The front of the packet gives students a place to write down the information. It is handy to use as a reference while they are still getting used to thinking about energy (and also later in the year when they forget an equation).

Here's the cover for the ETM packet. We've already explored the first inside page during our paradigm experiment. We come back to the cover on the second day of the unit.

We won’t need the equations just yet, so we’ll save that column for later. Some symbols, names, and the beginning of an understanding of what the type of energy is would be helpful to start.

Today is going to be one of those days where I do most of the talking (ugh). I try to make it as brief as possible so that they can get back to learning. To that end, we’re only going to capture four types (enough to get going with most problems we will consider in this class anyway) right now. There are plenty of spaces to record other types of energies as we recognize them.

English Problems

I missed this in the last post, but usually at the end of the spring/cart experiment (when we first say the word “energy”) I ask them to get out all of the English Language uses of the word energy that they can muster. As in: Ugh, I have no energy today. Turn off the lights and save energy. Energy drinks. 5 hour energy. She’s full of energy. Hey, yeah, you have a rad energy, man. Etc, etc. So we note the Physics is a Foreign Language That Sounds Just Like English problem (that we’ve been talking about since our 2nd unit—balanced forces). We’ll have to be really careful to define energy in physics and use that definition in class if we want our model to be good at making predictions.

Beauty—er, Energy—is Pain?

Here we go.

I choose the kid who I think will give me the best reactions (you’ll see what I mean in a minute or two). I walk over to them and quietly tell them to overreact. Then I give them a very dramatic (and very light) “punch” to the shoulder. They will usually cry out, “Ow!” or fall out of their chair (I did just tell them to overreact).

Moving back over to the front, I ask everyone what would happen if I put more energy into the punch. ["He would scream!" or basically, "It would hurt more."]

So pain would be a crude way to get a feel for how much energy is stored (and maybe going to be transferred) as we start thinking about the types of energy. [Some laughter from the kids. Maybe nervous laughter from the chosen kid.]

Kinetic Energy

For each type of energy, I try to make the name (and then symbol) the last piece of the discussion. First we need to identify the “new” way of storing energy, what it depends on, when it is present. Once we have that sense, then we can name it.

So, first up: Austin—let’s give the kid a name for easy description here. Anyway, so, Austin, would it be okay if I threw this ping pong ball at you with a speed of 1 m/s? You aren’t allowed to catch it. It has to bounce off of you. But 1 m/s. Slower than you walk. Are you okay with it?

[Sure, of course he is.] How about 5 m/s, a little faster than you jog? 10 m/s? [He's pretty much okay with all of that, though he starts getting a little more nervous about it at 10 m/s. Though, note: I do not ever throw anything at Austin.]

Okay, well. How about this baseball? Are you okay if I throw it at you at 1 m/s? Remember, it has to bounce off of you. [Yep, that's not that big of a deal.] 5 m/s? [Now we're getting nervous.] 10 m/s? [Well, no thank you.]

Fine. Then, [pulling the final ball up from its hidden place on the chair behind the table and eliciting a great reaction from everyone] how about this bowling ball? 1 m/s? 5 m/s? 10 m/s?

So it seems like there is a type of energy that is being stored in the motion of these objects. Austin is afraid of the pain that would be caused by them. What does it depend on? [They will pretty readily come up with mass and velocity (or speed).] Is it speed or velocity? [They usually quickly say that it is velocity, probably because that sounds like the more physics-y word (and not for any other reason).] Well, Austin, do you care if I throw the bowling ball at you from over here or over there? It is going to be going the same speed and bounce off of you either way. Okay, so the direction doesn’t matter. [Ah, speed then, not velocity.]

When is this type of energy present? [Something is moving.] Are you ready for a name? [Often there are some who gathered facts in middle school and are ready to give name it Kinetic Energy without you saying anything at all. But if not, they are fine with that name anyway.] We’ll use a big, capital K for the symbol. [Of course, different classes/books/teachers/etc might use slightly different symbols. These are just what I use with my students, and I think they are pretty typical ones.]

Gravitational Interaction Energy

[Pulling an extra chair over behind Austin.] Let me know when you start feeling worried. [Honestly, just saying that is pretty troubling, but he's willing to go with it.] Now? [Holding the ping pong ball just barely over Austin's head.] Now? [Holding it about a foot above his head.] How about now? [Now I'm standing on the chair and holding it as far above his head as possible.] None of those really worried you? Alright.

How about this? [Repeat entire sequence with baseball. Austin worries a little bit about the 1 foot distance, but really worries when I'm standing on the chair.]

Okay, then—[I can't even get through the sentence before the cries come from his classmates of, "Don't do it!" But of course I do it anyway.]—how about now? [Holding the bowling ball just above his head. And yes, he's already worried!] Now? And—[as I start climbing up on the chair]—it’s okay; I’ve only dropped this once. So how about now? [Yes! Very worried!]

So I think we’ve found another way of storing energy. What does it seem to depend on? [Weight (or mass). Height.]

Weight or mass? [Similarly to the speed/velocity question, some will decide mass just because it is the "physics word"(?!).] Okay, so would Austin be just as worried if we did the same exercise on the moon? [Well, no, not as worried.] How about if we did this far out in space, far away from all other things? [No, he wouldn't be worried at all. The ball wouldn't fall. This is often the first point at which they start to want to yell out their middle school memorized facts, and I try to hush the "potential" word usage as much as possible. We're not even ready for a name yet, anyway, much less a confusing one like that!] So, weight, then, right?

It depends on weight—and the other one you mentioned before was height. Would Austin be less worried if we did the same thing downstairs in the Bio Lab (directly below our classroom)? [Yes, that wouldn't matter.] So it’s not exactly height, right? [We get around to an idea that it is more like how high the ball is above Austin, not height above the floor, not height above the surface of the Earth, etc. They come to some sort of idea about how it depends on ∆y, though of course there was no ∆y in our exercise (just an imagined ∆y). But we also know that it doesn't really depend on Austin (because if it had been Brandon or Noah sitting in that seat, it seems like the same amount of energy would be stored in the raised bowling ball).]

So it depends on weight and also a relative height. And since it depends on weight, it would only exist if the object is near a planet. So it depends on the relative distance between an object and a planet. And it depends on there being an interaction between the object and the planet (the gravitational force).

There is a sort of class of energy types that depend on interactions and relative positions. We call them “Interaction Energies.” So this is one flavor of Interaction Energy. [To consider: was Kinetic Energy an Interaction Energy?] For interaction energies, we use a big capital U, then give it a subscript for the type of interaction energy. So for this (Gravitational Interaction Energy) we get Ug.

Spring Interaction Energy

There’s another way of storing energy that we’ve really already started thinking about. When we did the experiment with the springs giving their effect to the carts, there was some sort of transfer of energy, right? How did the carts store the energy? [As kinetic energy.] Where did it come from? [It came from the spring.] So what kind of energy was stored in the spring?

A new type, right? Okay, now is this type more like Ug (depends on an interaction and the relative position of multiple objects) or more like K (can be stored in a single object, does not depend on position)? [After a little talking, we decide it depends on how much the spring is stretched (or compressed), and that there has to be another object for there to be a spring force (interaction).]

So, spring interaction energy, then. And symbol? [Us.]

Change in Thermal Energy

Okay, check this out: I push the marker box and it starts sliding across the table. It has a bunch of kinetic energy and then—where did it go? [Immediate answer: friction.]

That’s a force, but before (in the cart/springs experiment), we saw that energy was transferred from one object to another [Us to K]. Is this different? Or is it being stored somewhere? What is storing the energy? [The table is storing it. Friction interaction energy? There's definitely an interaction, but does it depend on the relative position of the two objects? Not in the same way as the object/earth or object/spring from before.]

Let’s look at what happens with the matter models when you slide them against each other. Look at the atoms and see what happens to them.

The get jostled, right? They shake. Wait, the atoms in the table shake or the atoms in the box shake. [Try it again with the two matter models. The atoms in both shake!] Okay, so at first there was Kinetic Energy stored in the marker box. Then the box atoms and the table atoms jostled each other. So the box slows down, but the atoms are moving in faster random motion. So it is kind of still kinetic energy, but it is teeny tiny kinetic energies stored in the atoms moving randomly, not the whole box moving in one direction.

But do you ever see it happen in reverse? That is, everything gets colder and the marker box suddenly starts sliding across the table? That would freak you out, right? So there’s another thing that is different about this flavor of energy. Once energy is stored as the tiny random atom motion, it mostly seems to stay that way.

And one more thing: does this only happen when there is friction? Is there any other way that the atoms can get jostled and have faster random motion? [Try hitting the matter models against each other. So an impact (normal force) can also jostle the atoms.]

Now, aren’t the table atoms and box atoms already moving even before I slide the box across the table? How much teeny tiny kinetic energy is there beforehand? That’s hard to figure out. But it is pretty easy to see how much it changes (because it is easier to see how much macroscopic kinetic energy the box has when it is first sliding). So we usually just keep track of how much this type of energy changes.

