# Lenz’s Law Activity

This is the second year I’ve taught AP Physics C: E&M, and we’re getting to the final leg of the course: electromagnetism. I was preparing the unit’s opening activities when I came up against the struggles of Lenz’s Law. One pesky negative sign within Faraday’s Law creates more trouble than just about anything in this class.

At this point in the year, my students have studied electrostatics, including potential and Gauss’ Law, RC circuits, and magnetostatics, including Ampere’s Law.

I’ve never really understood how to use Lenz’s Law to consistently predict the correct direction of an induced current. I was trying to figure it out again a few days ago, and it ended with some choice 4-letter words and my head on my desk.

But I’ve got it now! And I’ve come up with an activity that will help students understand it as well all thanks to the HTML5 version of PhET’s Faraday’s Law simulation.

The HTML5 version is particularly good because of the option to display the magnetic field lines coming from the magnet. This is the key to the entire activity as it’s what allows students to reason through how the magnetic flux through the wire loop is changing. It also being an HTML5 sim allows it to run on phones and tablets. Also, it’s FREE.

I had students first explore Faraday’s Law through the old java version of the sim. This one allows you to vary the size of the loops, which the HTML5 version doesn’t. I ask students simply to play with the sim and figure out the conditions required for current to be generated in the wire as well as to list the factors that affect the magnitude and direction of the current. Students don’t have much trouble figuring all of this out.

We then have a quick discussion on how to predict the direction of the induced current, and this is where things get sticky. There are lots of patchwork theories that arise that are basically a list of if-then statements involving the direction of motion of the north or south end of the magnet relative to the loop.

This is ultimately unsatisfying because a list of if-then’s is not a good scientific model, especially situations that aren’t “moving a bar magnet near a wire loop.” I then take a few minutes to review flux, which they’d seen from electrostatics, and then introduce magnetic flux as basically the same thing, but with magnetic fields.

I conclude the discussion by emphasizing that looking at this from a “how is the flux changing” perspective is more generalized than “which end of the magnet is moving how” perspective and, thus, will result in a much more generalized and useful model.

# Data Collection

The goal of the activity is to collect “data” by drawing before-and-after pictures of the magnet moving into and out of the loop. Students use each set before-and-after drawings to figure out the change in magnetic flux due to the motion of the magnet, the voltage reading (whether it’s positive or negative) to determine the direction of the current, and then the right-hand rule (which they know from the previous unit) to figure out the field created by the wire.

Here’s one example of moving the north end of the magnet towards the loop. Having the “field lines” box checked is essential.

Before:

After:

In the “before” snapshot, students draw an arrow* indicating the direction of the flux through the loop. In the “after” snapshot, students draw another arrow showing the direction of the flux, longer if the flux increased and shorter if it decreased, then a dashed arrow showing the change in the flux. They also use the voltage (negative voltage = flow from positive terminal to negative terminal, positive = opposite) to determine the direction of the current, which they draw, and then they draw the direction of the field in the wire due to that current.

To figure out if the flux increases or decreases, they use the density of the field lines in the loop. More density = greater field = greater flux. The direction of the change is figured out by looking at the direction that they had to stretch or compress their initial flux arrow to turn it into the final flux arrow. For example, the first picture has a flux arrow pointing to the left, and the after has one longer, but still pointing to the left. If you wanted to make the first one look like the second, you’d have to stretch it to the left. Therefore, the change is to the left.

Students look at 4 scenarios, which require 2 drawings each:

• The north side of the magnet moves from to the right of the loop to the front edge being inside the loop (pictured above).
• The far end of the south side of the magnet moves from the center of the loop to the left of the loop (pictured below).
• The far end of the south side of the magnet moves from the left of the loop to the center of the loop.
• The far end of the north side of the magnet moves from the center of the loop to the right of the loop.

Basically they pull the magnet into and out of the loop from the right, then reverse and pull it into and out of the loop from the right.

*Since flux isn’t a vector, I’ve been careful not to call them vectors. Though, what we’re kind of doing is vector subtraction to figure out the direction of the change. I’m not quite sure why we can treat it like a vector and it still work out that way. Oh well.

# Data Summary

Once they’re done, they’ve got 8 drawings with all kinds of arrows, so it’s kind of a mess. The goal is to see a pattern that they can use to predict the direction of the induced current based on the change in flux. When they’re eventually figuring this out on their own, I want them to think about it like this:

1. Figure out the direction of the change in flux.
2. Figure out the direction of the field that would oppose that change.
3. Use the right-hand-rule to figure out the current required to generate that field.

