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31 December 2015

Does AP Physics 2 include thermal expansion?

Joanne, a veteran of two of my summer institutes, writes in with this question.  Before responding, I did a search for "thermal" and "expansion" in the curriculum guide.

Nothing shows up for "expansion."   Lots of hits for "thermal".  

My understanding is that that everything about "heat" in physics 2 is about energy transfer via heating -- transfer by conduction, convection, radiation (looks like nothing but qualitative for the latter two, maybe some semi-quantitative for the first).  And then a bunch about energy transfer in gasses, with kinetic theory, the microscopic source of the ideal gas law, PV diagrams, etc.  

Be very, very sure that students can describe and explain what it means, at a microscopic level, for energy to be transferred via heating.  They've gotta be able to say more than a vague "the molecules move around more."  Manipulation of equations, and rote problem solving techniques with PV diagrams, will not be of any particular use on the AP Physics 2 exam.  The understanding has to be deep and thorough.

But no thermal expansion, as far as I can tell.


29 December 2015

Notes from observing an English class

As part of my school's faculty development program, we're asked to observe a teacher of our choice outside our department.  I asked to watch John Amos's English class.  I chose him because I knew him to be an outstanding, experienced, creative, intelligent teacher.  More to the point, he teaches 9th grade like I do, but his style and personality are very, very different from mine.  I thought it would be useful to see how another craftsman uses a different skill set to achieve the same general goals.

So many "Physics Educators," and "educators" in general, have the Soviet attitude that if only everyone did things my way, students would learn better.  I disagree.

I've always been open at my workshops and on this blog: my ideas, philosophies, and suggestions are mine alone, developed in the context of my personal strengths and weaknesses, and shaped by the ecosystems of the three schools at which I've taught.  What I do cannot work for everyone.  Yet, it's still worth sharing my thoughts, techniques, and ideas.  Not in the sense of "do these things and you will become a great physics teacher;" but rather, "here are a few ideas you may not have considered; try them, and then either throw them out or adjust them to make them your own."

So here's my extensive reaction to John's class.  I will not be adopting wholesale any of his particular techniques; but I appreciate the exposure to some different ways of approaching my craft.  Many of John's ideas are in the back of my brain now, ready to manifest -- consciously or subconsciously -- in my own classes.  In other words, I bought myself a few new tools.  Whether and how I use them is discourse for a future time.

What happened in the class?

John included three or four segments in a 45 minute class:

1. Discussion of vocabulary words
2. Discussion of previous night's chapter in Bradbury's The Martian Chronicles
3. Instruction about responding to passage identification questions
4. Practice responding to passage identification questions

This was a 9th grade general English class that included many of the same students I've worked with this year.

My reaction:
I always thought I hated kibbe.* I dreaded when my mom tried to make it. Around age 30, I realized that I liked kibbe just fine -- what I hated was my mom's cooking of the kibbe.**

*Kibbe is a Lebanese dish with bulgur wheat, ground meat, onions, and spices.

**Mom's laham mishwe (little bites of spiced lamb and onions) is wonderful. Don't tell her I said anything about the kibbe.

Similarly, my personal experience with the classroom study of writing and literature has been universally negative. I've always been aware that it's been the poor teaching and poor classroom atmosphere that turned me off to English, not the discipline of English itself. But John's class brought the source of my negative reaction to the forefront.  Last week, I watched a master at work.

I've advocated to physics teachers that we give a short quiz at the beginning of every class. The purpose is as much to settle the class down as to use the quiz as a device for review. John likewise recognizes the necessity for a start-of-class routine, but does it differently. He throws vocabulary words, the ones that will be on the upcoming test, up on the screen. As soon as the first boy arrives, he begins a relaxed, informal discussion about the words.  Thus, even the boy who is second to arrive feels he's joining class in media res, and so gets his materials settled and ready for business right away. John's vocabulary discussion -- which is interesting and captivating anyway --  serves the same teaching purpose as my quiz, but is better suited to John's personality than mine.

It almost goes without saying that we moved through four activities before any of the four had a chance to get old or stale. This class could easily have gone on for 90 minutes. Like the best entertainers, John left the class wanting more -- better 5 minutes too short than 1 minute too long.

Now, part of what made the class great was the enthusiastic and substantive participation of the students. Most, including some I know not to be A+ students, jumped in with excellent and interesting things to say, listening to each other and advancing the conversation. It helped that we weren't reading Jane Eyre, we were reading about Martians.  Most of the class was invested in the book, and in the class discussion; those few who weren't sat quietly, listening, without causing distraction. Those who participated did so authentically, never playing a game of one-upsmanship, never ignoring a classmate's comment.