We use the word “heat” to mean something specific (and different from this) in physics. We call this Thermal Energy (and so we will keep track of Change in Thermal Energy, or ∆Etherm).

Interaction, not Potential

It will come up eventually (thank you, middle school), but I try to keep it from happening on the first day (for the sake of those not already burdened by the English Language problem of “potential”). We’ll talk about why “interaction” does a better job of helping them think about when the energy is present (when there is that type of interaction; also, more than one object has to be involved (can’t have an interaction between one object)) than “potential”. And I give them the money quote from a student my first year:

“Everything has potential energy. Someone could potentially come up and push it and then it would be moving.”

Now, packing 4 flavors of energy (20 to 40 minutes worth, just depending on how the students in that particular class react to everything), we’re ready to start drawing some pie charts (next post in this series, and coming soon).

Hey guys, bring a pencil and a calculator next door. I want to show you something that’s been bothering me a lot.

Springs are strange

I’ve been thinking a lot about springs.

They’re sort of odd, you know? When you hold them like this [hold spring looped to one finger on each hand and stretched a bit] and then like this [same as before, but move hands a farther apart so the spring is stretched more], there’s definitely something different. Right? [Right.] But Newton’s Laws (great as they are) don’t seem to cover it completely. I mean, everything is at rest both times, so the forces are balanced both times. [Right.] But something is definitely different.

What’s different about the spring?

So I have an idea about how to visualize what is different when a spring is stretched more or less. I was thinking that we could attach the spring to a cart. The spring would pull the cart as it “unstretched” and make the cart speed up.

We could do the same thing to two carts at once and see the difference in the effect on each cart. So it would be a sort of cart race to compare the spring effects.

We could use the “special” box of springs from back in the balanced force unit. Remember when we found the spring constants for them (during the Fs lab)? It will be convenient to already know those values.

If you open up the new packets to the first inside page, you’ll see that I put in spring force (vs spring stretch) graphs based on the data from your experiments back in September for these two springs (the two different versions of the longer spring in that box).

[Hand the two springs to one kid.] So which one is spring 1? [After a couple seconds, the kid realizes that she can figure that out from how "stretchy" the springs are and identifies spring 1.]

Spring effect on carts

Great idea: we could use two different springs in our race. If we could get them to give the same spring effect to each cart, then we would have a foothold in identifying what it is that’s different about the springs when you stretch them more or less. [Kids seem to think this is at least a decent idea. A minus of this experiment is that I'm not setting them up to have the great ideas about what to set up, though they do get to have the great ideas about how to get the carts moving with the same speed.]

We need two people who are going to be very careful in making measurements. And each of them needs a backup person to watch what they are doing and double-check the measurements. [Eventually two kids will agree. Usually, though, everyone knows who the careful measurers are, so they pressure them into doing the job. I use the names of the kids a lot to help everyone keep track of which spring/cart we are discussing, so let's name them Aaron and Bertie for the purposes of this post.]

Okay. The springs are hooked onto the carts at one end and onto paperclips tied to strings at the other end. I will hold the ends of the springs. Aaron and Bertie will move the carts so that the string is just barely taut. Then they will pull the carts back to stretch the springs. Make sure you look at the edge of the cart to measure the stretch, not the spring, because it will be easier to be precise in moving the cart.

Now we need an idea for how to stretch the springs so that they will give the carts the same effects.

[The first suggestion is almost always to give them the same stretch. Sometimes students will quickly dismiss that idea because the springs will have different forces. Even when they dismiss it at first (and then almost definitely decide to try the same force first), they usually then try the using the same stretch second (thinking maybe they were wrong that the different forces would matter since the same force didn't work). Overall, there are four usual suggestions. All four of these usually get suggested (though not all at first).]

Same stretch (run on the graph)

Okay, good idea. So let’s have Aaron and Bertie both stretch their springs 10 centimeters. The backup person should watch what they are doing and make sure the stretch is really 10 centimeters.

Remember that we aren’t necessarily looking for the carts to get to the end of the track at the same time. We are looking for the springs to give them the same effect, so we’re looking for them to have the same speed once the springs aren’t stretched anymore. So we should look careful at their motion relative to each other (not for which one reaches the end of the track first).

Ready? On the count of three… One, Two, Three!

Huh. That didn’t work? Let’s try that again. [When I say that, the kids often say something like, "Was it supposed to work?" They're so used to verification labs, even at the end of the first semester (or close to the end of the year in my regular class) that some are already willing for you to just tell them what was "supposed" to happen. Yikes. I respond, "I'm not sure. Let's try it again one or two times to make sure we keep seeing the same thing."] Wow. Bertie’s cart wins every time? [At this point, someone will note that the forces are different so it isn't really surprising that Bertie's cart would win. That leads us to the next idea...]

Same force (rise on the graph)

That makes sense. So let’s keep Bertie’s spring stretched to 10 centimeters. How much should Aaron stretch his spring? [Give them a few minutes to sort that out with the graphs.] Okay, so Bertie is stretching her spring how much? [10 cm] And Aaron is stretching his spring how much? [20 cm] Okay, ready to try it? Backup people, make sure to watch them measure.

Huh. That didn’t work either? Let’s try that again. Last time, Bertie’s cart won. This time, Aaron’s cart wins. So, at least we know that there must be some way of making them equal in between those values. But neither the run nor the rise worked for making that happen.

Well, is there any other feature of a graph that we’ve found to be physically meaningful? [Almost every time, the first answer will be to make the slopes equal.]

Same slope

Great! We’ve definitely seen the slope of a graph represent physical quantities before. So how do we change the slope for the spring? [After a few seconds, they will realize that they already know what the slope represents and that they can't change the spring constant without changing the spring. Back to the drawing board.]

Okay, so not the slope, then. Any other features of a graph that we’ve found meaningful this year? [It often takes a minute or two for them to think through this idea. They will usually either say area (yay) or displacement (boo... they think displacement is a word that means area on a graph, not a word that means change in position for an object).]

Same area

Another good idea. Let’s keep Bertie’s spring stretched to 10 centimeters. What’s the area under her spring’s graph if the spring is stretched to 10 centimeters? [Give them a few minutes to figure that out.] Okay. So we need to figure out how much to stretch Aaron’s spring so that his graph will have the same area. [This is absolutely the toughest part. In Honors Physics, some to most of them will figure it out without much prompting. In regular Physics! class, they usually need a lot more guidance on how to set up that kind of calculation. I relate it back to kinematics problems where they knew the slope (acceleration) and area (displacement). They have solved many problems like that in the same graphical manner. I might also briefly mention the ACT science section and applying graph skills to new contexts to make that connection for them.]

[Check that each person knows how much to stretch the spring.] Should we try it? Alright!

Hey! That looked pretty good! Let’s try it again and make sure it really works. Cool! [And yes, they are pretty psyched that they've found a way to make the spring effects the same for both carts.]

So… do you think the area has a physical meaning?

What other graphs have we used this year that had areas with physical meanings? [velocity-vs-time graphs (change in position), acceleration-vs-time graphs (change in velocity), force-vs-time graphs (change in momentum)]

How about graphs that didn’t have physically meaningful areas? [A few will quickly mention position-vs-time graphs as they have tried to use that area for something before!]

So each of those areas has always shown us a change in something. Interesting.

Do you think the area on this type of graph has a physical meaning? [Well, yes.] Why? [The carts had the same speed when we made the areas the same.]

—

At this point, we’re coming around to the idea that the area on this graph (a force vs displacement graph) represents a change in something meaningful. Having cleverly read the front of the packet, they will always suggest to call it energy. The big idea here: the area on a force-vs-displacement graph represents the change in energy. Some smaller ideas (like energy being transferred to the cart by the spring) are starting to percolate. We’re about out of time for one day, though, so we’ll have to keep building this model next time.

Follow-Up Posts in the ETM series:

This post details the first day (about 40 minutes) of my energy unit. We have just started building the model. There are a few more steps to piecing this whole model together (building a common vocabulary about energy and two new representations), and I think they warrant separate posts. I will update this post with the links as the next few are written.

* Common types of energy (ETM Cheat Sheet)

* Drawing energy pie charts

* Drawing LOL charts (Energy Bar Graphs)

Instructions for Starting the Date

We need all groups of two. Every group needs a whiteboard and a marker.

One person from each group, raise your hand. Just one person from each group. Okay, after a few minutes, you guys will go clockwise. Everyone else will go counterclockwise. So, everyone will move places.

Everyone is going to work on the same problem. So, let’s spend 5 minutes now working on problem 9. Work straight on the whiteboard. We’ll have time at the end for you to copy down anything you want to have in your packet. No pencils. Just straight on the whiteboard. Okay, go!

I tried this first in my regular classes, and we worked on this problem:

In one of the classes, most students had done a lot on the problem already. In the other class, most students had not done anything on the problem yet. It seemed to work just as well in both classes.

