Transitioning from Energy to Momentum

In my college level physics class we study Energy right before momentum. I really like this, particularly because we can begin our study of momentum as driven by the fact that a pattern emerges from data that is not explainable by Energy.

On the first day of my momentum unit I typically do a fun car crash activity to help students start thinking about how force and time are related in collisions. The next day we start building the momentum transfer model. (We’ll come back to force-time relationship at the end of this paradigm series) Last year, not having experience with Modeling Instruction, I just dove right in (chronicled starting with day 1 here). This year I wanted to utilize the discover, build, break cycle that Frank Noschese talked about in his TEDx talk. One of the tenants of modeling is that models are useful for certain cases and not for others. Thus I used an inelastic collision to springboard into momentum based on the fact that an energy analysis is not particularly useful for this situation.

When students walked in I showed them a scenario where a moving cart (A) collides with a stationary cart (B) of equal mass. I asked them to use the Energy Transfer Model (ETM) to predict the final velocity of the carts. A typical analysis looks something like this;

Assuming there is no conversion of energy to thermal energy, the kinetic energy of the first cart should end up as combined kinetic energy for both carts after the collision;

$\frac{1}{2}m_Av_{Ai}^2=\frac{1}{2}m_Av_{Af}^2+\frac{1}{2}m_Bv_{Bf}^2$

Noting that for this case $m_A=m_B$  and  $v_{Af}=v_{Bf}$,  the whole thing simplifies to

$v_{Ai}^2=2v_f^2$

Solving for the final velocity of the two carts together in terms of the initial velocity of the first one,

$v_f=\frac{v_{Ai}}{\sqrt{2}}$

Once we got to here I simply said “Go test it,” and they got to work in the lab.

Before I go on I want to comment on the lack of thermal energy in the above derivation. Many of my students correctly tried to include E_therm in their analysis. This is great, but I pointed out that today was a lab day and thus we need to be able to measure things. Me: “Can we easily measure E_therm?” Student:”Ummmm…no.” “Right, so let’s ignore it and see if the data upholds that assumption.” They almost always (correctly) want to include E_therm in every energy analysis, but we have done a couple situations in the lab where stored gravitational interaction energy transfers to kinetic energy for dynamics carts where assuming no changes in E_therm yielded good data. Thus students were primed for me to suggest that we could ignore E_therm. However, this is tempered with the fact that I do a demonstration showing that kinetic energy transfers to thermal energy in collisions (a couple weeks prior) and that they are used to me guiding towards ‘wrong’ answers. So I believe students went into lab cautiously optimistic that our the lab evidence would support the derived equation.

It doesn’t.

It only takes students 5-10 minutes to realize that the final velocities are closer to half the initial rather than the initial divided by the square root of two. Some of them try to justify the data (well, it seems kind of close to root two…), but after conferring with their classmates they give up and go with two. At that point I pulled them back up to the front of the room.

Me: So, did our equation work?
Students: Nope
M: But was their a pattern?
S: Yep. Final velocity is half the initial.
M: Wait, you mean that energy doesn’t predict the final velocity, but something else does?
S: Um…..

We had a quick discussion about how something must be going on that is different from energy. We also talked about how it makes sense that energy wouldn’t work; we expect some of the initial kinetic energy to convert to E_therm  after the collision.

From here I continued day 1 in pretty much the same way as last year. I found after a 45 minute period students were just about ready to talk about a relationship, just slightly behind where day 1 ended before adding the energy piece. My students are much more used to the idea of paradigm labs this year and are getting pretty good at looking for meaning in lab data, so I am not surprised that this addition didn’t significantly change the day one timeframe. Tomorrow we start with presenting the student derived relationships.

An Empirical Start to the Energy Transfer Model (Part 2)

At the end of the first post in this series I lamented that starting energy empirically meant that I couldn’t include changes in thermal energy like starting this modeling unit more traditionally does. I shouldn’t have worried. Turns out that emphasizing that changing the energy of a system through working, heating, or radiating helps them overall with energy conservation despite that thermal energy in particular isn’t address. But I’m getting ahead of myself.

Days 1-4 ish are outlined in the first post of this series. I’m now picking up at around Day 5.

Kinetic Energy

We started this unit by finding that the area under the force vs. postion graphs for two different springs, when made equal, yielded equal velocities when launching carts. I emphasized at this time (and over and over again as we went through the unit) that the area under graphs, if it has a physical meaning, means a change in something. In this case it’s a change in energy, though we hadn’t gotten that far yet. I just emphasized it’s a change in something. So in the first activity the change in something predicted velocities. In the second it correlated with a change in height. At that point we coined the term gravitational interaction energy, and we looked at how the final gravitational interaction energy was the same as the initial plus the change in energy (as found from the area under the F vs. x graph) The third, starting now, looks at the correlation of that change with velocity. They now know that this has something to do with kinetic energy, since we had the energy=pain talk, but not exactly how.

There are many variations of this lab, most using springs. I found that if you attach a force detector to a cart (which we did for the area vs. change in height experiment previously), you can just pull the cart with a rope and get pretty good data for area vs. v^2 even though the force isn’t constant. Which I think is extra cool. Basic setup for this experiment is below. Note the horizontal track.

