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07 October 2021

How a wave moves - conceptual physics question

An alumna of my Conceptual Physics Summer Institute was having some trouble with picturing the answer to this question from waves problem set 9.  She asked if I could help.  Of course!  This is an important but very difficult question which helps students understand how a wave moves along a string.

The question, which I've adapted from an old New York Regents physics exam: 

If you assign this, do NOT let students ask you questions!  Make them show their own personal understanding without you giving them hints.  I'd either give this as a quiz question to ensure it's students' own work; or allow collaboration among classmates so that they argue with one another, but can't in their minds simply appeal to the authority that "teacher said to think about <foo>" or "teacher said the answer is <bar>, so I'll make up some random bologna for my justification."  

And so, most students will get this wrong on first attempt.  Let them.  They need to struggle, to make their own mistakes such that they care about the solution you show them for a greater purpose than just getting a problem done.

How do I explain the answer?  I first put the PHET waves simulation on screen.  My students are familiar with this simulation, having played with it for 10 minutes as a previous assignment, and having seen it on screen a few times.

I set the simulation to "oscillate" and "no end," as in the screenshot below.  I turn the "damping" slider all the way off.  I tune the frequency slider to 1 Hz, meaning the wave has a period of 1 second.

I show the students that the wave moves to the right, while the pieces of the string move up and down.  (Of course I've shown this before!  I still need to show them again to set the context for this particular problem.)  I ask, how far does a wave crest travel in 1 second?

After a discussion, the class usually agrees that the wave travels one wavelength.  Great.  

Then I ask, how far does the wave crest travel in a tenth of a second?  Since we just discussed how far the crest travels in one second, they pretty quickly come up with 1/10 of a wavelength.  

But what does that mean for this particular problem?  Students still have a tough time connecting the top picture to the correct answer.  Many still think that since the wave moves 1/10 of a wavelength, that the wavelength itself is now much smaller, making the wave extra-squiggly.  I know, I know, this makes no sense to us as physics teachers; but that's a very frequent misconception.  Here's how I bust it.

I pause the simulation, and circle several positions, as in the picture on the problem set:


Then, I move the animation forward a few frames.  Everyone sees immediately what the new wave looks like (and that the wavelength hasn't changed!):



This is a good a-ha moment for the class!  It's not merely okay for most of the class to get something wrong on a quiz or on an assignment - it's on occasion absolutely necessary in order to advance the class's collective understanding.












12 September 2021

Mail Time: How (and especially *when*) I discuss the center of mass in AP Physics 1

I noticed that in the past couple years there've been a lot of center of mass questions on the AP exam. While my best students are capable of figuring these out, I wanted to try driving the point home on an exam with a good short answer justification-style question. I can't seem to make one that I'm satisfied with though. Preferably something that shows the center of mass can not change between two moving objects unless there is net force acting on them. 

I was thinking about an old AP question I saw regarding two balls moving in opposite directions on a moving train. Would it be a good idea to ask students to explain the velocity of the CoM based on the perspective of somebody on and off the train?

Ooh, I know that one!  It's a great question, from the official "practice exam" released in 2014.  

Me, I talk about center of mass very late in the year.  I make sure we're comfortable with the "simple" parts of N2L and momentum conservation first.  Next we do rotation.  I use the term "center of mass" where it's important, but I'm not asking students to truly understand collisions and systems from a center of mass perspective.  

Then, through the Pivot video "marble collides with can and wood block", and a bunch of examples including 2019 P1 #1 (about a velocity-time graph for the center of mass), the students start wrestling with the center of mass concept, and how the CoM obeys Newton's laws.  

The problem you suggest is a great one!  I'd just give it in March or April rather than now.

02 September 2021

Definition of acceleration lab, with a spark timer

A correspondent asked me about the "definition of acceleration lab`with dot machine." Is there a specific motion the students are doing? And the "dot machine" is like ticker tape/ strobe diagram? Where does that come in?

This exercise uses the tape timer or spark timer, one that makes 10 dots per second on a long string of paper.  (If you have the 60 dots per second machine, just have students graph every sixth dot!  :-)  )

Here's what I do with the students on lab day:

* Demo the dot machine from the front of the room - 1 minute.

* Divide into groups of 3 or so

* In the back, I have three dot machines [spark timers] set up.  I stand by one of them.  I work with the first group:

   * They adjust the angle of the track between 5 and 30 degrees, and measure that angle.

   * They tape the paper strip to their PASCO cart.  I thread the strip through the machine.

   * I start the machine, they release the cart, they grab their paper strip with dots on.

   * Once they verify that the machine worked, they go away to get position-time data; I start working with the next group.  They re-adjust the track angle, etc.

This takes only two-three minutes per group!  I run the machine because I know what to do, and I get down to business without putzing.  But, if a group doesn't want to wait for me to run the dot machine, they can use one of the other setups.  They see what I'm doing, so they figure things out pretty quickly.  

