Setting up authentic AP problems in lab - 2015 P1 #3

One of the all-time best sources for college-level, open-ended laboratory ideas is the AP exam itself.  While some AP problems are explicitly posed in an experimental setting, the large majority of the released problems - free response and multiple choice - can lead to an interesting laboratory investigation for students in the latter half of the school year.  See this post, this post, this post... you get the idea.

It took me several attempts over the years to get decent data for 2015 AP Physics 1 problem 3.  (Here's the link to the 2015 free response questions.)  To summarize, the question posits a block in contact with a compressed spring on a frictionless surface.  The spring is released from rest.  At the spring's equilibrium position, the block comes off the spring onto a rough surface.

The primary experimental challenge is to produce data verifying the answer to part (a)(i): Sketch a graph of the block's kinetic energy as a function of position.  In particular, we need to show the correct shape of the graph before and after the block reaches the spring's equilibrium position.

The theory: Okay, obviously the kinetic energy increases to a maximum at the D = 0 equilibrium position, then decreases back to zero, because the speed increases than decreases.  The functional form of the graph is the complicated bit.  It's easiest to see through an energy approach:

Before D = 0, the potential energy of the spring is given by (1/2)kD².  This means the potential energy drops to zero as D², i.e. parobolically.  Since the sum of kinetic and potential energy must be a constant value on this frictionless surface, the kinetic energy curve must be an upside-down parabola.

After D = 0, the block loses kinetic energy because work is done on the block by the friction force.  Work is force times distance traveled parallel to the force... that is, linear with distance.  Thus, the kinetic energy drops linearly until the block stops.

The experiment: You'll need a compressible spring, a way of keeping the block moving in a straight line, and a device to record speed as a function of position.

(You DON'T need to worry about the "frictionless" surface before D = 0.  The shape of the graph is still parabolic, even if there's work done by friction before the block is released.  Why?  Because both the with- and without-friction mathematical functions -- (c - kD²) and (c - fD - kD²) -- are parabolic.)

My students and I flipped a PASCO two-meter track upside down to find a groove just about the right size to fit one of those wooden felt-covered friction blocks.  We stuck a Vernier sonic motion detector in the groove about a meter away from the track's edge.  The detector was set to acquire data at the highest possible frequency - I think we used 50 points per second, but I'm not entirely sure.  At the edge of the track, we pushed the block against the spring and let go.  The spring uncompressed, the block slid toward the clicking detector. 

Next came some serious data presentation work.  We had to figure out how to use the Vernier Labquest to graph calculated data columns - it only automatically produces distance, velocity, and acceleration data.  But this is a matter of programming, not physics.  We got the device to output (1/2)mv² on the vertical axis; on the horizontal, we used a subtraction function to adjust the distance from the detector so that "zero" represented the location of the block with the spring uncompressed. 

And sure enough... though the function looks choppy because we only have one point every 0.02 s, it's the correct shape:

As an improvement, a student suggested using a PASCO smart cart on a track, attaching a crumpled piece of paper or similar to the front of the cart to produce some frictional drag on the track.  The motion encoder in the smart cart's wheels can take more frequent (and more precise) data than the sonic sensor.  However, I don't have enough familiarity with the sparkvue interface to create the derived graph from the raw data.  If you do, please try the experiment and email me the results - I'll post them here!

Ask not what your students *should* do. Ask what they *do* do.

I was in high school marching band.  We won the Kentucky state title in my senior year.  Please hold your applause.

"I'll bet youall practiced a lot," you say.  Sure: we had summer band camps, and after-school practices equivalent to those of varsity athletic teams.

So, yes, the volume of practice time was certainly helpful to our success.  Nevertheless, we routinely defeated other bands who practiced similar hours.  How we practiced was as important as how much we practiced. 

Two questions to ask about our band director's pedagogy:

Question 1: Should voluntary participants in an elite high school ensemble, for which we were graded and earned academic credit, be expected to do independent, self-motivated practice?  Should band members come to rehearsal with their parts mastered, ready to work on fine tuning and advanced ensemble work?

