My week-long kinematics approach, including the facts

In 9th grade AP Physics 1, my initial work with kinematics takes a week and a half.  That's it.  How do I do that?

* Monday (45 minutes): position-time graphs, learned through facts and a graph-matching exercise.  Homework is about position-time graphs.

* Wednesday (90 minutes): velocity-time facts and graph-matching exercise; acceleration facts with demos using the PASCO visual accelerometer; demonstrate free-fall acceleration with a motion detector.  Homework is about velocity-time graphs.

* Friday (90 minutes): motion diagrams with a 10-Hz dot machine; make a position-time graph from the dot machine output; use two slopes of that graph to find an acceleration.  Then, two quantitative demonstrations with the projectile launcher and algebraic kinematics.  Homework is about the definition of acceleration.

* Monday (45 minutes): finish dot machine lab, correct any issues with the first homeworks.  Homework is several algebraic kinematics problems.  

Then on Wednesday we're moving into equilibrium of forces.  (Those of you who have taken my workshops might be confused - for my upperclassmen, I start the year with equilibrium of forces, and then move into kinematics in the style above.  But for 3rd formers who are more at home with real inquiry from the beginning of the class, I dive into motion.)

How, you might ask, does this minimal treatment lead to deep understanding?

Well, it only kinda does right away.  It's the long-term re-visitation of these concepts, the integration of kinematics into problem solving with other topics, that truly ingrains deep understanding.  Yet, my students average a full two points higher than the national average on the AP Physics 1 exam.  They're getting kinematics just fine with my approach.

I use fact sheets, and demand direct reference to the facts on every problem.

A big part of why students struggle at first with understanding motion is that they rely on their prior knowledge.  I mean, AP physics students are generally at the top of their class.  They are used to half-listening in math or science class, then using their natural talent to reach in the direction of an answer or written justification.*

*Then they're used to using their debate skills to argue why their answer is technically correct and should earn points.

I don't provide the class with a lot of facts; but those facts get directly to the point of kinematics concepts.  And direct reference to these facts will lead students to correct answers and justifications... if the students can be arsed to use them.

Here are the facts.  No justification is accepted unless the student has quoted at least one of these facts nearly verbatim.  (When there's a numerical or semi-quantitative problem using the constant acceleration equations, those equations are used instead of these facts.)

And yes, really, these facts and a week of experiments/demonstrations/practice is all that's necessary to dive into kinematics.  In my next post, I'll explain how I use the acceleration facts with demonstration to stamp out misconceptions.

Definitions

Displacement indicates how far an object ends up from its initial position, regardless of its total distance traveled.

Average velocity is displacement divided by the time interval over which that displacement occurred.

Instantaneous velocity is how fast an object is moving at a specific moment in time.

Position-time graphs

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

To determine how fast an object is moving, look at the steepness (i.e. the slope) of the position-time graph.

To determine which way the object is moving, look at which way the position-time graph is sloped.

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.

Instantaneous velocity is found by taking the slope of the tangent line to a position-time graph

Velocity-time graphs

To determine how fast an object is moving, look at the vertical axis of the velocity-time graph.

To determine which way the object is moving, look at whether the velocity-time graph is above or below the horizontal axis.

An object is moving away from the detector if the velocity-time graph is above the horizontal axis.

An object is moving toward the detector if the velocity-time graph is below the horizontal axis. 

To determine how far an object travels, determine the area between the velocity-time graph and the horizontal axis.

On a velocity-time graph it is not possible to determine how far from the detector the object is located.

Most everyday motion can be represented with straight segments on a velocity-time graph.

Acceleration

Acceleration tells how much an object’s speed changes in one second.

When an object speeds up, its acceleration is in the direction of motion.

When an object slows down, its acceleration is opposite the direction of motion.

Objects in free fall gain or lose 10 m/s of speed every second

From Umpire School, 2008 - good and bad teaching from a student's point of view.

I wrote the following in 2008 at the Harry Wendelstedt Umpire School in Daytona Beach, Florida. This year, our faculty has been discussing and giving significant attention toward the relationships we build with our students. This post was a response to relationship building from a student's point of view - in this case, I was the student.

