Two complicated true-false questions addressing impulse-momentum misconceptions

Toward the end of the impulse-momentum unit, after my class has played conceptually and experimentally with the impulse-momentum theorem, I ask the following on a daily quiz:

1. True or false: Two identical-mass object that fall from the same height must experience the same force during the collision with the ground.

2. True or false: Two identical-mass objects that each collide with the ground for the same amount of time must experience the same force in the collision. 

These require complex reasoning, at the absolute limit of what I expect from conceptual students after building skills for most of the year; and dead-center of the reasoning level expected from AP Physics 1 or C students.

I'm addressing misconceptions involving the impulse-momentum theorem.  In particular, students invariably look at J=Ft and assume that the force involved is just the weight of the object.  No!  When an object hits the ground, F is the force of the ground on the object, which generally bears no relation to the weight.

What are the answers:

For 1, imagine that one object hits muddy ground, the other hits concrete.  Not the same force.  (From J=Ft, J is the same for both, but t is bigger for mud, so F is bigger for concrete.)  So false.

For 2, same time of collision doesn't mean same impulse, i.e. momentum change!  For example, consider a happy and sad ball.  One bounces, one sticks - but time of collision is about the same for both.  Or, one egg that splats on concrete from a high height, one egg that hits on concrete from a lower height.  About the same time of collision, but the egg dropped from higher height changes its momentum by more, so experiences a bigger force. Also false.

Is there any need to teach dimensional analysis in AP physics? (No.)

With respect to AP Physics 1 in particular, I was asked:

Do you expect AP students to use dimensional analysis (factor-label method) when converting units?  Do they come to you with that skill?  I am considering the importance of the factor/label method to chemistry and its importance as a prerequisite skill to AP physics. 

Students pick up converting units easier using ratios.  This seems like one of those skills once they get it, it seems very useful to them later on.  I have always just assumed my physics kids could do it.  I don’t know if I am just holding onto it just because I learned it that way though.  Any thoughts?

Interesting question... I think the last statement is a wee bit on the nose.  A lot of us hold on to teaching skills and topics because of the way we ourselves learned them.  :-)  

Dimensional analysis, converting units, etc. is not useful in AP Physics 1, 2, or C.  In the very rare occasion in my class (not on the AP exam!) when I have to convert, say, from 40 mL to cubic meters, I type into google "40 mL to cubic meters".  The answer is 4 x 10^-5 cubic meters.  :-)  But, only 2 of 76 released AP Physics 1 free response questions have included even a single numerical answer.  And neither of those required anything beyond 5th grade math to acquire.  Physics 2 and Physics C have included more numerical answers, none of which require any unit conversions.

When we've introduced unfamiliar units, I deliberately use simple comparisons.  A meter per second is about 2 miles per hour, or 4 kilometers per hour.  That's easily close enough to understand whether a speed is reasonable for an airplane / automobile / runner / small slimy creature - and that's all that matters, 'cause google can do precise conversions if they're necessary.  A meter is about a yard, a kilometer is half a mile, a kilogram weighs 2 pounds.

I vehemently reject the old-school approach to physics problem solving that says "just manipulate the units until they match."  No!  Start every problem with a fundamental fact or equation.  The AP Physics exams are not going to assign problems that end in "gotcha!" because a student didn't convert centimeters to meters before plugging and chugging.  And for the frequent questions asking for derivations or justifications, the response "I got the answer because the units of momentum mean we have to have something with kg and m and s involved" simply won't fly.

Yes, in chemistry, the factor-label method is useful as students get their heads around grams, moles, and the meaning of an atomic weight.  But I let the chemistry teacher deal with that.  In physics, it is so critical to convince students that it is NOT a math course that I want to do nothing that gives the impression of a math course!  

For argument's sake, let's say I did teach dimensional analysis... I doubt that the chemistry teachers would notice any meaningful difference the following year in students' ability to execute this skill.  In the age of google, unusual unit conversion and dimensional analysis is simply not a useful skill in our students' lives -  unless they become a chemist, in which case they will figure this technique out on their own with ease.

Athletic coaches are servants, just like teachers are

My favorite pro football coach is Mark Parsons of the Portland Thorns.

