Tales from a Secondary Implementation of ET: Part II

Hi again,

In a previous post, I discussed some of the principle benefites and possible limitations that might be associated with using ET as an instructional tool within the context of a mathematical college physics course (specifically an algebra-based course). I also detailed my experiences in leading my students through the first four steps of Moses' algebra project (Field Trip, Pictorial Representation, People Talk, Feature Talk). In this post I will discuss my experiences over the next two classes during which I formally introduced my students to Energy Theatre.

The Five Questions:

As I mentioned, I opened up Friday's class by readdressing the 5 questions developed during "feature talk." After reviewing these questions while writing my previous blog post, I realized that many of them (e.g. "what forms of energy are there?", "is energy being transferred?", and "where is the energy located?") were not a far cry from the questions that we might expect an expert or "good student" to ask during a formal energy-based problem solving session. Thus I decided to use these questions as the basis in which to anchor a mathematical analysis the way to bridge ET to the mathematical representation.

As part of their homework, my students had to come up with a complete description of a mousetrap cart using their 5 questions as a guide. By framing the previous night's homework as a test for their questions, I was able to lead a fairly meaningful discussion on what might need to be altered. Section C, for example, decided that "what does energy do?" wasn't terribly helpfull. Meanwhile, section B decided that "is energy being transferred?" should be spun off into "is enery being transformed?" By keeping track of the alterations that each section made, I hoped to instill a sense of ownership in my students.

I opened thenext full day of ET by again readdressing my students' 5 questions. Now that my students had had some experience in ET, I asked them to begin brainstorming, for each question, what types of answers they might expect. All three of my sections had previously generated a question along the lines of "what types of energy are there?" and I had them use this as a starting point. The result of this brainstorm was a list of different types of energy (e.g. kinetic, potential, spring, thermal, chemical, etc.). My sections also all had questions along the lines of "how would we measure the energy?" this question was used to generate a list of possible evidence for the different types of energy (e.g. is there movement? temperature? stretching or compressing springs? etc.).

With these lists in hand, I pointed out that they could also be used to address some of the students' other questions (e.g. "how much energy is there?", "is energy being transformed?", etc.). Again, by having my students continually refine their questions, I was bringing them to a point where they would be able to conduct a mathematical analysis with real teeth.

The Theatah, The Theatah

After our initial reassesment of the 5 questions, I introduced ET and we spent the rest of the day performing ET for the mousetrap cart. The students in my classes had been working in groups of 3-4 up until this point, but I merged the groups in each section into two super groups of roughly 12 students each (my smaller section had 9 each). Some groups were able to finish by the end of class while others needed a few minutes at the beginning of the next to finish.

On the second day of using ET, I gave my students three new situations: My pushing a 2 kg weight across a rough, horizontal surface at constant speed; An activated heat pack; and an activated cold pack. This final situation turned into a homework assignment for the students to practice using Energy Tracking Diagrams. Having spent the first day working out what exactly this ET thing was, my students took to these new situations rather easily.

The bigest difficulty that I encountered was getting my students to figure out exactly what I was asking of them. One group, for example, tried to create a sequence of "pictures" where the ropes represented an initial state and a final state. They kept the number of students constant, but each student was only featured in on "instant."  I also had to push many of the groups to come up with ways of distinguishing different types of students (kinetic, thermal, etc.). While many groups figured out different types of movement (my favorites were miming a chemist pouring chemicals for chemical energy, and jumping up and down for kinetic energy), some simply called out "I'm kinetic energy." One group tried to use different regeons within their rope loop to indicate that they were different typed of energy.

A further difficulty which I am beginning to notice now that we are fully involved with mathematical representations is the fact that ET (and ETD's) track the full "trajectory" of energy, while standard mathematical approaches only look at the initial and final states. I'll readress this point as I discuss bringing ET into math. I'm not sure how this will present itself on a mathematical analysis level, but many of my students have expressed some confusion about relating energy tracking to the mathematical statements, dispite being largely able to handle the math.

One logistical difficulty that I encountered was that there were too few of me. Since I had devided my class sections into two groups each, one had to perform out in the hall while the other used the class space (there were too many desks for both to be in the class). While I was able to wander back and forth and ask probing questions about the energy flow and about the ET representation, I got the distinct sence that the group whom I was not immediately attending to were busy in off-topic discussions. This seemed not to be a large issue during the I-RISE since there were three instructors, as well as many observers who functioned as authority figures. The in-service teachers also had a more developed sense of focus and responsibility.

