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25 September 2018

From Umpire School, 2008 - good and bad teaching from a student's point of view.


I wrote the following in 2008 at the Harry Wendelstedt Umpire School in Daytona Beach, Florida. This year, our faculty has been discussing and giving significant attention toward the relationships we build with our students. This post was a response to relationship building from a student's point of view - in this case, I was the student.

Woodberry Forest School has allowed me to come to Umpire School as the major part of my sabbatical.  In principle, the sabbatical should involve professional development that is somehow related to one’s role at the school.  Umpire School was not intended as true professional development, but rather was a lark, a way to get myself out of the classroom for a while so as to avoid burning out my enthusiasm for teaching.  It’s turned out, though, that this place has given me all kinds of worthwhile perspective about my day job.  Think about it…

I teach at a boys’ boarding school.  Here, I am a student at a “school” for 120 “boys”[1] who live not in a dorm but in a beachside hotel.  Woodberry is all about bonding with classmates and making friends, yet those friends are ever competitors for spots on varsity sports teams, in the plays, for valedictorian… here, though the student umpires are friendly and supportive to each other, we all know we’re competing for maybe 20 positions in the professional ranks.  In other words, my sabbatical has turned into role reversal.  Talk about gaining perspective…

So as the professional teacher thrust into the student role, I’ve continued to observe the instructors, what they do, how I and my classmates react.  I’ve already posted some thoughts on our major league instructors.  They’ve been uniformly awesome.  The instructors who are minor league umpires, though, have been a mixed bag.  A couple have been wonderful.  Most have been acceptable, though not special.  At least one is horrendous.  Though they all know their stuff, what separates the great from the just-okay is their attitude toward the students.  Too many of the minor leaguers are easily frustrated, occasionally obnoxious, or overeager to snap at reasonable questions.

My colleague Dan suggested, perhaps perceptively, that some minor leaguers might be teaching here for the cash and the politics rather than for a true love of teaching their craft; whereas, the major leaguers are already set financially and professionally, and so choose to come here for the right reasons.  While that’s an excellent point, I’ve chalked up much of the poor teaching to inexperience more than motivation.  I know that my own major deficiency in my first years of teaching was that I showed frustration too easily.

Thursday’s class included an hour-long review of the mechanics of the 2-person system that we’ve been learning all along.  The two highest ranking minor league umpires took the stage to run the review.  Boy, did they destroy the day’s morale… the timbre of their voice and their body language figuratively screamed, “My God, we’ve told you this already, why are you all too stupid to do it right?!?”  I do see where they’re coming from, ‘cause we do keep screwing up some of the basics on the field.  The review was necessary.  But an occasional smile, some sort of token admission that “you’re doing it all for the first time so you really aren’t dumb just inexperienced,” would have been appreciated.

Now, I’m not complaining about a bit of intensity, or even about them yelling at us.  We were warned from day one: the instructors will yell, not to embarrass us, but so that *everyone* can hear and thus everyone can learn from one person’s mistake.  Heck, that’s my philosophy in physics class.  Ask any of my students – I get loud and intense.  I tell you when you screwed up.  I try to do so with a smile on my face, but nevertheless, I yell.  Of course, I temper that yelling with encouragement, with whatever is necessary for the class to know that I love them even when they tell me that an object moving at constant speed must have a force acting on it.  Whether my students know it or not, I think deeply every day about whether I’ve shown enough love to temper my intensity.  Here at Umpire School, I have no problem being yelled at when I deserve it.

I’m concerned about instructors who assume that a student who messes up must not have been paying attention, or has a bad work ethic.  The students have heard at least seven lectures about how success at Umpire School requires individual effort beyond merely performing in drills.  Practice, study, attention while in line for drills, attention in class… all of these things are not really optional if we want to do well.  Well, the vast majority of the class seems to have taken this message to heart.  Many of us stay an extra hour or more at the fields to practice each day.  Others can be heard practicing on the beach.  My study group has been well attended, and I know that many other study groups can be found around the hotel.  Those in line for drills are often seen going through their mechanics.  I never see students talking in class or distracting their neighbors.  Everyone that I’ve seen has the right attitude.

Yet, I repeatedly observe instructors becoming angry or extremely frustrated with student(s), even though those students had shown considerable diligence.  In one case, at the huddle after a long drill, my field was reminded again[2] that we should be paying attention while waiting our turn.  “I’ve gotta tell you,” one instructor said with nods from his colleagues, “it gets really frustrating for us when we tell you the same thing again and again.  If you weren’t *$&#ing around in line, you wouldn’t make the same mistake that the guy in front of you made.  Don’t *$&# around in line, and then maybe we wouldn’t have to go over this same stuff so many times.  If you’re paying attention, you won’t screw up.”

This instructor’s statement contained two major fallacies.  For one,  I am capable of explaining exactly what I am supposed to do in any given drill.  But that does not mean that, when it comes time to make my body go through the actual motions, I won’t forget something.  For example, the first time I did the “pivot” drill I forgot to watch the ball in the outfield.  All the way until my next turn, I practiced in my mind, reminding myself, “watch the ball, watch the ball, ball, ball…”  When it came back to my turn, I started out watching the ball just fine; but then, after I properly glanced at first base to watch the runner touch, I forgot to turn my eyes back to watch the ball.  Now, I knew I’d get this eventually.  It’s not nuclear physics.[3]  But at that point, my mistake was simply born of inexperience rather than lack of dedication.  I paid attention; I still screwed up.

The second fallacy made me want to ask a smart-arse question.  I wanted to say, “Mr. Instructor, did you see anyone, anyone at all, *$&#ing around in line?”  I was smart enough to hold my tongue.

One instructor in particular, Jordan, has three times hollered at me as if I were a serf.  On Thursday, one of the fields needed some volunteers to bat – I didn’t need to be asked twice, especially because I had been sitting bored on the bench.  I grounded into a force play[4] to put runners on first and second with one out.  Now, when we are running the bases, we’re told to take two bases where possible in order to give the umpires something to call.  The next batter singled on a line drive to very, very shallow centerfield.  I properly held up, then ran when it was apparent the ball would not be caught.  As I approached second base, the ball was thrown toward the infield.  I was aware of the “go two bases” guideline, but the guy holding the ball probably would have been able to tag me out himself had I run to third.  So I stayed there.  After the third out, Jordan screamed across the field, “Greg Jacobs, how many times have we told you to go two bases on a base hit?  What’s your problem?”  I tried to defuse the situation… my intent was to say humbly, “I know, but the ball was in the infield while I was standing on second base… I thought running to third would be unrealistic.”[5]  As soon as three or four words were out of my mouth, Jordan snapped, “I don’t want to hear excuses, I want you to do what you’re told!”