I'm well aware that John's done considerable behind-the-scenes work over the first half of the year to set up the class I saw. At some point he's had to assert himself as alpha dog. For example:

One student -- he's from Vietnam, and in my AP physics class -- put forth some ideas which were initially confusing to the class, and even to me and John. The confusion came from many sources -- his language barrier and accent made it tough to follow him. This student's general intellectual level is well beyond that of most of the class, so his thoughts were more complex than we had yet considered. The class discussion was about linguistic metaphors for time, which necessitates some common cultural and idiomatic ground which isn't necessarily shared between Dixie and Southeast Asia.

I couldn't be more impressed with the class's reaction. I learned from experience in my own English classes: if I have an interesting but different take on a subject, keep my dang mouth shut, because if I don't explain it perfectly clearly right away such that everyone agrees with me, I'll have to deal with withering scorn from my classmates. Only occasionally was said scorn verbalized ("Oh, my gawd, the book's not that deep. Okay, I get it, you're smarter than we are.") Usually the negative response was manifested in body language, subtle dismissive gestures that ostracized me. My teachers either didn't notice, didn't care, or cared but didn't know how to take action.

In John's class, though, this student's classmates tried valiantly to get his point. No one made any rude snorts or eye rolls. Even those who were generally disengaged simply remained disengaged; they did not take the opportunity to get a nonverbal jab in at the smart nerdy kid.

How did John do it? How did he establish and maintain this atmosphere of genuine intellectual curiosity among 9th grade boys?

I mean, I do it... it takes every trick and tool I've ever learned, but I do it. I pounce on any student who makes a dismissive gesture, hollering loud enough for the sewage plant down the hill to hear me. I give out candy to the first student to give me a confident yet wrong response. I set up collaborative situations in which students must work with randomized class members. I have students grade each others' work so that right and wrong answers are transparent -- it's hard to make fun of someone when you know your own wrong answers will be out there for someone else to see.

But my strengths in setting tone -- my loudness, my subject's black-and-white nature -- are not in John's toolbox. He's softspoken, teaching a subject in which shades of gray are mandatory. So how does he do it?!?

(John did share one thing had done -- a different student, John says, had a difficult attitude for a while. John realized that this other student needs to be front and center, always with something to do or say; then he can be a very positive contributor. So, when John had the class read a passage out loud, he carefully appointed this student to read a major part. That kept him involved and invested, and less likely to turn to the Dark Side.)

I know there's more to say here... I wish I could have come to class the next day, when he was planning to give specific feedback to students' writing in response to reading passage identification questions.  But this should give you an idea of what I saw, what I thought about, as I observed this class to which I wish I could transport my 14 year old self.  No, I wouldn't have become an English major, but that's not the point.  :-)

23 December 2015

Momentum bar charts: worked-out examples

A large circular disk is initially stationary on a horizontal icy surface.  A person stands on the edge of the disk.  Without slipping on the disk, the person throws a large stone horizontally at initial speed vo relative to the ground from a height h above the ice in a radial direction, as shown in the figures above.  Consider the x-direction to be horizontal, and the y-direction to be vertical.  Consider the system consisting of the person, ball, and disk.  “Initial” refers to before the ball is thrown; “final” refers to the instant before the ball hits the ground.

The picture and some of the description is from an old AP Physics C exam question, which asked for detailed calculations of various quantities in terms of given variables and fundamental constants.  In AP Physics 1, there's no need to do the calculations;however, it's critical that we teach how to set up those calculations, or at least how to explain what is conserved and why.

I pose this and eleven other interesting situations in my energy and momentum bar chart exercises.  These are comprehensive, end-of-course activities that will challenge most physics teachers.  There's no algebra, none at all; just the requirement for careful understanding of the meaning of a "system", and then of an external force acting on that system.    

Can you make a qualitative impulse-momentum bar chart for the x-direction?

Of course you can.

Initially, nothing moves; so nothing has momentum.  No impulse acts on the person-ball-disk system.

What about the impulse due to the force of the person on the ball?

Since both the person and the ball are part of the system, the force of the person on the ball (and its Newton's 3rd law companion) are internal to the system.  The impulse column requires impulse applied by the net force external to the system -- only the net external force can change the momentum of a system.  In this case, there are no external forces in the horizontal direction.

The point of the bar chart is that it shows by inspection how the total system momentum is distributed: the bars on the left side plus the bars in the middle equal the bars on the left.  In this case, there must be zero total momentum after the throw.  How is that accomplished?  The ball moves right, so has what I'm calling positive momentum.  To maintain zero total momentum, the person and disk move left, giving them negative momentum.  The person and disk move together, giving them the same speed -- not the same momentum.  Since the disk is more massive than the person, the disk has a larger share of the system's negative momentum.  Note that the bars representing the person and disk add to about the same size as the bar representing the ball, showing that the total momentum remains zero.