Okay, it helps that I know the guy personally - he was my school's varsity soccer coach for about three years a decade ago, and I called his team's games on internet audio.  He moved on to coach professional soccer, has been with Portland for six years, and will become the coach of the Dutch national team at season's end.  I root hard for the Thorns, initially because of Mark's involvement - but now because I've grown to love the authenticity of the Thorns players, as well as the positive and inclusive Portland supporters' culture.

But why do I call Mark my favorite pro coach?  Well, he's good, as evidenced by his tremendous success over his years in the professional ranks.  More importantly, though, he understands the coach's role as a servant leader.  

I've been watching sports fanatically, quasi-religiously, even, for 40-odd years.  I've always believed that the game belongs to the players.  Coaches, umpires, broadcasters, and fans are ancillary.  I hate the "cult of the coach," in which the media portray coaches as godlike beings whose every move constitutes brilliant strategy.  This cult is worst in college basketball, where a player who gets a technical foul in the heat of the moment is said to require discipline for letting down their teammates; however, a coach who gets a technical is invariably trying to fire up his team in a calculated manner.  Spare me.

Somehow, we as a national culture have developed this deep-seeded idea that "leadership" from a coach must be egotistical and domineering.  That the success of a team is always due to - never in spite of - the quality of the coach.  Just look up the highest-paid government employee in each of the United States - in virtually every case, it's the state university's football or basketball coach.  

This cult makes me extra angry when I consider how physics teachers are treated.  Like coaches, we're judged negatively when our students don't do well.  But when we have outsized success on the AP exam, we're told "well, that's because you had the best students, no wonder they did well."  

Wait just a doggone second.  Firstly, why the eff do you think Nick Saban* is so successful?  He gets to pick only the best of the best high school athletes to play on his team.  A player who isn't doing well gets cut and replaced, with no consequence to Nick.  (Big consequences to the player, though, who loses his scholarship and has to go through significant bureaucratic hurdles to get permission to play for a different team.)  When Nick tried coaching in the NFL, which has a strong players' union and serious competition for players, Nick failed miserably, walking out on his team before season's end.  

*Head coach of University of Alabama gridiron football, $9.3 million annual salary for him, $0 average annual salary for his players

Yes, I have some students with serious natural talent in my class.  These folks need me.  They need the careful structure in the class that results in productive skill building.  They need me to help them bust misconceptions, or (better yet) to start them down the correct path in which they don't develop those misconceptions in the first place.  They need me to create a supportive class culture in which these talented students develop their confidence and understanding by helping their classmates.  Learning physics can be isolating and frustrating on one's own, even for the 800-SAT-math set.  These folks deeply appreciate a dedicated, skilled teacher.

And, unlike major college coaches, I have some students without top-level natural talent.  It's my job to work with these folks, too, to help them get better every day.  They might end up with 3s and 4s, not 5s, but without the careful course structure and supportive culture, they'd get 1s.  I am not allowed to ignore, bench, or cut these students.  They might not provide me personal glory for their top scores, but nevertheless I am charged to work carefully and diligently with them.  I am - and should be! - judged as much by how much these folks improve as by how well the natural-talent set perform.

In other words, I'm called to support all my students, to serve their needs, to meet them where they are to make them better.  Just like a coach should be.

In an interview last week, Mark Parsons explicitly articulated his calling to support his players.  Not to lead them, not to dictate strategy, but to - his word - "support" their development.  Mark praises his established superstars like Crystal Dunn and Lindsey Horan, but he also praises his top draft picks like Sophia Smith, and even the folks who don't start every game.   

When have you ever heard a coach speak of themselves as a servant, as a supporter for the players?  Sure, I have no doubt that a few prominent coaches do feel this way, but when have they ever articulated this approach publicly?  More often, the closest we hear is humblebrags about their tactical genius, or praise of a specific player after a win.

Mark's support-centered leadership is contagious, too.  Longtime player Meghan Klingenberg is a World Cup champion.  When she is asked about her role on the Thorns, she talks about her goal of making connections with her teammates, of supporting them, so that if they do ever end up having to have a tough conversation, all involved know that their words come from a place of love.  You ever hear a wide receiver or a first baseman talk like this?  No? Well, there's one big reason I love the Thorns.