Well, I’ll be danged… I avoided that argument by walking off the field, figuring that while I won’t get into a shouting match, I also won’t volunteer to take that kind of abuse. 

But sure enough, on Friday Jordan was in charge of our field during drills.  I ran out a ground ball to first base.  The first baseman booted the ball, and it trickled behind him.  I figured that I had a slight shot at making it to second base.  In a game, I would not likely have made the attempt; however, under the dictum of “make plays for the umpires,” and especially considering my verbal lashing the day before, I didn’t hesitate – I ran to second, beating the tag by half a step. 

And Jordan looked at me, shook his head angrily, and said to all, “That would never happen.  What’s wrong with you, Greg?  You’re supposed to run like you know what you’re doing!” 

Nothing I can do here short of getting into a screaming match, and there’s nothing to be gained with that.  I explained my conundrum privately to one of the better instructors, and I quietly go to the back of the running line when Jordan is on our field. 

Okay, so there’s my huge beef about the worst instructor here.  On a positive note, it’s time for a heartwarming story about Rob, a minor leaguer who earned our respect and made my day on Monday.  In one moment he showed more teaching talent than the rest of his compadres combined.

First of all, you must understand the nature of CJ the Crazy Braves Fan.  This 19 year old has had a difficult time of it at Umpire School.  To start with, he’s a bit of a natural social outcast.  His slight speech impediment makes him sound dumber than he actually is.  He has limited athletic ability – when he runs, he waves his arms, and he looks like he’s going to fall with every step.  CJ knows baseball, but he’s probably overly enthusiastic about the Braves and Bobby Cox.[6]  No one loves to play the game more than CJ, who puts himself first in line to bat (even though he can barely make contact), and who jumps at every chance to play the field (even though he can’t really throw or catch).  He shows that same enthusiasm for umpiring.  Everywhere you look around the fields, CJ can be seen practicing his “strike three!” or his ejection mechanic.  He keeps a list in his breast pocket of every instructor whom he has “thrown out” of our drills.  Unfortunately, CJ often has trouble getting his umpiring exactly right on the field.  At first a lot of students were a bit cruel to CJ, but by now the class has rallied around him… he’s almost a class mascot.  Most folks now treat him as a pleasant and amusing character.

CJ’s stated goal is to become a major league umpire, but he’s recently realizing that his talent might not be enough to carry him that far.  It was my group’s turn with the pitching machine, CJ was the umpire, and I was the pretend batter.[7]  Poor CJ just couldn’t get anything right this time.  He failed to see a swing; his mechanics were all over the place; Rob the instructor had to correct his stance two or three times.  For probably the first time at school, CJ hung his head.  He knew he had stunk it up, and it was hurting him.  His last two pitches were disasters, where CJ barely made any call at all.  He looked like he might cry at any moment.

Rather than giving CJ the typical formal evaluation that usually follows cage work, Rob brought CJ over to him and looked him in the eye.  “CJ, you can not hang your head,” Rob said.  “We think too much of you to allow you to give up on yourself like that.  Who here works harder than you?  Who here is more enthusiastic?  When everyone else is sitting on the bench trying to avoid helping, you’re the first one to volunteer to play, to bat, or to run.  We see that.  I see that.  The instructors appreciate your efforts, we know how much you care, we want you to be the best umpire you can be.  So we will NOT let you hang your head and give up on yourself just because you had a bad turn in the cage.  Think about how much you’ve improved in three weeks…” and so on, encouraging CJ firmly but supportively for about two minutes, obviously in earshot of a whole bunch of people. 

I kept a poker face, but inside I was rooting Rob on.  The staff might talk all the time about how much they want us all to succeed, but here was one instructor showing with his *actions* how much he cared about a student on the margins.  Me, I didn’t do so well in my drills on Monday.  Yet, Rob made my day.  I came off the fields feeling just that much better about my classmates and Umpire School.









[1] The “boys” range from 18 to 55 years of age, and our class includes a 39 year old “girl”
[2] For now the thirteenth time
[3] And I’ve done some nuclear physics.
[4] Making my batting stats on the season 7-14 with a double.
[5] What I WANTED to say was, “You idiot, what kind of baseball player takes third in that situation?  You lecture about umpires developing instincts, and then you expect us to make dumb plays like that?  What’s YOUR problem?”
[6] I can tell that it hurts him that seemingly every story about situations in the major leagues ends with “And then we had to throw Bobby out of the game.”
[7] The pitching machine is where we practice behind-the-plate mechanics.  The pretend batter holds a whiffle bat, and is occasionally instructed to execute a check swing, giving the plate umpire an opportunity to say “yes he did” or “no he didn’t”.

19 September 2018

We aren't publishing 1st marking period grades for freshmen. How do we communicate progress, then?

My school made the decision NOT to publish grades for 9th graders in the first marking period.*  This decision garnered substantial support from the faculty and an official academic committee.  We don't publish reviews of a theater performance during rehearsals; only intellectually vacuous sports media personalities desperate for ratings assign wins and losses to athletic teams before games begin.  In that vein, I'm thoroughly on board with delaying our assigning of grades until we have enough data for that grade to be meaningful.

*That doesn't mean we don't evaluate assignments, that doesn't mean we don't give graded tests... just that we do not publish or even assign an overall letter grade until after the first trimester exam.

During the summer, a representative group of faculty met to discuss how to implement this change, and also how to communicate about students in the absence of grades. In preparation for that meeting, the 9th grade conceptual physics teachers met to discuss our approach to communication.

Below is a version of a letter I sent to the working group explaining how the physics teachers intend to approach this gradeless marking period. 

Conceptual Physics: Communication plan without published grades at first

Philosophy: We started from Nolan LaVoie's “contract grading” experiment, which he presented to our faculty and to the International Boys School Coalition.  Nolan articulated the attributes which typically lead to success in history course; next, he described the various levels to which his students display those attributes.  While we don’t think it best to adopt contract grading whole-hog in physics, we do want to use attributes as the basis for our communication system.

