24 November 2014

Are we in the happiness business?

I spent a decade fine-tuning my elective general physics course to present about one-third of the material on the AP Physics B exam, but to the same level as that exam.  Students consistently did fantastic work, earning the equivalent of high 5s on the authentic AP-style tests I gave.

Then one year the population for the general physics course changed.  We began enforcing the requirement that all students take physics.  Those who had entered as 10th or 11th graders -- that is, those who didn't take 9th grade conceptual physics -- took this general physics course as a graduation requirement, not as an elective.

During that school year, I taught the same way, and I noticed no difference in performance.  As always, everyone who put forth a credible effort earned a B- or better; better than 1/3 of the class got As, with an overall average in the B+ range.  I was quite pleased with the year's work.

On the year-end course evaluation, though, I discovered significant dissatisfaction with the course.  "You're way too intense."  "You yell too much."  "Relax and back off."  I certainly was insistent and demanding in that class, as I had been for a full ten years teaching that course.  I had previously gotten only the very occasional complaint about my approach, coupled with significant thank-yous for bringing students through a difficult subject. In this particular year, though, a message was delivered unto me -- Back off.

And so I did.  I changed my approach to general physics for this new population.  I lowered the course expectations, so that they matched the New York Regents exam rather than part of the AP exam.  I made a conscious effort to use a calmer demeanor... instead of "NO!  BOUX!  ACCELERATION IS CERTAINLY *NOT* ALWAYS IN THE DIRECTION OF AN OBJECT'S MOTION!" it was, "So, Mr. Jones, could you please recall and repeat the facts we know about the direction of an object's acceleration?"  I truly did "back off."  What were the results?

* Happier students.  Year-end evaluations were quite positive, with no hints of the complains about me and my intensity.

* Poorer grades.  Only 20% or so As, and a class average in the low B range.

A large segment of the class continued making fundamental errors long into the year.  Many were content getting Cs.  But the class and I got along famously, and I've done well with the general-level students on this model for years now.

One day I recounted this story to a veteran teacher whom I greatly respect.  He began to redden a bit as I described the changes I made.  He finally exploded:  "Greg, we're not in the happiness business," he said.  "We're here to teach students the way we think best, not the way they think best -- that's what we're paid for."  

While I see this veteran's point, and agree with it wholeheartedly, I think part of teaching "the way I think best" is to respond and adjust to reasonable feedback.  Just as different levels of baseball call for different strike zones,* different audiences of student need different things from their physics courses.  I'll push my AP students as hard as I can.  They signed up for the varsity course, and they have the option to leave it it becomes more than they can handle.  But the general folks... they don't have a choice about taking physics.  Now that we're really requiring all of these folks to take physics, I'd rather they take away an enjoyable experience in exchange for a bit less depth of coverage.  I'd rather they be happy with a C than bitter with a B+.  And for those who want the greater challenge, they know how to sign up for AP next year.  They chose the general course, and for now, that's what they're going to get.

* And if you think the zone should be the same for major leaguers as for 8th graders, I challenge you to sit through an 8th grade game in which batter after batter waits for the inevitable walk.  If the pitch is hittable, I'm calling the strike.  I've never gotten pushback with this approach at the 8th grade or JV level -- and that is sort of the point.

POSTSCRIPT:  Interestingly, I am once again teaching the honors course this year, but I have maintained, for the most part, my lower-key, backed off demeanor.  And I'm not satisfied with my students' performance.

I have a gaggle of honors-level alumni who have given the Intense Greg positive feedback, who have mentioned how well they've been served by my course.  So why would I change my approach?  Nearly universally, graduates laugh at me, saying "Oh, I knew better than to confuse velocity and acceleration, I didn't want to get BOUXed!"  They knew I cared about them, and that I would work my arse off to teach them college-level physics the best way I knew how, they knew that a BOUX was never personal... but they also knew that they'd better not confuse acceleration and velocity.  

The toughest skill in physics teaching is adjusting your approach to the level of student in front of you, especially when different levels show up in your classroom back-to-back.  Even now that I have a clear game plan for each level, I still have difficulty pitching my tone and material just right.