To facilitate that, I had my students make a summary page that filtered out most of the data so that they could easily see the pattern. I put this up on the board and told them to fill in the rest from their data once they finished.

The conclusion to this was to figure out the pattern between the direction of the change in flux and the direction of the induced magnetic field. If done correctly, all of them should be opposite of one another, which students easily saw.

Here is an example of some student work.

# A few other things

The devil is in the details for this activity, so I walked through the first set of drawings with everyone to make sure they were doing everything correctly. I told them that they needed to draw the same number of field lines for each snapshot (I chose 6, the simulation draws 8), and that when drawing them, they needed to make sure and basically draw them as they’re drawn on the simulation. Doing this right is key to being able to use the density of field lines to deduce the magnitude of the field/flux within the loop.

My students also have lots of practice in figuring out the direction of change by looking at before and after vectors. Even if they hadn’t, explaining it as I did above (by looking at the direction required to stretch or compress one vector to the other), I don’t think it would have been too difficult for them to figure out.

I also made sure to check on each group frequently to make sure they were doing everything correctly because, again, getting everything correct is key to seeing the pattern at the end.

If you have any suggestions for improving this, please let me know! If you use this (or something similar) and would like to share your experience with it, please do so as well! And if you need help or clarification with anything here, leave a comment, and I’ll do my best to help out.

# Brainstorming a Special Relativity Activity

My AP Physics C: E&M class finished all the content we needed to get through with a few weeks to spare, so I decided (amidst their great excitement) to do a unit on relative motion and special relativity. Thankfully, the physics education twitter community is awesome, and I’ve been rescued from what would otherwise be certain doom with this unit, especially given that I had almost as much to learn about it as my students. Special thanks to @LCTTA and @kellyoshea for equipping me with a life preserver before I dove out into such choppy waters.

Through my various readings and video watchings, I came across this fantastic video by MinutePhysics. Take a moment to watch it before reading further; it’s only a 2 minute video, and it’ll save me a lot of typing. The inspiration for this activity came from what he call’s the switch-a-roo, in particular when “rotates” the slices vs. just sliding them (at about 1:03).

# Beginnings of an activity

My idea is really nothing more than making strips of paper that students can slide and rotate much like the “slices” shown in the MinutePhysics video. This will be given to them after a week of basic relative motion, so frames of reference and relative velocity are part of their vocabulary now. This will also go right after an introduction to the Michelson-Morley experiment and their “discovery” that the speed of light is constant in all frames of reference.

There will be two objects in motion relative to one another along with a photon. Both objects and the photon start at the same position. One object remains stationary, the other moves away with a constant velocity as does the photon in the same direction. Here’s how I’m imagining this might go:

Change the frame of reference such that the other object is at rest.

From this:To this:How does this violate the rules of special relativity? I would be looking for them to notice what’s in green above. I’m also curious as to what discussion the jaggedness of the photon’s line (look closely at the second picture) might generate.

How can you perform a switch-a-roo that doesn’t violate the rules of special relativity? I’m a little unsure how to guide them towards a condition for …doesn’t violate the rules of special relativity beyond that they have to keep the photon line “unbroken.” That makes it work out right, but I’d like it a little more grounded in physics. However, even if I can’t figure that out, it at least allows them to see the creation of a new time axis.

What do you think lines parallel to the bottom of each strip mean? It’s a new time axis! This will rely on their previous discussions about spacetime diagrams (which we’ve done for only non-relativistic scenarios in preparation for this part) about lines parallel to the time axis indicate constant position and vice-versa.

Does time in the new frame tick at the same rate as the first frame? Justify you claim with evidence and reasoning. This one’ll be a zinger! Time dilation!

Some other follow-up questions that I’ve yet to think of. Suggestions? Does the new frame have the same position axis as the old one? If not, what would a new one look like? See the next section on why I might ask this as I thought of it while typing it out. However, upon further reflection, I’m not even sure this can be done? Even if not through this particular example, it’s still a great discussion to have.

Some other follow-up questions that I’ve yet to think of. Suggestions?

# Ponderings

What I like: I think the most effective (and coolest) thing about this is that it gives students some kind of visual for how to think about time dilation and why the constancy of the speed of light necessitates such an effect. Linking the effects of special relativity to one of the key postulates in relativity, the speed of light in vacuum is constant in all frames of reference, was something that I never really understood until recently, and I want my students to appreciate that link. I think it also helps them appreciate the genius of the theory in that everything works out just fine if you just abandon the idea of absolute simultaneity. It sounds so simple when you say it like that, but it’s really rather profound!