The ultimate goal we have for our physics students is for them to be able to demonstrate an understanding of how the natural world works, and to communicate that understanding.  How do we know the level at which our students demonstrate and communicate their understanding of physics? Through performance on assessments, including weekly quizzes, monthly tests… and most importantly, in the year-end conceptual physics tournament.  Therefore, those assessments are the primary items on which the grade is based.

How do we prepare our students to demonstrate and communicate their understanding of physics?  We practice, just like a musical ensemble practices.  We practice as a group, we practice alone; we practice basic skills, we practice advanced skills; we practice the well-known pieces, we practice creative improvisation.  Individual members of the ensemble will have different skill levels.  Not everyone is ready to be a featured performer.  Yet, everyone in the group can improve their performance ability through authentic engagement in all forms of the ensemble’s practice. 

So, let’s articulate what forms of “practice” we undertake in physics, and how we expect our students to engage in that practice.  Let’s communicate how well each student meets those expectations - not just at the beginning when grades aren’t published, but throughout the year.  After all, good practice habits lead to strong performance whether or not a Juliard professor is evaluating musicians from the audience. 

Student attributes that lead to success in physics:

In-class practice
1. Participating in experimental and problem solving activities
2. Performing on daily knowledge checks, and working with classmates to evaluate and improve their work

Out-of-class practice
3. Using the fact/equation/calculation problem solving process on every assignment
4. Engaging with homework assignments initially, without using or seeking assistance from students or teachers.
5. Redoing assignments correctly, with assistance, when required or necessary




We have always evaluated these attributes by grading lab work, daily knowledge checks, problem sets, and test corrections.  We’ve always made performance on these attributes half of the student’s grade.  But since we’re no longer publishing grades at year’s beginning, we have the additional opportunity to communicate specifically how a student is progressing on these attributes.  For each, how well is he meeting the standard? Enthusiastically, appropriately, such that he needs improvement, or not at all? 

We intend to send a note to our students’ advisors every three weeks or so, at least at year’s beginning.  In that note, we will indicate how the student is performing with respect to each of these five attributes.  For example, the first sentence of the note would say one of the following:

He participates enthusiastically in experimental and problem solving activities, completing a large number of in-class exercises to a high standard.


He participates appropriately in experimental and problem solving activities, completing a sufficient number of in-class exercises to a reasonable standard.


His participation in experimental and problem solving activities needs improvement.  He has not completed a sufficient number of in-class exercises to a reasonable standard.


He does not participate appropriately in experimental and problem solving activities

The other sentences would similarly address the other attributes we’re observing.  We’d also include one sentence as to how the student is performing on weekly multiple choice quizzes, and on monthly tests.  Again, we’d assign no grade, just a narrative indicating the level of the student’s performance (something like “outstanding”, “high level”, “acceptable level”, or “needs improvement”).

Our hope is that these comments targeted directly to success-building attributes can communicate clearly what the student is doing, and how the student is making progress on all fronts.  A single grade can’t communicate like that. Even though we’ve written some extraordinarily detailed comments over the years, we feel that unless a student is in danger of failing, students, parents, and even advisors tend to look at the grade and ignore the rest.

Assigning grades too often causes our words, the very articulation of our love for our students, to be killed or swept aside.  We’re thrilled to be removing the grade for the first trimester.







.



17 September 2018

Don't get into a holding pattern on kinematics

I'm sure you know of a hundred fantastic activities regarding motion.  I can bring up a bunch off the top of my head that I learned about just in the past couple of years:

* Roll a ball down a ramp or off a table, and try to hit a moving cart
* Launch a ball through three or four rings placed along the ball's parabolic path
* Just heard about from Michael Magnuson: Predict the launch angle such that a ball just barely kisses the ceiling.  (Hint: it won't work right the first time, because most likely students will not account for the size of the ball.)
* Kinematics Card Sorts from Kelly O'shea

And that's just the new stuff!  I still use the old standby 10 Hz dot machine to make motion diagrams, linearize a graph of drop height vs. time measured by the g-ball, quantitative demonstrations with a projectile launcher, graph matching, and more. We have so many fun, straightforward, well-tested activities in our arsenal.  Fantastic!  Unless...

Unless... unless we're still doing kinematics activities and review when Thanksgiving or Christmas hits.

Whether you're teaching AP physics or a conceptual class, it's important to move along.  There's more to physics than motion with constant acceleration.  Students who grasp the concepts quickly deserve to be challenged by force, momentum, energy, and some non-mechanics topics.  Those who struggle will, in fact, catch up through review in context.  Once you've established kinematics ideas well enough that half the class is rolling their eyes at yet another set of multiple representations of motion, well, it's time.  Another day isn't going to help.  Move along to something new.

Have faith.  It's happened hundreds of times for me, that I grit my teeth feeling like I'm leaving some well-meaning but slow students in my dust... and then months later, a kinematics problem comes up in a seemingly unrelated situation.  "Oh, yeah, I remember when this seemed hard.  I get it now," they'll say.  

Move along.  I spend only two to three weeks focused exclusively on constant-acceleration motion.  I save some of the most interesting activities for later in the year, when my students have developed stronger laboratory skills, or during the exam review when there's no pressure to discuss new content.  Since we move along so quickly this time of year, my April and May can be extraordinarily relaxed. 

05 September 2018

CSI: Motion Experiment, Episode 1: The Detector Is Blind.

A reader is having an issue with motion detectors and semi-quantitative experimental results:

Hello there! I hope your year has started off well. Mine has. I am very happy with my results from last year, implementing your teaching/activity techniques with the students. Thank you very much for all of your guidance.

I am noticing that during the in class lab exercises kinematics - those are the ones where we have a track, cart, and motion detector, and double the time, then double the acceleration, then double the initial velocity - that the double time experiment yields very high percent errors for most students. I thought it might be a sensor issue, but I zeroed the sensors and did the experiment myself on the setups giving trouble, and I am getting the same thing the kids are. It's supposed to be a multiplier of 4 for the distance, but I am getting 2.6, 2.9, 3.3...very low to what it should be. I'm now thinking it may be an issue with friction, because usually the lower the incline the worse the result, but too high and we don't have enough space to get a good time interval (I only have 1 meter long tracks). I am using the metal pasco tracks with the plastic pasco carts. The carts are on the older side, so I'm thinking that friction with the wheels might be throwing off results. 

Do you have any input on this? Do you experience the same thing? 

Hey!  I've got some thoughts.  I don't think it's a friction problem - the friction is there even for the smaller time, and in any case is not going to cause that much of a difference between what's predicted and what's measured.