Woodberry Forest School has allowed me to come to Umpire School as the major part of my sabbatical.  In principle, the sabbatical should involve professional development that is somehow related to one’s role at the school.  Umpire School was not intended as true professional development, but rather was a lark, a way to get myself out of the classroom for a while so as to avoid burning out my enthusiasm for teaching.  It’s turned out, though, that this place has given me all kinds of worthwhile perspective about my day job.  Think about it…

I teach at a boys’ boarding school.  Here, I am a student at a “school” for 120 “boys”[1] who live not in a dorm but in a beachside hotel.  Woodberry is all about bonding with classmates and making friends, yet those friends are ever competitors for spots on varsity sports teams, in the plays, for valedictorian… here, though the student umpires are friendly and supportive to each other, we all know we’re competing for maybe 20 positions in the professional ranks.  In other words, my sabbatical has turned into role reversal.  Talk about gaining perspective…

So as the professional teacher thrust into the student role, I’ve continued to observe the instructors, what they do, how I and my classmates react.  I’ve already posted some thoughts on our major league instructors.  They’ve been uniformly awesome.  The instructors who are minor league umpires, though, have been a mixed bag.  A couple have been wonderful.  Most have been acceptable, though not special.  At least one is horrendous.  Though they all know their stuff, what separates the great from the just-okay is their attitude toward the students.  Too many of the minor leaguers are easily frustrated, occasionally obnoxious, or overeager to snap at reasonable questions.

My colleague Dan suggested, perhaps perceptively, that some minor leaguers might be teaching here for the cash and the politics rather than for a true love of teaching their craft; whereas, the major leaguers are already set financially and professionally, and so choose to come here for the right reasons.  While that’s an excellent point, I’ve chalked up much of the poor teaching to inexperience more than motivation.  I know that my own major deficiency in my first years of teaching was that I showed frustration too easily.

Thursday’s class included an hour-long review of the mechanics of the 2-person system that we’ve been learning all along.  The two highest ranking minor league umpires took the stage to run the review.  Boy, did they destroy the day’s morale… the timbre of their voice and their body language figuratively screamed, “My God, we’ve told you this already, why are you all too stupid to do it right?!?”  I do see where they’re coming from, ‘cause we do keep screwing up some of the basics on the field.  The review was necessary.  But an occasional smile, some sort of token admission that “you’re doing it all for the first time so you really aren’t dumb just inexperienced,” would have been appreciated.

Now, I’m not complaining about a bit of intensity, or even about them yelling at us.  We were warned from day one: the instructors will yell, not to embarrass us, but so that *everyone* can hear and thus everyone can learn from one person’s mistake.  Heck, that’s my philosophy in physics class.  Ask any of my students – I get loud and intense.  I tell you when you screwed up.  I try to do so with a smile on my face, but nevertheless, I yell.  Of course, I temper that yelling with encouragement, with whatever is necessary for the class to know that I love them even when they tell me that an object moving at constant speed must have a force acting on it.  Whether my students know it or not, I think deeply every day about whether I’ve shown enough love to temper my intensity.  Here at Umpire School, I have no problem being yelled at when I deserve it.

I’m concerned about instructors who assume that a student who messes up must not have been paying attention, or has a bad work ethic.  The students have heard at least seven lectures about how success at Umpire School requires individual effort beyond merely performing in drills.  Practice, study, attention while in line for drills, attention in class… all of these things are not really optional if we want to do well.  Well, the vast majority of the class seems to have taken this message to heart.  Many of us stay an extra hour or more at the fields to practice each day.  Others can be heard practicing on the beach.  My study group has been well attended, and I know that many other study groups can be found around the hotel.  Those in line for drills are often seen going through their mechanics.  I never see students talking in class or distracting their neighbors.  Everyone that I’ve seen has the right attitude.

Yet, I repeatedly observe instructors becoming angry or extremely frustrated with student(s), even though those students had shown considerable diligence.  In one case, at the huddle after a long drill, my field was reminded again[2] that we should be paying attention while waiting our turn.  “I’ve gotta tell you,” one instructor said with nods from his colleagues, “it gets really frustrating for us when we tell you the same thing again and again.  If you weren’t *$&#ing around in line, you wouldn’t make the same mistake that the guy in front of you made.  Don’t *$&# around in line, and then maybe we wouldn’t have to go over this same stuff so many times.  If you’re paying attention, you won’t screw up.”