How about the y-direction?

Sure, though it's a bit trickier.

Again, initially no movement or momentum.  Think for a moment: what causes the impulse in this case?

It's NOT the person pushing the ball.  That's a force (and thus an impulse) in the horizontal direction only.  And, that's internal to the system, anyway.

In the vertical direction, two external forces act on the system: the normal force of the ground on the system, and the force of the earth on the system.  The force of the earth is equal to the weight of the entire system; the normal force here is equal to just the weight of the person-disk part of the system (because the normal force is a contact force, and the ground is only in contact with the person-disk part of the system; the ball is in free fall).  So the net external force is equal to the weight of the ball.  That causes a downward impulse, represented by the bar in the chart above under the J.

Now inspect the bar chart: zero bars initially plus the impulse bar must equal the bars of total momentum when the ball is about to hit the ground.  The person and disk still don't move vertically, so they have zero momentum.  The ball must have a momentum equal to the impulse provided by the earth on it; that's represented in the chart by the ball's bar having the same size as the impulse bar.

That's enough for today.  But you can answer many, many more questions involving this situation.

What about an energy bar chart?  (Energy is a scalar, so you don't have x- and y- direction charts for energy.)  What if the earth is part of the system?  What if the system is JUST the person and disk?

See, the situation is rich, rich, rich with subtle questions.  Have fun with these.  Post thoughts in the comments.  Assign them to your students, and post the common misconceptions.  Go nuts...


14 December 2015

Cart on an incline: what qualifies as an "external force?"

When teaching about energy for AP Physics 1, one of the trickiest bits is defining an appropriate system, and then applying the work-energy theorem correctly to that system.  The question:

Hi Greg. From my understanding, an external force for a cart going down a [frictionless] incline would be the normal force acting on the cart. 

The weight is an internal or conservative force, so none of the external forces on a frictionless incline do work? I still consider Fg parallel to be an internal force for the system. Is this a correct assumption?

Not sure... gotta define your system first.

If your system is just the cart, then two external forces act: the weight (i.e. force of the earth on the cart), and the normal force.  Both are "external" forces because the forces are applied by objects that are not part of the defined system.  The normal force is perpendicular to displacement, so does no work.  The weight does work, because mg is parallel to the vertical component of displacement. This work is mgh, where h is the vertical component of displacement.  The cart acquires kinetic energy by the work-energy theorem -- the work done by the earth is equal to the cart's change in kinetic energy.

However -- if your system is the earth and cart together, then the only external force is the normal force, which does no work because it's perpendicular to displacement.  The work done by the earth on the cart is internal to the system, and conservative; so the system potential energy (equal to mgh) changes.  The system acquires kinetic energy by reducing potential energy, without any work done by external forces to change the total mechanical energy.

11 December 2015

Starting a Physics Lab From Scratch -- What Equipment Do You Buy?

In their December 2015 issue, the journal The Physics Teacher attempted to answer an important question that new teachers -- and teachers new to a school -- regularly ask:  "I don't have any equipment at all.  What do I need to order?"

Problem is, TPT asked the question of a university lab manager, who had ideas as far removed from a typical high school teaching situation as the troposphere is from the mantle.  No, sorry, you should NOT order $1400 AC power supplies, infrared cameras, or cloud chambers as your first purchases, unless, say, your top priority in setting up a banking office from scratch would be purchasing lie-flat seats for the executive jet.

No, folks, you want fundamental equipment to start your high school lab, equipment that is simple to use, durable, and (where possible) multi-use.  You want equipment that allows you to do demonstrations and laboratory activities in line with the first-year physics curriculum you cover.  

Here's my rough list of equipment, with caveats below.  You may think of other things; great.  Post a comment.  But be aware of my goal, here -- I'm not trying to be truly comprehensive in this list, and I'm not listing equipment for everyone's pet experiment.  

Rather, I'm answering the question: What would I buy for a high school's introductory physics program, given a one-time, not that big, start-up budget?

Enough for multiple lab groups:
PASCO carts and tracks with pulleys
PASCO hanging mass sets
Vernier Labquests, with motion sensors
Ohaus spring scales (just the 2.5 N and 5 N sizes)
Cheap breadboards, digital multimeters, resistors, and connecting wires
Lenses / curved mirrors
Batteries, miniature light bulbs with holders

Demonstration equipment*
Variable DC power supply, up to 20 V*
"Decade box" variable resistor
PASCO fan cart
Happy/sad balls
Vernier force probe*
Vernier force plate
Vernier light sensor*
Laser/fish tank
PASCO projectile launcher
PASCO string wave generator

*Where marked with an asterisk, it's worth getting enough for multiple lab groups if you have the money; otherwise, just get one unit for use in demonstrations.