One issue might be the 15 cm blind spot* for the sonic detector.  Depending on whether you're moving toward or away from the detector, you may well be missing a significant fraction of the distance the cart traveled.  After all, the blind spot is 15% of the entire track length!    Another less likely issue is that I've had students measure (and thus double) the time from when the detector was started, not the time that the cart was moving.  

*The green Vernier detectors that I use have a 15 cm blind spot.  The decade-old blue Vernier detectors have a 40 cm blind spot.  I don't know what the PASCO detector blind spot length is, but it exists.

The way I'd suggest doing this particular problem is in one trial.  Set the detector at the high end of the track.  Place the cart's back end 15 cm from the detector.  Press play, WAIT FOR THE CLICKS, and let the cart go once the detector has started running.  Use the position time graph made by the detector.  Check the distance traveled after the cart has moved, say, for 0.30 s.  (Not when the labquest says t = 0.30 s, 0.30 s after the cart begins to move.  You can check the velocity-time graph to see when the vertical axis value first moves away from zero.)  Then check the distance traveled after the cart has moved for 0.60 s.  I'll bet you come closer to a factor of four increase.

Do you have a PASCO smartcart?  Those will get much better data; and, you can use them on a long plank of wood instead of on the track - if the cart moves slightly off a straight line, the motion encoder in the smartcart's wheels will still work.

Hope this helps!

Epilogue:  Turns out the reader didn't know about the motion detector's blind spot, and so was especially confused that the cart moving toward the detector gave a consistently different result than a cart moving away from the detector.  She solved the problem using the experimental suggestion above.  Awesome.

26 August 2018

How to teach a group the use of a new software platform

Oy.  I’ve been stuck in jail faculty meetings all week, with barely an end in sight.  Every teacher knows that simply talking at a class from the front of the room for 90 minutes is unacceptable pedagogy; however, that’s how most faculty meetings are structured.  Even though it is often the leaders of these very meetings who are informing teachers not to talk at the class from the front of the room for 90 minutes.

In four of the last five years, our faculty has been asked to learn a new software platform - from google docs to Canvas to a bespoke boarding school check-in system.  For each platform, teachers have rightly asked for - demanded - training on how to use that platform.  How, pedagogically, should that training be conducted?


I can tell you first how it should NOT be conducted:


“Hi everyone!  I have a great joke about how frustrating this software is going to be for you.  Now open your computers.  Go to the login page and input the credentials we sent you via email.”

“Wait, what page?” “This page written on the top of my browser on the screen.”


“My login doesn’t work.”“Okay, if your login doesn’t work, open this tab and click 'reset password'.”


“Which tab?”  “The tab on this page here that I’m manipulating on the screen.”

“What do we do after we log in?”  “Great, I’ll tell you in a moment.  First let’s get everyone logged in.”

“Can we change the system to account for the differing needs of the history department?”  “As a matter of fact, [five minute digression of interest only to the history teacher who asked]”

“Which tab, again?”

Does this sound familiar?  I consider this sort of faculty meeting to be educational malpractice. If our classrooms should reflect pedagogical best practice, then our meetings as a faculty should reflect the best of best practices.

But my complaint here demands an understanding of what are best practices of teaching new software.  Many of us will need to do this in our classes - how do we avoid being responsible for the scene described above?  I mean, its not like the folks running these sorts of meetings or classes have extensive experience in computer pedagogy.  Such skills must be learned.

Here’s an approach that works, and wastes no one’s time.  It will require a change in mindset... because of the persistent meme throughout every level of our profession that if information is not "covered" orally by a leader in front of the entire group, no one knows or is expected to know said information.  But, I’ll bet you thousands of dollars that the approach below will cause better retention of information as well as far, far less resentment.

"Hi everyone! We have a new software platform that we all need to use this year. Today we need to make sure you can access the platform, and that you are familiar with its basic functioning.  In the process, we the people organizing the software platform need to debug, to find out what works, what is clear... and what isn't.

I've listed five tasks on the board.  Please open your computer, and access the email that gives screenshots and step-by-step instructions for each task.  

Then, please follow the directions and finish each of the five tasks.  If something doesn't work, if you're having trouble, ask a friend; help each other.  I and my partner will be walking around the room troubleshooting.

When you've done all five tasks, please come see us and let us know.  We're particularly interested if you encountered any problems or created suggestions.  After you've talked to us, you're done - I know you have things to do in your classrooms.  That said, if you'd like to stick around and help a colleague, I know that would be appreciated.

Go for it!"

That's all that needs to be done from the front of the room.

As the leaders circulate, it's quite important to deal appropriately with frustration.  Too many people in the audience act personally affronted that they have to learn something new, that it doesn't work perfectly the first time, and so on.  (Teachers are usually worse than students, here.) 

Yes, these folks need to get over themselves.  But the frustration is real, and often unavoidable.  Think of these frustrated participants as students who are continually wrong in their first exposure to free body diagrams. The leader must be calm and patient, yet insist on everyone being good teammates working toward a common goal of learning the new software.


14 August 2018

I'll be teaching an online physics course to help with teacher certification...

Hey, all... this is an ad, but an ad for something you or someone you know may be interested in.

I'll be teaching two online physics units through the Putnam-Westchester Industry & Science Teacher Alliance (PWISTA).  Check out the Science Teacher Mastery Program.  Each class in the program is equivalent to what would be a two-to-three week content unit in a first year college physics course, but aimed at students who are or intend to become physics teachers.

The goal is to provide a convenient and useful option for folks who need content-specific college coursework for their professional development or teaching certificate.  Do you know someone who is being asked to teach physics, but is primarily a biologist or chemist and thus needs some content support?  Or, do you know someone who is familiar with physics, but needs guidance in physics pedagogy, needs to know how to help her or his students understand physics?  Either way, this course will be of use.

I'm offering two classes: one on circuits, and one on impulse-momentum.

For each, you will get access to all of my topical course material, both when I teach at the high-school (Regents) level, and when I teach at the college (AP) level.  This includes the labs, problem sets, and quizzes that I assign.  I'll give you written guidance about how to use this material in your teaching, and for your own study.

Then, I will host five one-hour online sessions on Thursday nights this fall (see schedule below).  In each session, I'll spend the first half discussing practical pedagogy, just as I do in my workshops and on this blog.  In the second half, I'll discuss specific content, problem solving, and test preparation issues.