After 5 Minutes

Okay, time to switch! Leave your whiteboard where it is. If you raised your hand before, move clockwise. Everyone else move counterclockwise. [Note: After doing this once, we didn't need to go through the hand-raising routine on subsequent days. They were able to sort out having the two people from their first group just move in opposite directions.] Okay, great. 5 more minutes with this group. Ready, set, go.

Everyone is now with an entirely different partner (in many cases, the partners were pairings that had never happened by choice the entire semester!) and no one had their own work in front of them. There was a tense moment where I wondered whether they would just complain, be exasperated, shut down, or actually do the work of figuring out what the others had done and start adding to it. Amazingly, they started adding to it!

One group simply erased the entire whiteboard and started over, not understanding anything that had been left for them. I didn’t see that happen again in any of the next 4 times that I tried this activity. One group wasn’t making much progress until someone from the next table noticed them and said, “Hey, I’m going there next! Do some work for me!”

When the 5 minutes were up, I looked around and saw that we probably had about 5 more minutes worth of work to do in order to get the boards to a mostly-finished state. So we switched again.

Now, again, a different pairing and completely different work. Most boards are close to being finished and so some puzzling starts to happen. “Why did they do this?” Some had written mostly answers absent of work, and two generations of physics students down the line now had to figure out not only whether the answers were correct, but also how they had even gotten there.

At the end of the 5 minutes, we decided we were finished with the problem and had a board meeting (we all sit on the tables and hold the boards in front of us (but not in front of our faces) so that we can see everyone’s work and look for places we agree/disagree). It was a more interesting meeting than usual since everyone was holding work that wasn’t entirely their own. They sometimes had to try to explain something that they wouldn’t have chosen to do themselves. In some classes, the students voted on the board they thought was best and had that group simply present it. Since the ideas about approaches were rotating about the room, the boards looked similar, but not identical.

User Notes

There was some time pressure to get work on the board, but it was a good pressure that was absent of any kind of anxiety. The time limit was just about how long you had with that particular board, and when time was up, you were on to the same challenge, just remixed.

Most of the above was a description of how the whiteboarding went in my regular physics classes. In Honors Physics, they loved it so much that it got a mention on the course evaluations as a favorite activity after only trying it once. One class asked to do a momentum problem the same way in our next class meeting (our first try had been a goal-less energy transfer problem) because they knew they needed more practice on that topic before the exam, and they thought this activity would be the best thing to help them.

We wouldn’t want to do this kind of whiteboarding every time, but it seems to be a nice way to break things up. It probably wouldn’t work as well near the beginning of a unit (5 minutes would be a short and frustrating time while they are just developing skills), and it definitely requires a complex enough problem that there can be at least 3 “dates” worth of work done on it.

I will definitely be using this one as often as is reasonable (maybe a couple of times per unit) from now on.

On my course evaluations two weeks ago, I asked a couple of questions that had to do with how they spent their time outside of class and how they felt about being asked to choose how to spend their time (rather than being told how to spend it). I compiled the responses below so that you see both answers together from the each student. Emphasis added to the responses is my own.

The Questions

The homework policy in this class is probably different from most other classes you’ve had. What thoughts do you have about the way you’ve been asked to use your (physics) time outside of physics class?

About how much time did you spend on physics (outside of class) each day? What did you do with that time? How do the time and tasks compare to your other classes?

The Homework Policy

I assigned some homework in September (no more than ~20 minutes, not every night, and never collected (it would almost always be whiteboarded the next day)). A lot of students (especially in Honors) get nervous (!?!?!) when I tell them that I’m not going to assign homework, so it seemed like a good idea to wean them off of it. They also didn’t really need to be preparing for extra tests in September since we hadn’t learned much yet. Once September ended, I stopped assigning homework. I talked with them a bit about how they should use their out-of-class physics time (correcting tests, practicing skills that they needed to improve, meeting with me, signing up for and taking extra tests on Sundays, sleeping, etc). I found it interesting that no one mentioned the September homework in their responses at all. I think they’ve forgotten that we ever had assigned homework.

I do occasionally ask Honors Physics to do their weekly test as a take-home quiz. When I do that, I try to make sure it is really a 35 – 40 minute quiz, and I ask them to write down the time they start and stop (to keep them from spending hours on it, which I know some would do). I didn’t start doing that until December-ish.

The class website has some extra problems for each unit and a page with answers (but not solutions) to those questions.

I should note that compared to last year’s fall semester, when I taught these classes in a very similar way except that I did assign regular homework (including about 30 minutes every single night in Honors Physics), my classes covered almost exactly the same amount of material (one class of Honors ahead of last year, one class a few days behind; both classes of regular physics no more than one week behind last year’s classes). I haven’t seen the exams yet (next week), but I think my students are stronger this year than the kids last year were at this time if there is any difference at all.

The Responses: Regular Physics (Juniors, 1 Senior)

I generally try and do as little work as necessary for classes, so I think this has been a challenge for me to try to put in extra time.

I do not spend that much time on physics outside of class, but when I do, I usually try and rework the problems to see if I understand. I spend less time on physics than my other classes, mainly because I have so much required work to turn in.

—

Good because I get to invest my time in the objectives I need to focus on the most

20 minutes on average, depends if I have a quiz to study for or if I’m testing on a sunday. It’s about the same as my other classes a little less maybe because there isn’t regular homework

—

I enjoy how I have been asked to use my time outside of class.

Time to study which is less than other classes.

—

I actually like it, instead of loading us for 40 minutes you ask us to use as much time as we feel we need to study and learn the material.

I usually only study physics when we have a quiz, and that’s only about 15 minutes, so it’s very manageable.

—

I think it is fine, and you need to put in that work in order to succeed in the class.

Around 30 minutes working on the worksheets in our packet. It’s about the same as other classes.

—

I like it. I just use it for whatever else I need to be doing. I’ve worked it into my schedule so I don’t notice it anymore and it’s just more time.

I do other homework (English takes me a long time) and use the physics time to do it. If I’m done I’ll just watch a movie or something.

—

I usually just re-do worksheets to get ready for quizzes and I’ve been doing pretty well so far, so I don’t really have any complaints.

I usually only spent time on physics outside of class the night before an assessment. So I spent less time on physics outside of class than i did my other subjects.

—

it is reasonable and understandable we must look over our tests and review our notes. for most classes I do this anyway

around 20 mins of review and such.

—

I love it. Never change it. It gives me freedom to be flexible. Though I still have to completely figure it out (meaning study for quizes better) I think it is the best way to learn.

I spent much less time on Physics compared to other classes, though I probably spent a little less than 30 minutes a week those spent studying for quizes.

—

I think it is a good idea. There may be less homework but there are definitely more quizzes which makes me want to keep up with my reviewing. Its frustrating to go from a 2 to a 1 on an objective which is why I try to keep studying

Outside of class I review the packets we complete during class in order to study. I also go back to my old quizzes and see what I did wrong. The notes on my quizzes are helpful in letting me re-due the questions I got wrong. I spend around 15-30 minutes on Physics, 15 normally but 30 or a little more if studying for a quiz.

—

I think that it’s nice that we don’t have specific homework to do, but personally, I wouldn’t mind being asked to do a certain number of problems before the next class. That way, I’m studying physics as much as I need to and I don’t feel like I’m slacking off.

Since there is no assigned homework every night, there were some nights where I didn’t do physics. I worked for the longest when I was about to take a quiz on the weekend, and I spent about 2 hours altogether. The workload is completely manageable.

—

I feel as though it helps us prepare ourselves. Because since there is no literal homework, it puts pressure on us to make sure that we study, and make sure that we are pushing ourselves to understand the material.

I dont really spend time on physics after class. I just work in class, and i understand in mostly.

—

I don’t work on physics a lot outside of class, and I do much less work compared to my other classes. However, this is in no way one of my easier classes.

I usually only spend time of physics outside of class unless I know that I have a quiz the next day. I review what we did in class and do practice problems sometimes.

—

It is the best. It is BY FAR the best educational strategy I’ve ever had and has is the cause of my thousands of “2″s.

Uhmmmm, not much? I think about objectives sometimes and do practice if I feel inclined to. Physics is a mentally engaging, thought-provoking class which requires a lot of mental energy and input during the forty or eighty minutes.

—

I like how it is now and do not wish for it to change.

About 20 minutes. With that time I go over the past quizzes so that I may improve upon those skills that I did not do so well on. And some of that time is dedicated to going over the work done in class.

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I like it because it gives me the freedom to focus on what i need to work on instead of having to complete pre-made homework problems.

i spend about ten minutes outside of class. We do not have homework so the time spent on physics is lower than that of other classes.

—

It’s very helpful, because it allows me to focus on my other classes during study hours, so that come class time, I can spend 100% of my energy on physics.

Very little time, to be honest. I’d correct tests and catch up on work in the packet.

—

great. I love not having homework

20 minutes. I study for up coming quizzes. This class not take as much time outside of class like other classes. Thats sweet

—

I think that if you use your time wisely outside of class, it can really determine how you do in class. The more time you spend outside of class, the better you understand in doing a classroom activity. If you don’t spend time outside of class, it shows in class as well. The amount of energy you put into physics is really how you choose it to be and in that how you do it physics and what you remember is completely up to you.

