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26 December 2014

Teaching seniors after Christmas: hints and ideas

Our faculty is currently involved in a brainstorming exercise in which, without practical constraints, we suggest how the school could or should change programmatically to better address our students' needs.  Certainly I'm hearing some excellent ideas (though some of them are only excellent in the absence of friction and air resistance, so to speak).

A large number of these ideas suggest sweeping changes to the structure of the senior year.  I've many times heard our faculty -- and other faculties -- hold forth on the moral deficiencies of late-season seniors.  Amongst all the kvetching and suggestions for change, I wonder... are we trying to solve a problem that doesn't exist?  Or, at least, are we trying to solve a problem that could better be prevented than solved?

A number of teachers have quite positive in-class experiences with late-season seniors, without internships, final projects, field trips, or any other major gimmickry.*  If a class is truly important and useful, it should sustain students' interest regardless of whether those students need a good grade to ensure college admission.  To a very large extent it's the teacher's job to structure the class so as to keep students -- seniors included -- invested.

* MINOR gimmickry is abundant among the best senior teachers.

So how do successful teachers of seniors sustain interest, even though all seniors (to one extent or the other) have one foot out the door in the spring?  Here are some tips.  Some are from my own experience; many are from observation of and discussions with the best teachers of seniors that I know.  Please submit your thoughts in the comments.

* Deal with seniors are they are, not as we wish they were.  Seniors always prioritize things other than your class; as the spring advances, my class drops down the list.  I may not agree with their priorities, but it would be silly not to acknowledge them.  I set in my mind from the beginning that I am not going to take personal offense at seniors' attitudes, nor am I ever going to lecture them about their senior slide.  I vow to treat students with respect, even when their decisions don't command respect.

Front-load your course.  We know the senior slide is going to happen; conversely, we know that seniors are heavily invested early in the year, when their grades "matter."  So push, push, push the pace.  I cover at least half of my material in the first trimester.

Don't let one or two obnoxious seniors poison your mindset.  Even the best teachers of seniors don't have a 100% success rate.  When a student is being irrationally obstinate, do your best to patiently ignore him.  Don't let him rile you up.  If he's bringing the whole class down, dispassionately remove him from the situation (i.e. boot his arse out of class without drama); but whatever you do, don't engage or argue.  It's not going to help.  Think about how the rest of the class feels -- they're probably embarrassed about their obnoxious peer, but he's still a peer.  They don't want him disrupting class, but neither do they want the teacher to become angry or aggressive.  Be the welcome bringer of peace, not the fearsome champion of war.

* Develop positive relationships with the class early on.  While you are not expected to be best buddies with your students, they need to know that you care about them.  Expect the highest level of effort and performance, yes.  But in everything you do, from your words to your body language to your actions, show your students that you're doing it for them.  When someone screws up BEFORE the senior slide, treat him firmly, fairly, and compassionately.  Know that everyone is watching you, all the time.  If you react hostilely to one student, even if he deserves your hostile reaction, the rest of your class feels like you've reacted hostilely to them, too.  Don't underestimate the teenager's desire for vengeance against those who, in their view, take their authority too seriously.  

Conversely, don't underestimate teenagers' positive ethical underpinning.  If you are seen to be fair, patient, and on their side, the silent majority of your class will support you.  When that one bastard starts being a jerk to you in March, you want someone to take him aside and tell him "not cool, man, back off."  That does, in fact, happen... if you do the front-end work to earn such quiet support.

* Make even more effort to do something different every few days.  There's no cure-all for times when students would rather be cavorting in beautiful spring weather than sitting in your class.  Certainly the physics teaching literature, this blog, and shop talk will yield numerous suggestions of productive but different styles of class: whiteboarding, socrative, the physics walk, lab challenges, test corrections, and more are excellent ways to add variety.  Whatever the specific activities, it's that variety that's critical for seniors.  Freshman need routine; spring seniors need to break out of their routine.  

* Taper.  You might reasonably expect 45 minutes of work per night early in the year; by April, that expectation should be down to about 15 minutes.  It's a bad idea to stop giving homework altogether, or even to reduce the frequency with which assignments are due; however, each assignment can become smaller in scope.  Swimming and track coaches are familiar with this idea of "tapering" toward a championship meet.  The physics brain muscles are already strong from the hard work students have done early in the year.  In the spring, daily work is more about maintaining muscle memory, about remembering and cementing things students already know, rather than about learning new things and developing new ideas.  