Participants can get 15-hour CTLE certificates through Purchase College.  They can also get three graduate credits in science education through Manhattanville College - see the site for details about credits, certificates, and pricing.

I've appended the full course description via this google link.  (The impulse-momentum course has the same description.)

If you have further questions, please contact me via email or twitter; or, contact Mark Langella, head of PWISTA, through their site.  Mark teaches the chemistry courses, and has been a College Board consultant for many years - he's the varsity, in case you know anyone who wants a similar program in chemistry.

Schedule for PWISTA Physics fall 2018:

The following are Thursday nights.  The circuits course will meet at 8:00, the impulse-momentum course at 9:00, via Google Hangouts:

Sep. 20
Oct. 4
Oct. 18
Nov. 1
Nov. 15

01 August 2018

Stamp out political hyperbole in teaching: physics teachers are not "cruel."

Dad: Maybe if we tied it down so it couldn't move it wouldn't get so hungry.

Daughter: You can't do that, Dad, it's cruel!

Dad: Oh, everything's cruel according to you. Keeping him chained up in the backyard is cruel. Pulling on his tail is cruel. Yelling in his ears is cruel. Everything is cruel. So, excuse me if I'm cruel!

That's not a secret transcript of the director of the Gestapo ICE negotiating care for his family dog.  No, that's Homer Simpson discussing how to handle Bart's pet Stampy the elephant.  Homer: Now I've had my head in an elephant, a hippo, and a giant sloth.

I've been thinking an awful lot about cruelty lately... I mean actual, perpetrators-would-burn-in-hell-if-I-believed-in-hell cruelty.  For example, about how many people are willing to make excuses for sending refugee children to concentration camps.  I feel helpless and depressed.

Next, I've thought back to the times that I, personally, have been labeled "cruel" by students, parents, and colleagues.  Refusing to answer questions during a test: "cruel."  Insisting on a serious written attempt at a problem before I offer help: "cruel."

In the past, I've simply given matter-of-fact explanations for my approach to teaching, usually with a smile on my face.  "A test is my opportunity to see what my students can do on their own, not how well they can pump me for information."  "If I ‘help’ before you’ve thoroughly engaged with the problem, you won’t gain the critical experience that will help you figure out how to approach unfamiliar problems on exams.”  

I’ve let the overwrought label “cruel” deflect off of my mental armor unchallenged.  After all, who cares… by year’s end, the vast majority of students change their tune, ace their AP or final exam, and send me notes of thanks for holding them to high standards while still showing support for and belief in their ability.  

It's time to change our tune.  The more I think about it, we should *all* care about the insidious emotional manipulation of casually labeling a teacher as “cruel.”  I think we should stand firm, and forcefully correct anyone who deigns to use this epithet directed at any teacher.  I’ve got two important reasons for fighting back.

(1) Your reputation matters; Words and labels matter. When people call you cruel, they are fighting a modern political battle, using emotionally charged language alongside truth-neutral hyperbole to discredit you for their own purposes.  The endgame is to force you to reduce or eliminate your demands for rigorous intellectual engagement while delivering high grades.  This approach is the localized, small-scale version of Brexit’s “More money for the NHS” or 2016 America’s “Lock Her Up!”  Keep pounding the same talking points that hit the audience right in the feels, and then facts don’t matter.  

Colleagues and parents are already predisposed toward a negative opinion of the physics teacher.  The subject we teach is fundamentally different, as is good pedagogy in our subject.  But also, physics teachers themselves are generally different from our colleagues.  We are so often outsiders to the mainstream education community.  And as we’ve seen the past few years, it doesn’t take much discrediting nonsensical propaganda to turn a community’s outsiders into outcasts.  You might give the highest grades in the department, you might over the year assign less homework than any other AP teacher… but if the “cruel” label sticks, you’ll be in political trouble despite reality.


(2) Hyperbole of labeling a well-meaning teacher “cruel” dilutes the impact of calling out true cruelty.  Right now, powerful people are abusing their positions to direct acts of authentic, deep cruelty, and they’re doing so publicly and shamelessly.  When someone calls a teacher “cruel” they set up a dangerous false equivalence.  

You really think that me not allowing retests is on the level with harassing Sandy Hook victims’ parents until they must go into hiding?  That refusing to assign vacuous “extra credit” is the same as forcibly taking away children of asylum seekers, then lying about and profiting from the kidnapping?  Because that’s what you’re saying when you call me or my pedagogy “cruel.”  

I’m sorry your child or your advisee is going to have a harder time getting into Princeton if (s)he earns a B in physics.  I hope (s)he can turn that into an A eventually.  It is perhaps my most fervent wish that your kid’s B counted as the cruelest event to happen to an American teenager this year.  

Are you frustrated with me, with my course, with physics, with the entire hierarchical educational system?  That’s fine.  That’s fair. 

But it’s not cruel.  




22 July 2018

Mail Time: a tough mix for an upcoming AP Physics 1 class.

Nancy writes in:

I didn't have an AP class this past year because the numbers were too low. The class did make for this upcoming year, which starts in 8 days! I have 6 kids in my class. 3 had my honors physics class last year (and I feel have a good foundation for AP). The other 3 have never had physics. Any advice for how to start? Where? Any recommendations for folding in instruction for the newbies while reminding the trained without boring the one and losing the other (or me losing my mind)?


Yeek.  Looks like a tough mix... at least, though, there are only six students.  It's pretty easy to tailor the class with so few.  

I guess the answer depends most on how well prepared the three returnees are for the demands of AP Physics 1.  Is your honors class calculational, conceptual, or something in between?  

If your returning students had a calculational high school-level course similar to the New York Regents class, then I'd just teach the whole class AP Physics 1 together.  They'll all have to learn how to explain and write about physics.  Just be sure to begin the year with something clearly deeper and different from what they might have done last year; be sure to begin the year with a fast pace.

However, if your honors class was sort of AP Physics-lite, then you might want to do something further removed from a typical class.  Something like having returners teach the class occasionally, or assigning them as tutors for the new-to-physics students, or set up competitive lab exercises that partner returners with newbies, or... anything you can think of that makes the returning students the acknowledged leaders of the team so they barely even notice that they're covering the same topics again.

AP Physics 1 is intended as a first-year course.  In the long term, see if you can place more of your top-end first year students into the AP class.  That will allow you to cast a wider net for second-year students.  Even students with quite poor standardized test scores can do very well in AP Physics if they are seeing the topics for a second year, but that first year truly is not necessary for the majority of students.