It also sets them up for utilizing spacetime diagrams for relativistic scenarios, especially if we want to get into drawing the new time and position axes for a moving frame on top of those for a stationary frame, as shown here:

What I don’t like: I begin the activity by them seeing that applying a regular ‘ol switch-a-roo (i.e., the Galilean transformation) makes light travels a shorter distance in the same amount of time, thus violating special relativity. And that’s a great starting place, I think. But there’s not really a way to circle back to that to verify that the new switch-a-roo (i.e., the Lorentz transformation) succeeds where the old one fails. I see how that happens when the new position axis is drawn (like in the SparkNotes picture above), but I’m not sure my students will see that. Perhaps I should just ask them to discuss whether or not a new position axis is needed and, if so, what would it look like? Hmm..

I’ll be giving this to my students in a few days, and I’m hoping for the best!

# E&M Modeling: Inductance

This post is part of a series of posts documenting my efforts to keep with a modeling philosophy in my AP Physics C: E&M class where sticking to the Modeling method can often times be difficult. Getting exact measurements on things like electric field strength, electric and magnetic flux, and current changing over time can be difficult or outright impossible without a bunch of expensive equipment. Here’s another way that I’ve figured out how to adapt and keep as best I can do the method through the amazingly useful and 100% free PhET simulations paired with the Hudl Technique app.

# Sequencing and setup

This “lab” was conducted after a 2 week introduction to electromagnetism through Faraday’s Law and Lenz’s, which they constructed a conceptual model of by using the Faraday’s Electromagnetic Lab simulation. The remaining time was spent working the typical run-of-the-mill induced current/EMF problems, including my favorite E&M demonstration of dropping a magnet through a copper tube.

I began by drawing a simple circuit with nothing more than a DC voltage source and a loop of wire, and they discussed how the magnetic field within the loops would change as the current and number of loops increased producing a simple drawing like this:

I essentially wanted to get them thinking more about the time-behavior of circuits, which we haven’t done a lot of. Most of their experience has been that either the circuit is on or it’s off, no mention of anything in between.

Students then setup a simple RL circuit using the PhET Circuit Construction Kit (AC+DC) Virtual Lab simulation and answered a series of questions mostly aimed at making sure they noticed all of the things I wanted them to notice.

To accompany question 5, I asked them to model time time-behavior the potential difference across the bulb and the inductor using a diagram I came up with last year. The idea here was to both solidify their understanding of the time-behavior of the potential difference as well as to set them up to be able to explain the results using Lenz’s Law.

Recreation of what my students came up with.

They were already familiar with the negative sign due to Lenz’s Law within Faraday’s Law, but they viewed it from the context of determining current direction by looking at the direction of the change in magnetic flux. From here, I added to their drawing to help them understand exactly why the bulb started with no difference in potential across it.

The opposite emf induced by the inductor cancels out what would otherwise be a 10V potential difference across the bulb.

Armed with the beginnings of a conceptual understanding of what was going on in the circuit, they were now tasked with developing a quantitative model for the current and potential differences within the circuit.

# Obtaining and analyzing time-dependent behavior

I have neither the equipment, funding, or even the knowledge of what kind of equipment I would need to procure in order to get the kind of data I want. Instead, I had my students use the free Hudl Technique app, which not only turns any smartphone into a slow motion video camera, but also allows you to advance frame-by-frame through the video with the accompanying time-stamp of each frame. They placed an anmeter and voltmeter in frame of their camera, took a video, and then scrolled through afterwards in order to record the current and potential difference across the inductor at various points in time.

Armed with a notebook full of data, my students jumped into Plot.ly to determine equations for V(t) across the inductor and I(t) within the circuit. Below are their results.

R-squared of 0.9998. Current function I(t) = 0.998 – 0.992*exp(-0.0544*t)

Students quickly realized that the 0.998 and 0.992 were awfully close to the maximum current of 1 A so were easily able to generalize that part of the equation. The 0.0544, on the other hand, was not so obvious. They’ve yet to begin tackling that yet, though. They’re potential difference graphs produced equally solid results:

R-squared of 0.9999. Potential difference function V(t) = 0.0626 + 9.89*exp(-0.541*t)

Like with the maximum current, students saw the parallel to maximum potential difference. They also noticed that the term within the exponential was almost identical, though they’ve yet to delve into what that means.