* Be creative in holding students accountable.  Any assignment is useless if it's not taken seriously; any assignment, no matter how small, is useful if done with care.  Along with tapering comes the responsibility to ensure that students do the required work, and do it well.  Second semester seniors generally don't give a rip about their grades, especially if grades are used as negative incentive.  Use as many different positive incentives as possible.  I give exemptions from future work for particularly strong efforts.  I might announce an exciting activity like a physics walk, with the reminder that a complete assignment is required to go along.  Even small things like in-class music when everyone turns in the homework can help.

Whatever the incentives, though, be sure they are backed up with the inviolable requirement that all assigned work must be completed eventually and correctly.  Use every trick in your book to enforce this requirement, such that students recognize that it's easier and more fun to get the work done right and on time than to slack off.

* At some point, acknowledge the year is over.  Where that point begins is your judgement call.  But it's important, I think, to end the year on a high note.  I've had the class solder AM radio or robot kits; had them inventory and organize the lab; done the bridge building or egg drop contests... anything that requires no out-of-class effort.  

In late May, you're not teaching anything further to this year's seniors.  Instead, you're laying groundwork for the future.  Think about what you want this year's class to say to next year's.  Students talk to each other, and it's usually straight talk.  You want a reputation right in between "pushover" and "arsehole."  After a couple of years, that reputation will by itself minimize hostile relationships with seniors, as they will come to your course from the start with the expectation that the spring will be serious yet fun.  

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  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.)


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 than 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 satellite'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.

24 September 2014

Can an Electric Field Be Negative?

A correspondent writes in:

I've been telling my class that the electric field cannot be negative.  1. Its direction is set and then 2. the value is set.  And since the value corresponds to the predetermined direction, it is always positive.

One of my international students from China used the vector argument.  Since electric field is a vector quantity, can't we 1. choose our direction first - independent of the field and then 2. determine the direction of the electric field and how it meshes with our predetermined direction?  Was I terribly wrong to say that E-field cannot be negative?

My response:  I say an electric field can never "be negative."  Electric field is a vector -- it has magnitude and direction.

Sometimes in a 1-dimensional problem, by convention physicists choose one direction to be positive, one negative.  For example, if south is the negative direction, then a car slowing down moving north might have a "positive" velocity and "negative" acceleration.  And the kinematics equations require algebraic use of the negative signs.  Nevertheless, the magnitude of the acceleration vector would still be 4 m/s/s*, and the direction would be south; the magnitude of the acceleration can never be - 4 m/s/s.

*  not even positive 4 m/s/s, just plain ol' 4 m/s/s

It's legitimate, though crude, to apply the same reasoning to the electric field.  Define up as positive.  Then a 200 N/C electric field that points down could be called "-200 N/C."


(You can see some of my reasoning in this post: Never trust a student with a negative sign.)

Students get into trouble if they try to use F=qE, and plug in negative signs for q and E to get negative forces.  Negative forces?  What are they?  Forces also have magnitude and direction.  You can't have a -300 N force, just a 300 N force in the downward direction.*

* Again, pedants can argue that such notation can be made self-consistent.  I'm teaching introductory physics, with students who still struggle with the idea that "-300 N" doesn't mean "bad 300".  It's far more important to use notation that addresses the physical meaning of a quantity than notation that maybe, perhaps, with expertise, can be made mathematically reasonable.

So don't ever use negative signs with electric fields -- they're too easy to confuse with negative charges, which mean something completely different, and negative potentials, which are again different.  Have students state a magnitude and direction of an electric field without negative or positive signs:  "200 N/C, to the left."

15 September 2014

Giancoli's stoplight problem -- scale it down and set it up in the lab

A classic problem -- I think I first found it in the Giancoli text, but some variant is in all comprehensive problem sources -- asks for the tension in two angled ropes supporting a hanging object, given the mass of the object and the angles of the ropes.  The version I assign includes a 33 kg stoplight, a 37 degree angle, and a 53 degree angle.

Firstly, adapt the problem for AP Physics 1 rather than the traditional AP B course.  To do that, I begin the question by asking "Is it possible to calculate the tension in the left-hand rope?   If so, explain with words and without numbers how the tension could be calculated.  You need not actually do the calculations, but provide complete instructions so that another student could use them to calculate the tension."  It's okay if students choose to do the calculation first, then tell me how it's possible.  Of course, the obvious approach is to explain that we can set up two equilibrium equations (one vertical, one horizontal) with two unknowns, so the problem is solvable.

Next, I ask for the solution for the tension in the left rope.  They calculate something like 220 N.  

