Addressing AI use for school assignments - *It's not about AI!*

"I don't understand why using AI for assignments isn't allowed.  AI is a tool, right, like a phone or a computer?"  Peter made this comment in authentic good faith.  The tone was curious.  Peter, my student, wasn't being performative, or jockeying for social capital - no other students were even around.  He honestly wanted to know my thoughts.  And so I answered honestly and openly.

"I guess it depends on the purpose of the assignment," I told Peter.  "I agree, AI is a tool, a robot.  Would you use a robot to vacuum your floors?"

"Well, yes," he said.  "That's what a roomba is."

"Right," I said.  "Because the purpose of vacuuming floors is to have a clean floor."

I followed up.  "Would you use a robot to lift weights for you when the team goes to the weight room?"

"Of course not!  That's dumb," he said.

"Why is that dumb?"

"Because the purpose of weightlifting is to build muscles, not just to raise and lower a dumbbell."  Peter's eyes widened a bit.  "Oh, I get it.  That makes more sense now."

My analogy here is not likely novel or interesting to people reading this blog.  Conversations in which I explain simple ideas to teenagers are commonplace.  I mean, I teach 9th grade.  I'm used to student puzzlement about things that are obvious to me, things beyond Newton's third law.  For example, I had to explain the meaning of the word "sacred" the other day.  The student newspaper, edited by a senior, referenced "the Beatles rock musician John Lennon," which still provoked the question "what's a Beatle?"

So why do I relay my conversation about AI?  Well, because it's not only about AI.  AI is just the bogeyman of the day.*

*To paraphrase Neil DeGrasse Tyson, who was totally speaking tongue-in-cheek:  AI has been all around us for years.  It's only become a "problem" since humanities professors realized it could write students' papers for them.

The idea of a school assignment as authentic practice, in the same category as sports conditioning or musical scales, was foreign to Peter.  He had always thought of schoolwork as a chore, as a means to an end.  Get these answers right by any means necessary.  

Before you harumph at Peter, consider typical middle school or elementary school culture.  How often do you hear about parents who do their kids' homework for them?*  Even in 1983, a quick look around my class's "visual aids" would show twenty professional-level works of art, and two thrown together with watercolors and rubber bands.  Twice (in the 1990s) I took jobs tutoring middle school students.  Twice the parents stopped calling me when they realized that I wasn't just giving the student answers, and that I wasn't making myself available on short notice when said student forgot they had a major assignment due the next day.

*Well, the parents SAY "I never do my kids' homework for them!  But I always check it over to be sure their answers are correct.  If they're confused and I don't know how to help them, I ask my spouse.  Boy, do I hate it when a class covers material that we don't know about!"

Worse, my experience - in both public and Catholic school - was that teachers praised the students who produced high-end projects with, shall we say, heavy adult influence.  And the few of us with projects that looked like they were fully created by a middle schooler were either shamed or pitied.

I've often addressed assemblages of middle school parents who are considering sending their kid to my high school.  They ask, "what can we do to help our child be ready for the rigors of high school academics?"  My answer is always, "Make them do their homework on their own.  Don't help, check, read over, or discuss their assignments at all, ever.  Allow them to fail - and then let them recover.  Then they will know their successes are truly their own, not due to a 'support network.'"  

This response never fails to produce surprised looks.  Not hostile looks, as the parents are asking the question authentically and are willingly listening to the answer of an "expert".  It seems, from the reaction and the follow-up conversations, that most parents had simply never thought about the developmental purpose of authentic schoolwork.  

Just as Peter hadn't.

Joe Hicks, "in my judgment"

I attended the Harry Wendelstedt Professional Baseball Umpiring School in 2008, on school sabbatical.  For those readers who were not obsessed with national league baseball in the 1980s, Harry Wendelstedt was one of the best-known and most-respected* major league umpires during his 33 year career.  He was a very old man that year when I met him at the school.

*Respected, yes; but Wendelstedt wasn't God.  Doug Harvey was.

Toward the end of the five-week program, I asked some folks back home in central Virginia how I might get into umpiring at the high school level, now that I had serious training.  They told me to call local umpire supervisor Joe Hicks, a name I recognized.  I called.  I told the man on the phone with the Virginia down-home drawl that I was currently at the Wendelstedt school, and that I was interested in doing some umpiring when I returned.

"Oh, Harry!" Joe said.  "How's old Harry doing?  Tell him I said hi.  Oh, and we'll put you on our schedule this spring."  Okay.  That conversation went more easily, and more interestingly, than I anticipated.

Joe Hicks died last week, age 91.  At his funeral, no shortage of folks discussed Joe's friendliness, his kindness, his willingness to assume good faith of others and to offer help to those in need.  And yes, they discussed his baseball prowess.  They told of Joe helping his grandsons with their hitting when they asked.  They told how when Joe, age 70, was handed a bat during a game of stickball on the beach, his one swing ended the game - he hit a beach house that had been out of range for all others.  Joe was a small-town guy who became famous, yet remained humble, who never used his status for self-aggrandizement.  

I first met Joe and his umpiring partner Alex Smith in the early 2000s when I was coaching JV baseball.  They called virtually every game on campus, JV or varsity.  After the game, they would invariably head to our boarding school's dining hall for dinner.  I found out later that Joe deliberately assigned himself to Woodberry games because we were the only school who offered a free meal to go along with the $50 game check.  

I'd occasionally sit with Joe and Alex.  We'd talk baseball, and baseball umpiring.  Even before my foray to umpire school, I had a reputation on campus as a baseball rules expert; but here were two folks who were truly expert, and who were excited to teach me things.  Joe never let on about his history in the major leagues.  Alex let a couple things slip, bragging about how Joe had played for Casey Stengel, or how Joe had hit a walk-off home run off of Don Larson in the Polo Grounds.  Joe just said, "well, I did, but we didn't call it a 'walk-off' in those days."  

Joe welcomed me into the local association for the 2008 season.  He made sure I had a well-seasoned and supportive partner for my first-ever game.  After that game, Joe called me up to ask me how it went.  "Well, I didn't do anything crazy-bad, but I'm not happy with calling balls and strikes.  I know I missed two curve balls that dropped in for strikes."

"You only missed two pitches in the whole game?  I mean, that's great work!  You got hundreds right, then," he said.  Well done, Joe - being kind, building up the first-time umpire's confidence.  

What sticks with me about my umpiring conversations with Joe is how he taught me, and all umpires in the association, to handle conflict.  Again and again, an umpire would describe a tough situation they* had encountered; and Joe would recommend starting the explanation with a folksy, "coach, in my judgment..." 

* No, not necessarily "he".  Joe's association, in 2008, was the most diverse group of umpires I'd seen.  At umpire school, of 120 trainee umpires from all over the western hemisphere, 119 were white-looking folks, including one woman.  In Charlottesville, there were men of multiple colors, and many racially diverse women.  That's more usual in 2023, but Joe had reached across racial and gender lines before that was common in the hidebound world of umpires.

Joe's thesis was, the umpire is there for the express purpose of making judgments.  If the umpire sticks to that purpose, a coach has little room for argument.  An emphatic "I'm telling you, your runner was out" as a statement of fact practically demands the angry coach to riposte, "no he wasn't!"  But a calm "coach, in my judgment, the catcher put the tag on before the runner touched the plate" has a disarming quality.  Sure, the coach can give his version of events... but rather than emotionally charged statements of conflicting facts, the discussion becomes one of conflicting judgment.  And the umpire is the one paid to use their judgment to keep the game moving.  

I've used Joe's phrase - even his intonation! - "in my judgment," hundreds of time since 2008.  And only occasionally on the baseball field.  Usually, I'm discussing a student's placement (or lack of placement) in an advanced science course.  Or a failing student's plan to improve.  Or my observations of an interpersonal conflict on dorm.  Or a disciplinary matter at boarding school.  Or a problem I've graded.  "In my judgment, this response does not state that acceleration, not velocity, is to the left, and so does not earn the point."  I'm employed by my school precisely for my experience in putting forth this sort of physics judgment.  The 14 year old responding "well, in *my* judgment, it does" sounds silly.    

