Contract grading part 2: How we made it happen at the school level

(The previous post explained *why* I moved to contract grading with my 9th grade AP Physics 1 class. Today I'm discussing institutionally how I worked with my colleagues and my administration to make contract grading happen.  The next posts will discuss how I communicate with parents; and then how I make this particular style of contract grading work on a day to day basis with my class.)

A few years back, a history-teaching colleague presented to the faculty and at an external conference his experience with "contract grading".  His contracts for a required 9th grade course painstakingly listed the descriptive attributes of students who get grades of A, B, and C.  He allowed the students themselves to contract for whichever level best described them.  Then, he held the students to their contract, demanding levels of in-class engagement, paper rewrites, and out-of-class effort commensurate with what the students themselves had agreed to.

My approach is much simpler.  In an AP class, there's no such thing to me as settling for B-level effort.  Students who are good fits for AP physics do all the assigned work to the best of their ability, redo whatever they bombed the first time, engage enthusiastically and diligently with laboratory exercises, and finish all test corrections.  Someone who's only partially willing to do these things shouldn't get a low grade - they shouldn't be in this advanced class to begin with.

On this colleague's model, I proposed to the dean and the headmaster that all of my AP students would contract for an A, by pledging to do each of the items in the paragraph above.  They were quite receptive to the idea, especially as this history colleague had already demonstrated that non-traditional grading approaches neither brought forth the apocalypse, nor a flood of burdensome complaints. The headmaster made the very important suggestion that all students should contract not for an A but for an A-minus, on the grounds that nobody is perfect.  It turned out that this small change was critical to the success of the approach.

We ended up with the contract that you can read here.  

In practice, now, a small committee including the academic dean and the head of admissions select students who they think can handle the AP Physics 1 course as freshmen.  I've asked them to cast a wide net!  That is, they don't just rank by standardized test scores - which they can't anymore anyway since our school's admission process went test-optional.  These folks are all quite familiar with the incoming class.  They make their best guess at choosing a team.

Then, on the first day of class, I explain to the students (orally, and in writing on the course syllabus) that they have been selected for the AP physics section.  In three weeks, I tell them, I'll have an individual meeting with each student.  If by then they've lived up to the terms of the contract so far, and if I judge that they are likely to be successful in the college-level course, I will offer them the contract to sign - at which point they may choose to sign, or to switch into the general physics course.  I remind them that I have chosen them to be part of this team, so that I am invested in their success.  That I will be honest with them if I think they can't handle the course, so that they can just concentrate on each assignment and leave the long-term planning to me.

But what about their GPA?  

Here's what the contract says about grades:

Your marking period report will indicate an (unweighted) grade of A- each term during the year.

After AP score reports are released in July, your transcript will be adjusted according to the scale below.  This will increase the overall GPA for all those who earn 3 or above – which, historically, has been virtually everyone.

However, if your in-class performance is better than your AP score equivalent, your transcript will reflect the in-class performance.

AP Score     Transcript Grade

5             A and honors bump

4             A- and honors bump 

3             B+ and honors bump

1 or 2             B

Note the out that I've left myself and my students: someone who's done well all year won't be penalized for having one bad day on May 9.  That said, the AP exam is pretty darned consistent.  It's rare that someone significantly underperforms what I've seen from them all year.  In practice, my goal is to eventually counsel out anyone whose in-class performance is below the 3 level, so that *everyone* will earn a weighted B+ or better.  Those students who aren't getting 3s on most practice exams are invariably better off building skills in our very strong conceptual physics class, and then returning to the AP course junior or senior year.  

Here's where the headmaster's genius suggestion solved problems I hadn't anticipated.  A student who truly is trying to game the GPA system in the short term is better off with an earned A in general physics than the automatic A- in the AP class!  And a student willing to take a class below their intellectual level for the purpose of earning a higher grade is someone I don't need in AP physics, any more than the football team needs someone who only joined to impress potential sexual partners.  The students who choose to stay - which, so far, has been all of them - understand that they're taking a small GPA hit for now, but in return are freed from the angst of worrying incessantly about whether they're perfect.  