Once each group has their strip of paper, they make a table of position-time values.  They each get a copy of the response sheet, and they individually make the graph from their table.  The rest of the  response sheet is done as a come-and-show me where I check each part as they complete it.


30 August 2021

Mail time: using notation as stated in the problem stem

On an AP exam, are points awarded or not when a student doesn't use exactly the variable notation as stated in the problem (such as, M vs. m, or I vs Io)?

The answer is, it depends on the context.  There's no one universal approach, because each part of each problem is testing different skills, and the rubrics are developed independently by different leadership teams who might make slightly different decisions from year to year and problem to problem.  

When we develop each problem's rubric, the leadership spends a long time discussing just this question, looking at hundreds of samples to see the range of responses.  I'd say the line we try to draw is, we don't want to award a point where a student may have been ambiguous about communicating their physics understanding; but we don't want to be pedantic splitters of hairs.

To give a couple of examples from an AP question about a modified Atwood machine: on the free body diagrams, we didn't care about the specificity of the labels.  The objects were of different masses, m[a] and m[b].  But who cares whether they wrote "mg" or "m[a]g" on the free body!  They had communicated that each object experiences a downward force of the earth.  The fact that these forces were of different magnitudes wasn't relevant to the particular skill that was being tested in this part.  We accepted anything reasonable and unambiguous - Fg, mg, Fe (for force of earth), etc.  Failing to award points because "you didn't put the subscript on the m!" would have felt pedantic to those of us charged with creating the rubric, especially when each free body dot was even labeled "object a".  

But in the derivation in the very next part, it made a significant difference which mass the student was talking about!  Here, the problem was indeed checking to see whether the students understood, in "F=ma", which F, which m?  So here, we demanded the final answer have correct notation throughout.  I did not feel like a pedant when I failed to award points for no subscript on mg in the numerator of the final expression - such a result does not communicate a full understanding of the physics of the problem!

If you're not sure, ask yourself the question - are you splitting hairs, or are you demanding clear communication?  And if you're not sure, just pick one way and be consistent.  If you do corrections instead of handing back graded tests right away, then students won't notice or care - they'll learn from the correction that they needed, in that case, to use the notation given in the problem.  Which isn't an onerous ask.  :-)


12 August 2021

Demonstrations with the visual accelerometer

I introduce acceleration as how much an object's speed changes every second. No "delta-v over delta-t"  for me - this equation obscures the physical meaning of acceleration, and will invariably be used by students as simply v/t.  But a couple problem sets in which students write the definition of acceleration as their starting point and reason from that fact work wonders.

That said, before I even dig in to the meaning of the magnitude of acceleration, I work on the direction of acceleration.  We use two simple facts:

1. When an object speeds up, the object's acceleration is in the direction of motion.
2. When an object slows down, the object's acceleration is opposite the direction of motion.

First question, then: I release a cart from rest.  Now, as the cart rolls down an incline, what is the direction of the cart's acceleration?  
Anthony
(by @Aldescery)

No, Anthony, don't shout out an answer.  Start by reading a fact word-for-word, and then tell me how that fact answers the question.  

"When an object speeds up, the object's acceleration is in the direction of motion.  This cart speeds up while moving down the incline.  So the cart's acceleration is also down the incline."

Perfect. The concept is still extremely abstract to students, though.  On this first day of acceleration, my students are still translating "acceleration" to "speed" in their puppy-physicist heads.  They are answering this question by rote.  I need to show them, demonstrate for them, that their rote reasoning led to a physically-verifiable prediction.

I use the PASCO "visual accelerometer", pictured at the top of the post.  This particular device has been discontinued by PASCO - they offer a new device that attaches to the smart cart.  If one of your colleagues is good with the Arduino, then I've been told it's trivial to hook up some LEDs and an acceleration sensor to make a similar device to mount on a cart.

So next, I actually release a cart from rest at the top of an incline.  The visual accelerometer mounted on the cart lights up - the lights pointing down the incline light up.  Students see that the cart's acceleration was, in fact, down the incline. 

Second question: I push the cart and let go (without the visual accelerometer mounted).  While the cart is moving up the incline, right now! - I snap my fingers after I've let go, while the cart still is moving up the incline - what is the direction of the cart's acceleration?

"When an object slows down, the object's acceleration is opposite the direction of motion.  This cart is moving up the incline while slowing down, so the acceleration is opposite the direction of movement - acceleration is down the incline."

(Careful with language here - I try from the very first instance to stamp out the two uses of language that lead to serious misconceptions.  I don't allow students to use "accelerate" as a verb; and I don't allow students to say that acceleration "moves" in a direction.)

And I do the demonstration.  The lights pointing down the incline light up... even as the cart moves up the incline!