This instructor’s statement contained two major fallacies.  For one,  I am capable of explaining exactly what I am supposed to do in any given drill.  But that does not mean that, when it comes time to make my body go through the actual motions, I won’t forget something.  For example, the first time I did the “pivot” drill I forgot to watch the ball in the outfield.  All the way until my next turn, I practiced in my mind, reminding myself, “watch the ball, watch the ball, ball, ball…”  When it came back to my turn, I started out watching the ball just fine; but then, after I properly glanced at first base to watch the runner touch, I forgot to turn my eyes back to watch the ball.  Now, I knew I’d get this eventually.  It’s not nuclear physics.[3]  But at that point, my mistake was simply born of inexperience rather than lack of dedication.  I paid attention; I still screwed up.

The second fallacy made me want to ask a smart-arse question.  I wanted to say, “Mr. Instructor, did you see anyone, anyone at all, *$&#ing around in line?”  I was smart enough to hold my tongue.

One instructor in particular, Jordan, has three times hollered at me as if I were a serf.  On Thursday, one of the fields needed some volunteers to bat – I didn’t need to be asked twice, especially because I had been sitting bored on the bench.  I grounded into a force play[4] to put runners on first and second with one out.  Now, when we are running the bases, we’re told to take two bases where possible in order to give the umpires something to call.  The next batter singled on a line drive to very, very shallow centerfield.  I properly held up, then ran when it was apparent the ball would not be caught.  As I approached second base, the ball was thrown toward the infield.  I was aware of the “go two bases” guideline, but the guy holding the ball probably would have been able to tag me out himself had I run to third.  So I stayed there.  After the third out, Jordan screamed across the field, “Greg Jacobs, how many times have we told you to go two bases on a base hit?  What’s your problem?”  I tried to defuse the situation… my intent was to say humbly, “I know, but the ball was in the infield while I was standing on second base… I thought running to third would be unrealistic.”[5]  As soon as three or four words were out of my mouth, Jordan snapped, “I don’t want to hear excuses, I want you to do what you’re told!”

Well, I’ll be danged… I avoided that argument by walking off the field, figuring that while I won’t get into a shouting match, I also won’t volunteer to take that kind of abuse. 

But sure enough, on Friday Jordan was in charge of our field during drills.  I ran out a ground ball to first base.  The first baseman booted the ball, and it trickled behind him.  I figured that I had a slight shot at making it to second base.  In a game, I would not likely have made the attempt; however, under the dictum of “make plays for the umpires,” and especially considering my verbal lashing the day before, I didn’t hesitate – I ran to second, beating the tag by half a step. 

And Jordan looked at me, shook his head angrily, and said to all, “That would never happen.  What’s wrong with you, Greg?  You’re supposed to run like you know what you’re doing!” 

Nothing I can do here short of getting into a screaming match, and there’s nothing to be gained with that.  I explained my conundrum privately to one of the better instructors, and I quietly go to the back of the running line when Jordan is on our field. 

Okay, so there’s my huge beef about the worst instructor here.  On a positive note, it’s time for a heartwarming story about Rob, a minor leaguer who earned our respect and made my day on Monday.  In one moment he showed more teaching talent than the rest of his compadres combined.

First of all, you must understand the nature of CJ the Crazy Braves Fan.  This 19 year old has had a difficult time of it at Umpire School.  To start with, he’s a bit of a natural social outcast.  His slight speech impediment makes him sound dumber than he actually is.  He has limited athletic ability – when he runs, he waves his arms, and he looks like he’s going to fall with every step.  CJ knows baseball, but he’s probably overly enthusiastic about the Braves and Bobby Cox.[6]  No one loves to play the game more than CJ, who puts himself first in line to bat (even though he can barely make contact), and who jumps at every chance to play the field (even though he can’t really throw or catch).  He shows that same enthusiasm for umpiring.  Everywhere you look around the fields, CJ can be seen practicing his “strike three!” or his ejection mechanic.  He keeps a list in his breast pocket of every instructor whom he has “thrown out” of our drills.  Unfortunately, CJ often has trouble getting his umpiring exactly right on the field.  At first a lot of students were a bit cruel to CJ, but by now the class has rallied around him… he’s almost a class mascot.  Most folks now treat him as a pleasant and amusing character.