Answer: Yes.

Question 1a: In actuality, out of 50 band members, how many dove into said independent, self-motivated practice?

Answer: Two.  On a good weekend.

Importantly, the band director didn't nag us about practicing our instruments on our own time.

Instead, he worked with us on difficult passages during rehearsals.  He showed us techniques that would help us improve.  So, using the regularly-scheduled rehearsal time alone, we got pretty good.  When he did need us to do some practicing outside of rehearsal time, he'd give specific goals -- "on Monday, you must be able to play measures 98-116.  I'll pick a couple of you randomly to play for all of us."  No nebulous and shaming "make sure you practice this weekend!" for us.

Question 2: Should the participants in the school's highest-level ensemble, one that expects to be competitive with the best bands in the state, have mastered basic skills prior to important mid-year rehearsals?  Should the participants retain training from practice to practice, from week to week, such that the director does not need to re-teach basic skills and already-taught elements of the competition show?

Answer: Sure.

Question 2a: In actuality, how well does the band retain skills and show content if they're not reinforced on a very regular basis after band camp ends?

Answer: Not well at all.

The band director didn't nag us about retaining skills.  He didn't complain that we should have learned these things by now.  Instead, he drilled us such that we didn't forget.

Every practice, all season, began with marching fundamentals - everyone in a block, at the command of the drum major performing a number of basic maneuvers, all the while the director and his assistants watched like hawks for uniformity of technique.  Then came the musical warm-up, reinforcing basic skills - perhaps today we did an exercise based on the E-flat scale, maybe tomorrow was a tuning/blending exercise, the next day rhythm or embouchure drills. 

This all took at least 30 minutes of a two to three hour practice.  And was worth every moment.  (It was, honestly, a bit drudgerous.  However, the first 30 minutes of practice became ritualistic, such that we felt a hole in our collective soul on those rare occasions when we didn't do fundamentals and warm-up.  I recall a couple of occasions when the upperclassmen practically demanded to start practice the "right way" when someone proposed to skip warm-ups.)

Next, we'd re-teach pieces of the competition show in small chunks on a regular basis.  By season's end, each segment of the show had been taught in the summer, then re-taught two to three times.

Physics teaching connections:  

(1) While students in an AP -- read "college level" -- class *should* be able and willing to put in many hours of engaged homework time each week, in practice they're not.  It's our job to design the course with expectations about out-of-class work which students can and will meet.  Then it's our job to find a way to use class time to develop physics skills such that students can make the best possible use of what time they do devote to out-of-class study.  We need to solve problems in-class.  We need to teach how *not* to ask for help fifteen seconds after reading a problem.  We need to teach how to start an unfamiliar problem, and how to collaborate with classmates to communicate understanding.  

(2) While students in an AP class *should* be able to retain basic facts and problem solving techniques from week to week; while elite-level students *should* come to our class with algebra skills; fact is, they don't.  It's our job to design the course to teach/reteach even things they should have already learned.  Give fundamentals quizzes.  Don't give unit tests, give cumulative tests.  Assign problems that require students to circle back to already-mastered material.  

Look, if you know anything about my classes, you know that I'm as far from a fluffy no-standards teacher as it's possible to be.  Yet teaching rigorous physics doesn't mean we have to expect monkish devotion from our students.  When we complain to our students or our colleagues about how the kids just aren't studying like they should, we alienate the audience.  Meet the class where they are, not where they should be, and everyone will be happier and more successful.  Yes, of course require the class to know and use appropriate skills as the year progresses... but continue to teach those skills in context, too, so that even those with weak backgrounds and minimal out-of-class devotion can eventually catch up.

Hints for preparing students for a physics presentation

I'm thrilled when I hear about physics teachers using student presentations and formal student-led discussions as teaching tools.  Students should come out of our classes with the ability to explain physics orally as well as in writing.  But that's easier said than done.