In class, I remind everyone that any numerical solution to a physics problem is not really an "answer," but more accurately a "prediction" of the result of an experiment.  I should always be able to verify a prediction by setting up the suggested experiment.  Thing is, I don't have a 33 kg object to string up from ropes.  Why not?  Because, 33 kg is like 70 pounds.  The mass sets in my classroom don't go above about 1 kg.

And there lies the way to verify the prediction -- scale everything down by a factor of 100.  I do have 330 g to put on a hanger.  Then, I should get a tension in the left rope not of 220 N, but of 2.2 N.  

In the above picture, I've arranged the lengths of the ropes such that the angles are in the right neighborhood.  Sure enough, the left rope read a tension of 2.1 N, within the 0.2 to 0.3 N tolerance I expect on a typical classroom spring scale.

Not only does this experiment reinforce the physical meaning of the problem's solution, not only do we see whether the answer is "right" or not, this experiment can help emphasize why the answer "221.43 N" is utterly ridiculous.  The scale can't read better than about 2.2 N or 2.1 N -- it can't read 2.145 N.  Only two digits mean anything (not two decimal places, two DIGITS).  Seeing a "scale reading" rather than an "answer" is the first step toward internalizing that physics is about experiments, not numbers.

08 September 2014

Where do I get AP Physics 1 multiple choice test questions? The Big Amazing Resource. Update January 2019.

Testing isn't as simple as it used to be.  Over AP Physics B's 40+ years of existence, enough authentic multiple choice questions had been released to satisfy even the most prolific tester.  However, now that we've moved into the AP Physics 1 era, a lot of those questions are useless; even those that are in the spirit of the new exam need to be rephrased, especially to bring them down to four rather than five choices, and to minimize but not eliminate the questions that require calculation.

Of course, you can go to the College Board's official AP Physics 1 page via AP Central.  There you'll find some sample questions in a file conveniently marked "sample questions."  You can get more in the official "course and exam description.  Finally, if you've ever completed a course audit for AP Physics B or AP Physics 1, you'll be able to download the released practice exam.  Go to your account, go to "add a course," add AP Physics 1, and download the exam.

The 5 Steps to a 5: AP Physics 1 book includes a full practice exam, as well as some good questions at the end of the content chapters.  Or, try looking at the supplements to the Serway textbook's 10th edition; they've hired some seriously connected people to write sample questions for them.  And those of you who have attended my summer institutes or this past summer's open lab have a CD of materials.  Look in the "honors physics" folder, and then look at the quizzes.  Many of those daily quiz questions can be used either verbatim or with minimal revision.  

But the Big Amazing Resource for AP Physics 1 and 2 is the newest version of Matt Sckalor's AP Physics workbooks. About half a decade ago, Matt compiled every released AP Physics B multiple choice question into a single workbook, organized by topic.  Over the summer, a number of AP Physics consultants -- that is, people with intimate knowledge of the new courses -- rewrote these questions so that they meet the spirit of the new Physics 1 and 2 exams.  Now, this new and improved workbook is still not vetted by the committee.  It ain't perfect.  But it is a treasure trove for those who need to make some close-to-authentic tests.

How do I access this Amazing Resource?  The only way is to go through "Pretty Good Physics -- Secure."  Most of this blog's readers already have an account there.  If you don't, you should -- follow the link, and follow the instructions to sign up.  The process is simple but may take a few days, because it is critical that the site administrators verify that all members are honest-to-Bob physics teachers.  

Then, get into the site and search for "workbook."  Out will pop the new workbooks, all ready for you to copy and paste into your tests.

Do you know of another good resource?  Let us know in the comments.

Update January 2019: Okay, there's plenty of authentic AP Physics 1 and 2 questions available via your course audit - the College Board has released 40 of the 50 multiple choice from the international version of these exams each year since 2015.

But starting in 2019-20, audited AP teachers will have free access to a comprehensive online question bank that will include both released and unreleased items.  And more.  Stay tuned.  Still use the Big Amazing Resource, but it will be unnecessary shortly.

04 September 2014

My students are only averaging 80% on the daily quizzes. What do I do?

A frequent concern this time of year for both teachers and students is grades.  The optimism of the first few days of school has faded... the students have probably gotten back a bunch of quiz and test scores, jolting them into the reality that they're gonna fail this course, and then they won't make the honor society, nor get into college, or at least the right college that would allow their parents to brag at cocktail parties.  Holy #$&*, they'd better go drop this course RIGHT NOW.

