Today, Brian Carpenter tweeted the following

While I’d like to say this was intentional on our part in planning this gathering, it was more a factor of never really having tried something like this before and not knowing fully what to do, plus a bit of being to busy to really sit down and plan out detailed schedule of every day. But I think Brian is right, and I think it is important to think about how to bring some planned serendipity into any professional development opportunity, to say nothing of bringing this to the classroom.

### SBG discussion

While Standards Based Grading has been a frequent topic of conversation at our gathering, we decided to devote this morning to trying to hold some sort of discussion that might allow people to join us online. After working out some of the technological kinks, and a quick offer of help from Andy Rundquist, we brought the chat into illuminate and had 5 or so teachers from all over the east coast join in. Andy was also kind enough to record the conversation and archive the transcript and you can find both at the Global Physics Department.

The talk is definitely worth checking out if you’d like to hear some explanations on what SBG is, and then many different perspectives on how to implement it, along with advice on selling it to students, parents and administration. It’s also totally worth it to hear Kelly describe her revolutionary approach to semester exams and how she calculates the final grades—seeing what her students are able to accomplish under this system is truly amazing, and a great goal for me in my own teaching.

### Post game analysis

To me, the highlight of the day was a discussion of the idea of post game analysis, which began with Matt Greenwolfe asking us what master chess players (and athletes) do differently than lesser chess players. Matt said that one of the biggest differences is the the time and focus they bring to post game analysis. Chess players can spend hours after a match replaying the game in their heads, looking for the places they made mistakes, focusing on understanding those mistakes and how to avoid them in the future. Professional athletes do the same thing with game film. But developing or novice athletes tend to spend a minimal amount of time seriously critiquing past games, and when they do they tend to avoid or dismiss their errors and look only at their strengths, which can significantly hamper their improvement.

Matt then discussed how he’s trying to improve a number of his modeling discussions by focusing on drawing out more post game analysis—during discussions having kids get up to add an idea or a diagram to the post game analysis board, and after completing a deployment lab, stopping the class and asking them—”What is the post game analysis here? Where are the important mistakes you made in completing this lab, what are the key moves to overcome those mistakes, and what are the big understandings you should take away?”

We took this idea even further thinking of how you could, during lab, encourage students to focus on capturing “highlight reels” of mistakes and breakthroughs to share in postgame discussions. Frank went on to describe how he does something like this after assessments, where students must self record their scores on the assessment and then reflect on the mistakes they made and their plans for overcoming them.

It seems to me that bringing the sports/music/hobby metaphor to tie together all of these experiences with a bit of metacognitive discussion might really help to improve how students see the benefit of doing this work. Even the most novice 9th grade football player can tell you exactly how and why you should be watching game film, along with specific strategies for getting the most out of it. Helping students to see this connection better in the classroom seems like a great idea to me. This also seems to be the perfect answer to the “I’m not sure what I should get out of this” statement that crops up from time when students simply observe modeling discussions without much participation.

### Diagram tips and tricks

We had a number of discussions about helping students to see more connections between the diagrams they draw in physics and see how many diagrams are in fact derivative of one another. One particularly important diagram is the system schema (and we even discussed if this would be better, since most students don’t know what a schema is, to call these interaction diagrams).

Here’s the system schema for a book sliding across a table with friction. I learned you can improve these diagrams by adding labels to each of the interactions to indicate the force they’re associated with.

Then we moved on to talking about LOL (energy diagrams) and Matt finally cleared up my misunderstanding of the difference between LOL energy diagrams and pie charts. Pie charts show the evolution of energy transfers throughout the system, while LOL diagrams are focus only on initial and final states. Also, contrary to my previous understanding, pie charts can be used to address systems where the total energy changes—you just make them bigger/smaller as energy is added or removed from the system.

Matt does a few extra things to make sure his kids get a really deep understanding of energy:

• Students must draw energy pie charts above the LOL diagram to show how energy evloves.
• Students must solve each problem using at least two different systems.
• Finally, we discussed how you could really just use the the system schema in the LOL diagram to also show energy flows with block arrows. Here’s an example:

Let’s consider a block being pushed by a hand along the table with friction, starting from rest. Start with a system consisting only of the block. Here’s how the combined LOL/pie system schema would look.

Pro tip from Kelly: Place an ‘x’ in any column that you’ve thought about and know is zero. It lest you and the teacher distinguish between the 0 you know you understand, and you unintentionally not writing anything and the teacher mistaking it for understanding.

Now here’s the same situation, but for the system of the hand, book and block.

Notice that now we need chemical potential energy in order to account for the energy in the system, and there are no energy flow arrows, since all of the energy flows are internal, the total energy of the system does not change.

Constructing diagrams of this level of detail and synthesis will be a significant challenge for my students, but it also seems like a very worthy goal.