Good luck...

14 July 2018

2016 AP Physics 1 problem 5 waves on a vertical string - video from Walter Keeley

In my PWISTA* AP Summer Institute, participant Walter Keeley tried to set up the waves-on-a-vertical-string problem from the 2016 P1 exam.  (Click the link, and go to problem 5.)  The problem asks students to explain, in a paragraph, how a picture of standing waves on a vertical string provides experimental evidence that the wave speed depends directly on the tension in the string.

*Putnam-Westchester Industry & Science Teacher Alliance


The correct approach:  The picture shows a longer wavelength in the standing wave near the top, where the tension in the significantly-massive string is greater.  Since the frequency of vibration is provided by the wave generator and is the same throughout the string, by v=λf the larger wavelength means larger wave speed.


Walter initially had no more success setting this up than I had over the years.  The strings I've used have simply not been heavy enough.  Walter tried a seriously massive rope, but it wasn't flexible enough to show a clear pattern.

It was Lorren, one of our participants, who suggested using ball-chain to provide both mass and flexibility.  It was Tom who pointed out that you'd have more luck seeing the wave if the generator didn't merely vibrate left-and-right, but in a small circle.

So, when Walter had some downtime at robotics camp, he obtained some chain (from True Value Hardware at 40 cents per foot).  Walter had to build his own geared motor to vibrate the chain:
Photo credit Walter Keeley

Walter used his phone to create a video of the vibrating chain; the app Hudl Technique is what he (and my students, too) use for playback, because it does slow motion and precise timing.

And oh my goodness, look at Walter's video: 

Look how you can see -- and measure, if you want -- the wavelength change.  Walter even arranged - presumably by trial and error with the frequency selection - to have the same three-and-a-half antinodes that are shown in the original AP problem.

Do you have a beautiful experimental setup of a released AP Physics problem?  Send pictures, and I'll be happy to post it on the blog with credit to you.  If you've never set up released AP problems in your lab, well, that's an awesome April open-ended lab assignment.


04 July 2018

2017 AP Physics 1 problem 1 with the draining batteries: we set it up

On the last day of my AP Physics 1 summer institutes, participants are asked to pick a released exam question, solve it... and then set it up experimentally.  We always get some simple yet elegant setups, like Rebecca’s modified-Atwood-turned-projectile from the 1998 exam; some complicated setups that don’t quite work but point in the right direction, like Lorren’s attempt at the 2018 collision-on-a-horizontal-spring problem which got us thinking about vertical springs and velcro; and some complex and elegant creations that go beyond just the AP question, like Quinn’s measurement of the kinetic friction coefficient that can then be used to determine the mass of an unknown block.

Several free response problems over the last few years have presented significant experimental challenges, though.  When the bumpy track problem came out on the 2016 exam I heard from so many teachers, "this isn't real, no one would actually set that up.  Well, we did last summer. 

This year one participant, Frank, took on an even greater challenge: the paragraph question about draining batteries, from the 2017 AP Physics exam.  It postulates connecting light bulbs to a battery in three ways, and asks which will drain the battery soonest.  

Which battery drains first depends on the power dissipated by the circuit: since power is energy per time, the shortest time to drain the battery will come from the circuit dissipating the largest power. By V2/R with the battery always providing the same voltage, whichever circuit has the smallest equivalent resistance will dissipate the most power.  So the bulbs in parallel will drain the battery first, followed by the single bulb, followed by the two bulbs in series.  That's the theoretical solution.

Frank and I and our lab assistant Tom brainstormed three approaches to this experiment.

(1) We could finesse the problem by simply observing brightness, which correlates directly to power.  That's almost trivial - we connected three sets of bulbs to three identical batteries, and we saw the parallel bulbs brightest, the single bulb next brightest, and the series bulbs dimmest.  Great for a simple demo, but this sort of thing has been done before.    

(2) We could get three fresh batteries, hook them up, and set up an iphone to do a time lapse video.  I don't know offhand how long it would take to drain fresh AA batteries, but it's not gonna happen within a single lab period; and that's all we had at our institute.  I do hope that some reader will set up the time lapse and send it along.

(3) Tom noted that he had some "big blue" capacitors available.  These are 27,000 microfarads and can operate up to 25 V.  Though the study of capacitors is beyond the scope of AP Physics 1, it's not hard to explain to students that these things store a fixed amount of energy (for a given starting voltage), and then that energy dissipates rapidly.  

How rapidly?  Your students don't need to know, but the time constant of discharge depends on the product of the equivalent resistance and the capacitance.  We want an equivalent resistance in the dozens of ohms to get time constants on the order of seconds.  Frank and Tom found some Christmas lights; when these were connected via alligator clips, the dimming of the lights over a few seconds as the capacitor drained was easily visible.

Which drained first?  It was sorta hard to tell with the naked eye.  So we clothed our eyes with slow motion video on our phones.  

Frank charged the capacitors.  He connected a switch that, when thrown, would simultaneously connect each circuit to its capacitor.  Here's the result:


Just like we predicted - physics works.


01 June 2018

The Last Jedi - analysis of theme and Holdo, with (yes) tenuous physics teaching connections

I’m a big fan of Alastair Stephens’ podcasts*.  He’s done a 12-episode series on Story and Star Wars, a 60-plus episode series on Tolkien’s works, and a long-running Harry Potter podcast.  Alastair doesn’t just give a fan’s perspective, though he is certainly a fan.  He delves into the text of a story. He commits literature on what many consider merely nerdish-pop culture phenomena.

Update: Some credible, in my judgment, #metoo details about Stephens came out in August 2018.  I’m now unsubscribed from his work; I’ve removed the link to his site.

Alastair finally got around to talking about The Last Jedi a few weeks back.  I sent him a response to some of his analysis.  In doing so, I realized that there’s a physics teaching connection to a couple of these.  And you can’t go wrong discussing Star Wars amongst physics teachers.  

So in the spirit of love for intellectual Star Wars discussion... Here are three thoughts on The Last Jedi after listening to Story and Star Wars:

(1) Alastair spends some time searching for The Last Jedi’s overarching theme, which he points out is not at all clear.  I took the theme of the show, such as it is, to be contained in Rose's final line to Finn: "saving what we love, not killing what we hate."  Poe was demoted for violating that principle. Rey found the part of Kylo that she could love and save, not kill and hate.  Rose's trip to Canto was "worth it" only when she saved the camel creature. Problematic Holdo planned to save what she could rather than make a heroic last stand. Luke took action when he realized that while he couldn’t destroy the first order or Kylo, he could at least save Leia, Rey, and the rebels.  