CJ’s stated goal is to become a major league umpire, but he’s recently realizing that his talent might not be enough to carry him that far.  It was my group’s turn with the pitching machine, CJ was the umpire, and I was the pretend batter.[7]  Poor CJ just couldn’t get anything right this time.  He failed to see a swing; his mechanics were all over the place; Rob the instructor had to correct his stance two or three times.  For probably the first time at school, CJ hung his head.  He knew he had stunk it up, and it was hurting him.  His last two pitches were disasters, where CJ barely made any call at all.  He looked like he might cry at any moment.

Rather than giving CJ the typical formal evaluation that usually follows cage work, Rob brought CJ over to him and looked him in the eye.  “CJ, you can not hang your head,” Rob said.  “We think too much of you to allow you to give up on yourself like that.  Who here works harder than you?  Who here is more enthusiastic?  When everyone else is sitting on the bench trying to avoid helping, you’re the first one to volunteer to play, to bat, or to run.  We see that.  I see that.  The instructors appreciate your efforts, we know how much you care, we want you to be the best umpire you can be.  So we will NOT let you hang your head and give up on yourself just because you had a bad turn in the cage.  Think about how much you’ve improved in three weeks…” and so on, encouraging CJ firmly but supportively for about two minutes, obviously in earshot of a whole bunch of people. 

I kept a poker face, but inside I was rooting Rob on.  The staff might talk all the time about how much they want us all to succeed, but here was one instructor showing with his *actions* how much he cared about a student on the margins.  Me, I didn’t do so well in my drills on Monday.  Yet, Rob made my day.  I came off the fields feeling just that much better about my classmates and Umpire School.

---

[1] The “boys” range from 18 to 55 years of age, and our class includes a 39 year old “girl”

[2] For now the thirteenth time

[3] And I’ve done some nuclear physics.

[4] Making my batting stats on the season 7-14 with a double.

[5] What I WANTED to say was, “You idiot, what kind of baseball player takes third in that situation?  You lecture about umpires developing instincts, and then you expect us to make dumb plays like that?  What’s YOUR problem?”

[6] I can tell that it hurts him that seemingly every story about situations in the major leagues ends with “And then we had to throw Bobby out of the game.”

[7] The pitching machine is where we practice behind-the-plate mechanics.  The pretend batter holds a whiffle bat, and is occasionally instructed to execute a check swing, giving the plate umpire an opportunity to say “yes he did” or “no he didn’t”.

We aren't publishing 1st marking period grades for freshmen. How do we communicate progress, then?

My school made the decision NOT to publish grades for 9th graders in the first marking period.*  This decision garnered substantial support from the faculty and an official academic committee.  We don't publish reviews of a theater performance during rehearsals; only intellectually vacuous sports media personalities desperate for ratings assign wins and losses to athletic teams before games begin.  In that vein, I'm thoroughly on board with delaying our assigning of grades until we have enough data for that grade to be meaningful.

*That doesn't mean we don't evaluate assignments, that doesn't mean we don't give graded tests... just that we do not publish or even assign an overall letter grade until after the first trimester exam.

During the summer, a representative group of faculty met to discuss how to implement this change, and also how to communicate about students in the absence of grades. In preparation for that meeting, the 9th grade conceptual physics teachers met to discuss our approach to communication.

Below is a version of a letter I sent to the working group explaining how the physics teachers intend to approach this gradeless marking period. 

Conceptual Physics: Communication plan without published grades at first

Philosophy: We started from Nolan LaVoie's “contract grading” experiment, which he presented to our faculty and to the International Boys School Coalition.  Nolan articulated the attributes which typically lead to success in history course; next, he described the various levels to which his students display those attributes.  While we don’t think it best to adopt contract grading whole-hog in physics, we do want to use attributes as the basis for our communication system.