Once my students got the hang of ET, they were able to easily act out the additional situations of the heat pack and pushing the weights. Many of them also told me that they enjoyed the activity and one asked from where I got the idea!

Energy Tracking Diagrams

On the second full day of ET, after my students had acted out the first two ET situations, I introduced them to Energy Tracking Diagrams. Since this was yet a further abstraction of energy flow (an abstraction of an abstraction, really) I demonstrated ETDs for the first ET situation which my students had just enacted: my pushing the weights. I then had my students create ETDs for the heat pack. For homework, I had them create ETDs for the cold pack.

Two immediate benefites I found with ETDs was the ability to "homework-ize" energy theatre and the ability to have students work in smaller groups while still doing an ET-like activity.

Beyond these benefites, however, I found that my students actually had more difficulty with ETDs than they did with ET. Specifically, they were confused about how to represent the object, how to break a complex process into a few descrete stages, how to synchronize energy transformations with energy transfers in their diagrams, and which pieces of energy turn into other pieces of energy ("does K turn to T or is it the C that turns to T during this step?"). Many of these issues did not present themselves during ET. Another difficulty which I observed was that, while conservation is a built in consrtaint in ET, my students were very casual with the number of energy letters in their energy tracking diagrams.

In the end, while ETDs bring many benefites, I felt that spending time coaching their proper use would detract too much from the time I wanted to spend building up a mathematical formalizm. While ET provided a great kinesthetic introduction to energy and energy flow, ETDs seemed to add too much complexity. Perhaps there is a way to succesfully and meaningfully integrate these into a math-based-physics curriculum, however at the moment am not able to.

Bridging ET to Math

I closed out the second day of using ET by formally introducing the law of conservation of energy (Del_E = W + Q + Other energy inputs). I built up to this by generating a law for the conservation of students (Del_N = #Students who cross over a piece of rope). With this equation in hand, it was only a small jump to energy conservation.

The next difficulty was to introduce definitions of Work and Heat and to introduce the mathematical formulations of the varyous energy forms. This was one of the major points of departure from ET; while the theatre could only represent kinetic energy, say, as a group of students making running motions, in a mathematical representation we have to use a particular formula.

Over the next few days, I continued to draw upon the list of questions which the students developed and refined over the course of the week as a basis for mathematical analyses. When I and other expert problem-solvers approach problems from an energy standpoint, we generally have a list of questions we  try to address: "what is the system?", "what elements of the system are associated with energy?", "are any of these changeing?", "Is energy being transferred to or from the surroundings?", "if so, how?", "Are there convenient initial and final states to choose?", etc. Each of these questions addresses an aspect of setting up a mathematical solution and many of them were questions which the students needed to address when performing ET. Thus, while the conservation of students inherrant in ET makes an excellent conceptual bridge to a mathematical representation, the act of addressing these questions makes an excellent bridge of practice to using math.

Finally, I mentioned before that one other point of departure from the ET and ETD representations of enery and the mathematical representation is that ET and ETDs attempt to track the full "trajectories" of energy while the cannonical mathematical approach only looks at initial and final states. Again, my students haven't displayed any problem-solving difficulties apart from the standard abilities of this particular population, however some have expressed confsion about this point on a recent "quiz" question "list one thing that you're still confused about."

Some final thoughts:

Overall, I thought my students liked doing energy theatre. Two things that I feel that they have very clearly gotten out of it is a more tangible sense of conservation, and the idea that energy can change forms. Once I begin to discuss energy dissipation and efficiency, I hope to use the fact that students in ET tended to spread out and become thermal. This was an effect that some of my students explicitly pointed out to me and, I suspect, others noticed as well.

My experiences at I-RISE and what I observed

My final presentation, at long last:

I examined when the teachers acted as expert knowers and expert learners.

My patronus is a lynx and I'm awesome at saving scared people with it.

A bit about little old me.

These are my assumptions about I-RISE.

Why I think all of these good things happen in I-RISE. It's all about letting teacher engage in the creation of knowledge.

There are a variety of mechanisms that lead to the creation of these positive experiences.

So what do I really mean by expert knowers and learners? This is my operationalization of the terms.

My analysis of I-RISE is based in the concept of communities of practice.

Additionally, distributed cognition helps to inform my analysis of the cognition that occurs in I-RISE.

How tools can transform cognitive tasks.

My analysis specifically examined interactions between Akbar, Sarah, Nicole, and Jessica.

The idealized version of what I felt I had observed.

The relationship I hoped to find between teacher roles and the progress of their model building.

What I actually saw all four teachers doing.

A look at just the two teachers that I believed to be the most influential or telling of the group activities.

