanger, and starts spinning the coat hanger around his finger. He says this, “If the path of my finger at the end of the coat hanger goes straight at the end of the hook, then I couldn’t possibly twirl this coat hanger around my finger. He points out specifically that it only works when he spins the coat hanger really fast-fast enough to make it all keep curving around the gap.”

Two questions:

What’s the physics here?

What’s your next move with the student?

My lack of knowledge about student ideas about astronomy and the earth

Having not taught much astronomy, I can say that I am wholly unaware of some difficulties I should expect students to have, but I am learning.

Here are things I learned today about student thinking about east and west.

Several students discussed that if you begin heading east (along the equator for example), eventually you’ll be heading west again, like, for example, once you’ve gone half way around.

Several students also said things consistent with the idea that east is toward your right (no matter where you are looking). For example, a student said that they saw the crescent moon last night in the eastern sky last night. When I asked how they knew this, they said because it was to their right.

Several students also said things consistent with east is toward right on a drawing (no matter the perspective of drawing). We have been making various drawings of sun and earth, trying to make sense of and gather data about, and it is common to equate right-ward as east-ward, even if in the drawing it might be inward toward the center of the earth.

I spent a fair amount of time talking with a colleague about this one after class, and I’ve been thinking about it. We touched upon many things such maps, compasses, geo-political distinctions, east/west vs north south, spherical coordinates and geometry, non-cartesian unit vector, direction vs. location (or region), etc. I promise to write more about my thinking and our conversation, but I just wanted to quickly get this one out there.

What do people think?





Initial ideas about Sun, Moon, and Shadows

We are transitioning in inquiry to a *new-ish* topic, away from light, cameras, and the eye, and toward the sun, the moon, and shadows. The reason I saw new-ish, is because it’s still about light, but to everyone it feels like a new topic.

The launching activity was: “We are going to go outside in 10 minutes. Where will we have to look to find the sun, to the find the moon, and what will shadows look like?” … We discussed, made observations outside. Then we came back in, shared results, and a second question was asked, “What will the situation be in 2 hours when we go back out?” Then we went back out and made observations.

Here are a range of ideas, thoughts, and question I heard during our first day:

When we go outside we will find the sun toward the east, because the sun always rises in the east.

When we go outside, we will find the sun toward the south, because I remember seeing it that way recently.

The sun and the moon are (typically) on opposite sides of each other. Since the sun is out, the moon cannot be out. While many said this can’t always be true, because of an eclipse, many also realized that eclipses are rare events, so it’s an exception to the rule.

The sun and the moon are typically on opposite sides of each other, so if it is out, and the sun is toward the east, the moon should be toward the west.

The moon will mostly likely not be out, because it’s out less often during the day.

Since we found the sun in the southeast sky (and not exactly east), the sun will actually set in the northwest sky, making a big arc across the sky.

Since we found the sun in the southeast sky, the sun must stay to the south as it moves across the sky. They just couldn’t see how the sun could get to the north. Question: Is the sun never in the north?

Since we found the moon in the south-west sky, the moon will need to move toward the east as the day goes on. This is because the moon needs to be out at night, and the moon wouldn’t have enough time to go all the way around, and still be back in time for night time.

When the sun is at its highest point (around noon), there will be no shadows, because the sun will be directly over head

When the sun is at its highest point, there will be a split/double shadow, because it will cast a shadow both ways.

When the sun is at its highest point, there cannot be no shadow, because it doesn’t ever seem there are no shadows. Maybe the shadow will be small, but there will still be a shadow.

Shadows will grow, and then shrink and then grow throughout the day, as the sun goes up and then back down.

Shadows will shrink and twist throughout the day, possibly going around like a clock.

At noon, shadows will be facing north.

When we saw the moon, the lit part of the moon was facing the sun. Will that always be true?


Energy and Momentum

Before spring break, we had two days to talk about work and energy in physics class. Today, we are talking about momentum. For their online pre-class reading quiz, I decided to throw in the following question:

Explain what you think the major difference is between energy and momentum. Why do you think we need both concepts?

Here is a sample of student responses.

Momentum deals with mass and velocity, while energy deals with the work done over a period of time.

Momentum measures the ability of an object to continue moving in the same direction with the same speed, while energy measures the amount of force which an object has due to its mass and velocity.

Energy does not involve a collision specifically, it can be potential or kinetic. while momentum does involve a collision.

Energy is what it takes for something to move and momentum is how fast something is moving when it hits something else.

Energy is the capable of work and momentum is a mass in a motion. we need them both because without the work of energy we can not move a object and with out momentum we do not have enough force to keep the object from going fast or to slow down.

Energy is a transferable unit which can be stored and changed into other forms where as momentum is the directional energy that an object has due to its motion.

Energy is a scalor, and momentum is a vector. Energy is measured in foot pounds while momentum is in Joules. We need both concepts in order to find all possible answers for a problem

Momentum is needed to make energy and vice versa. Conservation of energy when collision.  Momentum of energy during movement.

Energy is a scalar quantity only expressing magnitude, momentum is a vector quantity and has a magnitude and direction. We need both because they represent different values in the same way that speed and velocity are not the same.

Momentum is a vector and energy is not. Energy can be converted in other forms of energy, while linear momentum can be converted only in linear momentum.