I miss you, Joe.  Rest in peace.

Center of mass calculations for AP Physics 1

The revisions to the AP Physics exams for 2025 are imminent.  I've posted about the formatting changes, which are truly no big deal for physics 1/2, and are so, so welcome in physics C.  (Doubling the time available for the exam, but not doubling the length of the exam, will allow students the time they need to approach complicated questions.)

The *content* changes are nonexistent in physics C. In P1, most folks are focused on the major change that adds fluid mechanics.  But what about the minor changes to P1?  They're there, too: the parallel axis theorem, quantitative questions about gravitational potential energy in orbits, and calculations with center of mass.

So what is there to know about center of mass quantitatively in AP Physics 1?

First of all, the conceptual treatment of center of mass motion that's already covered on this exam won't go away.  We still need to understand that the center of mass of a system obeys Newton's laws - with no unbalanced external force, the center of mass moves in a straight line at constant speed; with an unbalanced external force F, the acceleration of the center of mass is F/M where M is the system mass.

Then, the conceptual understanding of the location of a system's center of mass still is relevant.  For a symmetric object, the center of mass is in the, um, center.  For two equal-mass objects, the center of mass is right in between.  And for two unequal-mass objects, the center of mass is closer to the larger-mass object.

The new stuff is based on calculating the position of the center of mass using the equation m1x1 + m2x2 = Mtotal(xcm).  No, please don't write this equation using the notation from the updated official equation sheet, with summation notation!  Your students don't know what that ziggy-zaggy capital E is; and why is there an i in there?  We have to know about imaginary numbers now?!, they'll ask.*

*Yes, I'm aware that students must be able to calculate for more than two objects, in which case the equation I wrote is technically incomplete.  Students will figure out how to add a third or fourth object just fine once they have experience calculating for two objects.  In first year physics, complicated but precise mathematical notation obscures rather than elucidates meaning.  Sort of like any statement that includes the word "technically."

The AP Physics 1 exam famously has minimal use for numerical answers.  Only one of the ten revised "science practices", with which each AP Physics 1 exam question must align, includes calculating numerical quantities.  So while "here are two objects and their positions, calculate the location of their center of mass" is a legitimate question, expect this end-of-textbook-chapter-style problem to be rare.  But what else is there?  Think of the same kinds of questions that are asked about kinematics or energy:

* How would the center of mass position change if the left-hand object's mass were doubled?  If both masses were doubled?  If a third object were placed somewhere?

* Graph the position of the center of mass as a function of the mass of one object; graph the position of the center of mass as a function of time with this known external force acting on the system.

* Describe an experiment which will determine the center of mass position for this set of objects on a thin plank.  Now here's some data from that experiment; plot the data and use the slope of a best-fit line to determine the center of mass position.

All these questions start with the center of mass formula, but use the formula to make predictions, graphs, experimental conclusions.  And that's AP Physics 1 in a nutshell.

Why use energy bar charts?

The usefulness of graphical representations over straight-up equations and calculations for understanding energy concepts has been well established in physics teaching literature for years.  Yet, still only a fraction of physics teachers - especially at the college level, as reported to me by recent graduates - use such representations as an integral part of teaching energy.  

For most teachers I work with, their story parallels my own.  At first, reluctance to use energy bar charts seems to have three possible causes:

(1) I was never taught that way; I and my classmates understood energy with equations without trouble.

(2) It would be a LOT of work to change my materials not just to add in bar charts, but to de-emphasize algebraic algorithms.  And it doesn't make sense to do this work because...

(3) My current students are understanding just fine; they're getting answers right more often than not.

I resisted teaching energy bar charts for nearly the first two decades of my career - mainly for point (3) above.  For the most part, my students seemed to be learning energy without trouble.  The old calculational AP Physics B exam rewarded quantitative reasoning.  So I taught my class the most general form of an energy conservation equation I could:

W_NC = (KE_B – KE_A) + (PE_B – PE_A)

Students were taught to identify two positions A and B, take out any terms that were zero, plug in the KE and PE formulas, and solve.  This allowed students to get correct answers, or at least copious partial credit, for practically any Physics B problem you could imagine.

This algebraic formulation caused difficulty when students were asked to reason with energy.  Most students dutifully plugged in correct variables, or correct numbers for the correct variables.  But what they *saw* was a bunch of gobbletygook, as if the work-energy theorem were written in Klingon.  

Yes, I'm personally fluent enough in mathematical notation that I can quickly describe conceptually how a change in a physical situation would affect the calculation.  Physics Education Research has provided abundant, replicable evidence that the vast majority of students are nowhere near as fluent.  

(Some would argue that students in a college-level physics class should be good enough at mathematics to do advanced analysis with an equation this simple; after all, most of these folks are in a calculus class, and algebra of this sub-basic level was generally taught in 7th or 8th grade!  Yet, arguing what students should be able to do in the face of evidence to the contrary is not a recipe for success.)

When the AP Physics 1 exam came on line in 2014-15, its incessant demands for non-quantitative reasoning forced my hand.  I opened up the wardrobe to find and create energy bar chart exercises, labs, problem sets, etc.  And lo, a new conceptual world opened up Narnia-style.

Look, would I have ever taught Newton's second law without free body diagrams?  Of course not!  If you just teach "F = ma," then students plug in any old F to the equation.  If you tell them they've used the wrong expression or number for F, they'll pull another out of their tuckus at random.  But the free body diagram forces* students to represent all the forces acting, and thus to pay attention to why each force might or might not exist, before they do any math at all.  The diagram ensures that students can't just plug numbers into equations in search of being done - they have to do the problem right.

* ha!

The purpose of an annotated energy bar chart is identical.  With just an equation to work from, students are trained from birth or middle school to plug in numbers and solve; exactly what numbers they use don't matter.  But now, students have no choice but to describe briefly why they chose to include or not include each bar representing a form of energy.  The exact size of the bars isn't important - just as I don't demand a to-scale free body diagram, I don't demand a to-scale energy bar chart.  What matters is whether there are more or fewer bars for each form of energy, or whether there are bars at all.

And finally, the energy bar chart gives students a starting point to get them out of their "I can't do this" inertia.  Anyone in my class, no matter how weak, can start drawing a free body diagram or an energy bar chart.  If they pay attention to their annotations, they often catch their own faulty reasoning.  When they seek help from me or a friend, the discussion begins with the diagram rather than with mathematics.  It's difficult for a student to understand why their mathematical work is wrong - especially when the actual mathematical algorithms were done correctly, but the starting assumptions were incorrect.  It's simple for a student to see why a diagram isn't right, and then to redo the mathematics based on the correct starting point.

Proximity of the professor is a problem

Have you ever passed less than a meter from a working student's desk and had that student look up, see you, and ask a really basic question?  Especially a "question" that seems to be searching for the teacher's approval rather than for authentic feedback?

I had lunch with two art teachers yesterday.

James told us of the best of his undergraduate professors, someone who was legendary within the entire program.  Apparently, sometime in the middle of his three hour drawing intermediate class, the professor would walk out of class.  He'd walk down to The Corner for a coffee, returning with cup in hand maybe 45 minutes later.

At first James was taken aback, appalled, indignant.  "How could he leave us?  That's unprofessional.  We need his help!  How does this guy consider this "teaching?"

After a couple of times, James noticed what was happening.  James was a dedicated art student, someone who cared deeply about getting better at drawing.  So when the professor left, of course James continued to work diligently, alongside the other art majors.  