When someone inevitably asks in class about grades or GPAs, my response is gentle, but clear about two points:  (1) Read the contract for details, and (2) If GPA will have any influence on your decision to remain in the college-level section, you don't belong here;  I'm happy to help you switch into the general class, where you're likely to earn a natural A.  They get the message very, very quickly - such that the SECOND student who tries to ask about grades is hurriedly and firmly shushed by classmates.

The next post will describe how I communicate all of the above to parents and advisors.  Then I'll get to discussing the nitty-gritty of how the class works on a daily basis.

Contract grading in AP Physics 1 part 1: Why I do it.

The most important qualification for success in AP Physics 1 is the want-to barrier.  I mean, yes, there's a level of intellectual horsepower required.  Yet, the borderline students who willingly opt in to the challenge of a college level course tend to do well in the long term, while borderline students who are pushed by parents or counselors - or by the transactional potential of a higher GPA - to take AP physics tend to perform poorly.

Much more importantly, the borderline students who opt in for the right reasons don't bring their classmates or the class culture down.  And such students don't bring *me* down.  Rather, they make me happy.

A number of years ago, I decided I need to limit my work with advanced students to those who truly want to work with me.  I'm sick of fighting with smart students who use my class to game the college admission system.  I'm done with students who have no interest in physics, just in getting a weighted A on their GPA.   I have no patience left for those whose goal is to simultaneously maximize their honors grade while minimizing the engagement necessary to earn that grade.  

My first step was to focus my work on the youngest students.  Our boarding school 9th graders have already made the personal decision to seek out a challenging environment.  They could all have remained at their local public or independent high school.  Already these 14 year olds have shown themselves to be not entirely risk-averse.  They see their teachers as kindly parental figures whose goal is to know, challenge, and care for them.  They *don't* yet see teachers primarily as mean, demanding authoritarians who are obstacles to their success.

Yet, precisely because these barely-teenagers have just taken an enormous leap outside what was comfortable for them, they often don't want to compound leap upon leap.  Our freshmen congregate to the popular activities that their peers say are cool - mostly football and soccer in the fall, rarely theater or the outdoors program.  When we tried giving the freshmen the option to choose to join an AP physics section a few weeks after arrival, many qualified candidates stayed away.  They (and their parents) wanted a "solid start" to their boarding school career.  They were still gaining their footing in discovering who they were socially and athletically - they didn't want to risk "failing" academically.

So, we've gone to a contract grading system in the 9th grade AP Physics 1 class, in which all students in the course get an A- on each term report, no matter what.  After a year of just seven students opting in to AP Physics 1, I've had class sizes of 15, 20, and 20 - out of only 90 or so total 9th grade students at the school.  The students are happy, they're enthusiastic, they're fun to be around.  They're learning physics well enough to pass the AP exam (13/15 passing in 2020, 18/20 passing in 2021, probably similar in 2022.)

I'm sure you have two major questions:

(1) How did I and my school make this happen?  In a school that emphatically publishes grades six times per year, how do I get away with my class being such an outlier?

(2) Without term grades as a motivator, what techniques do I use to keep students invested and engaged for the long haul of a school year?

I'll address each of these questions in the next posts.  

Describing a laboratory procedure: speed of a cart at the bottom of a ramp

 Samar, who teaches in Maryland, called my attention to a question in the AP Physics 1 Workbook:  

In order to perform an experiment, two students need to determine the velocity of a cart just as it reaches the bottom of a ramp.  In a few short sentences, describe an experimental setup that they could use to determine the [instantaneous] velocity of the cart at the bottom of the ramp.

This is posed as an extra suggestion to discuss with students, and so doesn't have a solution in the teacher version.  Which of course - experimental physics is a creative endeavor, where right and wrong certainly exist, but where numerous correct approaches are available.  

Nevertheless, it's worth me giving a few examples of how I'd suggest answering the question such that (a) the procedure is correct, (b) the procedure is clearly communicated, and (c) the procedure is described in "just a few short sentences" rather than in a multi-page lab report full of vacuousness.

I've graded more AP experimental questions than anyone else on the planet*, so please trust me when I say that you shouldn't accept any response longer than about 80 words.  Seriously - no matter how thorough, no matter how accurate, a long response is no good!  For one thing, the student just used all sorts of time writing all these words here, when that time could have been more productively used elsewhere - on other problems in an exam, or perhaps at home playing with the family dog.  It's not possible to earn extra credit, or a "plus one!" on an AP exam.  Just answer the question, then stop.  If you "lose" a point for not saying something important, well, the extra five sentences you wrote at the end aren't gonna help.