It can be about 20 minutes each day, but before assessments a little longer. I will go over what was learned either in that day or in that week and figure out what I’m still foggy on so I know what to focus on the next class.

—

None.

I spend about twenty minutes a night on physics, usually practicing with other students. It compares about equally to other classes.

—

I find that it causes most – nearly all, in fact – of us to want to be more productive in the actual classtime.

About 30 minutes. But not every day. I review quizzes and try practice questions. The workload (outside of class) is overall generally less than that of my other classes. However in class one is much more productive than in other classes, generally speaking.

—

I think this is a perfect system, and our grades would reflect how we spend our time outside of class.

Each day I spend about 20-30 minutes on physics outside of class. I use that time to look over the work that we did in class, and go over the methods used to answer the questions. The only difference is that I can use this time to look over whatever I want regarding physics whereas in other classes, I would have to look over specific things regarding the homework.

—

I feel like it is useful to me, because when I do work outside of class and don’t understand something, it frustrates me and I think I continue doing it wrong. It was not only nice because I never felt completely swamped with work, but also nice because when I came to class I was ready for physics because I hadn’t done it the night before. I’m not sure if that makes complete sense, but that’s how I feel.

I didn’t spend much time on physics outside of class because I always worried I was doing a problem wrong when I did it by myself. I only spent time outside of class when I had a specific problem from class that I made a point to go back and review. I spent time outside of class on weekends preparing for extra tests, and taking the extra tests on Sundays.

The Responses: Honors Physics (70/30 split, Sophomores/Juniors)

maybe one or two problems assigned at he beginning of the week and due at the end of the week. So that we have to do work outside of class.

Not enough. Only when we are given take home quizzes… and then only 45-50 min.

I like this policy because it is based on my own judgment.
While in other classes, some teachers just hand out extra questions that is not the questions that I want but in this class, I can practice on my own on places that I know exactly and I think that is the best part about this class.
Also, if I don’t practice enough, the result comes out on quizzes.

I spend about an hour to an hour and a half.
I review the quizzes that we took in class.
Also, if I do not get an objective, I print out extra practice problems and practice more.

I don’t know, becuase i am a procrastinator, i won’t ever make myself do physics problems that aren’t required.

i spend very little time, most of the work i do for physics is done over break

—

I love not usually having assigned homework in this class. Even though no homework is usually assigned, I still occasionally study my notes and do extra practice if I am struggling with a topic. I am a strong supporter of the homework policy we have.

I usually do not spend time on physics outside of class. I only work outside of class if I am doing extra work to retest or on take-home quizzes. If this happens, I work usually about 40 minutes.

—

I really like it because I don’t feel pressed for time and it allows me to do physics in the smaller pockets of free time that I have.

15 minutes reviewing different equations and problem solving techniques
I do Physics more regularly then other classes but I don’t tend to spend as much time per night as I would on other classes.

i feel like quizzes outside of class just don’t work out as well and i would perhaps like a couple of problems here and there to be done outside of class but not in quiz form. it just keeps me from just not thinking about physics. but i do like the little to none homework approach because it makes the classes more important and more meaningful and there is a lot more focus in class due to the small amount of homework because i am not just tired out from doing it all the time.

i thought about it and looked over what we have done in class that day but i do not work very much outside of class. the time is minimal but it is better and it makes the classes better. much less than my other class.

—

I like it. It’s a good system. I’m not saying that we should kill a teacher every day just so I can lose weight, I’m just saying when tragedy strikes, we have to look on the bright side.

I don’t do it every day: I do it in big chunks (a couple hours at once…) It is more difficult than other classes and requires MUCH more studying and effort, but with less busywork. Testosterone is a great equalizer. It turns all men into morons. He will, however, get over it.
[Note: this is the same student from my last post who ended every response with a Buffy the Vampire Slayer quote]

—

I would hazard a guess that I am not the only one to say that the homework load from this class is quite nice. I think possibly assigning a problem could propel the class farther than where we are now, but I think that not really having “work” per say is also quite beneficial.

Round about 20 minutes some days, however most days 0. I sometimes do a quiz but mostly doing practice on those days that I do work outside of class. Although it sounds like I do no work for this class, but the main bulk of the learning is in class unlike my other classes. I would say that the time demanded from this class is very small in a scale with my other classes.

—

I really appreciate it. I’m much more likely to be eager and willing to do work and less stressed out about it since the workload doesn’t make me feel like I’m falling behind at all. Also, I can practice things that I actually need to work on, rather than doing exercises for homework that might not help me with what I struggle with at all.

I probably spend about an 1.5 hours per week on physics outside of class if I take a test on Sunday. If I don’t, I generally spend about 45 minutes. Compared to other classes, the workload outside of class is much smaller, but also less stressful. It’s less tiring to study since I’m not overwhelmed by the amount.

—

I like it because it is flexible, so that if I have a ton of other requirements, it is not that important that I get it done although I don’t master the skills as easily.

Depending on the section, and my level of comprehension my time varies a lot. I normally try to finish worksheets, or get help from people on dorm who are taking or have taken the course before on the problems I don’t understand.

—

I like it.

20- 40. Taking take-home quizzes. Most other classes don’t have take home quizzes.

—

It is efficient. Just need to take responsibility.

25 min. Went over old tests and worked in worksheet packets
spend equal amounts of time in other classes unless its a ‘big day’

—

it is nice, but very unstructured. This can sometimes be a problem as I am not always creative enough to come up with problems to work on.

10-20 minutes. Finishing problems or asking other people for help on things I am confused about. I spend less time on physics then other classes.

—

I think its really helpful not to have specific problems that we all have to work on so that you can spend your time focusing on the things that you are genuinely confused about.

it varies. sometimes I do up to 40 minutes, on quizes or practice but a lot of times I don’t do any.

—

I love it because we have very little homework while accomplishing a lot more learning in class because we are able to make mistakes while people are watching and able to correct us. By learning with partners and arguing about what to do I feel like I understand more deeply what we are doing.

I would spend about an hour on the take-home tests. Compared to my other classes an hour is a lot of time, but the take-home tests aren’t too frequent so it works.

—

I wish we had homework that way I could practice more outside of class.

About 30 minutes to an hour. The time is spent much more confused than my other classes.

—

I like not having homework.

None.

—

a bit disappointed for not finishing the work during the class.

20min. Review. I think we are spending just about right time for doing physics and we have little more tasks compared to Mr. Hammond’s physics class considering that they are behind us. But the workload is reasonable.

I think it is better because it allows you to determine your own grade in the class.

I take about thirty minutes of my time looking over my Physic’s work outside of classes. It takes about the same amount of time as my other classes.

—

It works a lot better than normal homework in other classes, because I don’t need to practice stuff that I don’t need to practice giving me time to focus on stuff where I need practice.

I’d spend about 40 minutes every other day on physics, reviewing stuff that I wasn’t sure how to do or needed practice on.

A Couple of My Thoughts

So far, I am happy with how this policy is working for my students. Some students need more guidance on how to structure their own time, so I need to make sure I make more explicit suggestions about how to use their time. Students asking for some assigned homework because they don’t know what else they could do to be more prepared for physics is a red flag for sure. I don’t think those students are using our class website since there are definitely extra problems there for them to do. I am convinced that working on mindset and “study skills” (how to practice, etc) with these guys is making them happier about the class and also making them stronger students, but I also know that there is room for doing this type of meta-work better.

I am also impressed by the kind of reflection my students were able to do here. They have some great ideas about how they have benefited from choosing their own out-of-class work, and they are seeing our class time as both valuable and where the learning happens. They also see the work they do outside of class as being beneficial, not time-consuming, and never busy work.

If anyone else is starting to question their own homework, I challenge them to give it up for a week, a unit, or a month. See what parts of the homework you and your students miss, and whittle it down to what is essential so that they can use the rest of their time in whatever way they’d like. If you find out that it is a necessary part of learning in your class, then you will be able to justify it even better. If, like me, you find out that you’ve been dictating how your students use their time when they aren’t even with you to essentially no end (see note about the lack of change to the pace and problem-solving ability), then you will be able to justify cutting way back or even giving it up entirely. It’s worth doing an experiment and finding out, isn’t it?

I’m hoping/planning to write more about my January course evaluations later (maybe after I get through exams). I especially want to write about/share the reactions to my “no assigned homework” scheme (preview: very positive! With very thoughtful responses from the kids!). After the semester exams (mine is on January 24th), I am also thinking about writing up a “State of the Physics Class” report for each class that summarizes their feedback, acknowledges what I’m hearing from them, and outlines some new ideas I have to find even better balance for everyone in class. I haven’t tried that before, and it might end up being a terrible (or fantastic!) idea. We’ll have to see.

For now, I wanted to get this new feedback on standards-based grading out there.

The Question

Consider the grading system that we use in physics class. What do you like/dislike about it? Has it had an impact on your learning and understanding of physics?
Give an example to help illustrate your thoughts.

Anonymous Student Responses

Note: any emphasis added is my own.