And so, James spent 45 focused minutes working on his own, without a safety net.  James didn't ask for approval when there was a decision to be made about his piece - he made the decision himself, and got on with things.  The professor wasn't there to offer advice, solicited or not; so James stopped worrying about what the professor might think, and instead advanced the piece the way he himself wanted.  When the professor returned, conversations with him became less of the tone "what do you want me to do next?" and more of the tone "here's my work, what advice do you have?"

Then James followed up with a thought about his six(!) children.  If James and his wife are in the room while the children are playing, they hear a neverending stream of complaints, requests for help, demands for justice, and so on.  The noise is deafening.  But, if the children are not in proximity to adults, in virtually every case they play in relative harmony.  Arguments are resolved quickly.  A kid who doesn't get their way either joins in with the others and does things their way, or just finds something else to do.  The adults in the house may get several dozens of minutes of peace.

Finally, Shari (proprietor of The Muddy Rabbit pottery, and ceramics teacher) said she often starts making her own projects during class.  Not only is she modeling appropriate technique, demeanor, and procedures in the studio, she is physically separate from the other students.  After a day or so, she says, learning how to throw clay on the wheel is a matter of playing around and finding out.  She's given all the advice she can - they simply need to practice, paying attention to what they're doing, powering through frustration, until muscle memory is established.  When she is working on her own project, she's close enough to answer questions posed out loud (whether or not the answer to that question is "keep trying!") and to notice when a student truly needs faculty intervention; but far enough away that students don't continually say "is this good, Mrs. Jacobs?" 

James and Shari were describing in different contexts why the ground state of my class consists of me at my computer in front of the room.  Students must physically walk to my desk to show me their progress or to ask a question.  When a student instead shouts a question, I ask them to come forward - you might not be surprised to know that this shouty student often stays put at their desk, seemingly having figured out either the answer to their question, or that their question wasn't as urgent as they had thought.

James said he's heard the term benign neglect to describe the technique of strategically ignoring his kids and his students.  Physics teacher Matt Greenwolfe adopted the term that I use, feedback inertia.

Whatever you call it, you're not letting your students down if you seemingly leave them alone for extended periods.  Be there for them... but only when they truly need you.

Mail Time: What's your demo using kinematics with a spring?!?

Logan writes in:

Hi Greg,

What's the "energy of a spring demo with kinematics/energy" [on your class-by-class planner]?

Logan, 

I think you're talking about the demo where I hang a 1 kg object from a vertical spring of known spring constant, displace the object 5 cm, and predict  how fast the object is going at equilibrium.  I do this using Newton's second law and kinematics.  Yes, really.  

Then I do the experiment (a motion detector placed underneath makes a velocity-time graphs, and we look at the maximum vertical axis value).  Off by 40%.  What?  Physics didn't work?

But energy gives an accurate prediction.

Point is for students to recognize when kinematics are applicable, and not applicable.  And to practice energy bar charts, o'course.

Lincoln, Nebraska for the 2023 college soccer tournament 2nd round

Last weekend, I traveled to Lincoln, Nebraska for the second round of the college women’s soccer championship tournament.  The University of Nebraska hosted two games on Friday, and I attended both.  This trip was a part of my school “sabbatical”, in which I’ve been traveling the country to see women’s soccer.  I’ll also be heading to the College Cup semifinals in December in Cary, North Carolina.  

I’d been to Lincoln back in 1999-2004 for the AP physics reading.  I didn’t get very far off campus in those years, ‘cause we had everything we needed right there; because I didn’t have a car; because I didn’t have the money to do anything expensive, including eating at restaurants.  Good news was, the food in the dining hall was amazing.  Every year, the first night we arrived we were given the choice of shrimp scampi or a bacon-wrapped filet.  And my request of “both, please” was always met with an enthusiastic smile.  Ah, the good ol’ days.  

Back then, we were bussed in from Omaha, 1.5 hours away.  This time, I flew straight to Lincoln’s airport, so a 10-minute Lyft ride got me to the hotel that was a short walk from the stadium.

First game: Gonzaga vs. UC Irvine.  I went in rooting for the UCI Anteaters over the Gonzaga Bulldogs, just because of the mascot.  (If Gonzaga had been the Huskies, I would have supported them.)  UCI went up very early with a goal from Aveka Singh - a junior from New Delhi, India.  I’m pretty sure the assist came from midfielder Tati Fung, who seemed the best player on the pitch.  When she had the ball, I had confidence in the Anteater attack.  

It was cold in Lincoln, at least cold for an outdoor spectator sport.  I wore like a thousand long sleeve shirts, thermal underwear, a parka, and my elephant hat.  Yes, my wife has knitted several animal hats for me, my favorite of which has elephant ears and a proboscis sticking out of the forehead.  Many, many Lincolnites admired my hat, but a good fraction thought it was an anteater in honor of UC Irvine.  

One man successfully identified the elephant, though, and told me so - he said he was a professor (of sociology) at UC Fullerton, whose mascot is an elephant.  He very much liked my hat.  Yet his daughter had become an anteater.  Go figure. 

The Anteater fans as a group - as a group of maybe 20 - were positive, enthusiastic, and kind.  They greeted their team enthusiastically after the game in the same way as a European team’s visiting support do, though with less drunken chanting.

UC Irvine had defeated national #1 UCLA in the first round, and were the underdog in this game against #8 Gonzaga.  Nevertheless, the Anteaters dominated the first half, slurping up a second early goal from Lilli Rask.  Gonzaga then grew into the game, finally breaking through five minutes before the half from freshperson Katelyn Rigg.*

*In the early 1990s, it seemed that a full third of the women I met at college were named some form of Cindy, or Cindi, or Cynthia, or Syndi, or similar.  Well, the same phenomenon in the 2020s seems to have shifted to Caitlyn, or Kaitlin, or… I suspect the latter to often be the offspring of the former.

It was a different first-year player, though, who was the danger woman for Gonzaga.  Emelia Warta kept gaining possession in advanced positions in midfield, after which she would rampage into the box.  Every time she touched the ball I expected her to create a chance. Warta and her team controlled the game more and more as the second half went on.

Yet the Anteaters weathered the storm, including a storm in which they themselves seeded the clouds - some dangerous passing under pressure in the back led to a giveaway and a ball cleared off the line with the goalkeeper out of her area.  Phew.  For the most part, UCI headed crosses away, got the ball to Fung in midfield, and passed out of trouble before trouble came right back toward them.

Tension mounted palpably as the clock ticked down* and Warta terrified the Anteaters as if she were a jaguar rather than a Bulldog.  In the last 15 minutes or so, the ball barely left the Anteaters’ half.  Yet a couple of final clearances through Fung sealed the deal.  And a couple dozen fans cheered.

*Yes, the college soccer clock counts down rather than up, ‘cause the NCAA knows better than the entire rest of the world how the game should work.  Phthphth.

Second game: Tennessee vs. Nebraska.  This was a home game for the Cornhuskers, who packed the stadium with a second-highest-all-time attendance of 2100 fans.  That’s like one of every 100 residents… whereas Portland gets one of every 25 residents at a Thorns game to make attendance figures more than 10 times larger.  (For comparison, Nebraska gridiron football gets something like one of every three residents to show up.  Football isn’t religion in Nebraska - it’s much more important than that.)

Perhaps because it was an NCAA tournament game, the stadium made a pretense of neutrality, playing the Tennessee fight song as the Volunteers entered.  It was fun to hear their entire team point in the air and “woooo” audibly - It’s good, old, Rocky Top (woooo!).  

Thing is, even though Nebraska was the highest of the four seeds, this game seemed of less quality than the first.  Both teams played helter-skelter, causing the wannabe-coach middle-aged men in the crowd to holler “settle!” with increasing intensity, becoming audibly angry when the players didn’t obey.  On occasions when the teams did settle possession in the midfield, neither could complete a pass to the forwards.  Seemingly every pass was too heavy, intercepted, out of touch, or simply astray.  