Finally, I asked them to plot the potential difference vs. the derivative of the current with respect to time as I knew that the slope of this graph would be the definition of inductance. They, of course, don’t know that yet. Taking the derivative of their current function and plotting it with respect to potential difference values gives the following:

R-squared of 0.9999. Potential difference function V = 182*dI/dt + 0.0762

Hey! It’s linear! And here’s why my students are for now, which we’ll pick up on the next time we meet. Everything after this is my attempt to explain everything out in the way that I’d want my students to see it. It will essentially be a record of me trying to figure out what all this means because I’m still not yet sure what inductance is beyond being able to qualitatively describe what higher or lower inductance does to a circuit’s behavior. But that’s ok because…

# But what is inductance really?

Dimensional analysis can be used to figure out that the units of the slope are volt-seconds per amp, which is a little difficult to explain in the typical For every ___ [unit 1], ____ changes by [unit 2] framework that my students (and me) are used to. It can be shown that the units can also be written in terms of tesla-meters-squared per amp, giving units of magnetic flux per amp, which is much easier to understand. Hey! Inductance basically is a measure of the magnetic field per amp that can be generated in an inductor. Neat.

However, that doesn’t quite help determine how the circuit behaves as the slope, i.e. the inductance, changes.

Solving the equation for dI/dt yields the following:

So, as the inductance increases, the rate of change of current decreases, meaning that it takes a longer amount of time for the circuit to reach the maximum current value. Since the current takes longer to ramp up, this means that the magnetic field generated within the inductor also takes longer to ramp up…

After running off and checking with the simulation, it turns out that I’m correct. Hooray! Though, to be honest, since both I and V are functions of time, I can’t quite shake why my logic feels a bit shakey even though the prediction is accurate. Something to think on.

Actually feeling like I understand inductance is a rather new feeling to me, but please let me know if I’m totally missing something here. You’ll do me and my students a huge service!

# Crisis Is the Best Motivation

I was stumped. Absolutely stumped. I’m teaching rotation for the first time and had just finished blazing through rotational kinematics. I wasn’t thinking more than a day or two ahead (still am… thankfully, spring break is next week). So Friday happened, and I had no idea where to go next.

Sunday evening rolled around, and still nothing. I was at the “google iterations of different phrases” stage of desperation. And at some point in my google hole, I was looking at a cook-book lab for torque. And then… huzzah! An idea.

I wasn’t sure at the time if it was going to work, but I didn’t have anything else to work with…

# It’s All About the Ratios

Students quickly notice that ratio nature of this lab. I stressed in the beginning to pick 2-3 combinations of masses that were even multiples of one another: “Picking a few data points where the ratio of masses is easy to see will help you see the pattern. Then, apply that pattern to your data points that aren’t even multiples to see if it still holds up.”

I wasn’t sure about giving them that tip when I did, but I knew that we didn’t have 2-3 days to spend on this. As it turns out, it was the right thing to do. Sure, it takes a little bit of the discovery away, but not in a way that lessens the benefit of an activity that essentially has them inventing torque.

Once most groups had noticed the pattern, I asked each group to write an equation for the pattern they’d discovered that included the force of both hanging masses and the distance of each from the center. Each group was instructed to include that on their results. All of the groups came up with a ratio equation, which later I asked them to “get all the R’s on one side and all the L’s on the other.”

At this point, everyone’s back in their desks ready to take notes. I introduce the concept of torque and talk for a few minutes about it being an analogue to force for rotational dynamics. I also include some snippets from the rant below.

What fascinates me about this lab is that it allows students to go through an incredibly authentic scientific experience because they essentially invent the torque quantity. This activity answers the question Why is torque = force*distance, which is something that I never understood. Because of this whole ratios thing! Nature has decided that if the force*distance on one side of a reference point is the same as the force*distance on the other side of that point, then the object’s angular velocity doesn’t change. The “invented quantity” aspect of this activity lays the entire foundation for rotational dynamics as everything else depends on knowing what a “torque” is.

All in all, this lab is simple and straightforward. No tricks, twists, or surprises. And I’m sure it’s not a new or unique approach in the grand ‘ol world of physics education, though it’s very new to me. But I think that’s a big part of why I like it. If you’ve got suggestions on how to improve it, I’d love to hear ’em!

# No rotation equipment? No problem!

Like many AP Physics 1 teachers, I’ve had to figure out how to teach rotation this year. As I’m still new to the profession, the amount of lead time I have on my lesson plans has shrunk to about 2-3 days by this time of year. Here I was with a few days to plan an entire unit that would ideally start off with a lab that I didn’t have equipment for. Thankfully, there exists a thing called Direct Measurement Videos that have got me covered. I wrote about why they’re awesome earlier in the school year. Later in this post, I’ll talk about how I integrated this with Desmos to get a match made in heaven.