Things not to get
Stopwatches (phones and watches will perform this function)
air tracks (PASCO tracks work better for 1/4 the price and 1/1000 the noise)

I'm assuming basics like metersticks, rulers, protractors, ringstands, string, computer printer with projector, copy machine, white or chalk board, desks, etc.  

I'm also not including things that can be found around the school, or jury-rigged for cheap: like using PVC pipe for waves or rotation demonstrations/labs; clear rectangular plastic containers filled with water instead of commercial plastic blocks for refraction labs; tennis balls and marbles; etc.

And finally, I'm assuming topic coverage approximately equal to the AP Physics 1 exam, regents exam, or my conceptual physics exam.  Obviously if you're not teaching lenses and mirrors, don't buy them; if you are teaching magnetism in your first year course, you might include other materials (like magnets, perhaps).

I'm sure I've left out some things.  Post a note in the comments.  Perhaps I'll edit based on your suggestion; regardless, readers of this post would benefit from other folks' different perspectives.  


06 December 2015

Waves unit: two experiments with standing waves

I start the waves unit with demonstrations of basic definitions.  I use a wave machine, snakey, and computer simulations to show wavelength, frequency, amplitude, transverse/longitudinal, interference, etc.  I get into standing waves pretty quickly, with conceptual demonstrations on a string vibrator.

We do two experiments:

1. We attach the 60 Hz string vibrator to a string that passes over a pulley, and which supports a hanging mass.  Varying the mass varies the wave speed; we can measure the wavelength with a meterstick.  A plot of speed vs. wavelength gives a slope of 60 Hz.

One very cool side outcome of this experiment is that it gives a visceral understanding of when standing waves can and can't form.  Students will change the wave speed, then see that the nodes and antinodes aren't happening.  They have to adjust the length of the string until the antinodes show up.  Without saying a word, I've shown my class that standing waves only occur when an integer number of half wavelengths fit into the length of the confined region.

This experiment works at any level, from conceptual physics to AP.

2. We create sound waves in an open pipe using an iphone as a variable frequency generator.  We measure the length of the pipe as a function of the frequency.  The slope of a f vs. 1/2L graph will be some multiple of the speed of sound; that multiple is the number of the harmonic.  Because we do this experiment after the one described above, many students recognize why they have to adjust the length of the pipe to get resonance; it's the same principle as when the standing wave was on a string.

It's not easy to get good data for this experiment.  I use two ~40 cm pieces of PVC that fit one inside the other, such that the total length can be adjusted continuously.  Some folks use a tub of water to provide a flexible length; that's good too, just graph f vs. 1/4L rather then 1/2L because you're using a closed pipe.

 The difficulty comes with ensuring that all the data is for the same harmonic.    I've taught my students too well to explore an entire parameter space -- they use all sorts of widely varying frequencies, and thus they jump from harmonic to harmonic, when our analysis has assumed that we control for the harmonic.  The frequency has to change very gradually, by 10 Hz or so.  When they do it right, the data looks lovely.

This experiment as described requires graph linearization, so is for honors/AP students only.  I would not do it at all with a 9th grade conceptual class -- the data collection process is two abstract, it's too difficult for 14 year olds to get good data, and plotting a recipricol requires too much calculation.

This will work for an 11th grade general class, though.  Tell the class ahead of time which range of frequencies to use.  You can arrange for everyone to use, say, the second harmonic, such that the pipe length IS the wavelength.  Then tell them to plot f vs. 1/L directly; the slope will be the speed of sound.  Because the students don't have to do the graph linearization, and because the slope is easily derived from v=λf to be the speed of sound, general-level students can handle this one.

01 December 2015

Mail Time: What is your test format in AP?

From Josh:

I'm a new AP physics teacher and have been struggling with designing a set format for my summative assessments.*  I've read a lot of what others do but I'd like to see if there's anything particular that you do in class.  Some teachers have suggested making the entire test out of 45 points with 15 MC and a FRQ or two.  

* i.e. TESTS

Also, do you scale your tests?  I've read a lot of teachers do but personally I find that skewing the data on the learning objectives and it hides what they learn.  I can see scaling an actual AP exam given in class. The students at my school get a bump in GPA for taking an AP course so to scale it on top of that provides a huge jump and I'm having a hard time justifying that.  