### Teaching fields and the inverse square law

Matt showed us this most excellent diagram that explains the synthesis of all fields (electric and gravitational):

This diagram shows all the connections between concepts of forces, fields, potential energies and potentials. Across the left side, you have vector quantities Force and Field. Across the right side, you have scalar quantities, potential energy and potential. Across the top, you have properties of the object in the field (force, and potential energy), and across the bottom, you have properties of the field itself (field and potential). Between the corners you have the ways of transitioning from one to the other, and you can present the transformation between vector and scalar quantities with a varying level of mathematical complexity:

• Algebraically: (divide by $-r$ to go from $V$ to $E$
• Graphically (find the negative slope on the V vs r graph).
• Calculus: $E=-\frac{dV}{dx}$
• Vector Calculus: $\vec{E}=-\nabla V$

We also shared 3 different approaches to teaching the inverse square law

• Kelly has the students think about the motion of the moon, and asks them which model describes the motion of the moon. Students argue whether it’s PMPM (projectile motion) or CFPM (central force motion) and eventually, they realize it’s both.

Then they they talk about some of the ancient experiments you can do to find the distance to the moon, and using this and the lunar period of 28 days, she asks students to find the acceleration of the moon. Since this motion is PMPM, they also realize that this is the value for local g at the location of the moon.

She then makes an argument that g on the surface of the earth is $9.8\;\frac{\textrm{m}}{\textrm{s}^2}$, and at the location of the moon, it’s $2.72 \times 10^{-3}\;\frac{\textrm{m}}{\textrm{s}^2}$. She then wonders how the two are connected.

The students figure out how many earth radii away the moon is (60), and then she asks them to divide the g on the surface of the earth buy 60, but there isn’t a match. She asks them to divide it again, and boom—you get a match.

This is an awesome moment, since it shows Newton’s big realization wasn’t that all things fall. His moment with the apple was probably more like a series of reasoning about what happens to the apparent size of the apple as he holds it further and further out, and eventually he kept to the idea that the force that pulls the apple to the ground is the same that keeps the moon in orbit.

• Matt has the students use a month’s worth of data from Project CLEA on the location of the 4 major moons of Jupiter, and plot a position vs time graph. Students see a sinusoid, and measure the period of the moons. Then they can discover Kepler’s 3rd law relating the radius and period $R^3\propto T^2$, and combining that with Newton’s second law shows them that the net force acting on the moons must change as $1/r^2$, and then they argue that N3 requires symmetry, and so you must have the product of both masses in the numerator.
• Frank does a nice virtual experiment using a Phet-like simulation online. Hopefully this will prompt him to share the link.
• I have my students do an open ended analysis with spreadsheet of data on all of the objects in the solar system, trying to discover relationships between various quantities. Eventually, they discover Kepler’s 3rd law, from this and use N2 to find the inverse square law.

There was some discussion about whether all students can handle the abstract reasoning required by the modeling curriculum, and the efforts of many schools to push more and more abstract thinking into lower grades, and whether some students might be too concrete in their current thinking to be ready for some aspects of the modeling curriculum. It was emphasized that concrete thinking isn’t a learning style, it’s more a state of cognitive development, a la Piaget.

We also discussed how to identify these students and two of the best resources mentioned were:

### Other quick tidbits

• Two really cool ideas for CVPM (Constant Velocity Particle model projects):
1. From Matt: Do a Mars Rover simulation using 2 buggies. Construct and obstacle course and use the buggies to serve as models of the mars rovers. Students can send commands to the rovers (turn, move forward, stop) to the buggies, but they must also figure out the time it takes for signals to travel to mars and factor this in (you could then write a simple program to contol when students are allowed to send signals to change the motion of the buggy).
2. From Rosalind: Have students write a proposal for adding a walking/jogging trail to a local park. Include places for stretching/exercise, then have them compute average velocity along the trail for various levels of exertion (running, walking, jogging).
• I got past my instant banning of the word deceleration. Other teachers helped me to see that often, asking “Could you clarify what you mean?” can help students both see the ambiguous nature of the word deceleration, and at the same time, show us that they do understand the motion of the object. Somewhere, I think Brian Frank must be a little more happy as I’m trying to find ways to build misconceptions into positive things.
• Kelly is an organizational genius. Since her classes don’t have a textbook, she gives each student a binder, preorganized with index dividers and the first few units already copied as booklets. Students are charged for these supplies, and since they are far cheaper than a \$150 textbook, they wind up saving a bundle. Her binder is really a thing of beauty:

Later this evening, our conversations switched to discussing the future of the modeling movement, and education reform, and Khan academy (what do you expect, with Frank Noschese in attendance?).

I’ll close with a paraphrase of a great quote by Matt that I think sums up most of the educational reform movement nicely.

The atom of education is the relationship between teacher and student. Because of all the stresses and demands placed on teachers and students today, these atoms are decaying. Education reform is entirely focused on structural changes—rearranging these decaying atoms into different shapes, but since all of these efforts do nothing to address the decay of the atom, they lead to crippled, ineffective reform that never brings about the transformative change it promises.