19 November 2014

Should I buy my students commercial AP Physics 1 or 2 review software? (NO.)

I'm regularly inundated with spam*  offering to sell me question banks for AP Physics.  And I'm regularly asked by physics teachers, "Should I buy these?  My students want as much AP Physics review as possible."  The answer is NO -- Don't waste your money.

* the electronic and paper version, but not the canned meat version

But why is it a waste to buy review materials?  I can go on and on, as I'm sure those of you who know me could attest.  Below are the major arguments.

Firstly, and most importantly:  Why the obsession with extracurricular "exam review"?  The AP Physics exam tests physics knowledge; presumably your class is teaching about physics all year long.  The process of reviewing for in-class tests and exams is utterly equivalent to reviewing for the AP exam.  I'm always amazed at how students beg for, and are willing to pay good money for, "SAT review" -- yet talk to those same students' English teachers, and find out how they haven't studied for a vocabulary quiz all year, and they didn't pay any kind of attention to the grammar and usage review that was intended to prepare them for the sentence completion section.  I don't recommend feeding the exam review obsession, at least not until I can work out how to profit mightily from it.  Just use every trick in your book to make your students take every problem set you assign seriously, and you'll be surprised how the need for "review" abates.  Maybe if we made the students pay $10 per graded assignment, they'd realize that the best AP Physics exam review is their AP Physics class...

Secondly, why pay for what is widely available for free?  Good physics questions, like pictures of naked people and cats, can be found online without difficulty.*  While quality can vary widely, you can find enough AP-style practice questions to satisfy even the most compulsive student.  

* Unless the Puritans at  your school block all the hardcore physics sites.  

Finally, let's talk about "quality."  Writing good physics questions is HARD.  Writing good physics questions that are in the style of the new AP Physics 1 and 2 exams is even harder.  Some people I know to be outstanding physics teachers and physicists nevertheless have trouble creating clear questions at an appropriate difficulty level.  And some of the worst sets of questions I've seen have been in commercially available AP prep books.  Just because you're paying doesn't mean that you're getting useful questions, let alone better questions that are available for free.

So  where do I get AP review questions for free, then?  Start with the College Board's AP Central site.  They've published half of an exam in the "Course Description," plus a smaller set of sample questions, plus a full practice test for those who have an AP Physics Course Audit account.  I'm told that they will, eventually, publish a set of questions from last year's AP Physics B exam that would be appropriate for the new courses.

Next, go to "Pretty Good Physics -- secure."  If you haven't signed up for an account with that site, do so right away.  You can then access the Big Amazing Resource.  Also, numerous teachers have posted their own activities and tests from which you can pull review exercises.  

Use the 5 Steps to a 5: AP Physics 1 book, which includes a full practice test; next year's edition will include a second practice test.  If you have a commercial textbook, look at some of their cumulative end-of-chapter exercises.  (Nick Giordano is on an AP Physics development committee, and Eugenia Etkina's work has been used extensively in College Board publications.  If you have a textbook by one of these authors, use questions from it as much as possible.)

For those who have been to my professional development, look through the CD I gave you.  Don't look exclusively at the AP Physics tests; some questions from Conceptual Physics or Regents Physics are perfectly good for AP Physics 1 and 2.  Some questions I used as problem sets or quizzes are good as test questions, or certainly as test review questions.  I'll continue to update that CD.  Come to one of my summer institutes in June, or to my free "Open Lab" in July, and everyone in attendance can share what they've created.

Or just pick a physics teacher you know and trust, and combine forces by sharing .  Point is, in the era of crowdsourcing and the internet, there's no need whatsoever for you to spend any money just for a question bank.  Don't buy a cow; milk is free.

13 November 2014

Why I make students graph data as they collect it

When I run a laboratory exercise, students are required to "graph as they go" -- that is, data are not written in a table for processing later, but are plotted directly and immediately on a graph.  The inevitable question, from students and fellow teachers, is why?  I mean, physics data don't go stale.  The graph is gonna look the same if it's plotted tomorrow.  What is the advantage to insisting on a live graph during the laboratory exercise? 