I learned one pretty neat trick when I performed the lab myself. For each trial, it doesn’t really matter where the end point is, as long as you find the area for some displacement and then record the final velocity that corresponds to the end point for that displacement (assuming you start from rest, which I did). So I had students graph force vs. position to find the area (change in energy) that we were interested in, and then plot velocity vs. position so that they easily find the corresponding ending velocity. This way they can set the integral (area) section to be the same for each trial, then quickly use the examine function in logger pro to find the ending velocity at that same endpoint for each trial. Slick.

Plotting change in energy vs. v looks like this. Note that since I took this data I actually called the area work, since that is the means by which the energy is changing in this case. I did not instruct them to do that, however.

It actually looks fairly linear, especially to kids who are looking for things to be linear. However, typically data was non-linear enough, and we linearized a quadratic doing central force, so most groups linearized using v^2 on the x axis.

When the data is linearized, it looks like this.

Certainly that looks more linear! Student data actually turned out good as well. Always nice when that happens.

The board meeting for this went amazingly fast. In the first class a student commented almost right away about the units of the slope. They started trying to figure out what the units should be, and I wrote on the board. With a little prodding we finally figured this out;

$\frac{\text{units of rise}}{\text{units of run}}=\frac{N\cdot m}{\frac{m^2}{s^2}}=\frac{kg\cdot\frac{m}{s^2}\cdot m}{\frac{m^2}{s^2}}=\frac{kg\cdot\frac{m^2}{s^2}}{\frac{m^2}{s^2}}=kg$

Whoa. All that simplifies to kg? Cool.

The classes did this in different orders, but essentially within 10 minutes they had figured out that the intercept was zero (both empirically from their data as well as logically by thinking through why it should be zero), that the slope was half the mass, and that the slope relating to the mass made sense because the units of the slope simplify to kg.

Thus

$\{\text{Area under F vs. x graph}\}=\frac{1}{2}mv^2$

From here we went on to be explicit about the names of everything. The area represented a change in energy. In the first case (pulling carts up ramps), it’s a change in gravitational interaction energy. In this case, it’s a change in kinetic energy.

This is more or less where day 5 ended. No, seriously, at this point they (keep in mind this is a college level class taught at the high school, so essentially top 20% kids) took data, whiteboarded it, and figured out meaning in a 45 minute class period.

Day 6 ish: Lab wrap up and transition to Energy Bar Charts

I started the day by teaching energy bar charts (LOLs). (Need a primer on energy bar charts? Kelly comes through again). We then went through the labs drawing the LOL for each one. This did two things; first, and most importantly, it emphasized that the area under the force vs. position graph found a value that measured how energy changed from the first snapshot to the second snapshot. Secondly, it was a way to show students how to draw LOLs. After drawing the LOLs for our two experiments, we had a conversation about how energy changes. The modeling instruction teacher notes lists that there are three ways energy changes; working, heating, and radiating. (Side note: I strongly prefer starting energy from a First Law of Thermodynamics perspective (strict conservation of energy) rather than from a Work-KE theorem perspective. More on that in a later post on partial truthsThey brought up convection and conduction, and I talked about how these are just two different ways for heat to transfer. We briefly talked about molecular interactions and KE transfer here, but I kept it quick. The point here was to plant the seed that what we are doing generalizes beyond work performing the energy transfers in and out of the system, but that for now we are going to focus on work (rather than heating or radiating) as a mechanism to transfer energy.

This took an entire day, as I have them draw the LOLs first, then we have a conversation about them. After today I assigned a worksheet on drawing LOLs and writing the qualitative energy conservation equations. This is a modified version of worksheet 3 in the standard modeling curriculum, modified by myself, Kelly O’Shea, and Marc Schrober (in reverse order?).

I’m hoping to write more about the development process, but overall I found, very anecdotally, that starting energy this way helped students see conservation on a system basis, and they have no problems with the idea that energy can enter or leave a system through working, heating, or radiating. It took a while to differentiate between energy stored in the system as thermal energy versus energy leaving the system through work done by friction, air resistance, or normal force (bouncing ball or other examples), but that’s to be expected no matter how this is done. My regular physics students certainly had trouble with that distinction despite starting ETM ‘traditionally.’ Both classes saw this demonstration (video here) to show that kinetic energy certainly does, often, transfer to thermal energy. The difficultly generally is tracking that energy; is it stored as a change in E_therm in the system, or does it leave via work? It took a while to work through that (pun intended).

Concluding Thoughts

I’m going to leave you with this. When I first started learning about Modeling Instruction, I assumed it was all about the labs, such as those outlined so far in this series. I have since learned, however, that though the labs provide a foundation for the concepts being learned, working through those concepts through whiteboarding is as much as important as the paradigm labs. Whiteboarding is where students flesh out the differences between what they think and what science demonstrates as a better truth, and where they hopefully cement their beliefs as those that align with science. Don’t underestimate the full framework of Modeling Instruction as a complete system for helping students through the process of learning like scientists.