Regular Physics (Almost all Juniors)

At first I found it very confusing, but it makes more sense now. I like being graded by showing what I actually know, instead of what I got right, but because I get so many grades on one thing, sometimes I don’t know where I am.

I like that I can always try again and that getting something wrong is encouraged in order to achieve full understanding

It has required me to remember things for the future which is not always the case in other classes.

I feel that this whole course hinges on the exam, yes there is a safety net, but it only saves you from getting a terrible grade, getting a halfway decent one instead, when the work you might have shown through the year could have been worth a stellar grade.

I like it a lot, because if you don’t understand something and do badly on a quiz, theres always opportunity to retake that quiz.

The grading system just means a lot less stress knowing that I can fix whatever mistakes I make on a quiz later. It makes classes and quizzes a lot easier and laid-back.

I like it because it makes me keep working on objectives even though I have a two in them.

that reciving a 1 is the same as reciving a zero. which is alittle anoying becuase when you get a one it recognizes that you understand something and yet still your grade is a zero

I like it, and I think that we should do this in math too. It has made Physics less formidable than it was before. I LIKE ITTTTT.

I started off not liking the activegrade grading system but now I think it a smart system. Its nice knowing that if you don’t fully understand something now you can work on it and still get a 2 by the end. I think it is also really helpful that you make sure everyone has there 1 objectives by the end of the semester. Something that has been frustrating though has been the fact that one can’t get partial credit on quizzes.

I like the grading system for physics and I wish that other classes did the same. I really like that the objectives that we don’t master are always there for us to come back to later. I don’t feel left behind in this class because I know there are opportunities outside of class to improve my grade.

I like that there are no literal number grades. Also that if I dont do to well on a quiz one week, I can always re- assess on sunday. I like that. I also like that the number grades depend on how many 2′s you have, because it makes you want to work harder so you can get the highest grade, and the most 2′s out of all your friends.

I like the grading system in that we can always re-do our tests, but I don’t like that we only have two chances per week to improve our grade.

Well, apart from the fact that all twos got me a 90 in the first quarter, it’s definitely a good system, as well as an interesting experiment in the realm of education. Once, I taught a cat to dance. When I thought its dances were good, I’d put a give it a thing of catnip or a snack with two written on it. When the cat’s dances weren’t quite up to snuff, I’d give it a gift that was sub-par to the catnip or snacks. And if the dances were terrible, I wouldn’t give it anything, besides maybe a dirty look. I think that helped a lot. BUT REALLY, it’s a good system. It has made me realize that I must actually *master* concepts and not just remember them for test day.

I like the system as a whole and it has had a large impact upon my understand of physics. Seeing that we only pass with complete understanding of the subject and being given multiple opportunities to do so, we learn MORE at a faster rate than we would in a traditional grading system.

i like that it allows me to learn ata certain pace without hindering my grade, but it is a little confusing, and sometimes its hard to know what my current status in the class is.

It’s good, I just wish that all 2′s didn’t get you only a 90, while a single problem is dependent of the extra 10 points. If anything, I think it should earn you a 95.

its great. Its nice that if I get something wrong I am able to go back and study and improve that grade again.

I like that if you don’t understand a concept, regardless of if you got the answer, you do not get credit for that. You instead have to work at truly mastering a concept to get the credit. It’s rewarding to know you get a concept and have a 2 on it, and it helps to remember concepts longer. I had a 2 on a concept for a while and in an assessment I was given a 1 and that showed I didn’t actually fully understand it and needed to review. When I got a 2 on it again, I knew I truly understood.

I really like the grading system because you never can just forget about material you learned early in the year, it keeps re-appearing with quizzes that have old objectives.

I think this grading system is good because it shows wether or not we actually understand the material. For example, you can’t see what you don’t understand if you get a 78%, but a 1 shows that you obviously don’t have a firm grasp of the material.

I think it is hard to say we should completely eliminate grades from a class, so even when we get our quizzes back and see what objectives I got or missed I feel like I’m being graded. Sometimes also, Sunday afternoons are difficult to extra test becasue it’s an akward time. I really wish we could extra test during the week like last year, because I wouldn’t stress myself about preparing for the extra test until I had time.

Honors Physics (70/30 split on Sophomores/Juniors)

Like- how I know what I have to specifically work on
Dislike- I don’t know where my numerical grade is which helps to motivate me to improve

Even though the grading system is different and much more harder and challenging to get a good score, I’ll have to admit that it helps me a lot in learning physics thoroughly.

it is really hard to get an A in the class. First off, it is hard to adjust to the rythme of things because it is such a different kind of learning, it definitely inhibited my learning in the beginning of the year.

I like the grading system we have, because it allows me to have a second chance if I have trouble with an objective the first time.

I think that the quarter grades are just stupid and inaccurate, but other than that I think that the system is very effective in keeping students, including myself, continually improving on their physics skillZZZZ

the grading system has not really meant much to me especially because all grades are meaningless until the end of the quarter/semester. i would like it if my grade depended on more than just quizzes and tests and had some application on hard work on packets and homework but its manageable.

I don’t like that you have to show extra creativity to get about a 90. How do I show extra creativity? Especially on the exam? I’m confused and I think it would help to know exactly what I need to do. Ahhh I’m so scared of blanking out on this exam and getting something completely wrong and failing… I don’t like spiders, okay? Their furry bodies, and their sticky webs, and what do they need all those legs for anyway? I’ll tell you – for crawling across your face in the middle of the night [NOTE: this student included Buffy the Vampire Slayer quotes in every one of their responses]

I do like the grading system in physics because it lays out the work before you and the grade is entirely up to you, because you decide when or how you do the work. When something is not done by a certain point the teacher steps in, which is great because you learn the material more thoroughly.

I like it because the fact that I didn’t understand something at first doesn’t affect how my final understanding of it is judged. For example, when I study a concept that I’m somewhat uncomfortable with, my grade isn’t brought down when I understand it completely. It gives me a clear picture of what I do and do not understand at the present moment, not an average of the past and present. I dislike it because even if I understand everything we are learning, I still only get a 90. I feel like it’s not very encouraging to know that you have to take extra quizzes to prove you really know the material.

I dislike the fact that it is harder to guess where you actually are in the class but I love the fact that it is clear that you want us to succeed because that is what school is really all about. I believe it has had a great effect on how I learn physics because you make it pretty impossible to be lazy or forget something.

I do not like that if you make any mistake you get a 1. And I do not like retesting.

Different. Not sure if it is good or bad, but im getting used to it.
Consistency is a priority

It allows me to fail without feeling like I am going to kill my grade. It makes me work hard to really learn about things and to remember them in the long run.

I like that your not understanding at the beginining doesn’t haunt you for the entire year if you eventually learn. It also seems to more accurately reflect my understanding of something, like if I get something right on a lucky chance, I know I haven’t passed it yet, but if I really understand the concept but made a small mistake, the whole objective isn’t seen as a failure.

I like the objective system because it shows when we understand something yet if frustrates me when I make silly mistakes involving direction and units that cause me to fail objectives.

I dislike that a 1 basically means the same thing as a zero because it means that you havent completed the objective and i feel defeated.

I dislike the system very much. Getting a zero for a right answer that you showed your work on because it wasn’t the “right work” is not fair.

I love it. It makes me to be more perfect with physics as I keep correcting my mistakes, but sometimes it is painful when I get certain objectives wrong for silly reasons.

I like the fact that one test grade won’t hurt your entire semester grade. But I also find the grading system really frustrating sometimes.

I like this grading system a lot better because your grade is a result of how much effort you put in and how much you have learned overall as opposed to how well you can study for a test (which usually allows people to study for something, take the test, and then they forget it) and you don’t get penalized for not understanding something before as long as you understand it at some point.

A couple of my thoughts

The kids seems to be, for the most part, really “getting it”. They understand and appreciate the ideas about improvement of understanding, learning from mistakes, and working toward mastery. Several of them rightly criticize the first quarter grade (not reported on transcripts for college, etc, so not as “crucial” of a grade for them, but it still was tough for them to get the chance to show they had understanding that should translate to better than a 90 at that point in the year). I think the third quarter grade will be easier. Especially combined with the new way we’re doing quizzes (where they get to choose their quiz flavor… or at least the flavor of the side dish).

I think the increased frequency of quizzes (every week instead of waiting for the end of the unit to have a test) has also helped make the system better. They are getting more frequent feedback and feeling less stress about each assessment. That has made it easier to get them to see quizzes as a conversation between them and me about how they’re doing in physics.

—

See how these comments compare to last year’s. 2011

The front of my BFPM packet gives a lot of structure to our little pre-model warm-up.

Here's the cover of my BFPM packet from this year. Most of it (excepting Newton's Laws) gets touched on the first day of the unit, and students refer back to this packet frequently throughout the year when they have a confusion about a type of force. Click to see it in a larger, more readable size.

So we start with the word itself.

What is your definition of “force”?