I'm sure virtually everyone reading this blog has confronted the described mentality.  One way to deal with it is reasoned logic. Explain rationally and calmly that...

Oh, yeah.  Reason and logic don't seem to be the strong points of students who get carried away with the dramahz.  So maybe we need a different approach that doesn't necessarily include a rational basis.

The first and most important step in damping out this particular fire is to develop a relationship with the college counselor and the director of academics -- that is, the person ultimately responsible for college placement, and the person ultimately responsible for course changes.  These folks generally do have a rationalist approach to their job, and they are used to dealing with artificial drama; what they often don't understand is the nature of a physics course.  Meet with them.  Talk to them informally as well as formally.  Bring them cases of beer.  

Explain how your course works, that it's not about memorizing facts as much as using facts in new situations.  Assure these folks that you don't intend to fail the majority of your students.  I explain that any student who diligently completes all assigned work will earn a minimum of a B- for the year, but that there may be pitfalls along the way.  John Burk likes to compare his class to a theatre production: after a week of rehearsal, the scenes are quite rough, the actors don't know their lines, and the chemistry among characters hasn't yet jelled.  So should we just give up 'cause it ain't perfect yet?  Certainly not... think of physics as year-long preparation to perform on a year-end exam.  Things are expected to be rough at the beginning.

Then work on the students.  There's vast literature -- including on this and other physics teaching blogs -- about how to develop a "growth mindset" among the class.  It's critical at the course's beginning that you NOT discuss points or grades or college plans with any student or parent.  Nevertheless, it's a reasonable expectation that students be put at ease that their 75% quiz score doesn't mean they're getting Cs and having their lives ruined.

My approach is to tell them once -- only once -- how I calculate grades.  For me, 80% is an A, 70% is a B, 60% is a C, and 50% is barely passing.  I've in the past used a "square root curve -- that works fine as well.  When we approach the first test, I show up front the AP scale, in which about 65% is a 5, 50% is a 4, and 35% is a 3.  Then I allow test corrections to earn half credit back for any points they miss.

The final, critical point to the physics teacher is: don't try too hard to make students "feel better" about being in a hard course.  

When my own offspring is upset that we -- GASP! -- ask him to mop the floor, I find that it doesn't help his mood when we sympathetically and pleasantly try to acknowledge his annoyance and assuage his irrational anger.  "Don't worry, it won't take very long" or "Hey, it's not that big a job today, the floor isn't particularly messy" provoke more tantrums from the boy than if we just go away and leave him to the task.  Similarly with your students.  The more you sympathize, the more you try to talk them through and acknowledge their irrational dramah, the more they play up said dramah and talk themselves into a negative spiral of emotion.

Just keep going with the course.  As more and more of your students start to experience success, those shrill, distraught voices will become as whispers in the wind, drowned out by the veritable thunderstorm of positive confidence.

28 August 2014

Is projectile motion part of AP Physics 1? YES.

I got a note last night asking me to help settle an argument.  Since it's the second or third time this summer I've heard the meme, I figured I should address it publicly.

The question:  Is projectile motion part of AP Physics 1?

Answer: Yes.

The argument:  But the Physics 1 curriculum framework does not include any learning objectives with the word "projectile" in them.*  No LOs even say "two-dimensional motion" or anything similar.  Since the problems must be written directly to the learning objectives, nothing about projectiles can be asked.

* The Physics 2 framework includes one learning objective that requires students to recognize the similarity between a charge moving through a uniform electric field and a projectile.

Well, that argument takes an overly literal interpretation of the curriculum framework, I believe.   

My rebuttal:

1. Projectile motion is explicitly mentioned within "essential knowledge" 3.E.1:  "The component of the net force exerted on an object perpendicular to the direction of the displacement of the object can change the direction of the motion of the object without changing the kinetic energy of the object. This should include uniform circular motion and projectile motion."

2. Granted, the subsequent 3.E.1 learning objectives don't explicitly refer to projectile motion.  But I certainly could find a way to write a good problem involving a projectile that matches the 3.E.1 learning objectives, as well as to several others.  Problems can be written to multiple learning objectives.

3. At the AP reading, one of the points made by a College Board representative warned us about mechanistic teaching to learning objectives.  She said that in the biology redesign, a good number of teachers were flummoxed after they spent the year posting the learning objectives and teaching a course narrowly tailored to doing literally and word-for-word what the LOs said to do.  Her point:  the learning objectives are meant to be interpreted in the context of the "essential knowledge" statements, and are all interrelated.  The AP development committees are creating science exams, not the Law School Admissions Tests.  The learning objectives are intended to be flexible enough to allow for coverage of all the course material described in the framework; they are not intended to be narrow prescriptions of the precise questions that will be asked on the exam.