# Introducing Rotational Motion

I first started with a simple video of a rotating disk with some markers on it. I talk briefly about the differences between translational and rotational motion and give them their first task: come up with a way to to measure the position of the dots in as simple a way as possible. Essentially, I asked them to invent the concept of angular position. A few groups proposed using the arc length that the dot traces out, bu once they saw how complicated the math would be they took a different approach.

I was surprised that it only took about 15 minutes for each group to independently settle on using the angle from a chosen reference point to measure position. I did this because it’s critical for students to have a strong conceptual understanding of the fundamentals of rotational motion. If they don’t understand the basic idea that position is measured relative to a reference point, then everything else becomes much more difficult. I wanted to pair that idea with their idea to measure the angle relative to the reference point. Since they’ve been in physics for a semester-and-a-half by now, it went fairly smoothly. Nonetheless, it’s a critical step, and the 30 total minutes they spent on the activity saves them (and me!) a bunch of time later on.

# Integrating Desmos

The next day, I use a different video, a disk accelerated by a falling mass, to be their first foray into exploring rotational kinematics relationships. This video is a good choice for several reasons:

1. The frame count starts at 0 when the ribbon is cut. This makes converting frames to time values much easier for students.
2. It has 3 different points marked on the disk. I had groups investigating different points. They’ll see at the end that the angular acceleration was the same for all the dots, which is surprising to them. It’s also sets a good time to differentiate between angular and translational quantities.
3. The disk only goes through about a 1/4 turn. It helps with the data turning out very clean as frictional, air resistance, etc. effects are minimal.

Students generate an angular position vs. time graph from their data. Now, normally, I’d have them open up a blank instance of Desmos, input their data, and then find the parent function that fits their data. This time, however, I used a template that I adapted from one of Desmos’ stock graphs, Calculus: Tangent Line. What I wanted was for students to first find the equation for angular position, and then use the slopes of the tangent lines to generate an angular velocity vs. time data table from which they could make another graph. This can be done by hand, of course, but we definitely don’t have time for that. I slightly modified the stock graph by adding a data table, changing some variable names, and adding some instructions specific to the activity. Once they’ve figured out the parent function (SPOILER: it’s quadratic.), they can use the slider to pick a point on the parabola through which a tangent line is drawn. The t point gives the time value, and the slope of that line gives the angular velocity at that time.

This screenshot doesn’t show any actual data points, just the parent function and tangent line.

Once they have an angular velocity vs. time graph, which I have them do on a new blank Desmos graph since they don’t need the template for a linear relationship, they find the equation of the line, find the slope, and start figuring out what it all means.

What I really like about the template (and Desmos in general) is that it allows students to play around with the different sliders and explore how the slope of the tangent line changes as it moves back-and-forth on the parabola. It gives a very convincing visual showing why this specific curve yields an increasing velocity; they can see the tangent line getting steeper and steeper right there in front of them! It also saves a lot of time. I had them do this by hand when we did translational kinematics at the beginning of the year, and it took two full 50 minute class periods. And, even then, I’m certain that many of my students weren’t fully understanding exactly what they were doing as they were so focused on carefully drawing lines, estimating points to calculate slopes, and all the other mechanics of doing this manually.

Desmos takes all that away and lets them only have to mess with the important stuff. For this activity, I had students using a set of iPads that my school has. This can just as easily be done on desktop computers, laptops, or even students’ phones. Here’s the template that I gave to my students. If you create an account and save it, you can modify it for your own purposes.

# Thoughts on Desmos

Ever since I found Desmos at the end of last school year, I’ve been finding more and more ways to integrate it into my classes. For example, at the beginning of our simple harmonic motion unit, students discovered that the position of a mass-on-a-spring follows the cos(x) function. After having been introduced to some vocabulary, I gave them this warm up the next day: I’ve also noticed throughout this year that students think that anything (and I mean anything) that’s not linear is automatically “exponential”. The joke ends up being on them, however, as nothing we graph ever ends up being truly exponential. This wasn’t a misconception I thought needed to be tackled, but we’ve knocked that one out nonetheless! When trying to find functions that fit the data, being able to effortlessly zoom in and out as well as change the range of the axes takes care of another problem I’d noticed when doing this by hand at the beginning of the year.