The most important advantage has to do with how students understand experiments. A data table just looks like a bunch of random numbers, both to students and to experienced physicists.  It's when the data is put on a graph that patterns can be seen and understood.  By graphing as they go, students develop for themselves an instinct about how much data is "enough," whether the full parameter space is covered, what further data is useful, etc.  

Science teachers are always talking about avoiding a cookbook mentality in the laboratory, in which students mindlessly follow directions trying desperately to get the "right" answer.  Well, here's one way to get students to connect intimately with their data -- as they see the graph develop, they think about and process how the data connects with the physical experiment.  They wonder whether the graph will end up straight or curved, they construct hypotheses in their heads which are borne out or not by the graph.  

The practical advantage of "graph as you go" is that students don't write down a bunch of numbers and assume they're done.  I get pushback if students have sat at their desks to construct a graph, then are told "ooh, let's get some further data in this region of the graph."  Aww, man, I thought we were finished.  I even put the track away.  Do we really have to get everything out again and do more?  Can we just do ONE more point, or do we have to do a lot?  Grrrr...

If all data is going on the graph right away, I can walk around the room and suggest right away how their data collection process is going.  Everyone expects and welcomes my input as part and parcel of the lab course.  Lab becomes about producing beautiful graphs, not about getting done and away from the annoying physics teacher.

03 November 2014

Direct Measurement Video assignment: Einstein Rides the Gravitron

I've discussed "Direct Measurement Videos" before, in the linked post.  These videos are wonderful, because instead of a presenting a sterile "imagine this situation" type of textbook problem, the situation doesn't have to be imagined -- it's right there on the video.

But what exactly do I do with these videos?  I've been asked that question a number of times.  Here is my AP Physics 1 class's assignment for Monday, verbatim:

In the video linked above, an Einstein doll on a rotating platform appears pinned to a wall, as shown in the screenshot.  As the platform slows its rotation rate, Einstein remains pinned in place until he eventually falls. 

You are to determine the maximum coefficient of static friction between Einstein and the wall.  Justify your answer thoroughly – this means you have to explain not only how you solved the problem, but how you obtained or estimated the necessary data from the video in order to solve the problem.  Start with a free body diagram of Einstein, obviously…

This worked out better than I could ever have imagined.  

See, I'm dealing with a number of students who are not appropriately connecting mathematics to physics.  They want to explain results without reference to equations; they want to do calculations (both in variables and in numbers) without any verbal explanations.  When they're asked to explain a calculation, they tend to explain the algebra ("I subtraced T from both sides to get T = Fnet +mg") rather than explaining where the equations come from, and where the values they need could come from.  These deficiencies are hardly unusual in an AP class; but I am struggling this year to bring my class into a real understanding of quantitative-qualitative translation.

This video assignment seemed to bring out my students' best.  Most of the class made the free body diagram, set the friction force equal to Einstein's weight, and set the normal force equal to mv2/r. They knew from practice that the speed v can be written as (2πr/T).  They used Ff/Fn to solve for the coefficient of friction.  They made a table of values to plug in, and got a reasonable coefficient.  Great.

But then something beautiful happened... virtually all my students, even the ones who had been struggling, wrote me crystal clear explanations to follow up on their mathematics.  They told me exactly what I told you in the previous paragraph -- sometimes in the very words I used.  They explained how many frames were in a revolution, and how they calculated the time for one revolution just before Einstein dropped.  (Or, how many frames were in a HALF revolution before the drop.)  They either explained that they estimated Einstein's mass, or that they noticed that his mass canceled out of the equations they derived.  They explained how the radius of curvature was determined from the video.  

In other words, they completed the most thorough quantitative-qualitative translation that they've done all year.  Somehow, my students have been unwilling or unable to describe the process behind a calculation from a textbook-style problem.  The video brought out the best in them.  Why?  I don't know.  But I like it.

31 October 2014

Are Kepler's Laws part of AP Physics 1? No and Yes.

Debby Heyes, who attended my open lab this summer,has a quick AP physics 1 question:

Are Kepler's Laws included in the course?  

Fast answer: no.  A search in the curriculum guide for "Kepler" gives no results.

Deeper answer: Yes AND No.  Kepler's laws by name are not part of the curriculum, but some of the behavior of planetary orbits described by Kepler's laws is part of AP Physics 1.