Doesn’t have to be a physics definition. That is, we want to know what comes to mind when you think of the word force, not what you think I want you to say! Think about it for a minute. Then talk at your table and write up a quick whiteboard with your definition. 3 minutes, max.  All good definitions in their own contexts.

Okay. Hold up your whiteboards at your tables. Let’s just see what everyone has in their heads and get it out there so it doesn’t hold us back. Some common responses (though really you can get just about anything from them): push, making someone do something, something about midi-chlorians, a type of energy, something that changes motion, power.

Those are all great, and they’re really useful in their particular English language contexts. I’m going to give you my definition for force. Mine isn’t necessarily superior to yours, but I think it will be a really useful one because if we stick to it, it will help us in explaining and predicting new situations.

A force is an interaction between two objects. Yep! That’s it. Pretty simple, but also pretty powerful.

Now I talk for a bit.

Which the kids, of course (and especially this early in the year), love. Some of them are just aching for me to stand up front and talk so they can comfortably take notes. I try to keep it as short as possible and I usually even remind them (ahead of time) that they aren’t going to learn any physics while I’m up there talking. They’ll start learning it once they play with the words and ideas themselves and put them into action.

We’re going to jump in and start building a model for forces soon, but we’ll need a common vocabulary in order to be able to talk about forces. It’s pretty clear from our various definitions that we could easily get confused about what we’re saying to each other if we don’t agree on some common terms first. So I’m going to give you 4 (or sometimes 5… just depending on how it goes) common forces. It will be just enough to get us started, but there are certainly other types of forces which you’ll identify when they come up (and we’ll have plenty of extra space in the table to make new entries when the time is right).

We only need the language right now, so we’ll leave the “Equation” column alone and just work on the other ones.

There’s a tricky moment here when I want to involve them in creating the table rather than just presenting to them, but it’s just riddled with danger. Filling in this table can so easily turn into a game of “Guess What’s In The Teacher’s Head” and that’s just no fun for anyone involved. Since this is the second unit, I do have a little bit of a feel for how the class is going to respond to my questions. There’s definitely a sliding scale here as to how much input I ask of them and how much I just tell them. I want to keep these 4 or 5 mini-discussions to a total of about 20 minutes, realizing that no matter how great the discussions end up seeming to me (or even to individual kids), there is very little gain for any student in the class here. I want to push through to the part where every kid (or at least almost every kid) is doing their all or most of her own thinking.

Gravitational Force

This forces is always always always the first one anyone names when I tentatively ask for types of forces. When I ask for direction, I usually get “down” and occasionally get “toward the center of the Earth”. Of course I am exerting a gravitational force back on the Earth which points in neither of those directions, but that idea would be crazytalk to the kids at this point. And “toward the center” of the object exerting the force is a pretty decent idea for our starting place (and better than down), so we go with something like that. The exact wording of everything here can shift a little this way or that way depending on whether a kid comes out with something I quite like or whether I want to hand them my more precise wording over whatever they’re saying. When I ask for when it’s present, I get “always”. Which, hey, is fairly true. But we usually settle on something like, “near a planet”, which is, in fact, always true for them.

Normal Force (aka Crunchy Force, aka Perpendicular Force, aka Force of Sterling)

Another one that they often name is the normal force, though I’ve never had anyone call it that on the first day of the unit. I latch onto someone saying something like “push force” or something to that effect. The best intro I’ve had came when, during the introduction of the previous force, it became clear that there was a large wasp ready to terrorize our classroom. It came down to smashing height, and one of my students (Sterling) crushed it with a binder, much to the delight of everyone on the room. When I asked for the next type of force and it became clear that we were talking about a push force, the kids started calling it the “Force of Sterling”.  Quite right.

So in any case, I definitely save the name as the very last bit to fill in for this force. First, we need to clarify what we’re saying. Something like the PASCO matter model is key here. I tell them that it is my model of the table and ask what the red things are (they always say “molecules” or “atoms”). We talk about how springs are a good way to represent how atoms interact since if you push them together, they push back apart, but if you pull them apart a bit, they pull back together. (They will sometimes mention magnets at that point, but magnets you have to turn around to get the other effect.) I put it on the table and put something (whatever’s around) on top of it. I ask what happens to the atoms when you put something on top of it (they get “squished” or “crunched” or “scrunched”). I put the same thing on top of the table and ask what happens to the table. Many are already willing to make the leap to the idea that the table atoms are getting crunched even though we can’t see them. Are you sure? (Getting down on eye level with the table.) It doesn’t look like the table is getting crunched! At which point they usually try assure me that atoms are really small.

So maybe now, but maybe in a few days, someone will say something that will prompt me to get out the overhead projector and do a little table crunching demo*, but I won’t pull that out until they are asking for some more convincing on the act-like-springs front. We usually also have a wire set up hanging in the next room with some mass on a hanger. It’s really convincing to put some extra masses on the hanger, see how much the wire stretches, then take the masses off and see the wire go back(!!) to the same length it was before we put on the extra masses. Whoa.

Now we’ve got the “when is it present” aspect (when atoms are getting crunched, man) and we need the “what direction” to continue describing this force. I push something against the matter model a bunch of different ways with something somewhat flat and ask them what direction the force is being exerted each time. We narrow it down to the pretty elegant “perpendicular to the surfaces” idea.

Strangely enough, the name that people usually use for this force has to do with the direction of the force rather than it being something about crunching atoms. And of course, we’ve got another major Physics Is A Foreign Language That Sounds Just Like English problem. Almost no one has ever gotten far enough in math at this point that they have seen the word “normal” used to describe something that is perpendicular (when do they do that… Calculus?). We call out a few definitions of this word in English to get them Out There (usual, regular, what usually happens, ordinary, etc).

And of course, in few days, in trots the Natural Force. Which, really, is just them remembering the English definition of “normal” rather than the math definition and then trying to place a word with the “n”. So it gets gently corrected each time. And each time we say “normal force” (for quite a while), we (or at least I) usually follow it immediately with “crunchy force” to try and make that connection stick.

Friction Force

After the normal force, it’s easy to follow right up with the friction force (really just two parts of the same interaction, but that’s a little beyond where we’re starting right now, huh). That matter model is, again, really key. In fact, it’s best if there are two pieces of it so that you can push them past one another.

Before they start shouting out ideas about direction and when the force is present, I try to grab two matter models and help them start visualizing what it looks like for two objects pushing past one another. They see pretty quickly that the atoms are shearing (and also that they are getting crunched). So we pretty quickly come up with the idea that the friction force is present when atoms are being sheared. Even though “sheared” isn’t a word that they’re using in everyday speech, it is pretty easy for them to connect it to what the matter models look like when they are pushing past each other. Considering all of the other language problems, it might even be better that it isn’t a commonly used word (so long as they pick up the meaning and start using it right away).

Once we start thinking about friction, it quickly becomes clear that there are two distinct flavors. There can be friction when two things are sliding past one another, and there can be friction when two things are pushing past one another but not sliding (commonly: I push the table a little and it doesn’t move. Hey, I can even push it a little harder and it still doesn’t move. Why not? Immediately they say, “friction” even though they had just said friction only happens when something is sliding.). In both cases, though, as seen with the matter models, the atoms are getting sheared when there is friction. (Another awesome part of this discussion: frequently someone will note that the atoms in both matter models get sheared (and crunched) each time. So apparently they are both experiencing friction. Score.)

Now we need a direction. We look more carefully at the matter models. The idea of “opposite the direction of motion” comes up quickly, but it is clearly not going to work since we have cases where there is friction and no motion. In every case, though, the force is along the surfaces. Parallel to the surfaces. That turns out to be a super helpful guideline (continuing all the way down the line, long past the end of the balanced forces unit). We then just have to look at the details of the problem at hand, think about which way the atoms are getting sheared, and go from there.

Tension Force

Only one more, now, of the forces necessary to dive into the model building activity. We’re almost to the point where I get to stop standing up at the board and we can sit down and play with some toys.

It is less common for a student to bring up the tension force unprompted, but it is pretty obvious to them as soon as you start talking about a rope. (If they do bring it up, it is the vague “pull” counterpart to the “push” they gave to start the normal force discussion.) The word tension is fine and sounds like ropes. There is some trouble nailing down exactly how to describe the direction of the force, but a quick sketch on the board of someone pulling something (or whatever) with a rope at an angle heads us right toward the idea of “along the rope”.

When is it present? When there is a rope. A rope just sitting there? Well, it has to be… stretched? Plug in the word “taut” (which middle schoolers tended not to know, when I did this with them, but which my 10th and 11th graders tend to find obvious) and you’re basically finished.

Last note about this one: I always use the word “rope” when talking about a tension force, even if that rope is a dinky little string. String sounds too much like spring, and it gets frustrating to keep correcting each other about which word we meant to say. No big deal, but it helps me.

And sometimes the Spring Force

If there’s a little slice of time left, or if someone brings it up, we’ll also hit spring force. If not, I just save it for when we get to the spring force experiment because it will be rather obvious to them at that point, we don’t need it right now, and I want to stop standing up there and talking so we can start learning already.