I’ve battled and battled, mostly unsuccessfully, to have students choose axis ranges that spread the data out as much as possible on graph paper. Because if they crowd the data in one corner, then it’s probably going to look linear. Not a problem in Desmos once I show them how to rescale and zoom. I had an additional idea while writing this post. I’ll make it happen eventually, or maybe you will and you can save us all the work! I’m imagining a “worksheet” utilizing the sliding tangent line idea. I could give them a set of premade position vs. time graphs of accelerated motion. They could slide the tangent line, observe the changes in slope, and use that to translate the position graph to a velocity vs. time graph. I could even use curly braces to piece together a section of motion that’s accelerated and then a section that’s constant velocity like this: y=x^2 {0 < x < 4} and y = 16 { x > 16}.

If this is your first time seeing Desmos, and your reaction is anything like mine… THE POSSIBILITIES ARE ENDLESS…! then my suggestion is to not look around for premade activities to suit your needs, but to instead just spend some time playing around with it. Look for every excuse you can to do something in Desmos. Once you’ve figured the basics out, look at the premade ones for more ideas. Eventually, ideas will just start coming to you! Above all else, Desmos is a sandbox, and the more you understand all the nuts and bolts, the better suited you are for bending it to suit your needs.

# Setting the Stage

I introduce the impulse-momentum theorem immediately after a lab introducing momentum. At this point, students have a general idea on what momentum is, including that it’s defined as the product of mass and velocity. The introduction lab helped them see the ratio-centric nature of momentum and interactions. All that said, the general understanding of momentum is still fairly basic and developing.

I start with a simple question that essentially has students state the impulse-momentum theorem conceptually.

I immediately get responses such as change the mass! and change the velocity!. It only takes a little digging to get them to expand upon change the velocity to include that an unbalanced force must be present on the object. Bam, impulse-momentum theorem:

To change the momentum of an object, the forces on that object must be unbalanced.

Then, we move to deriving it. I’ve been including more derivations lately, but I’ve been careful to only do it when I feel that the students can do it themselves (with a little poking in the right direction by myself). My only direction here was this:

So, we said above that a net force is required to change something’s momentum. But the only equation we have that includes net force says nothing about momentum. That doesn’t sit well with me. Let’s see if we can get momentum in there. Be sure to start from  $F_{net} = ma$

The “ideal” derivation I’d imagined looks something like this:

As it turns out, only a couple of students actually did it along the lines of the way I did it. Which is actually fine! There’s no single “right” way to go through stuff like this.What’s important is that most kids were able to figure out how to get a in there somewhere. What most students did was this:

And I was quite satisfied! My response fort when students asked the oft repeated physics class refrain Mr. Register, is this right?, was Almost! Watch me go through it and you’ll see… When I went through my version of the derivation, they seem to see the difference. What’s important is that they’ve gone through a pretty important physics derivation (mostly) on their own.

Ok, let’s move that delta-t over to the left side… and we have the impulse-momentum theorem!

# Enter the Mythbusters

Huzzah! We have an equation! It’s got a fancy sounding name! Let’s start plugging in numbers!

Nope.

I’m trying to put more focus on understanding equations conceptually, hence the full-stop on jumping straight to plug-n-chug. To accomplish that along with really grabbing my students’ attention, I use this clip from a Mythbusters episode.

I stop it before they actually crash the cars together and poll the room, which instantly explodes in conversation and wild theorizing. I have a few students share their thoughts, throw out a few Hmm…‘s and What do you mean by that?‘s, a few inquisitive looks here and there. A head tilt or two. At this point, students are biting at the bit to know the answer.

But finishing the video would, in my opinion, flop the entire lesson. While about half my students guessed the right answer, none of them had a fully well thought out explanation supported by even (in my opinion) a reasonable amount of evidence to support their claims. Essentially, they were guessing. Which is a fine starting point, but a poor ending one (see The Most Important Thing (TM) on this post for more of my thoughts on this). I’m also trying to develop my students’ scientific argument writing skills a la’ the Claim-Evidence-Reasoning framework.

I want my students to be able to explain, in detail, exactly why the answer is what it is.

# Analysis

The analysis I have my students do is aided greatly by momentum bar-charts, which they were briefly exposed to during the lab and notes introducing momentum. I also provide some data.

I chose to use tons and not pounds or kilograms because of the numbers involved. Using either of those gives momenta in the thousands, especially if the mi/hr is converted to m/s. Using tons and mi/hr keeps the numbers low. Students work through all the bars, and I go through with them to make sure they have a solid set of data from which they can later draw their conclusions. I give them the additional piece of information:

The time for every collision is the same.

The goal is for students to see that the change in momentum for the cars hitting each other is the same as the 50 mi/hr car hitting a wall. If the change in momentum is the same and the collision time, delta-t, is the same, then the net force on each car must be the same as the 50 mi/hr car hitting a wall.