Hey, Josh... you've asked a couple of million dollar questions.  There's no one best answer, obviously. I'll give some detailed thoughts below about what I do.

But first, the disclaimer: while it's important to assign a fair grade to a fair test, that's NOT the fundamental point of testing.  Our overriding goal is for students to get the right feedback in the right context to improve their long-term understanding of physics.  A test is the standard, useful tool for that feedback; grades and GPA are powerful motivators. But we don't want students lawyering for points at the expense of figuring out concepts.  To that end, I think you've got the right idea: come up with a standard approach for your class, so that the "rules of the game" are fixed and known.

So how do I structure AP Physics 1 tests?

I try to test during lab periods, to get the longest chunk of time possible.  Students do better on longer tests (because they have more opportunity to see problems they can handle, because they can knock off an easy-for-them problem quickly and have more time on the difficult problems), so I give as long a test as I can arrange.  When there's not a convenient long period, I've given, say, 40 minutes multiple choice one day, then 40 minutes free response the next to make a full test.

In constructing the test, I try to use exclusively old AP items, even though that means using physics B items as well as released physics 1 items.  That's fine for me, 'cause I figured out that it's best to start my class targeting the old Physics B exam, then introduce more writing and description as the course continues.  I've decided to include "short answer" items designed to take about three minutes to answer, as well as free response and multiple choice.  These short answer items are also straight off of released AP items: either multiple choice with "justify your answer," or a single part of a free response question.  

Whatever you do, I suggest being very consistent with the timing: new AP 1 multiple choice should be 1:45 or so per question, and free response should be 2 minutes per point, with 7 point and 12 point questions.  Students may run out of time on a test early in the year, and that's a fine learning experience.  As the year goes on, if you're consistent with test structure, students will learn the correct pace.  And then they will know exactly how to deal with time on the authentic AP exam.

As for scaling the tests... I wouldn't think in terms of "learning objectives" -- just teach physics.  The tests should reflect how the AP exam tests the material you're covering in class.  If you give authentic AP items -- thus approximately controlling the difficulty of the tests -- then you can make a reasonable guess that the approximate percentages from last year will hold.  Last year, about 70% was a 5, 55% a 4, 40% a 3.  [On the Physics B exam, the scale was five points lower -- that is, 65% was a 5.]  

When I convert the raw percentage on a test to a publishable school scale, I have two considerations:

(1) Corrections contribute half-credit back to the raw percentage.  See this post and search the blog for "corrections."

(2) Ideally, a 5 with corrections converts to an A; a 4 converts to a B or B+; and a 3 converts to a B or B-.  2s become Cs, 1s become Ds or Fs.

In the past I've used a "square root curve" to convert from the corrected test score to a 90-80-70-60 school scale.  Lately, especially as the raw standard for an AP score has increased, I've gone to a scale based on the New York Regents exam -- there, about an 85% converts to an A- equivalent, a 70% converts to a B- equivalent.

Exactly how you convert doesn't matter... the only important part here is that the conversion from raw scores to a "school scale" must be identical throughout the year, and NOT EVER based on performance.  "Curving" a test by, say, making the highest score an A creates a perverse set of incentives for students to tank, or for high-performing students to be ostracized.  (Would a baseball team ever encourage their star player to strike out to help everyone else's batting average look good?)  If the whole class earns 3s and 4s rather than 4s and 5s, then they get Bs not As -- oh well.  If everyone gets 5s and As, that's fine too.  The beauty of AP is that it gives you an external standard to aim for, one that you can blame on the "evil" College Board.  You're not the author of the students' grade, just the publisher.  

So what happens if your test scores are lower than you hoped?  Well, it might happen occasionally.  Just like a football team shouldn't fire the coach and change their team identity because they lose the first two games of a 16-game season, you shouldn't panic or change based on a few poor performances.  At final grade issuing time, you can adjust grades based on in-class work like quizzes and homework.  I always recommend adjusting the entire class -- that is, don't take pity on a borderline student and bump him from a B+ to an A-, but rather drop an extra quiz such that EVERYONE's course grade rises slightly.  This will achieve the same bump for borderline students without any perceived or real favoritism.  And if you find yourself bumping people who don't deserve the bump, then perhaps the bump you're considering is a bad idea for everyone.  :-)  I find that there is a nearly 100% long-term correlation between performance on homework/quizzes/lab work and performance on test -- so over the course of a year, small decisions about grades balance out to give fair overall grades.  

Good luck... if you come to one of my summer institutes, we can talk a lot, lot more about how to structure testing for maximum benefit.  And, the beauty of the institute is that it involves a bunch of other teachers, too, who can share their ideas.