AP Physics C in April - don't worry about math!

I'm working on the final set of test corrections with my Physics C - mechanics independent study student.  This person did well on the test - earned a 4 on a typical AP scale.  But that's only 50-65% of the available points, so there are plenty of items to correct.  

This student had AP Physics 1 with me two years ago.  He is in AP Calculus BC.  

In the first part of the year, I had him focus on the mathematics that overlay the concepts he learned in Physics 1.  He watched all the "AP Daily" videos for Physics C, he practiced new mathematical techniques like integration to find displacement/work/center-of-mass-location/rotational inertia.  He's got those techniques down, now - at least, he'll do the math right most of the time if he sets up the problem right.

And there's what we're concentrating on now - setting up the problem right.

AP Physics C students usually want to do math.  They plug into equations, manipulate, see if the answer is right... and if not, they try a new approach, until (a) they get what they think is the right answer, or (b) steam comes out of multiple orifices.  Neither result is useful.

I don't want to see much math right now, for these corrections.  I want to see facts and concepts.  How should this problem be approached?  How do you know the problem should be approached that way?

For example: I don't want to see plugging and chugging into energy or momentum equations until I see a clear statement of what is conserved and why.  How do we know?:

Mechanical energy is conserved when there is no net work done by external forces.  (And when there’s no internal energy conversion.)

Angular momentum is conserved when no net external torque acts. 

Momentum in a direction is conserved when no net external force acts in that direction.

I need to see these facts, along with a statement as to why they apply.  Then I need to see that they used the right formulas for each term - including direction of momentum - and/or that they made a correct energy bar chart.  That's it.  The actual mathematics to finish the problem isn't relevant right now.

As this student has brought me corrections, I've deliberately checked off a few which were set up correctly, but led to the wrong answer due to a math error.  And, I've send him back to try again for a few corrections in which he got the right answer, but didn't communicate the starting point clearly.

All this works, except when he notices that his answer is wrong, but I tell him the setup is correct.  "I've got to get it right!  It's going to bug me forever if I don't!"  I totally get it!  But, trying to find a math mistake is not a productive use of time.  Usually the issue here is something like a squared term not being copied correctly from step to step in the mathematics; or, accidentally canceling a 1/2 in most but not all terms. 

These little math mistakes are difficult to find in a half-page worth of work; but, given a new problem from scratch, this student - or any competent AP Physics C student - would NOT generally make such a mistake!  Rather than spend 20 minutes doing and redoing a problem until the math works out, why not move on to the next one?  

Most of the errors that students make come from starting with the wrong approach.  Most of the time, the right approach leads to the right answer.  So in our limited review time, we're going to focus on the right approach.  We'll let the chips fall where they may on whether the math gets done right.

Mail time: AP laboratory questions using "equipment usually found in a school physics laboratory"

A post to a physics teaching message board asked the (paraphrased) question:

I was wondering about "design a procedure" AP Physics questions that ask students to use "equipment usually found in a school physics laboratory".  What are the limits here?  Would readers take off if a student used, for example, an accelerometer?

An accelerometer is fine.  It's available in the Pasco/Vernier catalogs and on smartphones - that's way common enough for me!

In general, I wouldn't stress about what's "common" or not.  No one is lawyering up about "well, this is only used in 49.1% of high school physics classrooms, so minus two points from Gryffindor."

Much more importantly, make sure your students can (very briefly!) in their procedural description show that they know how the device is used.  "Plot acceleration as a function of time using an accelerometer mounted to the cart" makes sense.  "Carry a phone on the roller coaster, and look at the acceleration-time plot using the built-in accelerometer."  Those are fine.

"Point the accelerometer at the cart to get its acceleration" doesn't work.  :-)  An accelerometer isn't a radar gun, nor is it a magic wand*.  I often see this issue with e.g. a photogate - it's not a point-and-click device! 

*Using it as such *would*, in fact, result in minus two points from Gryffindor.

Similarly incorrect would be, "Launch the ball from the projectile launcher.  Use an accelerometer to get its acceleration during the launch."  Now, I suppose you might be able to crack open the ball, insert a miniature accelerometer, paste the ball back together, launch the ball... but no.  That's not at all "common".*

* If someone truly did go through all this description, though, the procedure works.  Way ridiculous and time-wastey, but would such a student show comprehension of experimental physics?  I'd say so.  Point is, just saying "use the accelerometer" in this case isn't good enough for the readers to infer this farfetched procedure.  But if they write out all this detail, then sure, they have demonstrated serious understanding.