Seconds before the half, Tennessee keeper Ally Zazzara slipped as she took a goal kick.  Oy.  The ball ran straight to Nebraska’s Sarah Weber, who punished the mistake that wasn’t even Zazzara’s fault.  Of course the crowd cheered, and they should!  No one taunted or laughed at the keeper’s misfortune.  But as a quasi-neutral, I cringed.  Cheering felt dirty.  The poor woman slipped!  The Tennessee team avoided their keeper, who was the last one into the locker room accompanied only by her (presumably) goalkeeper coach.  This surprised me - I thought the team would surround Zazzara, try to boost her confidence for the second half to come.  They did not.

And then the Tennessee players didn’t woooo when they returned after the half down 1-0. Rocky Top without the “woooo” sounds uncannily incomplete, like “shave and a haircut” without “two bits.”  I thought the team were finished.  Yet UT equalized moments into the second half.  

The game became tense, but never really picked up in quality.  Passes didn’t connect; fouls stopped attacking action.  

I was initially rooting for Nebraska.  I’d spent many weeks of my life in Lincoln; I own a hat shaped like an enormous ear of corn.  I wanted to celebrate with a crown of supporters.  The problem is, too many of these supporters were sorta toxic and probably inebriated middle-aged men.  

I mean, I understand and accept that when a call goes against the home team, the fans will howl.  When two players collided in the box after a Nebraska forward headed over the bar, the crowd ignorantly brayed for a penalty.  That’s part of tribalism.  When two players tussled at midfield and both went down, the crowd screamed bloody murder when the foul went Tennessee’s way.  These aren’t the fan reactions that bothered me; in fact, I’d probably be disappointed if the fans were not invested enough to howl at these incidents. 

As the game mounted in intensity, though, the drunk men turned their wrath toward the referee.  “Whaddaya mean that ball was out?  Are you blind?  What game are you watching?”  Every minor decision brought forth more whining, more intense personal attacks on the ref. Not after 50-50 foul calls, but offside decisions, which way the throw-in went, niggling complaints.  

I’ve had a number of conversations with colleagues about the boundary between legitimate tribalism and over-the-top abuse of opponents/referees.  I’m a referee myself; but I willingly accept the home team howling as an important part of the game.  I’m a commentator for my school’s sports teams, where I am always utterly respectful of the opponent; yet I also am supportive of student banter about who is gonna win, or about who won last year, etc.  Separating the in-game passion from the post-game handshake is, to me, a critical part of learning to function in a society in which many of us are often on different “teams”.  I still don’t exactly know where that line sits.  Yet I do know that these obnoxious Husker fans crossed it.

I finally snapped when the arsehole to my left screamed at the referee with five minutes left.  The ref stopped play and indicated a head injury - he asked the Nebraska athletic trainer to take a player off for treatment who seemed to show symptoms of a concussion.  This dude - and a few of his like-minded fans around him - went berserk.  “Let them play!”  “She’s fine!” “The game’s not about you!”  “Go back to the YMCA, butthead!”  “You’ve been a butthead all game!”  And the personal abuse toward the referee got progressively worse.  No one shut these folks up.

This is the bystander problem that we try to address with the 14 year olds in my care.  If you say nothing, you’re complicit.  “Well, he might have been out of line, but *I* didn’t do anything wrong, so I can’t be blamed for anything that happened” is simply unacceptable.  Did you speak up?  Did you leave the area?  Or did you just grin and grab the popcorn while someone, even someone in absentia, was abused?  

I wish one of this man’s relatives or friends had spoken up.  “Hey, that’s going too far” coming from a family member can do wonders.  Or “come on, man, cheer for our team and shut up about the ref” from a fellow Cornhusker - preferably one who’s been leading the “HUSKER! POWER!” chants all night - would have helped.  

I was in no position to say anything.  I had no prior relationship with the nasty man; I was not in any way part of Husker Nation.  I was just a weird guy with an elephant on my head.  So I moved to a different seat to watch the last few minutes.  

And oh, what a last few minutes.  The game looked to be heading to extra time.  But with less than a minute to play, defender Ella Guyott - who had earlier in the game repositioned as a forward due to a substitution - stayed calm at the far post when a cross went over everyone else’s heads.  She slotted the ball into the net with a finish that looked so-easy-anyone-could-do-it but I would likely miss 9 of 10 times.  And that was that.  Nebraska 2, Tennessee 1.  

The players took a victory lap around the stadium, giving the front row high fives - that right there is so much of what I love about women’s soccer.  The players show overt, enthusiastic thanks for their fans’ support.  The teams huddled together, in wondrous shock and catatonic shock, respectively.  And the crowd raced to their cars to beat the awful traffic surrounding the stadium.  Glad I could walk.

I planned to spend the next morning walking around town, finding a cafe in which to grade my trimester exams.  Unfortunately, I had chosen the hotel in a rundown strip mall next to the “MEAT & BEER”.*  No coffee, unless you count McDonalds.  

*At night, the lights for the ampersand and T didn’t work, so the store became MEA BEER.

I did eat at the strip mall’s Runza, that wonderful fast-food empire that only exists within 600 miles of Lincoln.  They serve fast-food meat pies that are part calzone, part Hamburger-Helper-in-a-bread-wrap.  I was first exposed to Runza in 2000, when the AP physics readers were served Runzas for lunch.  Runza Rex, their tyrannosaurus mascot, handed me a Runza baseball cap which I still own.  I ate three of these large sandwiches.  After which I fell asleep during the afternoon grading session - the only time I’ve ever fallen asleep at the reading.  (Since that day, I’ve not eaten any lunch at all during the AP reading.)

Eventually, a twenty minute walk brought me to an excellent coffee shop in the UNL “Innovation campus”.  No clue what they’re innovating, or whether they’re gonna rename the rest of the university the “stuck in the past campus.”  Guh.  But the coffee was good, the barista was friendly, the tables were spacious and clean with lots of windows.  Exams got graded.  

Directions of motion are "toward the detector" and "away from the detector".

A fundamental principle of teaching first year physics students is to never trust a student with a negative sign.  The linked post details ways that I avoid negative signs wherever possible.  

My conceptual class never gets to the full-on kinematic equations - for them, all motion either is constant speed, using d = vt; or starts/ends at rest, making d = (1/2)at^2 or d = v^2/2a valid.  Since we never discuss computationally an object that changes direction of motion, we can dispense with the negative signs!

AP-level algebraic kinematics is one place where I haven't found a way to avoid a negative sign.  Yet!  Before we ever touch computation with kinematics equations, my AP class learns about position-time graphs, velocity-time graphs, and the definition of acceleration without any negative signs.  In fact, both classes begin with the exact same facts and exercises.  For position-time graphs, the facts are:

The steeper the position-time graph, the faster the object is moving.

A position-time slope like a front slash / means the object is moving away from the detector.

A position-time slope like a back slash \ means the object is moving toward the detector.

To determine how far from the detector an object is located, look at the vertical axis of the position-time graph.

After a number of in-class laboratory exercises with motion detectors, students are used to relating the way a position-time graph is sloped to whether a cart moves toward or away from a detector.  This takes about a day of class for AP, about three days of class for conceptual.  They're ready for the next step.

A daily quiz question eventually asks, "A motion detector points north.  The position-time graph it produces is sloped like /.  Which way is the object moving?"

When we grade this quiz together, I cite the fact: "A position-time graph sloped like a front slash means the object is moving away from the detector.  Count the question correct if the student wrote 'away from the detector,' or even just 'away.'"  

But I go on. I call a student to the front of the room and hand them a motion detector.  "Please place this detector on the track and point it north."  I usually have to help the student figure out that "north" is different from "toward the ceiling."