One common thing I noticed is that some groups wanted to add the impulses from each of the 50 mi/hr cars hitting each other together to get 150. Once I pointed out that the impulse for each car was +75 and -75, which added to zero, they’d go back to the drawing board. Others ignored me completely and stuck to their guns. As it turns out, the total momentum being equal to zero is important, but that’s for another day.

Another thing I noticed and also found fascinating is that several of my students across different classes mentioned something their Driver’s Ed classes say. Apparently, they’re told that two cars getting hit head on at 50 is like hitting a wall at 100. I responded by asking the students if they thought their driver’s ed teachers were physicists or knew anything about physics.

Yeah, I guess?.

So, it’s true because somebody you perceive to be an authority told you so?

Yes. Uhh, no. Maybe?.

That was usually enough to get them to keep digging with the data they had.

Up until now, students were doing things in their notebooks. This was enough to fill a 50 minute class period. Day 2 consisted of them putting their arguments on whiteboards and debating with each other in small groups.

# Whiteboarding

I had students form pairs and each put their arguments in Claim-Evidence-Reasoning format. Then, I shuffled all the groups around the room so that each pair was presenting to another pair that doesn’t normally sit at their table. Each group was to present their argument and (heavily) encouraged to modify their own boards if they changed their mind as a result of seeing another group’s presentation. Or add more evidence to support their own arguments if both groups agreed.

This here was the highlight of my week.

Students explaining and defending their ideas to each other is so beyond more effective than me “sage on the stage”-ing it. And way more fun for them. Many groups got (playfully) passionate about their arguments. They were already biting at the bit for the answer at the end of the previous day. They were downright starving for it today.

Once I was satisfied that enough discussion had happened, I played the rest of the video. I then I went through the explanation myself.

I will absolutely be doing more stuff like this again. One thing I need to figure out is how to get groups to more readily consider the evidence and arguments of other groups. While the discussions were great, very few groups actually made any changes to their boards, especially if the two groups disagreed. While I enjoyed watching them defend their arguments, nobody seemed ready to budge. I’m not sure if this is even a problem, just unexpected.

This activity also ended up being a textbook example of confirmation bias. Students would make a claim, and then do whatever they could to justify that claim. Some would ignore the +75 and -75 and add them to 150 anyway because the 100 mi/hr car hitting a wall had a change in momentum of 150. They’d do this even after I pointed it out. When I asked them to justify adding the numbers in the first place, the response was simply that the cars were hitting each other. Which, as we know, isn’t wrong per se, but it doesn’t necessarily help answer the question. When I’d ask how net force fits into that, I couldn’t get a satisfying answer… but students would continue to dig in their heels. This is basic human nature, of course, but it was interesting to be confronted with it so blatantly. I gave a speech emphasizing to draw conclusions from data, not draw conclusion and then hunt to find a way to justify it. But that alone isn’t going to be nearly enough.

One thing I’ll do differently next time is allow one group that got it right to explain what happened instead of me. I was just pressed for time this time, but that shouldn’t be an issue next time as I’ve got a much better idea of how to pace things now.

# A Revelation!

Just before the holiday break I had a bit of a revelation. I’d heard of this “Claim, Evidence, Reasoning” thing (resources on this at the end of this post) as a framework for writing scientific arguments, and I was hooked from the start. This was it! This is how I get my students to stop staring at their papers blankly when I say “justify your answer.” Or flail about including as many fancy-sounding vocabulary words as possible in a desperate attempt to get something, anything right. I dug through a ton of resources, read a few papers, and I was set!

Before you go further, if you’re not at all familiar with what I’m talking about, take some time to read up. A quick Google search will turn up lots of great stuff. This example is an excellent start.

My original vision for using the CER framework was in writing good conclusions to lab reports. And it’s a fantastic tool for that! But that’s only one way to use it. It was especially problematic for me because I wanted to offer my students opportunities to practice, but that would require doing a lab and having them write a paragraph-length conclusion. And then I’d have to grade them. I did this for one lab. Some kids got it, most didn’t, and I didn’t have the energy to try again. Eventually, it dawned on me what I was doing wrong.

Additionally, I think that CER is the way to go about preparing AP Physics 1 and 2 students for the new writing-focused section of the Free-Response questions.

CER isn’t just for elaborate conclusion writing. It’s for anything that ends with “justify your answer” or “explain your reasoning” or some other clever iteration of the same thing we always want students to do: tell me why.

# Introducing CER

Disclaimer: the idea presented below was shamelessly ripped from Eric Brunsell‘s Edutopia article Designing Science Inquiry: Claim + Evidence + Reasoning = Explanation. You can find the slides I used here, and here is the graphic organizer that I use. The organizer is a PowerPoint slide, but it prints like a regular sheet of paper.