The three segments in time which I decided to focus. I felt that when one person deferred to authority that the others in the group stopped co-creating knowledge and primarily became passive listeners.

First I wanted to share an early time clip in which the primary deferrer to authority leaves the group and we see the group engage in productive co-creation of knowledge.

Summary: I-RISE Rocks

Gina's Congress Presentation

Here are the slides and video from my I-RISE Congress Presentation.  My apologies for taking two months to get these up.

 During my two weeks at I-RISE, I explored how the rules of Energy Theater affected teachers' representations of energy.

To start off my presentation, this is my spirit animal- a baby panda!

I attended I-RISE in the transitional summer between undergraduate and graduate studies.  I came in with some experience in interaction analysis and discourse but I still had a lot to learn.  

I am generally interested in the studying the many facets of how students experience their physics classes.  In particular, I enjoy studying open-ended, constructive learning environments like I-RISE.

I looked at the rules of Energy Theater and how they mediated the teachers' discussions about designing energy representations.

In this first clip, teachers are negotiating about their energy theater for a mousetrap car.  We see that rules play an important role here.  They first acknowledge that they are breaking representational rules.  Later we see that they realize they are not one unit of energy, which violates conservation of energy.  

In the next clip, the teachers are drawing out the energy story for the Gaussian Gun.  They are attempting to reconcile their knowledge that a small amount of energy is dissipated with the rule that energy can only exist in equal sized chunks.

Rules and norms came up in other areas as well.  With more time, I would have explored how Todd got the class on board with the MFer representation for the Gaussian Gun.  It would have also been interesting to study rules and rule-breaking of the social responsibilities outlined on the first day of class.  

In conclusion, I-RISE was awesome! 

Tales From a Secondary Implementation of ET

Energy Theatre, as we all have witnessed, is an incredibly salient conceptual model of energy and energy flow within a system. Not only is it used to help in-service teachers develop a deeper understanding of energy, but as a Physicist, it is fun for me to think about how ET might be used to represent ever more esoteric situations (I've had many conversations with Abby, for example,  concerning entropy and energy degredation, and I think I may have a satasfactory way, albeit an impractical one, to represent the negative potential energy. More on that later...) But this all raises the question of how might we use this tool in another instructional context, specifically college physics students.

As I am currently teaching three sections of college (algebra-based) mechanics to students, I thought I would try using Energy Theatre to introduce my students to the concept of energy. And I thought I'd blog about it.

My goals for these posts is to spark discussion about A) is ET something that could reasonably be used at the college (or HS) level and B) what modifications would need to be made, either to ET itself or to the instructional contexts in which it is introduced, so that more naturally fits in a college-level physics class. Secondary goals of mine are to provide some guidence for anyone who may be themselves using or prepairing to use ET in a college setting.

This first post will focus on some of the specific benefites that ET would bring to a college course as well as some of the difficulties that I expect to encounter. I will also provide a brief overview of my first day, which led up to, but did not involve, Energy Theatre. My next post will likely come after my class has mostly moved into mathematical representations of energy.

I should note that none of my students have signed consent forms, nor do I consider them to be participating in a formal study -- Thus I will not provide any information beyond anecdotes of my own experience.

Benefites of ET:
Let me first list benefites of ET. These will be familiar to most. I list them because they support the more formal model of energy encountered at the college level.

• Conservation of energy is built into the representation.
• Energy is represented as having different forms.
• Energy is represented as having different locations within a system.
• Energy can change both form and location.
• Deredation is built into the representation in-so-far as energy tends to become thermal energy and the thermal energy tends to spread both within a system and into the surroundings. 
• Quantization is built into the representation.

Restrictions of ET:
Let me now list some of the restrictions that ET will impose within a college-level instructional context. For each of these, I will briefly describe a possible soluton:

• Energy Theatre lacks a mathematical component.

This is perhaps the most salient draw back of using ET in a college physics class, but hope is not all lost; many aspects of the mathematical representation arrise naturally from ET. The statement of energy conservation, dE = W + dQ, for example, follows directly from the simple conservation of students. Additionally, the identification of different forms of energy and energy transfer that are featured in the mathematics is also present in ET. What doesn't follow from an ET representation are the specific mathematical formulations of the various types of energy (e.g. mgh, 1/2mv^2, etc.) and energy transfer (e.g. FdX, PdV, TdS, etc.). I will have to explicitly introduce these.

• Although in principle, ET can represent the relative amounts of different types of energy, in practice (i.e. using only 10 students) ET lacks a suitable way to describe this. 