I certainly see Alastair’s question about the movie’s confused, disparate, and unfocused themes.  No argument there.  But, is it possible that all the possible themes he mentioned - war/peace, leadership/heroism, harmony/disharmony, etc. - could be encompassed in saving/killing?

(And, combined with the borderline polemic scenes on Canto, I took this theme as as close to a current political message as you'll get from Star Wars.)

Physics teaching connection: In many a May as the school year draws to a close, I find myself a bit bitter.  All too often, a colleague close to me is leaving the school; or a rotten, racist student accepts his barely-earned diploma with a sh*t eating grin; or I have to play nice as an unprofessional kiss-arse of a teacher is lauded by those who don’t make the effort to know better.  

Saving and killing are, of course, supremely hyperbolic when referencing life at a bucolic boarding school.  Nevertheless, I find myself reciting Rose’s mantra to myself.  The negatives that stick in my craw are far outweighed by the positives. The colleagues I love who remain on faculty (and the new folks coming in), the myriad students who graduate with pride at a job well done, the outstanding teachers who win well-deserved recognition… I need to treasure those people I love rather than seethe at those things and people that bother me.  If Star Wars helps me to do that, so be it.

That doesn’t mean I should give up the fight to improve my school, my students, and my own teaching.  I merely have to keep in mind that losing the battle of Hoth doesn’t mean losing the war.  


(2) Alastair presented an analysis of Admiral Holdo’s actions.  Her opposition to Poe - and, to judge by the mutiny that commences, her opposition to most of the rebels below a certain age - contrasts with her heroism and her camaraderie with Leia.  

I talked to the son of a Marine officer about her. He said, "A Marine captain who demands big-picture details from an admiral in a public forum would be rightly thrown in the brig.  The captain's job is to follow orders.  Holdo's response to Poe's insubordination was mild."  

Fair point.  Yet, as a physics teacher I see her response to fair questions from her subordinate as deeply problematic.  On the podcast Alastair indicated exactly the response I'd expect from Holdo, and that I give to students who question my methods.  Something like, “Poe, please understand that we do have a throw of the dice left.  I can’t divulge the details now, because I’m worried that the First Order can hear us.  But I promise that we will not merely wait here stoically to die.  Please trust me as Leia did.”

I’d be personally okay with even, “Poe, back the eff off.  I’m using what fuel we have for transports; we’re headed to a secret abandoned base.  That’s the plan.  I’d love it if you could now please take BB8 to do the final maintenance check on every transport.  That’s an order, Captain.”

The "shut up" response should be reserved for when the subordinate's questions broach into tendentiousness or bad faith.  And even then, making direct personal insults to a subordinate - “I’ve dealt with flyboys like you” - is not only out of bounds, but the exact opposite of productive.  (What talented, prideful subordinate ever responds to a direct insult with “Oh, the boss showed me.  I guess I’d better shut up now and do what she says.”?)  A large part of leadership is effective communication and managing the personalities of talented underlings.  Holdo failed.  


Physics teaching connection: The education industry does not well tolerate people with exceptional ability, especially if those people are brash.  To mix my performing arts metaphors, administrators want their teachers to be Burrs, not Hamiltons.  And, to my profession’s shame, teachers usually want their students to be Burrs, not Hamiltons.  Especially when the teacher is more Charles Lee than George Washington.  (Okay, back to Star Wars references.)

What is your plan when you’re presented with a student who’s extraordinarily talented, but who is impatient and frustrated with the strictures or the pace of your class?  What is your administration’s plan to deal with the young, brilliant, popular teacher who has the political acumen of Jar Jar Binks?  You should have such a plan.  The plan should provide support and encouragement, while at the same time guiding the Padawan toward wisdom. 

If your plan is to do a Holdo, you’re in the wrong profession.  I’m rather disturbed that a number of fans I talk to blame *Poe* for the catastrophes at the end of the second act.  "If he had just shut up and followed orders..."  No, that's on Holdo.  "If she had just communicated her plan and built trust..."


(3) Mechanisms of the force: Luke's mother of all Jedi Mind Tricks - A colleague of mine put the final scene with Luke into perspective for me.  We've never seen a force hologram with such power.  What if, my colleague asked, in the final confrontation Luke is performing a Kenobi-style Jedi Mind Trick... but not just on one mind.  He's performing the Jedi Mind Trick on every single person watching.  He's convincing all of the 200 or so people present to see something that's not really there, and to see the same thing that's not really there. This would explain the long-distance nature of the projection, in that Luke must touch minds through the force, not physically project a hologram equivalent.  It would explain how Luke can fight as a hologram, and why sometimes he is substantial and sometimes not - Luke is not physically fighting, he's merely making Kylo and observers see and believe in a fight.  It would explain Luke's death better - that sort of performance took all of his remaining energy. If that's true, that would make Luke truly the most powerful Jedi ever, and even a greater legendary hero.

Physics teaching connection: There is none.  Other than that virtually all physicists have a personal understanding of Star Wars and the Force.

20 May 2018

Did you or your students get a nonstandard form for an AP Physics exam?

The vast majority of students who take an AP Physics exam get the “operational” version of the exam.  This is the one whose multiple choice questions are never released, but whose free response is available publicly 2 days after the exam date.

A small fraction of students take a different form of the exam.  In particular, students outside North America usually get this different form - otherwise, it’s possible for a particularly dirty player to reconstruct the exam and text details to a student in a different time zone.  Within the continental US, that’s difficult - the west coast has entered the exam before the east coast is finished.  In the fall the College Board releases the majority of this “international” version of the exam to teachers who have passed an official course audit.

For statistical purposes, occasional randomly-selected students stateside take the exam form that’s otherwise earmarked for the international audience.  Invariably, when a few students find out that they took a different test than their classmates did, they claim that (a) they took the harder version, and (b) no fair.

Claim (a) has a 50-50 shot of being true.  Claim (b) is utter, ignorant baloney.