Next  I call a different student up.  "Here is my pet hippopotamus Edna.  Please help her move along the track away from the detector."  The student does so.  "Which way was Edna moving, north or south?"  Now it's obvious that Edna was moving north.  "So, the best answer to this question is that the object moves north.  If a student wrote "north" as their answer, count it correct AND add one bonus point."

"From now on, if a question indicates the direction the motion detector is pointing, answers should no longer state just 'toward' or 'away from' the detector.  Your answers should be north, south, east, west, left, right, up, down, etc."  And I hold students to that.

The only difference for AP is, eventually they get to computational kinematics with changing direction of motion.  So we talk about defining directions as "positive" and "negative" so the math works out.  And we define that the direction "away from the detector" is the "positive" direction, by definition.

Interestingly, despite this roundabout and indirect way of introducing what "positive" and "negative" mean in the context of kinematics, my AP students don't generally have difficulty interpreting an exam question that does use negative signs to indicate direction!  They perform way above the national average on the exam, including on the unit 1 kinematics questions.  And those who do take calculus-based physics transition to using coordinate systems as if they were native Cartesians.

Students work at different paces. Let them.

By November, I've generally established a positive, authentic class culture in which everyone is working as a team to learn a difficult subject.  This class culture will look different for different teachers, different school ecosystems.  Point is, now the class clowns have been brought into the fold or at least neutralized; the folks who'd rather whine or lawyer up than learn have similarly changed their priorities - or left the class.  

So we're doing a lot of laboratory work and problem solving in class now, and for the remainder of the school year.  A typical class day starts with a 3-5 minute quiz, after which students work on a list of activities.  Each activity must be checked with me for completeness and correctness.  A typical day's "order of work" might look like:

• One position-time exercise
• Experimental graphs worksheet
• Power in a bulb exercise
• Test 2 corrections
• Test 3 corrections
• Two more position-time exercises complete
• Two circuit graphing exercises complete
• “Graph that motion” interactive

And this list might be substantially unchanged for a week or two.  This is "teaching like a video game" - students feel like they level up when they complete each item in the list.

The question I'm often asked is, how do I handle the class when some students are on level 8, but others are on level 2?

Remember - I'm comfortable with our class culture and that each student is working in good faith.  I must support a student who took two days to finish a single position-time exercise and is now struggling with the graphs worksheet, the same way I support the student who, in those same two days, is nearing the end of the list.  They're both working at their respective ability levels.

Firstly, I can subtly slow down fast students and speed up slow students.  I don't mean artificially!  A student who is good at physics and does everything right should be allowed and encouraged to proceed quickly through the order of work.  But after the first 20 minutes, I'll probably be a bit more exacting about the standard of evidence a fast student presents me; and I'm more likely to let a slower student move along despite minor errors of reasoning.  

Next, since we've built a good team atmosphere, a faster student often slows down naturally.  Everyone knows that the price of my assistance on a problem is to pay it forward - the next person who needs help on that problem gets sent to the student I helped previously.  Helping classmates takes time!  It's time extraordinarily well-spent, because teaching others is the best way to learn physics.  Fast students often recognize how much they're learning by teaching, and so keep teaching.  Or, they get a nice ego boost by being the go-to person for their classmates.  Sometimes deep friendships are built around in-class collaboration, as physics can be a great social leveler - the universe doesn't care how socially cool or uncool you are, just whether your predictions are right.  Helping classmates is good for physics achievement, but it's also kind, friendly, and the right thing to do.

But in the end, I'm always gonna have a few folks who, comparatively, barely make progress.  That's okay.  At some point, the class moves on to new material - at which point, my order of work resets to new activities.  It's important that I do NOT insist that everyone finish every activity!  

I prioritize test corrections - these absolutely must be finished. And I'll bring in students to extra help time, or assign corrections as homework, to meet this goal.  For everything else, though, we just move on when it's time to move on.  Some students will have finished everything.  They will have been given a next-level challenge, or just allowed to do work for other classes while they wait for their classmates to catch up.  Others may barely progress, because they're bogged down in corrections, or in an exercise that's just not clicking.  No worries!  Not everyone even got to level 8 in Super Mario 3, let alone beat the level.  Not everyone makes the state playoff final.  We move on - to the next sports season, to the next Mario release.  

The stated goal for all students is that they work hard, take care of each other, and get better every day.  Nothing in there about the pace of their work.  As long as students are meeting these three goals, they get as much done as they can, without complaint from me.

How do you double the speed of a cart?

I've shared broadly my "double the speed of a cart" in-class laboratory exercises.  This is my introduction to Bertha's Rule of Ones.  In each of four situations, students use simple kinematics equations and semi-quantitative reasoning to predict a factor of change.

One exercise asks students to roll a cart down an incline, then double the cart's mass - what happens to the maximum speed of the cart on the same incline?  It's easy to double the mass of a PASCO cart, just put a specially-fitted 250 g bar on top.

Another asks students to double the travel time for the cart rolling down the incline, and predict what happens to the distance traveled by the cart.  Again, simple - just release the cart from rest and use frame-by-frame video.  The PASCO tracks even have a centimeter scale taped on!

It seems like it would be more complicated to double a cart's acceleration, but it's not - the acceleration of a PASCO cart on an incline is gsinθ.  For small angles, doubling the angle θ will also double the acceleration.  Changing, say, from 6 degrees to 12 degrees gives a pretty obviously doubled acceleration.

The tough one is, how do I double the initial speed of a cart rolling up an incline?

Answer: use the plunger on the PASCO cart.  

Take a look at the photo.  On the plunger are three lines with numbers.  (These numbers are the same color as the translucent plastic - hard to get a clear photo!  I colored the lines for better visibility.)  When the plunger is depressed, it clicks and stops at each of these lines.  Then, a quick press of the button on top releases this plunger.

Put the plunger up against a wall, or against the stopper that can be attached to a PASCO track.  Push the plunger in to position 1; push the button to release.  The cart will move with some initial speed.  (No clue what speed!  But it will be a reasonably consistent speed each time.)

Then, push the plunger to position 2 and push the button to release.  The cart will move with twice the speed as when you used position 1.  And position 3 gives three times the speed of position 1.

Why does this work?  Because the plunger is converting spring potential to kinetic energy.  Set the spring potential formula (1/2)kx^2 equal to the kinetic energy formula (1/2)mv^2: the spring compression x has a linear relationship with the speed v.  

Mail time: using a fourth kinematics equation on the AP exam?

More mail about motion:

I was wondering if I could ask you an AP exam question.  I see on your algebraic kinematics information to memorize that the 3 given equations are on the AP equation sheet.  The fourth equation that 'may occasionally be useful' is not on the equation sheet.*  If students were to need it for a question on the AP exam, would it be provided?  Or would they need to derive it from the other 3 given equations?

*This is the equation x =  t(vf+vo)/2 

Also, do you allow your students to use the AP table of equations on the daily quiz?  Or do you expect them to have those equations memorized? 

Students are not allowed to use the equation sheet on the quizzes (though I do let them use handwritten notes, so many write the equations out).  My students get the equations for tests.  They memorize these equations through use, generally, though I don't formally "require" them to be memorized.

As for that fourth equation, it's really using the definition of average velocity with constant acceleration.  The exam will not give this equation, but it can be used if students know it.  It *can* be used as a starting point for a derivation or a justification.

Mail time: airplane and car with the same acceleration, which moves faster?

A summer institute participant asks: 

I had a quick physics question from one of your daily quizzes: Which is moving faster, a car with an acceleration of 2 m/s/s, or an airplane with an acceleration of 2 m/s/s? My answer was airplane but my students are not happy with that answer. Is there any way you could explain it to me so I make sure I am telling them the correct answer?

Awesome, important question - this is a "holy grail" question for understanding motion.  

Acceleration tells the CHANGE in speed every second.  Both the car and the airplane gain 2 m/s of speed each second.  