4. Look at the released AP Physics 1 practice exam:  questions 5 and 6 include a diagram with a projectile on it.  QED.

So teach projectiles.  Don't merely teach "here's how to plug numbers into equations to get answers to three significant figures," because that approach is just as doomed to failure in projectile problems as in other topics in AP Physics 1.  Be sure students understand the independence of vertical and horizontal motion, how a vertical acceleration alone produces a parabolic trajectory, how the velocity, acceleration, net force, kinetic energy of/on a projectile change or don't change depending on various aspects of its motion, etc.  But do teach projectiles.

22 August 2014

Required Reading: Kelly O'Shea's "Mistake Game"

Reason number 156 why I love teaching physics:  I don't care how long you or I have been doing this job, there's always something new to learn and to try.  

I looked again last night at Kelly's O'Shea's excellent "Physics! Blog!"  Kelly was the one who first articulated the holy grail of physics teaching, the ability of students to solve "goal-less problems."  While clicking some attractive links I discovered* not the holy grail, but perhaps the shroud of Turin:  Whiteboarding with the "Mistake Game."

* I also discovered that Kelly independently made a Clever Hans reference two years before I did.

I am well aware of the verb "to whiteboard," and I'm extensively tutored in its benefits.  It's not like I disagree with or disapprove of the technique; I just haven't yet found a place for it in my classes.  I've always managed to accomplish everything intended in a whiteboarding session by using pencil-and-paper.  Kelly's post has changed my mind, by introducing the critical element: the deliberate substantive mistake.

You should read Kelly's post directly for the details about her Mistake Game.  My quick summary:  Give several groups of students a problem to whiteboard... but each group is required to intentionally include one substantive mistake.*  The groups take turns presenting their solutions to the class.  Since they're charged with selling the solution, including the deliberate mistake, the students actively engage their audience.

* They're allowed to include as many unintentional mistakes as they'd like.

The mistakes are to be discovered through questioning.  Kelly says she has to teach audience members to ask substantive questions in pointing out the substantive mistakes -- not "hey, that's wrong, the slope is the wrong way" but "Which way was the car moving?" followed by "And how does a position-time graph indicate the direction of motion?"

I've always wanted to bring the methodology of the Physics Fight into my honors physics classroom, but I never found a way that made me comfortable.  Usually a typical honors-level problem is complex, but not complex enough to provoke real discussion and conversation except on rare special occasions.  As Kelly points out, the requirement of a substantive mistake facilitates that discussion -- the presenters vie to create a mistake that is "good" enough to pass the audience's examination, while the audience members vie not just to discover but to engage in conversation about the mistake.  Imagine that... to get authentic discussion, I need to require inauthentic but authentic-seeming mistakes.  Kelly, that's practically Zen.


15 August 2014

Mail Time: How much detailed attention to significant figures in AP Physics 1? (Answer: NONE.)

Mo here, a retired engineer teaching AP Cal AB & BC (for 13 yrs.), and now taking over the AP Physics program. 

I can’t seem to find clear information anywhere with regard to significant figures (SF) and how they’re handled by AP Physics readers. Being an engineer, you can imagine I tend to be very strict about SF, but I don’t want to overwhelm my students unnecessarily if the College Board does not stress it.

I would greatly appreciate any advice.

Hey, Mo... this is certainly a frequently asked question.  On one hand, don't harp on students about sig figs. If they put four rather than two sig figs, that's usually not in any way an issue.  However, if they're writing down every digit on their calculator, they're missing something, and they're possibly losing credit.  

The new exam does discuss experimental uncertainty.  Rather than stress rules of significant digits, instead you might talk in context about the uncertainty in a measurement.  Two measurements of 0.19 kg and 0.20 kg are equal, because by definition "0.19" means somewhere in bewteen 0.18 and 0.20.  However, two measurements of 0.191 g and 0.202 kg are NOT equal.  

But most importantly, your question about significant figures is nearly irrelevant for the new exams.  

Take a look at the released practice exam, and see how many questions require a calculated numerical answer.  Only one part of one free response question does:  that's 1(b), which asks for a calculation of external force on a cart based on a graph of experimental data.  Now look at the rubric for that part: of the four points awarded for this calculation, not a single one is awarded for the numerical answer.  