An Empirical Start to the Energy Transfer Model (Part 1)

I’ve been thinking a lot about the Energy Transfer Model (ETM). The Modeling Instruction curriculum seems to start this model by jumping right into the concept of Energy Transfer without much empirical model building, contrary to many of the earlier models. I really like the way Kelly starts energy, showing students how previous models don’t work to predict the desired outcome. Still, I was unsatisfied in that I felt like I would just be telling students what energy is and how it transfers without letting them get a feel for it for themselves. So I set out to design my own version of the beginning of ETM. I used this version of ETM in my college physics class after starting ETM the standard way in regular physics.

Day 1: Area of Force vs. Position graphs

Day 1 started just as Kelly’s post details above, though she has modified it since posting to use Pasco’s spring cart launcher instead of regular springs. The idea is simple. How can I make the final velocity of these carts the same if they are launched by two different springs? We spent 10 minutes playing with the carts, and I showed them at maximum compression, both at about 8 cm, the carts launch at different speeds. Predictably, the spring with the highest spring constant launches fastest. So how can we make them go the same speed using their Force vs Position graphs?

We (my colleague Ben, with whom I teach the regular class, and I) tested the springs and their constants fell very close to those stated in the documentation, so we used that to make expected F vs. x graphs rather than take real data. It worked just fine.

In all classes I did this (three different sections, one regular and two college), the first guess was to make the force equal for each spring. So we did that. My regular class just looked at the graph, saw that if we wanted a force just over 4 N we could use about 5 cm for the red spring and 3 cm for the blue one. For the college classes I asked them to choose an arbitrary compression for the red spring, then find the blue compression to give the same force.

Either way, it failed miserably.

Turns out that if two different springs are compressed to the same force value, they do in fact have the same average force, and thus the same average acceleration. However, the weaker spring has to be compressed further to get that same force value, and thus the same acceleration happens over a larger distance. The weaker spring actually gives a faster speed when the force each exerts is the same!

They get this. I asked them what would happen if you had two cars that had the same acceleration, but one accelerates for 10 meters and one for 20 meters. The 20 meter one ends up at a faster speed. Yep, that happens here too. The red spring car goes faster because it has the same acceleration on average as the blue spring but for a longer distance.

So anyway, what now? I had to guide them to check area. I did not do as awesome of a job as I would like using the area under velocity vs. time graphs to find displacement, and as a result area of graphs is not a formost thought for them. However, all classes jumped on the idea once I led them there (by referring back to kinematics graphs and the parts of those graphs that do in fact have physical meaning). Most students needed help with the idea that they should pick an arbitrary compression of the weak spring. Once there, however, we worked through the math and found the compression of the blue spring such that its area equaled that of the red spring with our arbitrary compression.

The launch was perfect. In all 3 sections.

Kids really like it when things work, and boy, does this work. It took about one 45 minute class period to get this done, but they definitely got the idea that the area under the F vs x graph meant something. I emphasized, over and over, that area under graphs, if it has a physical meaning, means a change in something. We don’t know, however, what that something is yet.

This is where the classes diverged. The regular class went into a lecture day on types of energy and energy pie charts. But that’s not what I want to write about.

To continue empirically, I wanted them to see that the area under the F vs. x graph (a change in something, as I kept calling it) was meaningful in other situations as well. So next we looked at ramps.

Day 2: Ramps and the Area of F vs. x graphs

On day 2 I told them we were going to again look at the Area of F vs. x graphs, but this time in a different situation. We started with a cart at rest at point A, arbitrary but constant. We wanted to end with the cart at rest at point B up the ramp, also arbitrary and constant. I had them pull carts from A to B in any way they wanted and to find the area under the F vs. x graph. Here’s a sample trial.

I learned some things. First of all, most of them didn’t end the cart at rest at point B at first. But we did, however, use that to establish that the faster the cart was going at B, the larger the area seemed to be. We will go back and quantify this later (part 3 or 4 of this series, I believe). So we went back and got some data for starting and ending at the same points each time, starting and ending at rest, but getting from A to B in different ways. Here’s some sample data.

In discussion it became evident that outliers appeared in one of two general cases; when the cart was difficult to actually stop at point B, and when the cart moved backward at some point. On the whole, it was pretty easy to convince them that the area was the same no matter how you got from A to B as long as the cart didn’t move backward and the cart was at rest again at B. Pretty awesome.

That same day I asked them what measurement would always correlate with the area. Horizontal distance up the ramp? Angle? Height? We were able to quickly show that though distance correlated with area, it didn’t work well if we kept the same distance and changed the angle (we got different areas then). Thus distance is not a universal predictor of the area. How about angle? Similar problem; for one angle you could get infinite areas. How about height? We spent the last minutes of this period showing that if we had an equal change in height, even for two different ramps (same cart of course), that the area was approximately the same. Cool.

Day 3 and 4: Finding the Correlation with Height and the Entrance of Energy

Day 3 was short classes, only 30 minutes because of a pep fest, and I think data collection and whiteboarding could probably be done in one class period. However, the conversation we had about types of energy at the end of day 4 fit really well and it was nice to have that there. But I’m getting ahead of myself.