But this doesn't say how fast either moves!  Sure, if the airplane is cruising and speeds up a bit, while the car is entering the freeway, the airplane moves faster.  But, say the airplane is starting from rest on the runway, and speeds up to 2 m/s after one second, 4 m/s after two seconds, etc.  Then say the car is on the freeway.  The car is initially moving 30 m/s, then 32 m/s, then 34 m/s, etc.  The car is moving faster - yet the objects have the same acceleration!

Hope this helps.  The answer is, WE DON'T KNOW.

GCJ

Don't make agreements you aren't willing to fulfill

In spring of 2021, a student asked me, "Hey, Mr. Jacobs, if we *all* pass the AP exam, can we cut your hair?"  I said, "sure."  The odds of every one of my 15-20 9th graders passing the AP Physics 1 exam were not great.  Not insurmountable, but unlikely.  And lo, that year most students did pass, but a couple did not.

I made the same deal with my class in 2022.  And again in 2023.  

But, whoops.  In early July I got the score report - all 17 students got 3s and above.  Gulp.  

A promise is a promise.  

It will grow out.  Eventually.  Congratulations to an awesome class.

The "Pretty Good Physics" mailing list has migrated! Here's how to join.

For many years now, the "Pretty Good Physics" email group has been one of the fundamental resources for physics teachers that I recommend in my summer institutes.  Teachers email questions to the group, and they're answered within hours, usually by people who know what they're talking about.  Most importantly, the PGP group is positive in culture.  It's not a forum to kvetch about our administrators, the dang kids these days, or that silly College Board.  It's just a place for professionals to collaborate with one another.

The problem:  The email group was hosted by google.  Then it wasn't.  Apparently a significant number of recipients marked emails from the group as "spam."  And thus, the email group is no longer hosted by google, pour encourager les autres.

The solution:  The PGP volunteers created a new google group intended for discussion only.  The other function of PGP is to share files among physics teachers - that functionality is still available the same way it was.  But discussion via email is the strength of PGP, and it can continue on this new group.  

The only difference now is that we may not share secure files via the discussion group.  If you have a question about, say, an AP question that is released only under the course audit, well, you need to be sorta cagey about your question.  You can't just send a copy of the question to the group.  Silly, I know, but them's the College Board's rules, and we've gotta obey them if we're gonna keep this discussion group going.

How do you join the new discussion group?  If you're logged in to a google account at which you want to receive discussion posts, go to this site.  If you prefer to join with a non-google address, then you need to email Dan Hosey via dan dot hosey at prettygoodphysics.org, letting him know the desired email address and whether you want to receive every post or just a weekly digest.

If you do sign up, never ever mark a post as spam.  Just unsubscribe if you're sick of us.  :-)

The people who make PGP happen:  Pretty Good Physics is a completely volunteer effort on the part of four amazing physics teachers.  If you get a chance, thank them profusely, buy them a coffee, chant their name at your local physics shrine.  We so, so appreciate the efforts by these folks to keep this service operating:

• Paul Lulai
• Robert Casao
• Dan Hosey
• Gardner Friedlander

Thanks, all.  Looking forward to seeing your posts to the new discussion group.

GCJ

Creating appropriate attitudes toward judged performance

I did a six-year tour in competitive marching band.  The band practiced longer hours than most varsity sports in preparation for weekly competitions in the autumn.  We usually won – sometimes we lost.  Yet the philosophy of preparing for judged performance has been ingrained in me, and has lasted for decades.

The band’s leaders – student leaders and adult leaders alike – emphasized controlling what was controllable.  There’s no “defense” in marching band!  We can control our own performance, but not what competing bands do; and not what a given judge might think of our performance on the day.  We got better every practice, with the goal of marching the theoretical “golden show”. 

After any competition, we listened carefully to judges’ comments and considered how to use constructive criticism to improve.  We gave full-on effort in practice five days a week, holding each other accountable for our level of effort, because, fundamentally, we wanted to WIN.  Without the chance to be declared winner, I doubt that we would have prepared as intensely.  Nevertheless, we knew when we had marched a nearly “golden show” without waiting for the judges to consecrate the performance with a score or ranking. 

This “control what is controllable” philosophy bled into my academic and then professional life.  To me, a grade is like a judge’s score – it provides validation and motivation, but is secondary to the pursuit of knowledge itself.  I remember friends in college being shocked when I earned a B+ rather than an A- in a political science class… then being even more shocked when I shrugged and said “yeah, but I probably deserved the B+ in Russian where they gave me an A-, so it all evens out.” 

Then I myself was shocked in my first years of teaching when I discovered such a philosophy was utterly foreign to the majority of my students.  They felt personally wounded when a grade was lower than they expected.  They wanted a prescription to earn a grade: do these things, get this grade.  The idea of learning for the sake of learning, of education as an end in itself rather than a means to an end, did not compute.

Thus, I’ve adapted my approach to grades over the years to reflect my marching-band-informed philosophy of preparing for judged performance.  Many years ago I made grades translucent; and recently in my AP class, made them irrelevant throughout the year by means of a contract.  (The band didn't get official judges' scores after every practice run-through - only at each contest, and then only the end-of-year state contest mattered for our collective memories.  Just as designed in my AP class's contract.)

More importantly, I've led my in-class culture in the direction of our band's culture.  Nowadays, my students know that I will hold them accountable for just three items: work hard, take care of one another, and get better every day.  We talk about how to accomplish each of these three goals, which are attainable for every student in my class, no matter their natural talent.  

Someone could get a good-enough-for-them grade while sleeping through class?  Well, that someone isn't making progress on any of the three goals, and thus is called out until they improve - just as a star football player who half-arses practice and taunts teammates is shunned until they change their attitude (and then welcomed back into the fold when they do, ala the Jamie Tartt arc).

The weakest student in the class meets all three goals?  Generally, such a student's grades improve throughout the year.  In the positive culture we've established, even low grades tend NOT to be perceived as a character judgment.  I've delivered my judgment on this student's character by trumpeting to their classmates, advisor, and parents that they are indeed working hard, taking care of classmates, and getting better every day.  We celebrate every success, even small successes.  Such a student is, in fact, controlling what is controllable, and achieving what they're capable of achieving.

Now, understand I'm in my 28th year of teaching, at a school with tremendous administrative support, and trusting parents who live hundreds if not thousands of miles away.  Even here, building my class culture to attain a positive attitude toward judged performance has been a long and treacherous road.  It only takes one not-dealt-with bad apple to ruin the barrel for everyone.  It's taken long-term investment such that I have confidence that colleagues, parents, and administrators will see the positive aspects of the culture we've built, and thus support my efforts to maintain that culture.  

And just as importantly, my long-term unflagging dedication to culture building means that those colleagues, parents, and administrators who don't agree with my approach to schooling at least recognize that it's not worth trying to fight me on culture issues. 

Our physics students have weak math skills. What to do?

I've heard for nearly three decades how weak our students' math skills are.  And such observations are not necessarily incorrect, though they do harken to a mythical, deified past which probably wasn't as great as some want to suggest.  

Fact is, whether or not the pandemic has worsened our students' math ability, even AP Physics students will cancel across a plus sign as in the picture.  They did so in 1999, they did so in 2023, they'll continue to do so even in 2053.

Let's not talk about how we can Make Our Students Great At Math Again.  They never were; and we can't anyway.  Instead, let's deal with our students as they actually are, rather than as we wish they would be.

But how do we do that, when mathematics is the language of physics?

The big deal is, de-emphasize math errors.  

I looked at an SAT math section a few years ago, for the first time since like 1996.  I was annoyed by the second half of the questions.

See, these were all good math questions, questions that good math students should be able to approach.  Each required multiple steps, often three or four or five(!) separate connections between concepts to get to the answer.  Nothing wrong with that - one of the prime differentiators between a middling and high-level math student is their ability to pile connection upon connection without getting lost or frustrated.  