An AP physics teacher is in the business of student development; results on the AP exam come from helping students get better every day.  Mark Parsons is that rare coach who recognizes that results on the field likewise come from helping players get better every day.  Regarding his philosophy coaching the youngest-ever American professional soccer player:  "The development path, we all think it's like this [mimes a line with positive slope], but we all know it's more like this [up-and-down motion whose trendline has a positive slope].  We are going to stay out of her way when she's doing great; and we'll catch her when she's doing not so great, to make sure she knows that we believe in her."

Would you rather be on a team with Parsons and Klingenberg?  Or with the domineering men who tend to coach in the mainstream American sports?  

Knowing the answer, I consciously emulate the rare coaches and player-leaders who carefully cultivate a positive team culture.  My students are on my team.  I stay out of their way when they're doing great, and I catch them when they're doing not so great, to make sure they know that I believe in them.

How to speed grading #4 - instant replay

I've talked extensively in the previous three posts about using a referee's mindset while grading.  Make the best call you can, get the ball in play, and move the game along.  Whether a tight judgement call goes one way or the other isn't something a referee can dwell on.

But, yes, sometimes referees do make egregious errors.  And that's why instant replay, or the Video Assistant Referee, exists.  Please understand, though, that in virtually all sports, instant replay has become something other than what was intended.  

In the 1985 World Series, Don Denkinger called a runner safe at first, when the runner should have been out by a country mile.  A replay review could have, within moments, determined that Denkinger's call was crazy-wrong - and Denkinger himself would have welcomed a quick word in his ear correcting his career-defining mishap.  That would have been the correct use of instant replay.

In virtually every college or professional football game nowadays, officials make a call that causes the commentator to say "I don't know about that one."  Then the game stops, the commentator yaps on in ignorance of the rules, frame-by-frame video of the event plays for five minutes or more... the referee announces the final decision, and the crowd, commentator, coaches, and players still complain vehemently.  That's the use of replay that has caused me to stop watching so much American football.

In your physics classroom, it's worth making a version of "instant replay," a route of appeal, available to students to right egregious grading errors.  The following are errors in need of correction:

• You meant to write a score of 11, but you wrote 1 instead.
• You didn't notice that the student had referred you to the rest of their response on the next page.
• The copy machine misprinted a student's test page, changing the substance of a test question.

Egregious errors are rare.  As you're well aware, though, students will grasp at straws, hoping against hope that they can convince you that you made several egregious errors on every one of their tests - enough to make their grade go up a notch, anyway.  To allow students to make tendentious arguments about judgement calls, especially in front of their classmates, destroys culture and drains your spirit.  You didn't sign up to be a prosecutor or a debate coach.

Long Islander Matt Sckalor delivers the Word of God when it comes to physics teaching, on this and every issue.  Matt's response to a student who thinks they see a clear and obvious grading error could be mimicked by every teacher:

"I can't talk about this now.  Please put your test in this folder here.  Tonight,  I'll re-grade the entire test for you."

Problem solved!  You've checkmated the student's attempt to use their debate skills to argue a better grade, because you're not listening.  You've checkmated those whose primary interest was performative complaining about the grading in front of their sympathetic friends.  

And you've checkmated those who were grasping at straws, hoping against hope that they might find one more point.  Watch these folks' body language.  As soon as you emphasize that you will regrade the entire test, their faces will drop.  They'll do some mental recalculation.  They'll recognize the implication - it's just as likely you'll find a place where you awarded one too many rather than one too few points.  They'll sigh, mutter some passive-aggressive comments, and walk away.  

Point is, by taking away the public or even private discussion, you're using your and your class's time more appropriately, doing test corrections and lab activities rather than grade discussion.  Other students who might have been preparing with their own defense attorneys will see the lack of success from the first student, and so give up the argument.