Day 3, 30 minutes, was spent collecting area vs. change in height data. Some students changed the height just by pulling the cart further up the ramp, and some by changing the angle of the ramp, or a combination of the two. Part of the awesomeness of this lab is that it doesn’t matter; no matter how they change the height, if they collect data consistently and correctly, the results turn out well. (Students won’t, by the way, take data consistently and correctly; I had at least 2 groups in each class with non-sensical data. They don’t set the endpoints of the integral in Loggerpro correctly, or they don’t change the endpoints (thus making the change in height the same for all trials), or they measure change in distance rather than height, or they do one of I’m sure many other things that yield poor results. It’s a learning experience though, and the conversations that come from ‘bad’ data are often just as useful as those that come from ‘good.’)

In any case, the graphs were decently linear. Through a board meeting (circle sharing) groups quickly noticed that the intercept was zero, and that that made sense as if we don’t have any change in height, we shouldn’t have gone anywhere, so the area of F vs x would also be zero. They then noticed that some groups (conveniently with carts of different masses, *cough cough*) had different slopes. At some point someone notices that the slope appears to be approximately 10 times the mass. Hmmm, isn’t g really close to 10? Then we look at units. The slope must have units of Newtons, as y axis has units N*m and the x has units of meters. If the slope was mass times g, then the units would be in Newtons. Hmm. Note: In all this, I try to at ask questions with a couple of words max and let the conversation take its course.

This was convincing enough for my students that the slope should be mg. It was, pretty close, for the groups that had decent data. I then asked them to write a general equation to model our data. Most were able to get here;

$A=mg(\Delta h)$

where A is the area under the Force vs Position graph, in N*m.

I pointed out that even though this was a different situation than day 1, the area still gave us something meaningful. But seemingly unrelated to speed! We’re getting there. Let’s rearrange the above equation a bit.

$A=mg(\Delta h)=mgh_2-mgh_1$

$mgh_1+A=mgh_2$

Here is where I finally defined that the quantity mgh is called Gravitational Interaction (or Potential) Energy. I took a side trip for a bit on energy as pain, as described very well (better than I could) in Kelly’s aforementioned post on building the ETM.

Thus what we have found is that the initial gravitational interaction energy plus a the Area under F vs x (which recall we had emphasized as a change something) gave us the final gravitational interaction energy. So I guess the area is a change in Energy, huh?

Starting with Day 5 we are going to look at how the area correlates with speed, and use that to figure out Kinetic Energy. We will then use that to transition in to Energy Bar Charts and the rest of the energy unit. More on that in later posts (I think 1731 words is enough for now, huh?)

Concluding thoughts, for now.

I really like that this method strongly emphasizes that the energy is changing due to the Work done (though we haven’t used that word yet), and I plan to use it to strengthen both their methods of using graphs and multiple representations to solve problems as well as to help with the idea of Work itself, which when taught traditionally has really only served to confuse my students. I don’t like, however, that for now I am ignoring changes in thermal energy, which the typical intro to ETM in Modeling Instruction emphasizes from the get go. I used to teach energy where we would ignore friction for weeks, then finally add it in and start all over, and didn’t like that. I think, however, that the idea that the F vs x graph influences the transfer of energy will transfer (hehe) to friction as well. We’ll see, and I’ll keep you updated.

A Physics PLC: Collaboration at a Distance

This year my school district, like many others, implemented PLCs (Professional Learning Communities) as the driving force behind how we collaborate to help students learn. The directive was that all teachers should meet in a PLC weekly for approximately 30 minutes. This sounds, and can be, great, but I had a problem.

You’re Gonna Need Some Background Info

For 7 years I had been the only physics teacher. This year I took on technology integration half-time, and in addition we have more physics sections, so there are now three of us who teach physics part time. The other two also teach math and chemistry. When the PLC directive came out I was excited to have someone to work with, finally. However, it was not to be. All three of us each teach a different course (I teach a college level course, the math teacher has regular physics, and the chem teacher has ‘applied’ physics, essentially a conceptual class). Since none of us teach the same course and PLC work was important with the other courses those teachers were teaching, they both decided to go with their other courses. Great, I’m a singleton. Again.

Enter Twitter. I’ve been on Twitter almost two years now, and I have learned more on Twitter in these two years than the previous six, which included a masters degree. Among other things I have managed to build a pretty awesome PLN (Personal Learning Network) that includes  a couple hundred incredible physics and math teachers from around the country. In particular, the physics Modeling Instruction community is active and extremely helpful on Twitter. So I decided I’d try to find out if there was anyone else in the same boat as I, or anyone else who simply wanted to use student work to inform instruction. I posted a short tweet with a link to a Google doc with this request;

My name is Casey Rutherford. I am entering teaching for the 8th year, my 7th teaching physics, and my first using Modeling Instruction. I have a relatively odd request.

My school is implementing PLCs, certainly a worthy task. The problem is that at this point there is not a logical person with whom I would form a PLC. Thus my request. I am wondering if any of you would like to form an online PLC with me, working together approximately 30 minutes/week to compare student work. My thought is that we can do a lot with formative assessments, using photos of student whiteboards to form the basis for our conversations. I am, however, open to other ideas as well.