* I'm probably not kidding. Guinness Book, please contact me!

So, how would I answer?  Here are four ideas off the top of my head.  I'm sure others will chime in with other thoughts!  

1. Put a dual-beam photogate above the cart at the position where the cart leaves the track.  Tape a thin slice of an index card to the top of the cart, such that the card breaks the photogate beam.  Then drop the cart down the ramp, and the photogate will read the instantaneous speed at the bottom.

2. Place a meterstick horizontally at the bottom of the track.  Record the cart's movement on video.  Pause the video in consecutive frames when the cart is at the bottom of the track.  The distance the cart traveled between frames - read on the meterstick - divided by the time for each frame (known from the video camera) is the instantaneous speed.

3. Place a motion detector behind the cart.  Have the detector create a velocity-time graph for the cart's motion down the ramp.  The maximum reading on the vertical axis is the cart's instantaneous speed at the bottom.

4. Use a smartcart that can create a velocity-time graph of the cart's motion down the ramp.  The maximum reading on the vertical axis is the cart's instantaneous speed at the bottom.

Bean Dad and physics pedagogy: they're not the same at all, but I can understand why people have this impression.

I truly hope you missed the brief internet celebrity of "Bean Dad." Brief, tragic summary: a less-than-empathetic parent tried to teach his hungry six-year-old daughter to use a manual can opener by denying her food until she, without help, figured out how to open a can of beans.

Well, true to the spirit of Twitter, it took no time at all for the no-context sweeping generalizations to be pronounced.  I tend to ignore ridiculous Twitter debates that don't involve football, but an author whom I greatly respect jumped in with a barb that hurt: 

"The Bean Dad approach is STEM pedagogy in a nutshell," @jonnysun said.  (He's since deleted the tweet, I think - I found a reference to it, but I cannot find the tweet itself.)

I know other teachers heard similar not-so-flattering remarks about how science is taught.  Folks got defensive about their methodology.  And that way madness lies.

I mean, any good science teacher teaches by inquiry, by modeling, by discovery, or by whatever buzzword means "don't just talk about science, do science".  And none of these buzzword approaches, done correctly, bears any serious resemblance to Bean Dad.

Yet, before we turn our shoulders in a huff... please consider why so many intelligent people think that STEM pedagogy is like Bean Dad.  Fact is, this is a general perception of our craft.  Why?  That's an uncomfortable question.

I know that my very own students have this perception early in every school year. And in my first few years of teaching, I didn't know how to help students and parents and colleagues understand the difference between Bean Dad and "I can't help you with a blank page, I need to see your serious written attempt."  Insisting that students engage authentically with the material rather than demand that I solve their problems for them means that I will always, forever, deal with the charge that I "refuse to help."

And, well... a lot of our peers try to teach via inquiry or the like, but don't really understand what they're doing.  They don't lecture, but in good faith they don't know what guidance to give, just that they're not supposed to lecture.  Or in not-so-good faith they don't care what guidance to give.  Or they assume that since they figured things out on their own, so should their students.  These folks are, in fact, the school version of Bean Dad.  

We're deluding ourselves if we don't acknowledge the existence - maybe even prevalence! - of Bean Dad science teachers.  Their well-poisoning means that everyone else has to work ten times as hard to establish a positive class culture that gives appropriate guidance, but also allows students appropriate freedom to make mistakes.

We can't avoid complaints.  Yet, we can help students, parents, and colleagues understand our methods.  We can be transparent about our pedagogy.  We can de-emphasize the value of right answers and over-emphasize the value of correct approaches.  We can publicly prioritize progress over performance, long-term goals over short-term goals.  We can stand up for colleagues who share our values.  

And we should, must, keep on going in the face of pressure each fall.  When alumni of your course are the ones shutting down the complaints that "Mr. Lipshutz doesn't help us learn," then you know you've done well.

An ill-posed problem involving the work-energy theorem

A source of physics questions showed a diagram like the one to the right.  A person can exert a 150 N force parallel to the frictionless ramp.  How much work does this person do on the 20 kg box to bring it from the bottom to the top of the ramp?