Often the kids come up with a way of saying the direction of the force (which is along the spring, but opposite the direction the spring is being pushed / pulled) that is less awkward than whatever I was about to write for them. The force is pretty obviously present when there is a spring (no kidding!) that is being stretched or compressed (spring just chilling? No spring force for you.).

And yes, tension force and spring force could easily be the same thing. It just depends on how you want to view things.

Naming the Force

The curly brackets outline a phrase for naming forces that is a really useful touchstone to have as we keep traveling along the physics road. I’m not sure the origin of this phrase (Arons, maybe?), but we’ve been using it as long as Mark‘s been teaching here.

It tends to stick with the kids, so that when they are fumbling while trying to talk about something, prompting them for “that sentence we use to name forces” (even though it’s not a sentence) or for “the something something force…” gets them to quickly clarify what they’re trying to say.

It is über-helpful with Newton’s 3rd Law (N3L) because finding the name of the pair force means using the same phrase with only the objects flipped.

If the timing works out, we might talk about it right after putting together the force table. It can be a quick interjection at any point during the unit, though.

All of the above (definition of force, common types table, and possibly the naming phrase) should be around 40 minutes worth.

Notation Note: Types of forces vs Objects exerting the force

This bit doesn’t much affect any of the above, but it seems a relevant ending note.

There has been some discussion about which (naming forces by type or by object exerting the force— e.g. vs ) is better to use. There are lots of notations for labeling forces on free body diagrams (those above, object-agent notation, etc), and I suspect that different groups of students would find different notations more or less helpful.

To fill out the description of what I do in my classes, I’ll muse about both parts (type and agent) and describe what my students use.

Why the type of force matters: The type of force seems important in identifying interactions. Thinking about atoms being crunched or sheared, ropes being taut, planets being nearby—all of that seems to help students identify when there is a force or when the Aristotle in their gut is leading them astray. For example, during a discussion, one student comments, ”There is still the residual force that the hand exerts on the box.” It’s beautiful to watch kids explain that kind of statement away from each other by calling them out on the type of force. Is it a normal force? But is the hand still crunching the box’s atoms? Shoot. There can’t still be a normal force.

Why the object exerting the force matters: Fictitious forces show up on FBDs as labelled with the type (, most often) but with no object in parentheses. (“I know there’s a force here but I don’t know what the object is…”) Suggest drawing a system schema, and usually they will immediately just erase the fake force. They’ve already drawn or thought about the system schema and know there’s no object. So there can’t be a force there. Even when thinking intentionally about objects and interactions, it is still so tempting to draw in those gut-created forces. Without thinking about the object exerting the force each time (which you have to do when it is part of the label), it would be even easier to include the invented ones on a diagram.

So I think both are important. My students use a notation that includes the type of force as a subscript and is followed by the object exerting the force in parentheses (e.g. ) for a while. They definitely use it throughout the entire balanced forces unit. By the time the Honors kids get to unbalanced forces, they might be ready to stop writing the object in parentheses every time. The regular Physics! students keep it up for most or all of the year. I basically tell them that when they are drawing their FBDs correctly every time, they can stop writing the object exerting the force on them. Even still, most students will still write the object in situations where there are two of the same type of force (a box on a table that is also being pushed by a person, say). And they don’t stop thinking about what object exerts the force, which you can easily test by just asking about an FBD during any whiteboard presentation. There are clearly a lot of viable options for this notation, and the best way to do it probably depends in part on the students in the particular class and the method might be malleable as the year unfolds.

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* Put projector on table. Draw vertical line on whiteboard. Draw vertical line on transparency. Line them up as perfectly as possible. Stand on table next to table with projector. Step onto table with projector and stand very still. Then step back. Do that a few times and get them to see how the line shifts (but then stays steady and apart from the whiteboard line as you stand still), then shifts right back to where it was when you get back off the table. A similar demo with a laser and a mirror is in the MI teacher materials.

Now that we’re pros (Wheaties box, here we come) at drawing velocity-vs-time graphs, we need to be able to turn those graphs into equations if we want to use them as tools for solving problems.

One big stumbling block in solving constant acceleration (CAPM) problems is that, very very often, we are looking at situations where the object starts from rest (in no small part because the algebra can get a lot more involved for situations where the initial velocity isn’t 0 m/s, and we (or I) don’t necessarily want them spending their time solving a bunch of quadratic equations rather than playing with more graphs and physics problems. But anyway.). So the velocity graph they are drawing for the problems that they encounter almost always looks like one of these two:

And the area we care about, from the start of the object’s motion until some particular time (or through some particular displacement) is, indeed, .

Pretty soon, though, that () is the automatic response from a student when they want to find the displacement— even when the velocity does not start from 0 m/s. And pretty soon after that, they can’t solve any problem if the object doesn’t start from rest.

So. How to go about fixing this issue?

Annotations for the win

At my school (and maybe elsewhere, too?), the students are very familiar with the idea of annotating a text. When I would tell them to “label” their graph, though, that meant to them that they should draw dozens of tiny tick marks and unit-less (aka naked) numbers along the axes. That’s not what I meant at all! So I shifted to the language that they already hear all the time in their other classes (annotate) and gave them some guidelines on what it looks like to do a good job of annotating a graph.

Here's a classically "labeled" graph. The endless tick marks make solving the problem difficult because they often don't even want to commit to really drawing the graph since they can't just plot out points without already knowing all of the info. They never add symbols to the graph for the quantities that they don't know, and then they predictably have trouble finding out those unknown quantities.

This graph is more on track with drawing the qualitative shape of the graph, using symbols, and doing legit annotations. It's also displaying one of the strange habits a lot of my students have. Once she solved the problem, she felt she needed to go back to the original graph she drew and add in the numbers that she now knows (vf and ∆t in this case). Some of them really don't like putting symbols on a graph!

The first step to solving a problem is definitely having a qualitative, but annotated, graph. Once you put in the annotations, you create a language you can use to talk about your graph. You hear this again and again when you listen to students going from bumbling explanations about how they are solving a problem to eloquently talking about the area as they add in the annotations.

Write an equation in symbols first

Now that we have a vocabulary, we can put it to use in writing a sentence to describe the area on this graph. So here’s where the intervention needs to happen. Many students were making beautiful annotations, then completely ignoring their graphs as they wrote down (what else?) . When you are standing next to them and watching them do this, you can actually see that they don’t look at the graph at all while they write that equation. They have just memorized it now!

Enter the new worksheet. I am thinking about adding this to my CAPM packet next year, and I will be auditioning it during our exam review this January. I’ve done this exercise with a few kids one-on-one as they’ve come to see me about solving CAPM problems and it has been really useful, so I have high hopes for this working well with the larger class.

Links to the document: PDF | DOC | PAGES

Here’s an example of what I will expect them to do (but they just need to use one of the methods for finding the area):

Pretty simple and quick exercise. But if the kids aren’t writing the equations for area using their graphs, they must just not know how to do it (or what I mean when I say it). These guys definitely know how to find areas of triangles and rectangles (and therefore trapezoids), so I think they will be able to augment this skill really quickly and easily. Get a little consistency going and—BAM! Then they can solve any CAPM problem with (relative) ease.

Extra note: In case it is confusing why I would have my students go to all of this trouble— we actually don’t derive any of the usual kinematics equations. We use the graphs to solve problems. All year. Some of the kids start noticing patterns and figure out for themselves all the equations that they’ll see in a book the next time they take physics, but I ask them to solve everything graphically in this first-year high school class.

So after rambling a bit myself, I threw it over to Twitter to see what other people had to say.

Question asked in the comments on my blog: "What do you think is the essential toolkit for a first time SBG implementer?" So... #sbar folk?

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  (@kellyoshea) December 19, 2011

Here’s what I got.

@kellyoshea 1. commitment to the philosophy 2. nerves of steel 3. a towel

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Kate Nowak (@k8nowak) December 19, 2011

@kellyoshea theory first...stick to your guns. Communicate and communicate and communicate.

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Matt Townsley (@mctownsley) December 19, 2011

@kellyoshea 1. administrator support 2. spouse/family support 3. A great PLN 4. a good sales pitch for student/parent buy-in

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Fran Poodry (@MsPoodry) December 19, 2011

@kellyoshea 1) Commitment! 2) Sales pitch! 3) Dan's starter kit: blog.mrmeyer.com/?p=346#more-346

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eddi vulic (@zidaya) December 20, 2011

@kellyoshea checklist of philosoph principles to ensure its right for u. samples of standards, syllabi, grade tracking systems.

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Frank Lee (@TheyCalMeMister) December 20, 2011

A lot of good advice! Know your philosophy, commit, and communicate. From a more day-to-day view, you also of course need your list of standards (not too many or you’ll go crazy… I limited myself to 5 per unit this year, and many units have fewer than 5), a way to keep track of everything (like ActiveGrade or some such), and people to bounce your ideas off of and commiserate with as you go. I think you also need to have a good vision of your endgame when you start (assuming you’re going to have to translate this all back into a letter or number grade in the end— how does that happen?).