I am very interested in Standards Based Grading as well; however, this particular class is articulated through the University of Minnesota (in fact, it is U of MN Physics 1101 and they get a college transcript upon completing the course), and thus I am not able to implement SBG for this course. It is the only class I am teaching this semester due to a new half-time gig as a technology integration specialist. Thus I think I would like to focus on the impact of modeling on student learning.

I was blown away from the response. Initially I had over 10 people who were interested (ok, so it’s not like that’s hundreds, but I didn’t know if anyone would!). We spent a couple of weeks trying to accommodate multiple, mutually exclusive, schedules. I must admit I got a bit caught up in wanting to include the masses; I thought it was fun that so many people thought this was something worthwhile. However, at some point Kelly, who ended up in the core group, said that this really only made sense if it was something one could attend regularly.

Duh. PLC. Norms, relationships, student work.

The Core Group

We ended up with a core group of six of us; myself, Kelly, Fran, Meg, Leah, and Matt.

This group is both diverse and similar. All of us use Modeling as our primary mode of instruction. We are all at least open to Standards Based Grading, if not practicing it. We are all already on Twitter and thus relatively connected to the larger physics education community. We all like to learn and to work towards increasing student learning.

On the other hand, we all teach in very different settings. Fran, Matt, and I teach in very different public schools in Minnesota, Iowa, and Pennsylvania. Kelly teaches at a private boarding school in Delaware  Leah at a private, girls,  Jewish high school in New York City, and Meg at a public charter school in upstate New York. That diversity of perspective has been awesome.

The Hangout

We typically meet on Thursday nights for about an hour, though that time frame is flexible depending on what people bring to look at. When we started we thought that despite teaching in different settings with different classes that we could try doing some common formative assessments. We developed a formative assessment for constant velocity motion, and a number of us assigned it to our students. We then took a week to look at the data for the first teacher who was already ahead of the rest of us. It was pretty fascinating that the students were using a particular reference, ‘the motion detector’, in answering the questions despite the fact that no detector was mentioned in the problem. It turned out they had done much of the development of the concept using motion detectors, thus they thought of detectors as a universal reference point. Turns out looking at student work informs instruction!

In the next week or two after we then looked at other teachers’ students answers, but there was a problem. The sheer amount of information from the Google Form was pretty overwhelming. We spent a significant amount of time just sifting through it and trying to get the other PLC members to see the same cell. We did some color coding, but didn’t have a very well-defined system.

A Different Way to Analyze Student Work

We fairly organically decided that it would be easier, especially because of very different pacing for our different classes, to simply have volunteers ‘bring’ student work to look at for each meeting. Thus whenever I give a quiz I scan or take a picture of some examples that represent common or interesting mistakes students made on the quiz. Others do the same. Not only do we get the chance to see how each others students are responding to similar questions (it really helps here that we all use, at the core, the Modeling Instruction curriculum), but we can discuss how to best help students avoid pitfalls and misunderstandings. A typical night starts with a check in on how things are going and, often, advice for someone who is struggling with something. Then someone posts a link to a quiz and we take a minute or two to look over it. Someone notices something, and discussion ensues. As discussion slows on one quiz someone posts another. There is no rule or defined procedure here, but it seems to work well.

Often these quizzes lead to discussions on instructional techniques. One week Kelly was sharing her thoughts on having students use vector addition diagrams rather than the traditional use of components, for solving force problems. She then opened a shared Google Drawings window and demonstrated their usefulness. I introduced this diagram to my kids the next day and was blown away by how much they liked it. Collaboration for the win!

Building Relationships

Since the start of our gatherings I’ve thought a lot about Kelly’s statement that it would make more sense with a regular group. As we’ve been meeting for almost half a year now, I have found that I’ve become very comfortable with the other members. It’s humbling and sometimes embarrassing to share work that your students produced that is not perfect. A great PLC meets those imperfections with empathy and advice rather than with judgement. We’re all in this together, and all students make mistakes. In fact, one thing that I have become more convinced of as a result of our meetings is that the very process of making mistakes is essential to learning. Lots of research in science education, physics in particular, points to the idea that in order to learn and retain scientific reasoning, students must first wrestle with the dissonance between their own thinking and scientific explanations. (citations needed, I know; call me out if you want and I’ll dig some up for you! Here’s a bit to tide you over.) Anyway, the point is that as teachers it is hard to open up and be vulnerable, but the so far my experience is that my learning about student learning has been very worth it.

One highlight for me was that when I was in the NYC area over winter break I was able to meet Leah in person for coffee. It is really fun getting a chance to meet someone in person whom you  previously only knew in an online environment! I look forward to continue to build relationships with my PLC, and I hope to meet more of them in person eventually.

Why G+ Hangouts?

G+ hangouts were a natural choice for us. We all had Google accounts already, and G+ allows us to video chat, share documents, chat on the side (which also helps in posting links to student work stored in Dropbox, Evernote, or Drive), and even to use Google Drawings or screenshare. G+ also allows for recording hangouts, but we have not done that as there was consensus that recording would  take away from the ‘safe harbor’ aspect of the meeting.  There are certainly other options to G+; the Global Physics Department uses an enterprise version of Blackboard  Collaborate and the Global Math Department uses Big Marker. We never even considered anything else, however, as G+ hangouts has performed as well as we need it to.