Approach 1:  Define the system as the box-only.  Ignore the work done by the earth, because the problem asks only for the work done by the person on the box.  Because the force of the person is parallel to the ramp, the work done is just force times distance - (150 N)(5 m) = 750 J.

Approach 2:  Define the system as the box-earth.  The work done by the person should equal the potential energy gain of the box-earth system.  That's mgh, where h is the 2.5 m vertical displacement (i.e. 5 m times sine of 30 degrees).  The work done is thus (20 kg)(10 N/kg)(2.5 m) = 500 J.

Which is correct?  

Neither.  But the problem is ill-posed.

The easiest way to see the ill-posediness is to try to draw an energy bar chart.  Let's use the box-earth system.

The gravitational potential energy bars are easy - from zero at the bottom of the ramp to something at the top.  

On an energy bar chart, conservation of energy is written by equating the number of bars on the left plus the bars of work done by an external force with the number of bars on the right - I describe the process in this video as "bars plus bars equal bars."  Right away, you can see why the problem is ill-defined!  What's going on with the kinetic energy?

We could assume constant speed.  Then the bar chart shows that we need the same amount of work done by the person as the gravitational energy at the top of the ramp.  That's a totally reasonable assumption!  This gives the work done by the person as 500 J, as in approach 2.  

But then what of approach 1?  The 150 N force applied over 5 m does give 750 J of work done!  But that would cause the box to have 250 J of kinetic energy at the top of the ramp!  Is that okay?  Well, sure, but wouldn't the box fly off the top of the ramp, then?!  I suppose, the problem said the person "can" exert 150 N of force, so perhaps the person is applying less force than they "can"?!?  But then I'm sounding like a lawyer, so by definition I'm wrong!!!

Creating multiple exclamation points in a blog post means the problem is ill posed.  Now, "ill-posed" doesn't mean "One student personally can't figure out the answer."  Were such a problem to accidentally show up on an in-class or standardized exam, I'd expect a student to explain the issue in writing - not to come to the front of the room to argue with the proctor. 

Most frequently, this sort of question asks the minimum amount of work the person needs to do to bring the box to the top of the ramp without specifying the force applied by the person.  Then the assumption of constant speed is not just reasonable but required to find the minimum work.  It's the additional specification of the force of the person on the box that causes the issue.

That doesn't mean this scenario couldn't be used for a well-posed problem!   "Explain why this problem is unsolvable without knowing how the box changes speed on the ramp" would be an excellent question.  Or, remove the "frictionless" statement, specify that the block is at rest at the bottom and the top, and ask for a justification of whether the ramp is frictionless or not.

Describing motion from position-time graphs

 

The position-time graph to the right represents the motion of a cart on a track.  The motion detector points to the left.  Explain how to reproduce this graph.

When describing motion, students only need to address two elements: 

a. Which way is the cart moving?

b. Is the cart speeding up or slowing down?

Yet, students trying to answer this question will tie themselves in knots addressing how the cart is "accelerating", trying to use words like displacement, velocity, vector, negative, positive, etc.

Don't even give your class the string with which to tie knots.  Get them in the habit of addressing each of these two questions only; and get them starting every response with a fact of physics.

For the initial foray into position-time graphs, only three facts are relevant: 

1. A position-time slope like a front slash / means the object is moving away from the detector.
2. A position-time slope like a back slash \ means the object is moving toward the detector.
3. To determine how fast an object is moving, look at the steepness of the position-time graph.

a. Which way is the cart moving?  Do NOT accept an answer that begins with "The cart is moving right."  I don't care what else this response says, it is wrong on its face.  A response must begin with a fact of physics.*

*"But that's not fair, Greg! A student who says "the cart is moving west because the slope is negative" is right!"  See, I'm not concerned with whether this particular answer is right or wrong - I'm concerned with my students developing a long-term deep understanding of position-time graphs, such that they can handle any question on a high-stakes exam as easily as Serena Williams handles a shoulder-high volley at the net.  Imaging Serena as a wee lass asking someone to hit her volleys for practice... and that someone kept lobbing her.  "Please hit me volleys."  "But I won the point!" says her suddenly FORMER practice partner.