Is the international version harder?
Sometimes, sometimes not.  Is this year’s exam harder than last year’s?  It depends on your perspective, what you’re personally good at, and random chance.  The development committee attempts to construct exams of similar difficulty in each year, in each form. If you have access to the released international exams, take a look through.  Some questions are harder, some easier, most about the same.  Once many years ago I was in the super secret room where the international and alternate forms of the exam are graded - on pain of pain, I’m not allowed to tell you any details about the exams I saw.  That’s just as well, because I don’t remember details.  Yet, I can tell you that the questions read exactly like the operational exams - I perceived no difference in difficulty, no difference in the range of student responses.

Are the AP scores lower for the international version?
No.  The difficulty of exam questions does not matter when AP scores are compiled!

On each exam, a subset of multiple choice questions are repeated from previous years.  These serve as a control on exam difficulty.  Even when an exam consists of demonstrably more difficult questions, the meaning of a 5, 4, 3 is identical.  This subset of multiple choice ensures that desired outcome.

Let’s say that all students taking the international version got 40% of the available points, while all students taking the operational version got 50% of the available points.  There are two possible explanations for this discrepancy:

(1) The international exam consists of more difficult questions than the operational exam.
(2) The population of students taking the international exam is weaker.

Performance on the subset of repeated multiple choice questions can differentiate between the two hypotheses.  

If there was no statistical difference in performance on the repeated subset, then explanation (1) applies.  The same level of student getting fewer points means the exam is harder.  Thus, the cutoff percentages for 5, 4, 3 would be dropped.

However, if the students on the international exam scored similarly worse on the subset of repeated questions, then hypothesis (2) is confirmed.  Even on the exact same questions, these students performed to a lower standard.  The cutoff percentages would reflect that lower level of performance.


The overarching goal is that a 5, 4, or 3 means the same level of performance from year to year.  Yes, it is true that for AP Physics 1, about 70% generally works out to a 5, 55% to a 4; those numbers are variable to serve the overarching goal.  Similarly, it is true that about 5% of the student population gets a 5 on AP Physics 1.  But that's also variable, dependent on the performance of this year's students.  There's nothing preventing teachers and students getting better year to year, such that suddenly half the country earns a 5.  I mean, that's unlikely... but the College Board would be utterly thrilled if that happened.

Scores are not manipulated for political reasons.  In the very first year the AP Physics 1 and 2 exams were administered, a diverse committee was assembled and teachers/professors were surveyed to determine the standard of performance appropriate to each score.  While statistics were used copiously, this original score setting included some subjective as well as objective input.  

Once those original scores were set, though, the standard of performance for each score was also set in stone.  The scores this year will be what they will be... if more people get high scores (as has been happening very gradually across the last few years), that represents authentic improvement in the student population taking the exam.  No one is pulling strings behind a curtain trying to depress or increase scores.  Those who promulgate conspiracy theories do so out of malicious ignorance.  The numerous ETS statisticians, the chief readers, the College Board representatives, the development committees... all these people would have to be part of a such a grand conspiracy.  I know many of these folks - I know them to be people of considerable integrity.  They wouldn't stand for fudging scores.  It's not happening.

Similarly, there's no conspiracy to give half of your school a harder exam with worse scores.  If you happened to get a nonstandard form, well, everything will come out in the wash.  Your exam score will reflect your knowledge of physics.  As it's supposed to.  :-)



16 May 2018

Chimera: The skill of learning from a textbook

I was asked whether I still use just fact sheets, or whether I encourage the use of a textbook like OpenStax.

I'm still using fact sheets, and nothing but fact sheets. 

Many people have argued with me that they want to promote learning new physics from a textbook.  Reading a textbook is a skill, one that seems to be demanded in college physics courses.  Fact sheets and videos, they argue, eliminate textbook learning.

True.  And I desperately want to eliminate textbook learning.  

Textbooks are interesting and useful and fun to read for those who already have context.  In history, where the vocabulary and general situations (kings, wars, human conflict and leadership, etc) it's easy to learn from a textbook.  Life science texts with outstanding diagrams can lead to good learning.  Even language texts can be strong, especially if they include easily navigated glossaries and grammatical summary tables.

Physics cannot be learned from a textbook, I don't think.  Instead, students can learn facts from a fact sheet by rote. Then they can learn the skills of applying those facts to interesting situations, and experimental skills in lab, and how experiment connects to prediction... and finally, at the end of the year, students can go read a textbook successfully because they have the context for understanding.  

I think that process holds in first year physics as well as advanced physics - everyone I knew struggled to understand our quantum text, or advanced fluids text, or advanced E&M text.  I thought I was stupid because I couldn't read and understand the textbook.  My friends either also thought they were stupid, or thumped their chest and pretended to understand.  

We all figured these subjects out eventually, as we did problems and learned facts from our teacher and practiced with each other.  But the idea that it's a useful or even attainable skill to read a text and understand new physics the first time you read it?  Utter baloney, in my mind.  :-)

14 May 2018

The Jacobs Physics Podcast, ep. 3: 2017 AP Physics 2 problem 2, resistivity experiment

The 2018 AP Physics 1 exam involved an experimental graph to determine resistivity of an unknown material.  Interestingly, so did the 2017 AP Physics 2 exam.  This week's podcast deconstructs the problem and rubric from the 2017 P2 problem, including digressions about:

* writing procedures
* how I feel about formal lab reports (i.e. don't do them unless you're truly dedicated to the process)
* BAD GRAPHS
* the 1/4 page or 1/2 page rule for graphs
* how I feel about science fairs (i.e. don't do them unless you're truly dedicated to the process)

Click on this link to listen to this week's podcast.

Feel free to send feedback via email.  I've already addressed a couple of peoples' questions on the podcast; I'd love to have more.  If you want me to use your name, say so!

GCJ

10 May 2018

2018 AP Physics 1 Solutions

What a great exam this year... I particularly loved #3, the quantitative-qualitative translation question in which students have to work through a non-constant torque graphically and conceptually.  The paragraph question which combines energy and momentum concepts is likely to show up at our year-end conceptual physics tournament in the near future.

My solutions can be found at this TEACHERS ONLY link.  Yes, really, teachers only.  If you ask for access as a student or parent, Gardner, who runs that site, will take away your birthday, and for extra measure, he'll lay a little spell on you right there.  He'll turn you into stone, or a dog, or a chair.

Teachers, if you'd like access, please follow the instructions at the site.  Send Gardner a request to join, along with evidence that you are a physics teacher.

The official solutions will be available in the fall on the College Board's AP central website.  I'll be grading problem 3 - woo-hoo!  (No, I've no clue yet what the rubric will look like, just that I'll be grading thousands upon thousands of problems 3.)

GCJ