At the End of the Day…

What’s better about my teaching now? So far this year my PLC meetings have resulted in changes in unit placement, improvements in teaching specific topics, additions of representations to help student visualizations, improvements in my understanding of student misconceptions, and an overall increase in the big picture view of learning physics through a cyclic treatment of the various models (rather than treating topics as isolated units). I can only imagine what further meetings will lead to!

Teaching a University Course at the High School Level

I have the privilege of teaching a course that is articulated through the University of Minnesota. I have been wanting for some time to write about it, particularly because it has become an interesting mash-up of some cool physics ed stuff;

• Modeling Instruction
• Context-Rich Problem Solving
• In-depth study of content (as opposed to AP Physics B)
• Significant lab/writing component
• Standards Based Grading (sort of…you’ll have to read on to find out more!)

The course is called College in the Schools (CIS) Introduction to College Physics. CIS is a program run by the University of Minnesota where students take college classes, get college credit (complete with a U of M transcript), while being taught by high school teachers at a high school. CIS Physics is PHYS 1101W, where the W stands for the fact that students get one of their required writing credits due to the 5 lab reports written throughout the course.

I was first accepted to teach CIS physics as part of a four teacher pilot for the year 10-11 (the 2nd year of the pilot), and now the course has expanded to around 10 schools total, all in Minnesota. I have very much enjoyed the course as an alternative to AP Physics B, though admittedly the change to Physics 1 and 2 could render some of the benefits of CIS less potent. I moved towards CIS physics because I was tired of three aspects of AP B;

1. I felt like we raced through the material and, because of that, students weren’t learning to their full potential (we taught it as a first year course)
2. I felt there was no time for lab, and thus labs were few and far between.
3. Many students worked extremely hard only to fall just short on one single measure of their physics understanding at the end of the year.

CIS physics is a one semester course at the U, taught over a full year at the HS level. This decision was made because the course requires 6.5 hours of contact time each week (3 hours of lecture, 2.5 hours of lab, and 1 hour of discussion), which we cannot touch with 46 minute classes. I love, however, that even at the U, more than half the time is spent with students working rather than listening. My classroom is much more than half, but we’ll get to that in a bit.

Aspects of the U of M course

Lecture: U of M introductory physics courses run into the hundreds of students, and as such they have developed a system to manage aspects of learning physics while trying as best as possible to stay true to researched pedagogy. That said, lecture is still the content delivery method, and is given by faculty in the department. Students attend lecture three days a week for an hour each day. This component of the course is greatly reduced in my version due to my use of Modeling Instruction (MI). More on that in a bit.

Lab: The U of M developed a laboratory manual with 3-5 lab “problems” for each unit. Conveniently, many of these labs align well with MI, with the remainder providing good opportunities for verification labs. I love that I am expected to use almost half my class time for lab!

Lab reports: As much as I hate grading them, I like that this course has a technical writing component. I have received significant positive feedback from former students, both in regular and CIS physics, about their preparation for future lab reports because of my class. More importantly, I think it is important that students learn, generally, how to use data to make a logical argument. Lab reports also help me gain important insights on the reasoning skills and physics understandings of my students.

Discussion: This is the U of M’s main contribution within Physics Education Research (PER). The U’s PER group has done significant research into the use of Context Rich Problems solved collaboratively by groups of students.  This is an awesome part of the course, where students work in groups to solve difficult problems.

CIS Physics in my Classroom

The main difference between the U and my courses is numbers. They have hundreds of students per section, while (somewhat ironically) the CIS program limits our sections to 24 students. For me this has meant that I can effectively integrate a modified form of Modeling Instruction (MI) into the course, which largely replaces lecture (read more about why I use MI).Currently, this modified MI cycle, mashed together with some of the U of MN’s parts of the class, looks something like this;

1. Paradigm lab: The purpose of a paradigm lab is to introduce the concept at hand, usually by investigating a specific relationship. Kelly has lots of great examples of paradigm labs, and their connection to model building, here. This works very well with the labs from the U, as slight tweaking allows for use of ‘official’ U labs for paradigm purposes.
2. Conceptual aspects of model building: Though not universally true, I tend to start model building after the paradigm lab by looking at the conceptual aspects of the model. This tends to involve heavy use of the traditional MI worksheets and whiteboarding.
3. Problem Solving: This tends to start with a couple of days where students work through problems and I move around the classroom giving help where needed. Sometimes we whiteboard solutions, sometimes students just check their work and move on when they understand.
4. Context Rich Problem Solving: Students work on problems that are more difficult than those they can solve individually in the given time frame. Here is an example of a context rich problem that I wrote.
5. Verification Lab: Usually units end by applying the model to a situation to verify it’s ability to make successful predictions. These labs come from the U’s ‘official’ lab manual and are usually complex, yet at the same time give convincing results.