What if the student puts the test in the envelope?  Well, then regrade the whole test.  If the student is questioning one close judgement call, then look at every close judgement call.  I don't recommend deciding in retrospect that maybe the student deserved the one point they wanted to argue about.  I recommend leaving everything the way it was originally graded unless you totally screwed up.  It will help your piece of mind if you truly look carefully at the whole exam, including at the places where, in retrospect, the student hadn't said something explicitly enough but you awarded credit anyway.  Look everywhere, not just at the cherry-picked example that the student felt wronged about.  

And if you did in fact make the rare substantial error that was clear and obvious, just correct it.

Put the test in the student's box the next day.  Try to avoid handing it personally to a student before or during class - make it so they look at the test later, out of your presence, and preferably out of their friends' presence.  This is important whether or not you made any changes to their grade!  Teenagers live in the moment.  Chances are, they've forgotten about the minor issue about which they were so passionate about yesterday.  No need to remind them.  Let the argument die, put the ball in play, and move on.

How to speed grading #3: *When in doubt...*

In the first post of this series, I encouraged teachers to adapt an umpire's mindset when grading your students' work.  Don't think about why a student wrote what they did, don't think about what the student might have meant... just read with they did write, score it, and move on.

Next, I gave advice about how to prevent complaints on your test grading, by doing corrections before students see their original work.  Then there's no need to write comments that students won't read, anyway.

Even after taking these first two pieces of advice, teachers can still get stuck in the figurative mud while they wade through a stack of papers.  A rubric can't cover every possible answer, every possible approach to a problem.  In a stack of 50 problems, maybe 10 or 20 of them will cause you to pause and say, well... I dunno.  

Often times a student's answer lives in a quantum superposition state of earning or not earning a point.  If you're going to spend less than a three-hour-tour grading your tests, you simply must become comfortable resolving that wavefunction quickly and without regret. 

That's easy to say, difficult for a caring professional to do.  Try as we might, teachers live in the moment sometimes, too.  We want desperately for our students to do well on this particular test.  We want to be absolutely sure we've given every benefit of the doubt to a student response.  (We want to be prepared to defend ourselves against the inevitable lawyerly whine, too, but see the previous post about that.)  So we hem and haw.

Umpires and referees simply have no room for hemming.*  They must make a call in the moment.  So they train with "when in doubt" statements.

*Or hawing.

• When in doubt, it was an incomplete pass - not a catch-and-fumble.
• When in doubt, the runner is out at first on a bang-bang play.
• When in doubt, the player receiving the ball was NOT offside.
• When in doubt, the batter was in the box when she was hit with her own batted ball (so the ruling is "foul ball", not "out".)

These guidelines have been developed over years of veterans' experience.  They usually lead to a correct ruling.*  But that's not entirely the point!  These "when in doubt" statements also allow the game to go on with a minimum of fuss even if a parent's grainy video later shows that the referee got the call wrong by a centimeter.  We try not to disallow a goal or declare a turnover on a 50-50 call.  Instead, we make the expected call, the call that's not only more likely to be correct, but is least likely to turn the game in an unexpected direction.

* Professional trainers have published some experimental evidence on the second and third of these.  Yes, I read Referee magazine religiously.

Fans and players simply must get their heads around the idea that many situations in sports require split-second judgement by an official.  It's not good for the game for everyone to sit for ten minutes while the officials discuss amongst themselves, weighing arguments from opposing sets of players, then finally making a weak decision that only provokes further complaining.  No, it's best for the game for the official to make the best call they can, and get the ball in play again right away.

Two "when in doubt" statements I'd suggest that will help physics teachers make tight decisions:

• When in doubt, on a "derive" or "calculate" problem, if the final answer is right and some reasonable work is shown, award full credit.
• When in doubt, on a "justify" or "explain" question, doubt means do NOT award credit.

I mean, first and foremost, follow the rubric that the College Board or you have created for each problem.  Nevertheless.  When you're stuck, when you're not sure, use these guidelines and just move on.  The world won't end.  You'll end up with just as many (or as few!) arguments either way.  

In the end, an AP Physics test requires only 65-70% of the points to earn a 5, and 35-40% to "pass". It's not dignified to argue about the officiating.  Rather than complain about the one point that might have allowed them meet the passing threshold, perhaps the student should instead consider what happened on the other 60% of the points they crapped the bed on.