Energy is length times force while momentum is mass times velocity. We need to know both concepts to figure out things we do daily in life.

g as the “Specific Work” Near Earth’s Surface

Here are two common and useful ways of thinking about the quantity g:

g is the acceleration of objects near the surface of the earth: 10 meters per second gained (or lost) in 1 second

g is also the gravitational field strength near earth’s surface: 10 Newton’s of force pulling for each 1 kg

And here is a another, less common, but still useful way of thinking about it:

g is the “specific work” of gravity near the earth’s surface: 10 Joules of energy transferred for each 1 kg that moves 1 meter

By “specific work”, I mean something much like specific heat. Of course, it tells us about work and not heat, so it’s about changes in meters and not changes in temperature. And specific heat is characteristic of substances (e.g., copper or water), while specific work (at least in this context) is characteristic of planets. Different planets have different specific works (near to their surfaces) just as different materials have different specific heats. And just like the specific heats of materials aren’t really constant over a really wide range of temperatures, specific work of a planet is not really constant over whole range of distances. But it’s constant enough over a range to make the construct useful.

I realize I’m not the first person to have seen the parallel between specific heat and g (as a kind of specific work), but it’s a cool idea. And I should mention that this idea, which I had in my sleep, is the result of my brain mulling over Leslie’s class’s realization that falling objects gain 20 (m/s)^2  in every 1 meter.


Post script: I hadn’t really thought about the structural similarity of the equations this morning, but this provides another entry point for thinking about why it makes sense to think of g as the “specific work capacity”

Q = m c ΔT

W = – m Δy

Of course this means that the force, “mg” is the (non-specific) work capacity of any particular object being lifted away from the earth. The word “capacity” also resonates with me thinking of the gravitational field as being capable of storing energy.

Energy Theatre Debrief

Today was the first time I did an energy theater activity as an instructor. I decided to do this because

(1) I have been wanting to do some more physics (not just physics education stuff) with students in my teaching physics course

(2) I have been wanting to get them be engaged in some meaningful learning and learning activities, not just reading, talking, writing, and observing (although all of those are important, too)

(3) I wanted to shift our content focus, which has been heavily force and motion, to other topics.

(4) Today was a good day to be outside doing energy theater–it was sunny and 70 degrees!

Somethings that are really nice about energy theater include

(1) The rules are minimal but still provide a lot of structure, and the scenarios tied with rules provide a clear goal

(2) The activity just launches well–meaning that students start doing productive things, without looking to instructor, and without instructor having to answer a million question, or prod anything along. I spent most of my time away from the students listening, meandering back to ask a question or two, and then disappearing.

(3) There is lots to do, lots to negotiate, and lots of ways to participate–understanding the situation, deciding how many objects, what kinds of energy, what the signs for energy will be, how to mark the ground, who will start where, how many people they need, how things will evolve, how big a space they’ll need to fit everyone. The doing that happens, is by virtue of the physical space and the physical activity, seems naturally conducive for collaboration, listening, and discussing well.

(4) Different ideas about how to represent the situation arise (which is great), but, at the same time, much of this variations is reliable and predictable –has anyone done the submerged basket ball without the idea of buoyant energy coming up? The balance of diversity of ideas, with ability of instructor to anticipate and manage is nice.

(5) Students have to make decisions about how simple or complex to model the situation… should we include the air, or just the ground? Do we need to worry about the thermal energy of the ball? Do we need to give the rubberband some kinetic energy, or can we just say it gets potential energy directly? It’s easy for me to let them own these decisions.

(6) It is also easy, as an instructor, to see, feel, and hear how things are going and where they might be going. They are talking, moving, arranging, etc. It is also easy to ask questions that are helpful but not disruptive– “Did you guys decide how many objects there will be?” or “Have you guys discussed where everyone will need to start?” or “What’s this spot on the floor?” … or “Oooh. What’s that the sign for?”

(7) It’s also easy to suggest productive directions when they stall: “Well it sounds like you guys have two different ideas about how we should do this–Could we start by trying to actually do one and see how it works out, and then go back and focus on the other?” … “I have some whiteboards over there if you think it will help to try diagramming this out.” I like the ability to “do” things to see how they work, or write in order to plan more carefully. The talking, doing, writing aspects draw out different ideas, constraints, and realizations.

(8) Lots of issues and questions come up, including questions about choosing where “zero” energy will be? Whether or not energy needs to flow through object, or whether it can just jump straight over. Questions about whether energy can transfer and transform at the same time or whether it needs to do one or the other. Questions about how much thermal energy needs to be in each object, and whether they need to be the same. Questions about whether energy can be in an intermediate place where it’s not yet in second object but has left the first object, questions about can we invent new kinds of energy, questions about whether potential energy should be in objects or not, questions about whether all kinds of forces have respective kinds of energy, etc. etc. etc.

All and all in was a good day with energy theater. Students seems to notice right away that they’ve never been asked to do something like this where they keep track of what the energy is doing–that they typically are only asked to consider initial and final states, and maybe maybe some intermediate state, but not detailed tracking of where and how energy moves and changes.

Some of the most interesting discussions were when we had two plausible ways to model the situation, but individuals had different reasons to favor one or the other, or reasons to think that both were valid. It was interesting for me to see that some ways of solving the problems just “looked” better than others… and I wondered how much of that was aesthetic vs. scientific, or even both, because flow can be very aesthetic and is part of the science here.

The last part that was good about today was that students were “in” the moment a lot of the time, meaning that they were absorbed in the doing of arguing, listening, deciding, etc. It wasn’t forced or contrived.

OK one more things. The medium is just very good for negotiating and troubleshooting. If I had to be this picky about students diagrams (at first), it would seem like I was being an annoying teacher, but when the question is, “wait, where am I supposed to go next?”… Or “Wait, which of us is going to change to KE and which to PE when we step?”… it seems natural. Of course we need to know who and when and how, otherwise how will we move ourselves correctly. I can’t imagine a student with a static representation, student being so open to questions about the micro-details of energy transfers. I’d be nagging them.

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