I would like to add a couple of things in the future as I revise and re-write CIS Physics;

1. Wow-factors that drive learning. I have recently been inspired by Shawn Cornally and his emphasis of using something awesome to inspire learning. I want more awesome.
2. Breaking the Model, as Frank addresses at the 7:45 mark of his TEDx talk. I want to provide more coherence between models, and part of that is addressing the shortfalls of the current model so we have a reason to move to the next.
3. Standards Based Grading (SBG). There is a 5-10% category that is flexible, per the U’s guidelines for the CIS class. This is because the course at the U changes with the instructor (grading and all), and often the category is participation-based. It has been clicker questions, notecard answers, and other things in the past. I currently wrap that 10% into my other categories (Lab reports, Exams, and Final; I don’t believe in giving participation points or grading homework, but that’s a different post), but next year I would like to use it for standards checks. Most of the exams are problem based with some aspects that require implicitly conceptual understand rather than an explicit display of that understanding. I plan to have weekly standards quizzes (which I already do to some extent) that address 3-4 standards per unit so that students are getting more feedback on those conceptual and otherwise scaffolding pieces that lead up to the exams. The quizzes would be 100% retake-able  and each standard would be graded on a binary scale: either they’ve got it or they don’t. It’s not full SBG like I would like, but I think it will really help students to know their progress before the big exams.

That’s my current and future CIS Physics class in a nutshell. Feel free to ask questions or make suggestions!

The Flipped Classroom and Student Dialogue (or, Why I Became a Modeler)

Recently I have become fascinated with the research around how students learn though dialogue. My favorite piece of quick evidence is Derek Muller’s TED application video where he presents his research about videos for learning.

You really should take the six minutes to watch the video, but the summary is that he tested two types of instructional videos; direct instruction and instruction through dialogue. Students who watched the direct instruction videos said they were clear and easy to understand, yet their test scores did not increase. Students who watched the dialogue videos said they were confusing and didn’t like them, but their scores increased significantly. Interesting.

Similarly interesting to me is the recent obsession in the education world with the ‘flipped classroom.’ There seems to be some evidence that flipping the classroom does indeed increase learning; my question is why. The article on flipping linked above has an entire section on how student-student and student-teacher interactions significantly increase with the flipped model. Is this the primary reason flipping succeeds? If so, then why the obsession with video lectures and programs like Khan Academy? Is the video piece even necessary? Before I dive into this I want to give you a picture of where I am coming from with all of this.

I have taken a long road to get to where I am today as a teacher. I started teaching physics in the fall of 2005 with very little knowledge of how students learn, particularly the vast amounts of Physics Education Research (PER) that has been conducted in the last 30 years since the development of the Force Concept Inventory (FCI). I started a Masters degree in 2007, and through the research for my thesis on inquiry in physics I stumbled upon the FCI. I pre-posted my students for the first time in the 07-08 school year. Though my average postest score of 47% is above a national average for traditional teaching of 42%, I was pretty dismayed. Really? After a whole year of physics my students can’t even answer half of the FCI questions correctly? Not ok.

My research showed slightly higher student gains with inquiry, and, particularly interesting, that the standard deviation of the scores shrunk. My interpretation was that the high end learners gained about the same, while the low end learners gained more with inquiry. That’s good. But it wasn’t enough. In 5 years, my scores never got above 50%.1

I knew my kids weren’t really getting it, but I didn’t know what to do about it. Enter grad school #2. I decided in the spring of 2010 that I wanted to learn more about Educational Technology, so I enrolled in online courses at Mankato State University. I decided to research clickers (student response systems) for one of my papers, and I stumbled upon Eric Mazur’s work on Peer Instruction (PI). PI is a technique developed primarily for large lecture clases. The idea is that a multiple choice conceptual question is posed, and students answer via clickers (though this can work with low-tech solutions like raising a piece of paper with the answer on it). Particularly if the distribution is evenly split, the instructor has the students talk to each other, and then re-answer. More often than not (in my own experience) the distribution shifts towards the correct answer. Mazur has some great research out there about how students are able to reason to each other better than an expert, thus their explanations often make more sense. More importantly, the process of the discussion is another form of the dialogue used by Muller, and my suspicion is that in this lies the reason for understanding gains.

The following summer a colleague from another school in Minnesota mentioned Modeling Instruction (MI) to me. Dialogue and Inquiry are both central to MI. The modeling cycle typically starts with a paradigm lab where students use guided inquiry to investigate a phenomena. From there the phenomena, or Model, is expanded and refined, often through White Boarding. The idea is that student interaction, questioning, and revising of ideas drives the learning. And it works.

So we have Muller and his video instruction with dialogue, Peer Instruction with dialogue in large lecture classes, Modeling with dialogue in the form of white boarding, and the general idea of flipping the classroom. Most of the praise I have heard about for flipping is that it provides more time for projects, problem solving, and other more interactive methods of learning than when the teachers ‘had’ to lecture during the hour. I have to wonder if the problem is simply that lecture doesn’t work, period? Does flipping work only because teachers who flip are using techniques during class that actually do help students learn? Do the videos really have anything to do with it, if they are just direct instruction?