When looking at certain cannonical situations ( e.g. orbits, electron excitations, chemical proceses) it is important to look at relative amounts of energy (comparing kinetic to the total, for example, or comparing the total to kT). I suspect that with the introduction of mathematical relations, this will not be a significant problem.

• Potential energy difficult to represent in ET both because it is a negative quantity and because it is not located in an object.

For the second issue, Rachel has suggested allowing the students to use fields as part of a system where energy can go or allowing the students to simply use the system as a whole. I expect that I will have to make use of one of these two modifications as I will want to maintain a certain mathematical rigour. For the first issue (negative PE), I have an intriguing if highly impractical solution: If I allow students to become rest energy in addition to chemical, kinetic, etc. then potential energy can be represented, not as an additional type of energy, but as a deficit in rest energy (for example, students who were rest energy could become kinetic energy). Obviously, I would run into the issue of relative amounts of energy to pull this off. Beyond this, I haven't figured out a satisfactory way of introducing negative energy. Since most situations near Earth's surface can be analyzed using a positive potential energy, perhaps I can get away with only treating those situations.

• What is there to grade (beyond participation)?

Rachel suggested that I also introduce energy tracking diagrams as a gradeable proxy. Good idea!

• Finally, while instructors of the in-service teacher workshops can afford to present energy as a sufficient picture of the world, my implementation will come in the context of a physics course which includes forces, particles, momentum and kinematics. Thus I must treat energy as a necesary, but incomplete picture of the world.  

A Walkthrough of Day 1:
First I should note that the population of students I am teaching are, by and large, sophomore and junior life science majors, though there is certainly a spectrum. Thus many of these students enter my class with an existing familiarity with chemical and biological concepts, such as photosynthesis, electrolysis, chloroplasts, ATP, and photons. Additionally, these students have likely had physics as recently as highschool, and thus already have a passign familiarity with names like "kinetic" and "potential" as well as their mathematical formulation. Also, they are college students who "have" to take a class as opposed to in-service teachers who volunteer to develop their understanding. In other words, there are motivational and attitudinal differences.

For the first day, I took my students through the first four steps of R. Moses' algebra project. First, I led my students on a brief nature walk outside of the physics building. They were instructed to find examples of "energy doing what ever it is that energy does."Because many students are life-science majors, many people identified photosynthesis, wind energy, and solar energy. Many students also identified motion or kinetic energy. The nature walk fo my 2nd section happened to coincide with recess for the neighboring elementary school, so my students got to use kids running around and playing on swings as examples of energy (Says one student: "those students running around have lots of energy" before promptly sitting down on the grass).

This process took about 10 minutes before discussions strayed off topic. The next step was for the students to come up with diagrams of what they saw. Interestingly, there were very little "strobe" immages. This contrasts with what Rachel et al. have seen at this stage of the workshops. Rather, my students drew single pictures of objects (the sun, a tree, a leaf) and had arrows or other symbols indicating an energy transfer of some sort. I was actually quite impressed with these picutres since they included many different processes and often explicitly labeled different types of energy.

For the "people talk" step, I had to push a lot of the discussion about common elements accross the students' pictures. I suspect that this was due to a combination of the nebulousness of this task and my studnets being college students.

For the fourth step (and the final one of the day), "Feature Talk,"  I had my students brainstorm "a list of questions that if answered, would provide the most informaiton about what energy is doing in each (or any conceivable) scenario." (this was the same prompt given in the EP workshop). My students generated many great questions and each section narrowed down a top 5 (presented by section):

1. How is energy measured? How is energy transformed? How much energy is there? Where did it come from/ where did it go? What forms of energy are there?
2. Where did the energy come from/ go? How can we measure it/ how much energy is there? What types of energy are there? Is the energy being transfered? What is the form/ state of the object? 
3. How is the energy measured? What forms of energy are there? How is the energy transfered? Where does the energy come from? What does the energy do?

Many of these questions are excellent! Though some of them are quite big or too philosophical. (I had to dissuade my 3rd section from using "what is energy?" on the grounds that it wouldn't add anything to an analysis of a system). I told the students that these would remain provisional lists and that they should feel free to modify them if other questions occured during our exploration of energy.

I left my students with the following homework assignment:
Watch the following video of a mousetrap cart and generate as complete a description of the energy within the cart as possible. Use your section's list of questions as a starting point, but also consider this a test for the list -- are there other questions that you find that you need to ask? Are there questions that you find that you don't need to ask?
Be as thorough as you can; be prepaired to use your description in the next class.

... this, of course, will form the basis for the students' first encounter with Energy Theatre.