One idea that I had was about doing more of the student initiated assessments during class since, even if you could get 150 kids to quickly and earnestly buy in, it would become pretty unwieldy to meet with all, most, or honestly even half of them every week or two outside of class. These in-class opportunities would have to give students choice over what they want to test, but it would also be impractical for a teacher to be making 150 different quizzes each time. Even if most of the students had many of the same problems on their quiz, putting them together in nearly endless combinations would still take too long to be a sustainable practice.

But, so. My idea* is to offer a menu with a few flavors of test (say, 3 or 4) and let students choose a day or two in advance which test they’d like to have. It’s not so much trouble to make up only 3 or 4 different tests (especially compared to 20, 50, or 150). It would be pretty easy to have kids mark their names down on a sign up sheet as they left class one day, or to throw together a Google form if students were likely to use it. Here’s a quick example of four choices I might offer around this time:

It’s easy to scan ActiveGrade and see what flavors would be useful to a lot of kids at the moment (just look for vertical stripes of trouble). Here’s a snapshot of one of my Honors classes at the moment (well, a bit behind, actually, since I haven’t finished looking at the quiz they took right before they left for break, but still). Click to make it a little bigger.

So without a lot of work, it would be easy to see what the menu choices should probably be and to make up a few quizzes (tests, whatever) along those lines.

A couple of ideas for implementing this kind of menu test on a regular basis:

• Alternate weeks of teacher-chosen tests and student-choice tests. Teacher-chosen tests could still cover any objective (even quite old ones), but everyone would take the same test. Student-choice weeks would have them picking from a menu (of 2, 3, 4… whatever makes sense in the number of choices) created that week.
• 50/50 tests — Students get a choice every week (after the first few when there are too few objectives on the table for there to be any choosing), but they only choose the flavor of the 2nd half of the test. So everyone has the same first page, but they get their choice of a few different 2nd pages.

In my classes, we’ll return from break for just over 2 weeks of classes before the exam. I’m thinking about trying this method of student-choice testing to help my students feel more in control of how they are preparing for the end of the semester and to give them more than the two Sunday test opportunities to choose skills that they want to show me. I think they will like it.

Does anyone have other ideas for low-maintenance in-class assessments (or re-assessments, if you call them that) that can lower the stakes for teachers trying standards-based grading? And let me know if you try something like this in your classes (and how it works, for better or for worse…)!

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* I’m sure that I’m not the first to come up with an idea like this one.

While building the momentum transfer model, we need a new representation for thinking about how momentum is transferred between objects. It has to include a before and an after portion since we use the model to talk about what happens over a change in time. And in fact, we usually are talking about some (relatively) exciting thing that happens by analyzing the states of the objects immediately before and after the event occurs.

Some IF chart examples

How about the general situation happening in our momentum transfer paradigm experiment first? So a moving cart hits a stationary cart. They stick together after the collision. Let’s say (for the sake of concrete examples) that the moving cart has twice the mass of the stationary cart (so, 2 bricks vs 1 brick) and is initially moving at a speed of 0.5 m/s.

For the next example, let’s say that we have two carts that are initially  stuck together at rest, then “explode” (via the spring in the plunger cart) and move off in different directions. Let’s make the carts have masses of 3 bricks and 1 brick.

How about one more. This time both carts are initially moving in the same direction, but at two different speeds. They collide but do not stick together.

Features of the IF chart

The name (IF chart) stands for Initial – Final chart. I originally referred to these as “momentum bar charts”, but that was soon shortened by students to “bar charts” and then became confusing to them once we had energy bar charts as well later in the year. So we now call the momentum bar charts IF Charts and the energy bar charts LOLs (post coming later this year), and the confusion is gone.

The bar charts themselves have velocity on the vertical axis and mass on the horizontal axis. Or to say it another way, the height of the bar shows the speed and direction while the width of the bar shows the mass. In order for the charts to be useful visualizations of the situation, it’s important to exaggerate differences between objects in their mass and speed (some students like to draw most everything the same height or width and need prompting to get into the habit of making these features meaningful).

Once you draw your first chart and have everyone sit back to consider it for a moment, students will pretty notice that the area represents the momentum of the object (area of a rectangle being the base times the height, so the mass times the velocity for these bars).

So. If momentum is conserved for a given situation (that is, if there is no momentum transferred into or out of the system), then the total area on the I chart should equal the total area on the F chart since the area of each bar represents the momentum of the object and the total initial and final momentum of the system should be equal. Cool! That idea (conservation of momentum –> conservation of IF chart area) also usually makes a lot of sense to students.

A couple of (picky) notes on usual usage:

• For some students, it seems to make most sense to them to combine objects that move with the same speed into one bar. That practice drives me a bit crazy, but I let them do it because I think I’m just bothered by it visually, and who am I to impose my aesthetics over someone else’s sense-making?
• Many students are very resistant to drawing in a final bar if they don’t know the final velocity of that object. I push them to draw it in anyway and to make a tick-mark on the velocity axis (as I did in the examples above) labeled (or some other physically meaningful symbol… and definitely not !!). If momentum is conserved (and it usually is if they are drawing IF charts!), they should have a good sense of the direction and relative size of the speed just by looking at the other areas. And if they just leave the chart blank, it both looks very unfinished and, I think, loses a lot of the charm and usefulness for setting up an equation.
• One more important and picky point: If an object has a velocity of 0 m/s, then they should draw an x on the axis in the relevant spot (as I did in the examples above). The x on the axis means, “I’ve thought about it, and it’s zero.” If they just leave it blank, it gets confusing or looks like they just didn’t finish drawing it (see my previous picky point above).

And there you go! But, of course, we’re not finished with the diagram yet. Now that we’ve qualitatively modeled the situation, we want to use our diagram to make a more quantitative description. And we want to put it to use in solving problems.

Using the diagram to write an equation

As with our other favorite diagrams (velocity-vs-time graphs, free body diagrams… hmm, two more subjects for future posts!), IF charts start to become more powerful when you annotate them and use them to write equations. The diagrams in the examples above have already been annotated, so we’re ready for the next step.

In each of the example situations, let’s assume that there’s no outside net force to transfer momentum into or out of the system. In other words, momentum is conserved in those three situations. We can write equations for each by stating that the total initial area (momentum) is equal to the total final area (momentum).

For the three above examples:

1. 
   
2. 
   
   Note: I always use addition to add up the areas. I let the signs work themselves out. We’re expecting to find a negative value for , and if we put in a positive velocity for , that’s just what we’ll get.
3. 
   

You end up with a simple-to-solve equation and no formula to memorize. You write your own equation using the IF chart every time!

2-D problems and double IF charts

The charts scale well for two dimensional problems. The similarities between doing a Newton’s 2nd Law analysis in component form and doing double IF charts are also pretty evident. (I only do 2-D momentum problems with my Honors Physics students. We stick to 1-D problem in the regular class.) When we talk about 2-D problems, we note that we have two ways to solve them: using double IF charts or drawing a vector diagram (which we start by writing an equation in symbols and isolating the quantity we want to find). Drawing the vector diagram takes a lot less time and makes good sense to many students, so a lot of them actually choose to do 2-D problems that way instead of breaking the vectors into components. Double IF charts are always an option, though.

The future of IF charts… IFF charts

As useful as they are, IF charts are really lacking when you’re representing a problem that has a net outside force (and therefore momentum being transferred into or out of the system). The IF charts are now “unbalanced” (like an FBD that shows there is a net force on the particle), but you can’t represent how unbalanced they are in an obvious way. In fact, students tend to think you can’t use the charts at all if momentum isn’t conserved.

So I’m planning to try out a tweak on IF charts when we get there with my regular classes (we’re about ready to start the unit when we return from Christmas Break in January). We’ll try drawing IFF charts (if and only if charts…?). The extra F (in the middle, if you couldn’t tell) is for a Force-vs-time graph. Here’s what I’m thinking…

An example of a “balanced” situation where there is no net outside force:

An example of an “unbalanced” situation where there is a net outside force on the system:

Suddenly the charts became a whole heck of a lot more meaningful and powerful.

I haven’t tried these in my classes yet, so I don’t know how students are going to respond to and interact with them. If they work out well for the regular Physics! kids, I’ll share them with the Honors guys when we circle back to our second unit on momentum (now with energy!) this spring.

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Postscript

Edited 12/29/11 to add in some more details via Kathy Harper on the AMTA listserv.

I just wanted to add to the discussion that the original work-energy bar charts were developed by Alan Van Heuvelen.  (If you can manage to get a copy of his Active Learning Problem Sheets, or ALPS kits, I highly recommend it.  There are lots of nuggets in there, including great exercises to instruct students in the bar chat approach.  The kits are technically out-of-print, but I understand there are still ways of tracking down copies.)

The first person I saw take the chart idea to other domains, including momentum and angular momentum, is Tom O’Kuma at Lee College in Texas.  He is very active in AAPT, particularly on the two-year college scene.  I would suggest that we think of momentum bar charts as “impulse – momentum” charts, which would address some of the issues brought up in the previous post.