I will say that with both PI and MI require that before the conversation takes place students should be familiar with the problem at hand. I recall research (but can’t find at the moment) that showed gains in understanding when students worked on a problem before it was used as an example in class. The standard MI white boarding process involves students first working on the problems on their own (often as homework), then comparing in their group, then presenting their agreed upon solution to the class for more dialogue. PI requires them to first answer with their own reasoning, then compare that to another’s. Do out of class videos serve this same purpose?

I don’t feel like I have an answer to lots of the questions I have posed above. However, the main point I want to get across is that I think it is silly to focus the flipped classroom conversation on what takes place outside of  class; the power of flipping (which I would then argue is really the power of quality instruction) is the changes that can be made inside the class to promote student learning. Let’s just focus on how students actually learn, then teach them guide them to understanding using effective methods.

UPDATE: Here’s another resource that discusses the use of dialogue in Physics classes, though some of the information is the same as those listed above. The Art (and Science) of  Questioning via Clickers (podcast).

1 This is for the general level physics classes. It is noteworthy that my advanced classes have scored significantly higher. In the two years I have been testing them they have posttest averaged around 70%. Though this number is much higher, I am not satisfied with what would equate (in a standard grading scale) to a C- average, particularly with advanced kids. I do think it is interesting, however, that with essentially the same type of instruction these kids score so much higher. It is probably a combination of three things, in my estimation. 1) Higher scientific reasoning skills, which makes me wish I had given Lawson’s Classroom Test of Scientific Reasoning. I don’t want to over-test though. 2) More depth, both mathematical and conceptual, in the advanced class.   3) The idea that students who make it to the advanced classes are those who are able to have more internal dialogue and compare what they are learning to their own understanding without the need for the external dialogue. This may correlate to number 1, though.

What is a Model?

(The image above is part of The Modeling Comic that one of my students created last year)

I’ve been struggling for some time with the idea of a Model (within the construct of Modeling Instruction). Back up with me for a bit. In the summer of 2011 a colleague who teaches at another school in Minnesota introduced me briefly to Modeling Instruction. Being who I am, that is, someone who loves to learn, I promptly found a community of modelers on Twitter and learned quite a bit from blogs by Kelly O’shea, Frank Noschese, and Scott Thomas. I found out the hard way, however, that I had a fairly limited view of what a Model actually is.

In my excitement to get started Modeling I got stuck in a rut of thinking that 1) equations were physics (a statement I would never say to students but found myself thinking), and 2) that a model was an equation. For example, the CVPM model, to me, was x=xi+vt. Through the process of attempting modeling throughout the year, failing some, succeeding some, reading blogs, and finally taking the Modeling Instruction training this summer, I think I have a much better picture of what a Model actually is.  The training was instrumental in my formation of a definition of a model, as was Sam Evan’s post on what it means to model. So let’s get to the good stuff.

I believe that a Model could be defined as a particular phenomenon that is described using a set of representations (diagrams, equations, descriptions, charts, graphs, and more). These representations should produce accurate and reproducible predictions for and explanations of the phenomenon, within the limitations of the model. This makes it very hard to use a representation to describe the model, because the model is about the phenomena, not the representation. The Constant Velocity Particle Model (CVPM) is not linear position vs. time graphs nor equally spaced motion diagrams. CVPM is a type of motion that occurs when neither speed nor direction are of an object are changing.

To demonstrate what I think a model is in terms of MI, I am going to use a model that is well known to the science community; the Bohr model.

The Bohr model is a the idea (concept? model?) that the nucleus of an atom is surrounded by electrons whipping around in fixed orbits.

The Bohr Model was proposed by Niels Bohr in an attempt to explain emission spectra, which it did fairly well for Hydrogen. Representations for The Bohr Model include the planetary-style diagram shown above and energy level diagrams (below).

Two notable equations are used to represent The Bohr Model; the allowed Bohr radii formula

and the allowed energy levels known as the Rydberg energies

.

The Rydberg energies also have a more general form for atoms with more than one proton in the nucleus;

.

We have a number of representations above that attempt to describe the model. The cool thing, I think, in using The Bohr Model as an analogy for how Modeling Instruction is structured is that the model can be broken. That is, the model is useful under certain conditions, but must be modified when extending beyond those conditions. It turns out that the phenomena of atoms is more complex than the relatively simple Bohr Model had suggested.

This is actually a good analogy to CVPM leading into the Constant Accleration Particle Model (CAPM),  as CVPM is really a subset of CAPM for acceleration=0. The Bohr model works well for hydrogen because there are no other electrons interacting with the one that is ‘orbiting,’ thus Bohr’s assumptions work well; as soon as you add more electrons, the predicted emission spectra differs from the actual spectra and the model is broken. Using constant velocity to try to solve more complex motion problems where acceleration takes place is a bad idea, because the assumptions for CVPM no longer hold.

Still, because students need scaffolding and baby steps, it is pedagogically appropriate to teach CV before CA as a stepping stone; one could just teach CA, but it would be a bigger step to expect students to take. Similarly, the Bohr Model is the first step toward understanding quantum mechanics; in fact, it was a giant conceptual leap that allowed those who followed after Bohr to expand the model into something more complete.

I hope I have given some credence to what a Model is within the framework of Modeling Instruction. I very much appreciate any feedback you can give me!