Third question:  This time, I'm letting the cart go from rest, the cart moves down the incline, and I catch the cart in my hand.  While my hand is touching the cart - I snap my fingers as I catch the cart - which direction is the cart's acceleration?

"When an object slows down, the object's acceleration is opposite the direction of motion.  While you're touching the cart, the cart is slowing down, so the acceleration should be opposite the motion, up the incline."  This one is a bit harder, because students have to recognize that the cart slows down AND still is moving down the incline while I'm catching it.  But seeing me execute this motion helps them understand.  If I need to, I exaggerate the contact time, so that they can see the cart slow down for longer.

Of course, physics works - the down-the-incline lights are on until I touch the cart, at which point the up-the-incline lights instantly appear.  Nice.

Final question, which I generally save for another day once the class has practiced a good bit with acceleration concepts:  Now I push the cart up the incline and let go.  Right at the top - CLAP! - when the cart briefly stops, I want to know the direction of acceleration.

(I answer this one myself.)

The cart's speed is momentarily zero at the top of the incline.  If an object's speed is zero, its acceleration must also be zero.  So the lights on the device will flick off briefly when the cart reaches the top.

As I busy myself with mounting the visual accelerometer on the cart, I usually can hear some students grousing a bit.  "Um, you didn't use a fact," one might say.  Or, "why does acceleration have to be zero when speed is zero?"  Those who have had physics before or those with amazing intuition might complain that gravity is still acting down, so the acceleration has to always be down the incline.  The majority of the class sits and listens... they had agreed with me because I'm the teacher and I spoke confidently.  They're a bit uncomfortable that classmates are objecting.  

It doesn't matter exactly what students say.  I move on and do the experiment - experiment is always the arbiter of truth.  

And, of course, the lights emphatically do not flicker off.  Even if I make the incline really steep.  

I stay away from a force explanation for now... I ask a student to read the definition of acceleration.  Acceleration is how much an object's speed changes every second.  So, if the cart's acceleration were truly zero at the top of the incline, the cart's speed wouldn't change.  The cart has zero speed for an instant... with zero acceleration, the cart would stay at rest at the top!  And then I push the cart up the incline, grab the cart at the top to keep the cart at rest while the lights blink off.  The class sees what it means for the lights to blink off at zero acceleration - the cart's speed couldn't change!

Please don't think this demonstration is the One Weird Trick for understanding acceleration!  Yes, it helps a lot.  But getting students to stop conflating acceleration and velocity is a battle of attrition, demanding multiple methods of misconception-busting over the course of a full year.  If you can get even 25 of 30 students to get a question like "A ball is thrown upwards with speed 5 m/s, what is the magnitude of its acceleration at the peak of its flight?" correct on an end-of-year test, you are a physics teaching virtuoso.  

05 August 2021

Newton's first law on a rafting trip

 Yesterday, my family and I took a rafting trip down the Colorado River.  

The trip began with the obligatory safety and instructional lecture.  Dylan the perky guide assured us in an enthusiastic voice that we were about to have FUNNNN!  And then when we didn't holler in ecstasy, he asked us again if we were about to have FUNNNN!  Thank goodness the parents with two enthusiastic ten year olds in tow gave the requisite response so that Dylan moved on.

In a spiel that reminded me of the boat operators on Disney's Jungle Cruise, Dylan went on to explain truly important safety information like what to do if you fall out of the raft, how not to accidentally whack your seatmate with an oar, and so on.  Next came navigational instructions.  After demonstrating proper paddling technique, he described the commands we might hear.

"When I say 'forward one', everyone paddles one stroke - only one stroke! - forward.  Everyone show me 'forward one'!"  Everyone dutifully mimed a single stroke.

"Now show me what you do when I say 'backward one'!"  The assembled masses pretended to paddle backward once.

"Sometimes I'll have you paddle 'full forward'!  What do you think that means?" Some shouts from the ten year olds suggesting that we should keep paddling forward.  "Good!"

"And finally, if I say "all stop," then hold on to your paddle, but keep it out of the water.  What do you think happens to the boat?"

My moment had arrived!  "The boat continues to move at a constant speed, due to Newton's first law!" I said loudly enough to get a Look from the fellow rafters, including, especially, from my own family members.  Dylan looked a bit hurt that I had anticipated his punchline.  But, he cheered up a wee bit when the ten year olds shouted that the boat would stop.  "No, the boat is on a river, it's gonna keep going! Dylan cheerily told everyone, while he looked sidelong at me.  Sometimes it's a social curse to know physics.  

Tune in next episode when I describe how I explained the phenomenon of concave acoustic mirrors to a flummoxed guide on our Savannah, Georgia Ghost Tour.


22 July 2021

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.

20 July 2021

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.

10 July 2021

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.





08 July 2021

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.