I start off with some definitions that I pieced together through a few minutes of Googling. I’m not sure how useful copying definitions is for the students, but it feels like the right thing to start with. And it probably doesn’t hurt, so why not?

I spend a few minutes talking about each one, mostly to fill the silence while they dutifully copy. I answer “what’s olfactory?” a few times, too. Next, the video:

First off, the little girl is adorable. And the commercial is rather amusing, which helps with engaging students. Most importantly, as odd as it may sound, it’s very straightforward. She states that she has evidence and then lists off what that evidence is. Very little room for interpretation here. This is nice because it allows the discussion to focus on what I feel is actually the most difficult part of CER: the reasoning. And this is where student creativity can shine.

# Here Comes the Hard Part

Why is the reasoning difficult? Because it is generated solely by the student. It requires the student to connect the dots from evidence to claim. The best example I saw of this creativity was from this piece of evidence that the little girl provides:

He says he’s from Albuquerque? I’m not buying it.

My handout only has spaces for 4 pieces of evidence, but she presents 5. The Albuquerque one was the one that was left off the most often. To be perfectly honest, I didn’t consider it a viable piece of evidence until my students chimed in. I love it when I’m wrong! Here are some responses:

• It’s a very strange sounding name for a city. She thought he made it up.
• She’s never heard of this place before, so it couldn’t exist.
• He slipped and spoke some of his “weird language.”

My favorite bit of reasoning was in response to the He speaks a weird language piece of evidence: no other human language requires water to be spoken.

Making a claim is easy. Students do this all the time. Finding evidence to support it can also be easy. Just throw some numbers and vocab words out there and see what sticks. The true test of understanding is if the student can link it together with reasoning. Another reason why this video is a great start to the topic is because coming up with reasoning for the evidence presented is still fairly simple. It illustrates the idea to the students without imposing too much of a cognitive demand.

The reasoning is, in my opinion, the most critical part of the CER structure. It’s the glue that holds it all together. And, despite the relative ease of the introductory example, I maintain that it’s the most difficult part.

# And Now, a Physics Example

I formally introduced CER in the middle of my energy unit, so I used this as a follow-up example.

In both my AP and College-Prep classes, students quickly and easily identified that the car slowed down (claim) because it lost kinetic energy (evidence). However, I was awash with blank faces when I asked “So, class, who wants to share their reasoning?”

*crickets chirping*

It’s actually quite difficult for a student in an intro physics class to answer the seemingly simple question of “Why does an object slow down if it loses kinetic energy?”

Many students said “well, it’s going uphill (a claim unto itself) because it’s losing gravitational potential energy (evidence).” To which my response was “How do you know the driver doesn’t have their foot on the gas pedal? You can speed up and go up a hill at the same time, ya know…”

I was satisfied with one of two responses:

• Kinetic energy is the energy of motion. If kinetic energy decreases, then the motion decreases. – I was less a fan of this because of how vague “motion decreases” is.
• The equation for kinetic energy is (1/2)mv^2. If you plug in a bigger number for v, then the kinetic energy increases. If you plug in a smaller number for v, then kinetic energy goes down. – I like this response much better because it references an equation in a conceptual way.

To help students see the connection to the equation, I wrote it up on the board and asked a few leading questions.

• Which of these variables are constant? Which changes?
• Think about how each variable “interacts” mathematically. Are they added, multiplied, divided by, exponentiated, something else?
• Imagine you are making up numbers to plug into each of these variables. Now imagine plugging in a larger number, think about what that means physically, and figure out how that affects the kinetic energy. Do the same for a smaller number.

This was also the first time that I’d asked students to think about equations conceptually in this way (which I need to do more of!), so they struggled for a bit. When I asked them to do the same for question 2, it went much more smoothly.

# What’s Next?

While the introduction to CER went exceptionally well, my students still need lots of practice. I’m going to spend the next week or so doing warm ups that are exclusively this. One way to scaffold this is to simply ask them to write C: E: R: on three lines on their paper, and to fill in the blanks.

Another great candidate for using CER is the nTIPERS book. It’s swimming in problems begging to have CER slapped on them.

This also ties into a new framework that my colleague came up with for writing learning goals. I’m dividing them up by qualitative, quantitative, graph/data interpretation, and lab.

Who knows if this will work out at all as I haven’t tried any of it yet, but it’s nice that the CER thing seems to work well with it.

# Update

I’m loving how this is turning out. My students are rockin’ it so far!