The ultimate goal we have for our physics students is for them to be able to demonstrate an understanding of how the natural world works, and to communicate that understanding.  How do we know the level at which our students demonstrate and communicate their understanding of physics? Through performance on assessments, including weekly quizzes, monthly tests… and most importantly, in the year-end conceptual physics tournament.  Therefore, those assessments are the primary items on which the grade is based.

How do we prepare our students to demonstrate and communicate their understanding of physics?  We practice, just like a musical ensemble practices.  We practice as a group, we practice alone; we practice basic skills, we practice advanced skills; we practice the well-known pieces, we practice creative improvisation.  Individual members of the ensemble will have different skill levels.  Not everyone is ready to be a featured performer.  Yet, everyone in the group can improve their performance ability through authentic engagement in all forms of the ensemble’s practice. 

So, let’s articulate what forms of “practice” we undertake in physics, and how we expect our students to engage in that practice.  Let’s communicate how well each student meets those expectations - not just at the beginning when grades aren’t published, but throughout the year.  After all, good practice habits lead to strong performance whether or not a Juliard professor is evaluating musicians from the audience. 

Student attributes that lead to success in physics:

In-class practice
1. Participating in experimental and problem solving activities
2. Performing on daily knowledge checks, and working with classmates to evaluate and improve their work

Out-of-class practice
3. Using the fact/equation/calculation problem solving process on every assignment
4. Engaging with homework assignments initially, without using or seeking assistance from students or teachers.
5. Redoing assignments correctly, with assistance, when required or necessary




We have always evaluated these attributes by grading lab work, daily knowledge checks, problem sets, and test corrections.  We’ve always made performance on these attributes half of the student’s grade.  But since we’re no longer publishing grades at year’s beginning, we have the additional opportunity to communicate specifically how a student is progressing on these attributes.  For each, how well is he meeting the standard? Enthusiastically, appropriately, such that he needs improvement, or not at all? 

We intend to send a note to our students’ advisors every three weeks or so, at least at year’s beginning.  In that note, we will indicate how the student is performing with respect to each of these five attributes.  For example, the first sentence of the note would say one of the following:

• He participates enthusiastically in experimental and problem solving activities, completing a large number of in-class exercises to a high standard.


• He participates appropriately in experimental and problem solving activities, completing a sufficient number of in-class exercises to a reasonable standard.


• His participation in experimental and problem solving activities needs improvement.  He has not completed a sufficient number of in-class exercises to a reasonable standard.


• He does not participate appropriately in experimental and problem solving activities

The other sentences would similarly address the other attributes we’re observing.  We’d also include one sentence as to how the student is performing on weekly multiple choice quizzes, and on monthly tests.  Again, we’d assign no grade, just a narrative indicating the level of the student’s performance (something like “outstanding”, “high level”, “acceptable level”, or “needs improvement”).

Our hope is that these comments targeted directly to success-building attributes can communicate clearly what the student is doing, and how the student is making progress on all fronts.  A single grade can’t communicate like that. Even though we’ve written some extraordinarily detailed comments over the years, we feel that unless a student is in danger of failing, students, parents, and even advisors tend to look at the grade and ignore the rest.

Assigning grades too often causes our words, the very articulation of our love for our students, to be killed or swept aside.  We’re thrilled to be removing the grade for the first trimester.

.

Don't get into a holding pattern on kinematics

I'm sure you know of a hundred fantastic activities regarding motion.  I can bring up a bunch off the top of my head that I learned about just in the past couple of years:

* Roll a ball down a ramp or off a table, and try to hit a moving cart

* Launch a ball through three or four rings placed along the ball's parabolic path

* Just heard about from Michael Magnuson: Predict the launch angle such that a ball just barely kisses the ceiling.  (Hint: it won't work right the first time, because most likely students will not account for the size of the ball.)

* Kinematics Card Sorts from Kelly O'shea

And that's just the new stuff!  I still use the old standby 10 Hz dot machine to make motion diagrams, linearize a graph of drop height vs. time measured by the g-ball, quantitative demonstrations with a projectile launcher, graph matching, and more. We have so many fun, straightforward, well-tested activities in our arsenal.  Fantastic!  Unless...