"A position-time slope like a back slash \ means the object is moving toward the detector.  This graph is always a back slash, so the cart moves opposite the way the detector is pointing - the cart moves RIGHT."

b. Is the cart speeding up or slowing down?  Similarly, do not accept any answer that doesn't start with a fact of physics - especially do not accept an answer that references acceleration.  Yes, it is technically possible for an experienced physicist with a deep understanding of mathematical physics to recognize that the concave-down graph means the second time derivative is negative, and the negative slope means negative velocity, and to connect that to the magnitude of the velocity vector getting larger.  Aarrgh!  No!  No introductory physics student thinks this way!*

* And the vanishingly rare unicorn who can in fact think this way should have no trouble whatsoever using the much simpler facts above to reason through this graph.  So make the unicorn do so.

"To determine how fast an object is moving, look at the steepness of the position-time graph.  This graph is always getting steeper, so the cart always speeds up."

c. Now go reproduce the graph with a motion detector and cart on a track.  Amazingly, even after answering these two questions correctly, about 20% of the class will still set up the situation incorrectly.  They'll claim they need a curved track.  They'll have the cart moving away from the detector because "the graph is sloped down", even though they just wrote clearly on their own paper that the cart moves toward the detector!

Let them mess up.  

When the students have trouble reproducing this graph, they're confronting their personal misconceptions.  Even if a friend just shows them what to do, they'll see for themselves, "oh, the cart had to move toward the detector and speed up!  Now I get it!"  Or, you can ask them to read back to you what they wrote: "Which way is the cart moving, again?  And is the cart speeding up or slowing down?  So did you set up the cart moving toward the detector and speeding up?"

I don't like having students use their hands or their bodies to reproduce motion.  You'll end up in arguments about whether the graph does or doesn't look like it's supposed to, because it's really tough to keep a hand or a whole body continually speeding up for a second or two.  No, use a cart on a track!  This can be done with a fan cart on a flat track, or with a free-wheeling cart on a slanted track.  Insist on seeing one full second of motion - then you won't see just the 0.1 s when the student pushed the cart to get it started on the incorrect motion, and you won't have to argue about why that's wrong.  It's pretty much impossible to do this wrong and get a good-looking graph that's at least one second long.

"The answer is D because..."

Test corrections are the most valuable and productive use of my students' time I can think of.  Nowadays, I don't even return graded tests; rather, I give each student a blank copy of the test, along with notation about which questions they didn't earn full credit on.  They can see the original graded test (and their grade) only after getting all corrections checked off.

But test corrections are only useful if students explain their understanding thoroughly and correctly.

The first time we do test corrections, a few clueless (or intellectually lazy) students just write "I put C, but now I know the answer is D."  Um, really?  You call that a correction?  How does that help you understand the original problem?  More to the point, how does that convince *me* that you understand the original problem?  Begone, foul dwimmerlaik, and bear thy feeble "correction" with thee to the houses of lamentation.

Of course, there are teachers in other subjects who accept such baloney as a "correction."  Which is why many of us get pushback when we give credit for test corrections - parents and administrators and colleagues default to "oh, whoops, the answer was B, I've learned that now" in their own understanding of what "test corrections" mean.  No.  Duh.  They're much more than that.

However.  Even though most students and most physics teachers recognize that justification of the correct answer is required... it's still all too easy to accept a correction that doesn't truly show understanding.

A block of mass m is not touching a surface.  You pull up on the block with a tension T which is bigger than the weight of the block.  Which way is the block moving?

(A) down

(B) up

(C) the block can not move

(D) the block could be moving up or down.

"The answer is D because the net force is upward here."  How does this show understanding?  I mean, the net force is indeed upward.  And the answer is indeed D.  But has this student shown their personal understanding?  Or have they just quoted the answer their friend gave them with a vague handwave at a physics term?  Thing is, I don't know.  And so a better correction is necessary.

"The answer is D because the object could be slowing down or speeding up."  Well, this is also a true statement that doesn't show understanding.  How do you know the object could be speeding up or slowing down?  And what does that have to do with the direction of motion?

At this point, a student is likely to be getting frustrated with me.  They keep saying correct things, and I keep sending them back to the dungeons!  What do they have to do to get a correction checked off around here?!?

