In my intro physics course, we have many table-size whiteboards for students to work on, but the room I’m in also has 10 large whiteboards on the walls. Today, I told students to stop using the portable whiteboards and to start doing problems on wall boards. This did several amazing things.

- It allowed me to easily see from across the room whether or not groups had simply gotten stuck or were making progress.
- It allowed all the students in a group to have access to the board without anyone having to look upside down or become boxed out.
- It provide students much more space to write and draw, which dramatically boosted organization and clarity of their work.
- It helped me not hover over students when I came around, lending more agency and authority in their direction.

Ultimately, all of this helped me more quickly and accurately assess student progress and also provided them with a more effective collaborative space. Students really liked it. I really liked it. I think I’ll keep it, for now at least.

Aside: I’m becoming sold on energy pie charts.

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Brian,

This is a good point. I’ve also thought of driling holes in the top of the whiteboards and hooking them on the walls so students could write on them standing up.

Talk more about the pie charts?

First, I had my future physics teachers drawing energy pie charts on Tuesday Night. At first, kinetic energy was only the kind of energy (shown in the pie charts) and work was a way of talking about the energy that flowed in or out (shown by arrows) that explained the change in energy (or change in size of the pie chart). I modeled for them how to draw a pie chart for block speeding up along a frictionless surface because of a push. I talked about it in terms of me giving energy (the snickers bar I ate in front of them) to the chair.

Then I asked them to draw charts for a block sliding on a frictionless surface with no change in speed and block being pushed at constant speed on a rough surface. It was a big deal to talk about why the energy pie charts were the same size for both of these, but how the reason for the constant energy (and pie chart size) was different across the situations. Talking about no energy flow vs. not net energy flow.

Then I had them do a block sliding across a rough surface to a stop vs. a block sliding up and then back down an incline. We spent a good amount of time talking about why friction took energy away, but why gravity took energy away and then gave it back. This led us to talking about positive and negative work more specifically. But more importantly, this eventually led us to talking about why we physicists sometimes choose to think about some work out (a negative quantity) as potential energy gain (a positive quantity). Gravity seems to give that energy back more easily than energy taken away from friction.

I then had modeled for them how we could re-model the ramp situation with energy pie charts that included both KE and PE in the piechart. The last thing I asked them to do was draw a KE-only pie chart for a block sliding up and down a ramp with friction, and then a a KE-PE pie chart for the same situation. This was hard, but very fruitful. The best part of the conversation was around how big to draw the “work” arrows showing the energy flowing in and out at various points. They had lots of questions about how much energy was flowing in/out right at the top.

At some point in the night we were also talking about energy storage and energy transfer in analogy to savings and checkings accounts, and withdrawals, deposits, and transfers. Checking account was like KE, and savings account was like PE. We didn’t talk about negative energy.

Two days later, I had my intro physics students do it, but we had to start from KE/PE perspective, and use those piecharts to help us write down equations. It was by far one of the easiest days in terms of students (1) having somewhere to start with problems and (2) them being able to write down equations that made sense to them. It also afforded some interesting reasoning…largely in terms of “fractions”, I think afforded by pie chart. For example, several groups, instead of calculating initial and final PE for a roller coaster around a loop problem, they just said, “20 cm is 1/4th of 80 cm, so there must be 75% of the energy left for KE at the top of the loop.

Thanks, I’m enjoying thinking about this. I have not used pie charts myself and am interested in figuring out how they compare to my own favorite representation. You said arrows show the energy flowing in or out of the system of interest. Is the energy explicitly represented, i.e. if there was kinetic energy in the box does it then get shown outside the box? Or does the box-pie just get smaller, showing that there is now less energy in the box?

Is a work-arrow the same as any energy-flow-arrow?

By “gravity took energy away and then gave it back” do you mean that gravity took away kinetic energy, but gave back gravitational energy? Or do you mean gravity took kinetic energy away on the way up, then gave it back on the way down?

I definitely don’t think that pie charts tell the whole story, but then again what does? But I think they do seem to have some strong affordances as a starting place. It got us going somewhere. For that reason, what was explicitly represented or what a representation distinguished (or didn’t) changed a lot from first 10 minutes to the last 10 minutes with my future physics teachers.

I just set some of the rules for drawing pie charts:

Size of pie chart shows how much total energy is associated with the system (or object) of interest

Labels in the pie chart (can) show what kind of energy there is

Arrows can be used to show energy flowing in or out of the system of interest.

Then were off, discussing situations.

Throughout the hour:

We argued about what rules meant, and how and where things should be labeled. Our labels evolved and changed… what arrows meant changed, and whether the length or direction of arrows were significant changed.. whether or not arrows showed was currently happening or what happened in the intervening time to the next pie chart “snap shot”. What labels could be or should be in the pie chart changed. Whether or not the slices of the pie chart should be qualitatively correct… etc. How arrows should be drawn was discussed—from pie chart to pie chart, or away and towards pie charts. Should we label the flow of energy as Work or Energy, or label at all.

Some of these things we resolved, but much of it we didn’t.

It was much different with the intro physics course, where I really have to get my students somewhere specific because someone will test them in very narrow ways on an exam in the near future. For them, the piecharts were really a schematic for organizing some very limited forms of thinking that would help them thinking about how initial, final, and work-flow related energies relate. In that game, there was PE and KE in the object of interest, and non-conservation work was how KE was put in or taken away from the system.