Think back to your high school (or college) days.  How did you feel about listening to your classmates when they did formal presentations?  (Not how did you feel about giving presentations -- since you became a teacher, you might have liked that just fine.)  Did you look forward to presentation day?  I doubt it.  Possibly you were neutral, taking the "at least we don't have to listen to the teacher for an hour today" approach.  

More likely, you dreaded those classes.  Student after poorly-prepared student with minimal public speaking skill, some reading (badly) straight off of hastily-written notes.  Aargh, it was academic torture.

So don't make your own students suffer.  If you're going to do formal presentations, prepare for them with tremendous care and detail.

Set time limits, and enforce them.  Set a timer on your phone with a loud alarm at the end.  The students must know going in that if the buzzer goes off before they're done, they're done anyway.  No pity, no remorse, no exceptions.  Don't yield to the temptation to allow a student just to finish a thought, or to give them just a bit more time because they didn't quite get to the important part of the presentation.  You're teaching a life skill here.  Let them fail - then next time they probably won't fail.

Presentations can be very, very short and still be useful.  Even a long-term project can often be summarized in three minutes.  In fact, it is a valuable skill to learn how to communicate complicated ideas in such a short period.  What makes student presentations so painful is often the attention they give to irrelevant details, while the audience rolls its collective eyes saying "arrgh, get to the point."

Do not allow powerpoint.  Slides are too often used as a substitute for substantive communication.  See also this post. 

Practice, practice, practice.  Ideally, you'll go through the class for several days before the presentations, watching each student in turn and giving feedback.  You'll also have students giving their presentations to each other for days before the actual event, giving each other feedback.  Make a video recording of students speaking - it's painful but important for students to see themselves droning on without eye contact, repeating themselves without communicating anything important.  Force students to see these mistakes while they still have the opportunity to correct them before presentation day.

If nothing else, assign presentations for homework - require three dry runs in front of another human.  I mean, you know darned well that typically students try to wing presentations without appropriate preparation.  So require that preparation in and out of class.  Give the students a homework sheet that asks for the signature of the person who watched each presentation.  If each presentation is only three minutes without powerpoint, that's not a burden at all - it's a ten minute assignment.  

Too many teachers throughout the years have assumed that their students know already about basic speaking-to-an-audience skills, have assumed their students will be self-motivated to practice and perfect their presentation.  Then when the horrible presentation starts, everyone is embarrassed, just like when the kid at the talent show didn't practice his clarinet solo and now has no choice but to honk on.  It's our job to insist on the practice that we know teenagers won't likely do.  It's our job to teach the speaking skills that students haven't internalized yet.  

Eyes up.  The first thing I do in practice is start making faces at the students who stare at the whiteboard or at their notes instead of making eye contact with the audience.  Pretty soon, the whole class is helping each other keep their eyes up.  This good posture subsequently encourages students to speak naturally, telling their story to the audience rather than talking to themselves.

Who is the audience?  It's not good enough to tell the class "you will be speaking to your classmates and two other science teachers - all of whom are familiar with the first-year physics that you have learned."  It's not even good enough to explain what that means in front of the class.  You must allow the students to make mistakes in their assumptions about the audience, and then learn from those mistakes.

For example, a student will write an equation like d = vt, then spend 45 s of their three minutes umming and hmmming through an explanation of what d and v and t stand for.  It's never occurred to this student that the audience is familiar with this equation. That all they need to say is "We use d = vt because the cart's speed is unchanging." That the audience is more interested in the physical prediction made by this equation, and how that prediction is verified experimentally.  

So tell this student right now!  Right now, your feedback is in context.  You're not droning on about something that your quite intelligent and experienced-at-school student thinks that she already knows.  You're gently correcting a serious error immediately after it's made.  Your student can't tune you out, or say to herself "whatever, I know that."  She's just screwed up.  If you speak firmly and with love, showing with your whole being that you are helping prevent a mistake on a bigger stage, your student will listen, and appreciate your helpful feedback.

And the message will spread throughout the class.  The student you just critiqued will, in turn, share that feedback with the person she watches for practice.  And everyone will get better, as a team.