Yet these were numerical multiple choice, or grid-the-numerical-answer questions.  There was nothing to differentiate near-perfect reasoning from guesswork.  

I'm used to conceptual physics and AP Physics 1*, where the multiple choice questions are usually difficult but straightforward; and the free response usually awards credit for each step in the reasoning process.  When there are five-step problems, a student who makes 4/5 of the connections earns 4/5 of the points... and a top score on the exam.  On this SAT, though, it was all or nothing.  Make all the connections just right, or get no credit at all.

*Sometimes called conceptual physics on steroids

Now, I'm well aware that the purpose of the last questions on an SAT math section are for the purpose of differentiating the toppiest-top math students from the mere outstanding math students; I'm also aware that substantial psychometric data exists to demonstrate that these questions attain their purpose.  And I'm acutely aware that it's not in any way practical to design and score a free-response SAT math section.  My concern here is NOT about ETS or the College Board or the existence of the SAT math section.  

My concern is about those teachers, students, and parents who - possibly informed by the all-or-nothing nature of SAT questions - act as though the final numerical answer to a complicated math question represents a judgment from the Almighty Themself of a student's math ability, and of that student's personal worth.  No.  The 15 year old upstart who falls to Serena 7-6 in the third set has, in fact, performed far better than the player who was destroyed 6-0 6-0... even though both folks lost and are out of the tournament.  The Vikings and Bills may have lost four Super Bowls, but they made it to four Super Bowls - as opposed to the perennial sad-sack Lions, who aren't even sure what a Super Bowl is or how a team might be selected to play in it.  

But my students keep getting answers wrong, just as the Vikings keep losing in the postseason.  What can I do?

Separate the math from the physics.  Did the student begin with a fact, relevant equation, or standard approach (like a free body diagram or energy bar chart)?  Did the student use the fact to make a connection, use the equation in the correct context, do the appropriate next step in the standard approach?  If so, then praise them.  And move on.  

If I see a silly math error on a problem set, I usually ignore it.  Maybe I'll put "14/15" as a score on a graded assignment; maybe in class I'll just stamp the paper and move on.  Those who make significant conceptual errors must come back to redo the problem... but math errors don't really matter in this context.

A huge fraction of my student's practice is done in the context of making laboratory predictions.  Here again, I'll ignore minor math errors a lot of the time.  Billy forgot to square the 2 and so made an incorrect prediction that the speed would double, not quadruple?  I don't need to correct Billy.  The universe will correct Billy.  He'll go measure the cart's speed... and the cart's speed won't double like he said it would.  At that point, I'll show Billy that he did everything right but made a math error.  Yet, Billy doesn't feel like he's being shamed or even corrected by a teacher; Billy feels like the teacher is helping him figure out why his prediction didn't match reality.  And Billy's less likely to make that mistake again next time (though the likelihood will never drop to zero).

And finally, all incorrect answers on a test must be corrected, whether the reason for the incorrectness was math- or physics- related.  In this context, students care very much about getting the right answer, because they want to get their correction checked off, and they want to figure out how to improve their next test.  Importantly, students do NOT see their original test!  Thus, often a math error that led to a wrong original answer isn't repeated.  "Why do you think I got this wrong the first time?"  "Don't worry about it!  You likely made a math error.  Not worth thinking about.  You know how to do it just fine.  Move on."  

But when they bring me the correction with that math error repeated, the context is exactly right for me to show them the error.  "Look here.  There's a plus sign in the denominator.  You're not allowed to cancel across a plus sign."  Often the student hits themself in the forehead... goes back to their seat... and does the problem perfectly.  They knew the math concept!  They just didn't apply the math concept when the time was right.

I haven't had a mathematical breakthrough with this student, such that they'll never make such a mistake again!  The message I've sent isn't "I'm teaching you a math skill you should have already known."  No, the message is, "Here's a math concept that you knew, but you reverted to a misconception under pressure.  But your physics was just right!"  

"Conservation" of [foo] does not mean that all objects have the same [foo] - and 2023 AP1 #1

Conservation of momentum compares a total value before and after a collision.  It does not compare the momentum in one collision to the momentum in a different collision.

That was the fundamental error on the 2022 AP Physics 1 paragraph question.  Well, the same concept showed up again on the 2023 AP Physics 1 exam, on problem 1.  But this time, it was about conservation of energy.  These questions are both checking a student's understanding of what "conservation" means in each context, in each system being considered.  

The pumpkin pie I* baked has a mass of 2.0 kilograms.  The total mass of pie is 2.0 kg whether it's cut into four 0.50 kg pieces, or eight 0.25 kg pieces, or... all the pieces are always gonna add to 2.0 kg.  That's conservation of mass.  

*well, that my wife Shari baked.  And therefore it's probably a pumpkin cheesecake, not mere pie.  Mmmm.

Conservation of mass does NOT mean that every pie in the universe has 2.0 kg of mass.  

In the 2023 P1 problem 1, the maximum potential energy of a spring-cart system is 4 J.  Part (a) of the problem asks for an explanation of why the maximum kinetic energy of this system is also 4 J.  That's conservation of energy - the total PE + KE will be the same for any cart position.  Maximum PE means zero KE.  Then when PE is zero, all 4 J of PE has converted to KE.  

But part (c) of this problem has a block dropped on the cart when the spring is at its maximum stretch.  The maximum PE (and the maximum KE) of the cart-spring-block system still is 4 J.  Why?  The answer is emphatically not "conservation of energy."

In this case, we're asked to compare the maximum potential energy of two different systems: the cart-spring system from part (a), and the cart-spring-block system.  We're not comparing the mass of my pie-cut-in-two-slices to the mass of my pie-cut-in-four-slices; we're comparing the mass of my pumpkin pie to that of someone else's lemon méringue pie.  Two different pies.

Now, in this particular case, the pies both have 2.0 kg of mass the systems both have 4 J of total energy.  The potential energy of both systems is due to the stretched spring, and thus is given by the formula (1/2)kx^2 and is not affected by the system mass. The spring is stretched the same maximum distance, so the system potential energy is 4 J either way.  

That's not how they checked the map

Trivia night last Thursday.  My team is down eight points to the couple with the beautiful dog at the next table.  Final question coming.  Category: African geography.  Twenty points on the line.  They get it, they win (but we win if we're right and they're wrong).  Here it comes.

Put these Mediterranean countries in order from east to west: Algeria, Egypt, Libya, Morocco, and Tunisia.

We can do this!  Some quiet discussion ensues at both tables.  We turn in our cards.  It's over, though we don't know the result.  Time for petting the dog, along with idle conversation.  We know we're probably toast - we tell the other team how impressed we are with their knowledge of television legal dramas, the category in which we fell way behind.  We discuss the final question.  "We think we got it," we said.  "But I'll bet you did too, so you're winning."

Remember, I grew up in the 1980s.  I remembered Gorbachev and Tears for Fears, both of which were useful on the night.

"I wasn't sure at first," said the woman on the leading team.  "But I checked when I was in the bathroom just now, and we were right!"

"Oh, that's very cool," I said,  "that the bar has a map of Africa hanging in the women's bathroom!"

Cue laughter as I realized what I said, and what she meant, and how old I must have seemed.

Visual Accelerometer: Noah Segal's (free!) iphone version

I've been a fan for decades of PASCO's visual accelerometer.  The linked post describes the demonstrations I use when introducing the meaning of the direction of acceleration.

Thing is, the visual accelerometer with the red and green LED display has been discontinued by PASCO.  They offer the Smart Cart vector display, which is great in that it does the same thing as the visual accelerometer AND it can be set to display force or velocity instead of acceleration.  But the display itself is $109 plus shipping, and it requires plugging into a $199 smart cart.  

How can you do the visual accelerometer demonstrations for free?