Unless... unless we're still doing kinematics activities and review when Thanksgiving or Christmas hits.

Whether you're teaching AP physics or a conceptual class, it's important to move along.  There's more to physics than motion with constant acceleration.  Students who grasp the concepts quickly deserve to be challenged by force, momentum, energy, and some non-mechanics topics.  Those who struggle will, in fact, catch up through review in context.  Once you've established kinematics ideas well enough that half the class is rolling their eyes at yet another set of multiple representations of motion, well, it's time.  Another day isn't going to help.  Move along to something new.

Have faith.  It's happened hundreds of times for me, that I grit my teeth feeling like I'm leaving some well-meaning but slow students in my dust... and then months later, a kinematics problem comes up in a seemingly unrelated situation.  "Oh, yeah, I remember when this seemed hard.  I get it now," they'll say.  

Move along.  I spend only two to three weeks focused exclusively on constant-acceleration motion.  I save some of the most interesting activities for later in the year, when my students have developed stronger laboratory skills, or during the exam review when there's no pressure to discuss new content.  Since we move along so quickly this time of year, my April and May can be extraordinarily relaxed. 

CSI: Motion Experiment, Episode 1: The Detector Is Blind.

A reader is having an issue with motion detectors and semi-quantitative experimental results:

Hello there! I hope your year has started off well. Mine has. I am very happy with my results from last year, implementing your teaching/activity techniques with the students. Thank you very much for all of your guidance.

I am noticing that during the in class lab exercises kinematics - those are the ones where we have a track, cart, and motion detector, and double the time, then double the acceleration, then double the initial velocity - that the double time experiment yields very high percent errors for most students. I thought it might be a sensor issue, but I zeroed the sensors and did the experiment myself on the setups giving trouble, and I am getting the same thing the kids are. It's supposed to be a multiplier of 4 for the distance, but I am getting 2.6, 2.9, 3.3...very low to what it should be. I'm now thinking it may be an issue with friction, because usually the lower the incline the worse the result, but too high and we don't have enough space to get a good time interval (I only have 1 meter long tracks). I am using the metal pasco tracks with the plastic pasco carts. The carts are on the older side, so I'm thinking that friction with the wheels might be throwing off results. 

Do you have any input on this? Do you experience the same thing? 

Hey!  I've got some thoughts.  I don't think it's a friction problem - the friction is there even for the smaller time, and in any case is not going to cause that much of a difference between what's predicted and what's measured.

One issue might be the 15 cm blind spot* for the sonic detector.  Depending on whether you're moving toward or away from the detector, you may well be missing a significant fraction of the distance the cart traveled.  After all, the blind spot is 15% of the entire track length!    Another less likely issue is that I've had students measure (and thus double) the time from when the detector was started, not the time that the cart was moving.  

*The green Vernier detectors that I use have a 15 cm blind spot.  The decade-old blue Vernier detectors have a 40 cm blind spot.  I don't know what the PASCO detector blind spot length is, but it exists.

The way I'd suggest doing this particular problem is in one trial.  Set the detector at the high end of the track.  Place the cart's back end 15 cm from the detector.  Press play, WAIT FOR THE CLICKS, and let the cart go once the detector has started running.  Use the position time graph made by the detector.  Check the distance traveled after the cart has moved, say, for 0.30 s.  (Not when the labquest says t = 0.30 s, 0.30 s after the cart begins to move.  You can check the velocity-time graph to see when the vertical axis value first moves away from zero.)  Then check the distance traveled after the cart has moved for 0.60 s.  I'll bet you come closer to a factor of four increase.

Do you have a PASCO smartcart?  Those will get much better data; and, you can use them on a long plank of wood instead of on the track - if the cart moves slightly off a straight line, the motion encoder in the smartcart's wheels will still work.

Hope this helps!

Epilogue:  Turns out the reader didn't know about the motion detector's blind spot, and so was especially confused that the cart moving toward the detector gave a consistently different result than a cart moving away from the detector.  She solved the problem using the experimental suggestion above.  Awesome.