As with everything on the new exams, rote rules about arithmetic are far subordinate to the physical meaning of predictions and experimental results.  And calculation -- whatever the number of significant figures on the answer -- is far subordinate to explanation and description.  

Hope this helps...


13 August 2014

AP Physics 1: Define the system carefully when doing energy problems

For years I've taught energy conservation via an equation.  Write the energy conservation equation for the object in question, identify each term, and solve.  That gets the right answer most of the time.  However, in AP Physics 1, getting the right answer is not as important as describing clearly how to get the right answer, and why the right answer is in fact the right answer.  I need to dig deeper for this new course.

In particular, I've always been fluffy about defining the system experiencing these energy changes.  I implicitly was referring to the single object experiencing a change in position or velocity.  That's "fluffy" because potential energy is created through an interaction within a system of multiple objects; and because I'm making all sorts of assumptions about what forces doing work should be included on the left side of this equation.  The students could use this equation to get the right answer, but they could not have described in careful, correct language the energy transfer.

The NTIPERS book provided me with a guide to teaching my students to use a deeper approach.  In each energy problem presented by this book, the authors clearly define the system being analyzed, and they list the forms of energy the system could possibly possess before, during, and after the process in question.  NTIPERS suggests making a bar graph for each problem listing the amount of each energy; words and numbers are probably enough, but the bar graph is a nice approach, too.

As an example: consider 50 kg Tarzan dropping on a vine from rest, as on the 2014 AP Physics B exam problem 1.  One part asks the student to calculate the speed of Tarzan as he swings through his lowest position (call it 2 m below his starting point), neglecting air resistance.  We can approach this two equivalent ways:

1. Treating the Tarzan-Earth system:  Systems can have potential energy due to their interaction.  Systems can also have kinetic energy, which is equal to the sum of the kinetic energies of the component parts of the system.  Define the lowest position of Tarzan as the zero of gravitational energy for the system.  That means the Tarzan-Earth system begins with mgh = 1000 J of gravitational energy, and (because nothing is moving) no kinetic energy, giving 1000 J of system mechanical energy at the start.  During the process, no work is done by an object external to the Tarzan-Earth system -- the only other object exerting a force on any part of the system is the rope, and the rope is always pulling perpendicular to Tarzan's velocity, so does no work.  Since the gravitational energy is zero at the bottom point, the entire 1000 J of system mechanical energy must be converted to kinetic energy.  Now use the kinetic energy formula to calculate speed.

Summarizing: 1000 J gravitational energy before --> no work during --> 1000 J kinetic energy after.

2. Treating Tarzan as a single object:  Objects can have kinetic energy, but not potential energy.  So Tarzan begins with no kinetic energy.  During the process, two forces act on Tarzan: the force of the string, and the force of the earth.  The string force does no work on Tarzan because it is always perpendicular to Tarzan's velocity.  The earth does work on Tarzan equal to Tarzan's weight multiplied by the distance Tarzan travels parallel to the weight, or 1000 J.  This is positive work, because the force of gravity is parallel, not antiparallel, to the downward component of Tarzan's displacement.  At the bottom, then, we know 1000 J of work has been done on Tarzan; this must change Tarzan's kinetic energy by 1000 J, since we're not treating Tarzan as a system with internal structure.  Now use the kinetic formula to calculate speed.

Summarizing: 0 J total energy before --> 1000 J work done by gravity during -->  1000 J kinetic energy after.

This may sound like semantics to you.  It certainly does to me.  But I'm telling you, the new exam will ask students to explain energy conversion and conservation with direct reference to an appropriate object or system.*  We must teach the students to describe energy conversion in the kind of language I've included above.

* Look at learning objective 5.B.1.2 in the curriculum framework, for example.

Furthermore, the students are expected to be able to understand when the model of an object or system fails.*  What does that mean?  We calculated 6.3 m/s for Tarzan at the bottom.  A follow-up question might suggest that Tarzan was actually moving 5.0 m/s at the bottom, and experiments verify that air resistance has no measurable effect on Tarzan.  The question may ask for a resolution of this discrepancy.

* That's LO 5.B.2.1 for those of you with an education doctorate.

A reasonable explanation is that treating Tarzan as an object isn't reasonable.  He could be spinning; the "missing" mechanical energy is accounted for by his rotational kinetic energy.  Similar questions could be posed in which an object seems to have less energy than predicted by a point-object model, but some internal structure in motion accounts for the total mechanical energy budget.