Answer: They have to start with a fact of physics.  

Legitimate starting points for all justifications include facts from our fact sheet (like "acceleration is defined as the change in speed every second"), problem solving procedures we've learned (like 1. free body diagram, 2. components, 3. write newton's second law in each direction), or equations (like "x = vot + 1/2at^2).  

I think we should all train our students that any other starting point at all, especially "The answer is D because..." is incorrect on its face.

"When an object speeds up, acceleration is in the direction of motion; when an object slows down, acceleration is opposite the direction of motion.  [These are facts from our fact sheet.]  Here the acceleration is upward, because the problem says the unbalanced force is upward, and acceleration is in the direction of the unbalanced force.  So the object could be moving up and speeding up, or moving down and slowing down.  D."

There's no way this student doesn't understand the problem.  There's no way that this student is merely parroting what a friend told them.  (At least, if they've obeyed the five-foot rule.  A friend might have told them what to do, but the student must have phrased the answer in their own words because they can't just copy.  And the five-foot rule is easy-peasy to enforce in class.)

Most importantly, this student has corrected a misconception. They likely originally said the object was moving upward because the unbalanced force was upward.  By quoting the facts, they are forced to confront how their intuition about how the world works is at odds with how physics actually works.  

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.

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.

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.

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.  :-)

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.  

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.

Two complicated true-false questions addressing impulse-momentum misconceptions

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

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

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

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

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

What are the answers:

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

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

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

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

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

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

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

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

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

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

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

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

Athletic coaches are servants, just like teachers are

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

How to speed grading #4 - instant replay

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

*Or hawing.

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

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

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

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

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

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

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

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

How to speed grading #2 - preventing complaints - corrections, not comments

Yesterday I wrote about getting into an umpire's mindset when grading.  You're not paralyzed or prejudiced by considering what your students might be thinking - you're simply grading what is on the page, according to the rubric.  No pity, no remorse, no exceptions.

I don't write comments on any student work!  I mean, we all know darned well that students don't read those comments anyway, except with the attitude of a defense attorney trying to find a legal loophole.  Writing comments takes an enormous amount of time, time that is usually wasted - and time that doesn't prevent complaints, but perversely encourages arguments.

Greg, that's easy to say in principle.  In practice, aren't all your tough calls mercilessly nitpicked by students, and then by their parents and your colleagues?  Isn't a student going to argue about every little point they lose, especially if that point was lost on a judgment call?

No one can argue if you don't give a marked-up test back right away.

Rather than write comments, I merely indicate which parts are not fully correct, and I make notes for myself for the purpose of tallying points.  I print out a blank copy of the test for each student, on the front page of which I indicate which parts of which problems were incorrect.  (Not how many points were lost or gained - just which parts weren't entirely correct.)

I return the blank copies to the class ASAP after a test.  The next assignment is test corrections, which are done collaboratively.  

So, no one can argue points!  If someone does ask - as they do early on in the year - why they got the problem wrong, I don't engage.  I just ask them just to do the correction.  Once they've done all the corrections and I've checked each one off as correct, the students can have their original test back.

(I write everyone's name on the board when the test is returned.  Then, when a student finishes all corrections, that student is asked to erase their name.  Between the opportunity to erase their name AND the opportunity to see their original graded test, that's some powerful not-grade-based motivation for getting corrections done!)

It's amazing the difference in response when a student gets their test back this way, compared to getting their test back immediately.  In the olden days, I'd give back a graded test and watch the whining, sour-grapes justifications of poor performance, arguing, and performative embarrassment* commence.  No one who didn't get a top score was ever satisfied.   A "bad" grade would send a student into conniptions (and then into even more conniptions when they saw that no one was paying attention to their first conniptions).

*Like when we got our school pictures in middle school.  Every last student turned the picture upside down so no one could see, while telling everyone loudly how terrible they looked, hoping that their crush would ask to see and say how they looked great, really.  It was all just dumb performance art.

Not any more.  Now, students look at the grade, and a gritty determination sets in.  They rationalize up rather than down!  Not "man, it's not fair, teacher shouldn't have taken off points here."  But rather, "dangit, of these points I missed, most were simple mistakes. I knew how to do these, next time I'm not going to screw up the easy questions!"