The "equal areas / equal times" law can be stated as a consequence of angular momentum conservation.  An orbiting planet experiences no torque relative to the central star (because the gravitational force always points back to the center of rotation, meaning the distance term in "torque = force * distance" is zero).  Therefore, the planet's angular momentum about the central star is conserved.  Treating the planet as a point object, its angular momentum is given by mvr, where r is the distance to the central star.  When r goes down -- i.e. when the planet is closer to the sun -- v goes up, meaning the planet moves faster in its orbit.  That's essentially Kepler's law.

The "period proportional to the 3/2 power of the radius" law is merely a consequence of Newton's second law and circular motion, at least if we consider circular orbits only (which we emphatically do in AP Physics 1).  Set the gravitataional force equal to ma, where the acceleration in circular motion is v2/r.  Then the speed of an object in circular motion is the circumference divided by the orbital period.  Solving for period gives the Kepler's law relationship -- and we should be able to do that and understand it in AP Physics 1.

The law that says "all orbits are ellipses with the sun at one focus" is not in any way on the AP Physics 1 exam that I can tell.

An exercise I'm running...  I'm asking students what happens to the speed necessary to maintain a circular orbit if (a) the central star's mass is doubled, (b) the planet's mass is doubled, or (c) the planet's distance from the central star is doubled.  I hand everyone a different half-page of paper with one of these three questions asked; for more variety, some of the papers say "tripled" or "quadrupled" rather than doubled.  Students are guided to solve in variables for the speed, then to use semi-quantitative reasoning to see what happens to the speed.

Then, I pull up "my solar system", a phet simulation.  Using the "sun and planet" preset, students are asked to change the simulation as described on their paper to see if they get a circular orbit.  (Those who told me that changing the planet's mass changes its orbital speed as well become confused a bit when the simulation doesn't verify their answer.)

28 October 2014

When do you give your first test?

Barry Panas, the John Oliver of AP Physics consultants, writes in with a question:

How long does it take you to reach your first full physics test in your "first" course of physics with any group of students? I'm specifically thinking of the course that introduces student to kinematics (etc.). How long do you spend in that very first unit to the point of a test?

Complex answer.  Start with this year in AP Physics 1: I've been giving a 10 question multiple choice test once a week, then every third week I instead give a 40 minute free response test.   So the very first test happened after three weeks.  That was enough to get through graphical and algebraic kinematics, plus Newton's second law in one dimension. 

Since I only have 40 minutes to test, I decided to go with two AP-style 7 point problems plus three "short answer" questions.  All my tests this year will be in this format.  My trimester exams -- one to be given in November, one in March -- will be 30 minutes for 17 multiple choice questions, followed by a full-on 90 minute, 5 question AP Physics 1 style free response exam (three 7-pointers, and two 12-pointers).

Historically in my upper-level intro classes:  I've given tests every four weeks.  These tests have been 80 minutes or so long, including free response, short answer, and multiple choice.  In the regular-level sections, this has gotten me through virtually all of kinematics.

The advantage of shorter but more frequent tests is obvious -- they get more frequent feedback, and tests aren't as big a deal.  However, the advantage of longer tests is that students usually do better the longer the test.  More questions mean more likelihood to find something easy to knock out, leaving time to play with a tougher question.  

Either way, I've always stuck to a few guiding principles:  

All tests are of identical format.  Just as students are taught not to read the directions on an SAT or AP test (if you don't know the directions ahead of time, you're sunk), they shouldn't be asked to read directions to any types of questions they haven't seen before.  I publish the instruction sheet and the test structure before test day.

The time per problem is identical on all tests.  In AP, I use the AP time ratio of about two minutes per point free response, and just about two minutes per multiple choice item.  In lower level classes, I make sure to keep the same time-per-item-type ratio on all tests throughout the year.

All my tests are cumulative, meaning there's no need to schedule unit tests:  wherever we are in the course, the test covers everything to that point.  The test DATES are set from year's beginning.