Noah Segal, on the PrettyGoodPhysics teacher message board, shared his solution: he programmed a website to display the output from the iphone's accelerometer exactly like the old visual accelerometer - right down to the red and blue colors.

Turn on the orientation lock on your iphone.  Then, go to the site indicated by the QR code at the top of the post.  You'll need to give the site permission to use your sensor.  Then hit "toggle mode" to see the 1-d red and green output.  Don't like the scale?  Zoom in and out with the + and - buttons.

Best of all, it's free.  Until your phone flies off a cart, hits the wall, and shatters.  Then it is a rather expensive toy.  But for now, just mount the phone securely!  :-)

Thanks, Noah.  

Mail Time: Gravitational potential energy in orbits

One of the Fundamentals Quiz questions in the leadup to the 2023 AP exams asked about gravitational potential energy in orbits: 

118. Satellite A is in low-earth orbit; satellite B orbits much farther from earth's surface.  Which has greater gravitational potential energy: the satellite A-earth system, or the satellite B-earth system?

A reader asks,

Can you explain why satellite B is greater.  Physics is not my strong suit and I understand why using Ug = mgh.  But when using Ug = - GMm / r , wouldn’t the gravitational potential energy be greater for A?  I’m a little confused.

Ah, this is the million dollar question in gravitation.  The negative sign is extra important here.  Energy is a scalar - the negative sign doesn't just indicate direction, as it does for force or acceleration.  A potential energy of -50 J is LESS than a potential energy of -25 J!  

So, for the satellite farther away, the denominator of your equation is greater, the whole fraction has a smaller absolute value... but the negative sign matters.  The negative sign ensures mathematically that objects farther away from each other have larger gravitational potential energy .

For AP Physics 1, I just write this last sentence as a fact - you almost never need to use this equation for gravitational potential energy.  (This will be true for the 2024 exam; for the 2025 exams and beyond, students may well need to use the negative sign fluently.  We'll see. Either way, I'd *start* by using the fact and ignoring the equation.)  For AP Physics C, use of the negative sign in the gravitational potential energy equation is an important concept mathematically as well as conceptually.

Breaking news: AP Physics updates, to take effect with the 2025 exam

The universe now has clarity about forthcoming changes to all four AP Physics exams.  I'm thoroughly impressed with the work being done by the College Board team and the development committees.  Here's what you need to know!

The changes I describe below will take effect with the 2025 exams.  The 2024 exams will be identical in form and content to those since 2015.

Let's start with content changes:

Physics 1 will now include fluids - just teach the current P2 fluids unit, or old Physics B material.  That's the major change.  Minor additions include the parallel axis theorem, the center-of-mass formula, and quantitative understanding of elliptical orbits.

Physics 2 will add in sound, specific heart, blackbody radiation, and a non-quantitative treatment of transient behavior in RC circuits.  Physics 2 removes special relativity and quantum wave functions (keeping E=mc^2).

Neither Physics C course will change its content significantly.  The new Course and Exam Description will include explicit references to some topics such as physical pendula which have been tested before but not named in old CEDs.

Now, what about the exam format changes?  These are rather significant.  The College Board representatives emphasize, as do I, that the style of questions on each exam are not changing much at all.  The format changes are for the purpose of clarity of expectation.  The CB wants students to know what sorts of questions to expect on each exam, such that they can worry less about reading directions and instead show their physics knowledge.  The CB further wants to be able to better differentiate the level of the 1/2 exams from the C exams.  A consistent format makes it easier to separate the skills of "being a good physicist" and "being a good test taker".

So there's no need to throw out the questions you've been using on your classroom tests!  You can cut out parts or add parts... but everything that's been given since 2015, and everything you can find on AP classroom as aligned to the exam, is still perfectly useful.

All four AP Physics exams will have the same format.  That format includes 50 multiple choice questions, each with four choices and a single correct answer; and 4 FRQs.  The timing will be 90 minutes for multiple choice, followed by 90 minutes of free response.  The equation sheets for all exams will be aligned.

The four free response questions on all exams will follow the same order and point distribution:

1. Mathematical Routines, 10 points.  This will include calculations and derivations; on the 1/2 exams especially there will likely be a part requiring multi-step verbal reasoning as well.

2. Translating Between Representations, 12 points.  Physics concepts can be communicated in many ways beyond merely equations and words.  This question will test students' ability to understand more than just one of these communication methods.

3. Experimental Design and Analysis, 10 points.  This will be very similar to the current questions on all exams that are posed in a laboratory setting.  It will likely include data collection techniques, even on the C exams.

4. Qualitative/Quantitative Translation, 8 points.  This is a shorter version of the style of question that has been on the 1/2 exams since 2015.  Fewer points allows the question to get straight to the point - describe a situation verbally, describe a situation with equations, and then show how the equations relate to the words.

That's all.  These changes are all made with the idea of transparency - if students knows exactly what to expect on the exam, then they can focus on showing their physics knowledge in each situation which is presented to them.

The College Board will be releasing three all-new practice tests in each course for teachers - they'll be available in 2024 after you pass the course audit.  Therefore, I'd recommend that you read these, and then cut and paste into the classroom tests that you're already using. 

The other exciting news, especially for P1 teachers, is that a new standard setting will happen for the 2025 exams.  That means a new set of comparisons between AP students and college students taking a similar exam.  And, that means re-evaluated cut scores to earn 5, 4, 3, etc.  The hope and likelihood is that more P1 students will be qualified for higher scores.  But stay tuned.  

Greetings from Physics Camp

Something like two dozen AP physics readers descended upon Gates Barbecue this evening on "dine out night", the night when the College Board was paying our restaurant tabs.  I had fun conversations on the walk there, during dinner, on the walk back, and in the Westin lobby where two different sets of physicists were playing two different card games.  

Regular blog followers know how much I love the AP reading. Grading papers all day for two weeks is intense, in the same way the football two-a-day practice week or band camp are intense.  The skills built for the season pay enormous dividends in the long term; and the camaraderie, the relationships created, can't be replicated in less intense venues.

I have lots of thoughts for future posts, including a discussion of the physics meaning of the colloquial word "faster", what the word "conservation" means in our students' minds, and the physical reasons for an experimental discrepancy.  But eight hours of brain work requires sleep sometimes... so I'll be back in a week or two, when perhaps I've recovered.  

Take me down to Kansas City

Where the rubric's clean and we take no pity

Oh won't you please take me home...

Paid lab organization day at my school in central Virginia - old equipment for giveaway!

Update June 17 - we have enough folks for this event!  Thank you...

Alongside my five AP workshops and the rapidly filling Conceptual Physics Summer Institute, I need to do some work with my department to organize the physics floor for the upcoming school year.

See, because virtually all of my school's students take physics, I work with two other physics teachers.  One of these is leaving; the other is transitioning into more environmental science than physics.  And a new teacher is joining us, taking over one of the physics classrooms.  We need to, for the first time in a decade, do a full inventory and re-organization of the physics floor.  

We'd love to hire some help.  We're looking for 6-8 people - hopefully physics teachers, people who know what a motion detector looks like, and what that weird thing in the drawer is used for - to work with us from 9am until about 4pm on Friday June 30 2023.  We will pay $105 for your time... plus:

We're looking to shed some old equipment.  We have a bobzillion Vernier Labpros and Labquests, for example.  Some are fully functional; I know that many of the others would work with a bit of TLC from someone who put in the time to troubleshoot.  Rather than toss these in the electronics recycling, I'd like some physics teachers to have a chance to repurpose these.  

And we'll be getting rid of a TON of textbooks, hard copy materials, etc.  Including a full VHS library of Julius Sumner Miller demonstration videos.  Participating teachers can take what they'd like from the getting rid of pile!

If you'd like to join us June 30 at Woodberry Forest School, please send me an email - I'm easy to contact via the woodberry.org academics page.  

GCJ