A diagram can do the work of the words here, too.  If a student shows the accelerometer attached to a cart, or a phone mounted to a cart or something, then it's clear the student understands what an accelerometer is and how it works.

Hope this helps!

Greg

A birthday at Chuck E Cheese - and "good intentions"

As part of my boarding school responsibilities, I serve as "advisor" to a group of students.  Yes, I help them choose classes, but my role as advisor goes well beyond pure academic advising.  I'm the first point of contact for their parents with the school, and for these eight students when they have questions about anything at all in the complex ecosystem in which we live.  We eat together once a week as a group, giving us a chance to share stories, to get to know one another.  

And, in my group, I arrange a birthday celebration for each student.  Usually these past couple of pandemic years, that's meant simply me getting take-out from a restaurant of the birthday boy's choice, plus cake and a chorus of "happy birthday."  Sorta predictable, but a meaningful diversion in a busy, demanding schedule.

Well, we're clear to take the students out to restaurants again.  Yay!  When it was Alexander's turn to choose the birthday event, he did ask to go out.  To Chuck E. Cheese.  

Sounds like fun, I said.  I remember going to several birthday parties at Chuck E. Cheese when I was younger.  It was a rather commonplace event - my wife says she used to go to "Showtime Pizza", which seems like the same sort of thing.  But Alexander - and five of the seven students who ended up on the trip - did not grow up in America.  A Chuck E. Cheese party was an exploration of American culture, similar to attending a baseball game, a Broadway musical, or a rural county fair.

I made the party reservation, on which I had to indicate the age of the birthday boy or girl.  The form did in fact allow me to input Alexander's new age: 19.

Most of these boys didn't know what to expect.  All got on the bus for the hour-long drive on a Sunday morning with a mix of excitement and skepticism.  Would this be fun, or stupid?  Or both?  Time is the currency of our school.  They were committing something like four hours of their precious free time to this event.  Will this be worth it?!?

Our wonderful host Reyna greeted me and the group, and quickly upsold us on more food.  (I knew ahead of time that two small slices of a medium pie each would not cut the mustard for these 16-19 year old boys.  Make 'em extra larges, let Alexander choose the toppings, and make it four or five slices each.  Plentiful food is a boarding school social lubricant, as would be alcohol for an adult gathering.)  She gave everyone wristbands for the games, and sent the students on their way to play.

After plentiful skee-ball, pop-a-shot, and other arcade games, the pizza arrived.  Two students seemed to have disappeared, but they emerged from the Mario Kart cave eventually.  (If they had been 7, I would have worried at their absence!  I figured these rather bigger boys would show up for food.)

My wife Shari and I were a bit disappointed that the restaurant no longer features an animatronic rat band.  That was the big feature of 1980s Chuck E. Cheese birthdays - the serenade by the creepy clicking plastic figures.  Instead we got just a video screen welcome.  But...

Apparently someone told the salad bar operator to go put on the rat costume, because OUT CAME CHUCK E. CHEESE HIMSELF!!!  The video board played a birthday song, and Reyna encouraged all of us to do a birthday dance with Chuck.  In the event, only one of my group - Taeho, the man from Gangnam, Seoul - danced.  Alongside every 7 year old in the restaurant and the poor soul in the rat costume.  The rest of my advisees looked on... but they were smiling.  They were, indeed, entertained.  I have pictures.  Not that I'm going to show you, because I want my advisees to be employable in the future.  But I have pictures.  Everyone, Alexander included, enjoyed the party.  It was worth the time and effort.

Why am I writing about Chuck E. Cheese on a physics teaching blog?!?  Because of the conversation I had with Reyna while the 16-19 year old "boys" cashed in their arcade tickets.

"Thank you for working with us," I told her.  "I expect you're not used to teenagers."  I didn't expect her response - Reyna was effusive about the experience.

"I was nervous at first," she said.  "I saw that Alexander was 19.  We do get people who come with bad intentions - 23 year olds who just want to make fun, or insult, or be stupid.  But I could tell when I first talked to your group that they were excited.

"You, and they, came with good intentions.  I can tell they had a great time.  And I was glad to be a part of that."

That's the lesson.  Teenagers are in fact a despised underclass outside the confines of a school - and, if you listen to too many teachers kvetching in the faculty lounge, often even within schools.  Reyna pushed through her prejudice, even though her prejudice was born of authentic experience.  She kept an open mind, and treated my teenaged, ethnically-diverse advisees with respect, with the assumption of good faith.  And we were all the better for it.  (Especially the restaurant's bottom line.  Rat pizza ain't cheap.)

Thanks, Reyna.