21 October 2014

Friction coefficient on an object of unknown mass -- lab, homework simulation, or test question

I've been a fan of Phet's "Force and Motion: Basics" simulation for several years now.  It includes several tabs: the "tug of war" which inspired a daily quiz that I'll likely post soon; a "motion" tab that allows you to apply forces and see the speed change, but in animation and in a speedometer; and an "acceleration lab" tab that allows for all sorts of investigations connecting net force, acceleration, mass, and speed.  I'd suggest downloading the java version and playing with it for a while.  In fact, I give extra credit to my students merely for noodling around with this simulation for at least ten minutes one night.

A few weeks ago, I discovered the "friction" tab.  You can see a screen shot above.  By clicking on the "applied force" slider, you cause the stick figure to push on the box in either direction with any amount of force.  The checkboxes in the yellow area allow you to display the net force, the individual forces, the masses of the objects, and a speedometer.  Students can see that pushing the box doesn't cause the box to move immediately in the direction of the push; rather, the box slows down or speeds up based on the direction of the net force.  That analog speedometer does more to bust the misconception of net force being in the direction of velocity than anything I can do or say in class.  

But wait -- there's more.  I clicked the checkbox that says "masses."  As you might expect, the mass of each object is displayed.  You can make the girl sit on the box, and she'll even hold the 200 kg refrigerator without complaint if you make her.  Great.  Students can see how the speed changes more or less rapidly when different masses and forces are involved.

Take a careful look at that wrapped present in the bottom right corner.  Its mass is displayed as a question mark.  Ooh... that seems like an invitation to an open-ended investigation.

My question: determine the coefficient of friction between that present and the surface (with the default setting for the friction slider).  That's not a simple plug-and-chug problem because the mass of the present isn't known -- okay, the simulation displays the value of the friction force, but it doesn't tell you the value of speed or acceleration.  So neither "Fnet = ma" nor "Ff = μFn" gives enough information to solve with a single trial and single equation.

Students are asked to write up their solution in a single page, as if this question were a job audition for their engineering firm.  I have a different teacher or an advanced student rank all the submissions, placing each in one of four categories:

"Hired" (one submission only)
"Recommended to other companies"
"No recommendation"

Hints about using this idea:  For one thing, be sure to open the simulation in java.  I unfortunately had one class open using html5, which is simpler to use and which works on ipads.  But on that version of the simulation, the mass of the present is displayed for all to see.  Oops.

Secondly, there's no reason to stick with this as a pure simulation.  Use wooden blocks, or the PASCO friction apparatus (which is just an open plastic box with a rough bottom surface and a place to attach a string).  Don't allow anyone to measure the mass of the wooden block, but ask them to determine that and the coefficient of kinetic friction using force probes or spring scales only.  The only reason I did this with the simulation rather than as a live, hands-on laboratory exercise is that we had done enough already with that friction apparatus this year.

And finally, this would make a great AP Physics 1 essay-style short answer question:  "In a clear, coherent, paragraph-length response, describe how you would determine the coefficient of kinetic friction between the block and the surface using a spring scale and other known masses."

09 October 2014

Fan cart on an incline, and the beginnings of an AP Physics 1-style problem

I started my presentation on inclined planes the way I've always started it -- with a quantitative demonstration.  I placed my venerable rechargeable 310-g PASCO fan cart, whose fan produces a force of 0.26 N, on a PASCO track.  To what angle should I incline the track so that the cart remains on the track in equilibrium?

I demonstrate the solution using the standard three-step Newton's Law problem solving procedure -- draw a free body, break the weight into components, and write Fnet = ma in both directions.  In this case, because acceleration is zero, the weight component down the incline mg sin θ equals the 0.26 N force of the fan.  Solving for θ gives an angle of about 5 degrees.  That's easy (and impressive) to verify with an angle indicator.

The next problem I pose posits the same cart released from the top of a 10 degree incline; what will be the cart's acceleration?  This time, instead of solving myself in front of the class, I have each student work through the problem himself.  When someone gets an answer, I hand him one of the fan carts, a motion detector, and a labquest -- it's his job to verify the answer.  Usually we predict an acceleration of 0.87 m/s/s, and we measure something in the neighborhood of 0.77 to 0.86 m/s/s.  I'm happy with that -- at most 11% off from the prediction.

