13 December 2014

AP in-class laboratory exercise: Energy (And more on different approaches in 9th and 12th grade)


Above is an example of an in-class lab exercise for AP-level seniors
When I introduce a new topic in 9th grade conceptual physics, I hand out a sheet with a few facts and equations, then I dive directly into guided laboratory exercises.  You can see one set of such exercises, about collisions, here


I don't do any discussion, or example problems, or anything at all with me talking to the class. There's no point -- the freshmen don't have the attention span to listen, and they don't have the abstraction skills to apply what I show them to future problems.  Therefore, the 9th grade in-class laboratory exercises walk the students step-by-step through the solution to a problem, then guide them through the experimental verification of their solution.  No one can tune me out, because I'm not talking. Instead, each student himself has to wrestle with the problem, showing me his answer to each step. When someone does a step incorrectly, I help him, and send him back to his seat to try again.

When I tried the same approach with AP-level seniors this year, it didn't work.  

A freshman who's told his answer is wrong generally looks sheepish, goes back to his desk, does the problem right, and finally looks happy as a mollusk to move on.  

A senior takes the wrongness of his answer personally.  While the freshman just accepts my word that his answer was wrong, the senior tends to make ever-more-ridiculous arguments at me to justify his incorrect reasoning.  Seniors aren't sheepish about wrong answers; no, they're defiant, as if it were my fault that the universe doesn't work the way they want it to.  

On the other hand, I've had good success over the years holding seniors' attention with quantitative demonstration lectures.  So after Thanksgiving break, I went back to my previous approach in teaching the work-energy theorem.  It went well... I raced through a bunch of energy problems at the board over just a few days.

Then, after those few days of me solving problems and showing demonstrations, after a few days of problem solving on each night's homework, I handed out this in-class lab exercise.  

Each student got a different sheet.  The picture above shows problem 1 -- but the link includes seven different sheets, with seven different energy problems.  Three involve carts on a track, three involve objects on vertical springs, and one involves a sliding block.  Each problem requires students to solve in variables, then use semi-quantitative reasoning to produce a prediction.  The experimental verification can be done with motion detectors and/or photogates -- no other equipment required.

The seniors did much, much better this time.  They were no longer hostile -- they felt like I had shown them how to solve the problems, so that if they got something wrong, it was their own dang fault.  

And that was interesting... the freshmen never worried about blaming themselves or me for a wrong answer -- it was just wrong.  The seniors got very snarky if they felt that I hadn't showed them the correct approach at the board, or if I hadn't mentioned all relevant background information out loud in class.  They pouted at their seat if they were turned back more than once to try again.  

But once I had done my duty lecturing at the front of the room, the seniors enthusiastically took to the same kind of open-ended independent lab exercises at which they had thumbed their noses earlier in the year.

I will likely come to some broader conclusions about seniors in the new AP course after I experiment a bit more with my class this year.  I'd love to hear other teachers' experience with these or similar in-class exercises.  

03 December 2014

Using cell phones in class -- Socrative

My school today legitimized the (responsible) use of cell phones on campus.  In honor of that momentous event,* I posted the following to our faculty folder.  I first found out about socrative through AP Physics consultants Dolores Gende and David Jones, so thanks to them... hope you consider using it, and I hope that your cell phone never rings during assembly.

* which produced a level of rejoicing on dorm more appropriate for the destruction of a Death Star

Hey, folks... in the spirit of sharing, consider checking out "socrative" via www.socrative.com.  It's a free service that uses cell phones or any web browser as "clickers" for classroom surveys, questions, and quizzes.  Students respond to the questions on their phones, and the results are aggregated on the teacher's page so that they can be projected on-screen.  For those of us of a certain age, think of it as the ending to America's Funniest Home Videos where they polled the audience about their favorite, and displayed the results -- just using cell phones.

At the site, log in with your gmail account, or create a unique socrative account.  Tell it to ask a "quick question."  The website displays a room number, which students enter on their phones; then the students can participate.  (The students do not need an account.)  This sets up for use the first time in about two minutes.

I don't always use clickers.  But when I do, I use socrative.  (At least, I do now that cell phones are ubiquitous.)

GCJ

01 December 2014

Teaching semi-quantitative reasoning: first, ask students to derive a useful equation.

Two identical arrows, one with speed v and one with speed 2v, are fired into a bale of hay.  Assume that the hay exerts the same friction force on each arrow.  Use the work-energy theorem to determine how many times farther into the hay the faster arrow penetrates.

Typical students know how to apply the work-energy theorem if the problem is stated in numbers.  In fact, if you told these students to answer this question by calculating the distances penetrated by a 10 m/s arrow and then by a 20 m/s arrow, they'd get the answer right.

But if those students try to solve in variables only, without making a couple of calculations with made-up numbers, they get lost.  They don't know where to put the factor of 2... they solve for v rather than for the distance penetrated... they get lost doing random algebra.  (Don't believe me?  Try assigning this problem.)  Nevertheless, I need to teach even my not-so-mathematically-fluent students how to answer this type of question with algebra rather than numbers.  

The trick, I think, is to rephrase the question.  Consider this version:

Two identical arrows, one with twice the speed of the other, are fired into a bale of hay.  Assume that the hay exerts the same friction force on each arrow.

(a)       Use the work-energy theorem to determine an expression for the distance into the hay that an arrow of speed v will penetrate.

(b)       How many times farther into the hay will the faster arrow penetrate?  Justify your answer.

When I explicitly require an algebraic solution for the relevant variable -- the distance penetrated -- in terms of the variable v rather than 2v, the question becomes straightforward.  Students see that the speed v appears in the numerator, and squared; so, doubling v quadruples the penetration distance.

The difficult part of the problem was figuring out to solve for distance in terms of v.  So I've told them to do that first.  As the year goes on, I will gradually take off the training wheels, and ask the question straight-up, like at the top of this post.  However, I want to start establishing good habits of answering problems involving semi-quantitative reasoning, so I'll guide students to deriving a useful equation first.  

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"
"Blacklisted"

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."