However:  Yesterday a group kept getting between 0.56 and 0.60 m/s/s for the acceleration of the cart.  Now, rather than 11% off, this group was 31%-35% off.  That didn't seem right.  What was going on?

The first words everyone spewed were "because of friction."  Stop it.  It's rare that the true cause of a laboratory discrepancy can be attributed solely to neglecting or miscalculating friction.  And in that rare case that friction is indeed the issue, "because of friction" is never an appropriate answer.  Explain how the force of friction, or the work done by friction, would change the relevant equation; and then convince me that the measurement is different from the prediction in a way that would be accounted for by that force of or work done by friction.

This group measured an acceleration that was smaller than predicted; but the other groups were pretty much right on.  That implied that the carts might have been different in some way.

These PASCO fan carts operate on a rechargeable battery.  "Could our cart's battery be dying?" the group asked.  Let's see... the weight component down the incline of mgsinθ = 0.54 N is independent of the fan.  It's the force of the fan up the incline that would change depending on the battery, and that  fan force is subtracted from 0.54 N to calculate the net force.  A smaller fan force due to a dying battery would mean that the net force down the plane would be greater, not smaller, giving more than the predicted acceleration.

So the cart's battery wasn't dying.  We realized that two of my three carts were newly purchased over the summer.  I used a force probe to measure the force of the fan on the new carts -- I got 0.32 N, more than the 0.26 N from the old fan.  Aha!

What a wonderful AP Physics 1 problem you've discovered.  You could describe the situation... then ask some of the questions below:

* How would you experimentally measure the cart's acceleration after it's released from the top of the 10 degree incline?
* Predict the cart's acceleration after it's released from the top of the 10 degree incline.
* How would the cart's acceleration change if rather than being released from rest it were instead given a brief shove to cause it to move up the 10 degree incline?
* The cart's acceleration is measured to be substantially less than the prediction.  Does that mean that the force of the fan was greater or less than the assumed 0.26 N?
* How could you experimentally measure the force provided by the fan?

I know when I write any sort of physics problem -- whether for the College Board, for my book, or for my class -- I often begin with an actual situation I've encountered in my laboratory.  Do you have an experiment that lends itself to a good AP Physics 1-style verbal response sort of question?  Post it in the comments, or email me; maybe I'll use that as the basis for a "Mail Time!" post.


08 October 2014

5 Steps to a 5: AP Physics 1 Teacher's Manual now available

As part of the 5 Steps to a 5: AP Physics 1 book, I wrote a Teacher's Manual.  It's finally available... you can go to this page here to get it.  (You need to give McGraw-Hill your name and school address... uncheck the box about upcoming promotions, and I don't believe they will spam you about anything.)

I've listed many of my quantitative demonstrations in this manual, along with some general pieces of teaching advice which reprise things I've posted on this blog.  I've approached the manual under the conceit of "5 steps for you to help your students get 5s."  Hope you like it... Please send comments.


26 September 2014

Mail time: velocity-time graph that crosses the horizontal axis

A correspondent asks:

Hi Greg. I was doing some questions and I'm unsure about a certain response. I'm looking at a velocity vs time graph where the graph is linear and cuts right through the x-axis going in the neg. direction. At EXACTLY the point of intersection do we state that the acceleration is negative because the slope is negative or zero because at that instant the object has zero velocity?

My instincts want me to say negative, but last year I went with zero, sooooooo I'm not really sure.

I've made a graph of what I think you're looking at... see the picture.  You want to know, "What is the direction of the acceleration at point A?"  This is a classic question, with a corresponding classic point of student confusion.  This graph could represent, among other things, a ball thrown upward in free-fall -- it moves upward, slows, stops briefly, and speeds back up toward earth.  

Two ways I'd phrase my answer:

(1) Just because velocity is zero does not mean that acceleration is zero.  Otherwise, gravity would have to turn off just because a ball reaches the peak of its flight.

(2) Acceleration is the slope of a v-t graph.  The horizontal axis isn't special -- the slope of that line doesn't change anywhere, so the acceleration is negative everywhere, both for positive and negative and zero velocities.