Multiple Choice appropriate for General Physics

For juniors and seniors, my school offers only two levels of physics that don't require a prerequisite:  AP physics B and General Physics.  I will have a number of students taking General Physics as a graduation requirement, so this course must be accessible to folks of all academic abilities.  My approach to General Physics has been to teach mechanics, waves, circuits, and optics to the AP-B standard.  The goal is that if my students could take the AP physics B exam, but strip out all of the topics that we haven't covered, they'd all pass.  That makes for a slow-moving but powerful course.  On my February exam, I do give a long set of AP free response questions, on which my students perform easily to passing standard.

I've already detailed the free response questions, most of which are at the AP level, that will be on this spring's final exam.  But I want to give a set of multiple choice questions as well.  Most of the multiple choice questions available in the physics universe are at the AP level.  Since I have not spent any time this year with the General class practicing the correct approach to multiple choice questions, and since they have not had multiple choice questions on any other test, and since I want the multiple choice to HELP their performance rather than to serve as an additional challenge... I need some straightforward multiple choice. 

Enter the National Science League.

The NSL is a shamelessly commercial organization which sells science (and math!) contests at all levels from elementary to high school.  Their business plan is sound -- create straightforward multiple choice tests annually, promote the tests as a national "contest," and get schools nationwide to open their wallets.  In return for a sum of money, the school gets the test itself, some certificates and medals, and recognition on the NSL website on which schools are ranked in each subject by the performance of their top 10 students.

I personally have no trouble with the commercialism.  The NSL is filling an open economic niche.  From a competitive standpoint, the "contest" is worthless:  the 40-question multiple choice physics test is written such that any AP student who misses even one should be flogged.  Commercially, though, that makes a lot of sense... more teachers will be willing to give the NSL contest, and thus pay money for it, if they know that their students will feel successful.  Nothing wrong with that.

I use the NSL physics contest not as a contest, but as a set of multiple choice questions uniquely suited to my general physics class.  By coincidence, the topics of the NSL questions align nicely with my own choices:  mainly mechanics; some waves, optics, and circuits.  There are always a few thermodynamics or electrostatics questions that I have to cut out, but usually at least 35 of the 40 questions are right in the General Physics wheelhouse.

As part of my final exam this year, I will give the 2010 NSL.  As an added benefit, I have a built-in review packet: for practice leading up to the final exam, I have given out a previous year's NSL.  My students are consistently missing no more than 3-6 questions out of nearly 40. 

GCJ

Remarks on preparation for the cumulative final exam

Physics is by nature a cumulative subject.  Good physics problems, whether they be exam problems or active research problems, tend to combine multiple topics.  For example, a problem I've seen a million times involves two blocks colliding at the edge of a cliff.  To find the landing point of the blocks, it's necessary to use both momentum conservation AND projectile kinematics.  The student who passed the kinematics test and then forgot all about it finds himself up a creek on such a problem.

I'm regularly asked, at least early in my course, "Will this test be cumulative?"  The initial answer is usually something mildly sarcastic, like "Are you asking for my permission to forget everything we covered last month?"  One time, and one time only, I explain the rationale for the cumulative test, usually with a specific example of how physics topics mesh to form interesting problems.

That said, this time of year a student is faced with an enormous amount of information to digest in preparation for a cumulative final. It's been nine months, after all.  In the last marking period we've covered optics, circuits, and astronomy -- all of which have little immediate relationship to the mechanics topics from the first 2/3 of the course.

Rather than give my class the daunting and hopelessness-inspiring mandate to "just study everything," I try to focus the class's preparation.  This exam is not designed as a "gotcha!" final, is not intended to show what the students don't know.  No, I'm trying to set my class up for success on a serious yet managable set of problems.

How do I set them up for success?  Let me start with what I will *not* do.  I will never stoop to that scourge of high school teaching in which the teacher offers a "review session" at which he essentially gives out answers.  Nor will I answer questions during the test such as "What are you asking on this problem?"  "Success" on an exam doesn't necessarly mean a grade of 100%, it means demonstrating physics problem solving skills in an atmosphere of authentic evaluation.

I don't consider it inauthentic to state the overall topic of each problem. In fact, I do this before February's cumulative midterm as well.  Students get the cover page of the exam with instructions, along with a grading sheet.  The grading sheet, with the topic of each question, is the picture at the top of the post.  The instructions:

Instructions:

o Part I consists of 40 multiple choice questions.

o A calculator is allowed but not necessary.

o Do not spend more than 45 minutes on these, though that is not a firm limit.

o Answer on the scantron

o Students in general physics should SKIP the questions marked “AP.” General physics will only answer 32 questions.

o Part 2 consists of four free response questions

o AP students should answer only the first three. You may look at problem 4 (about astronomy), but I will not grade your answers.

o General physics students should answer all four questions.

 

The list of topics doesn't truly give away anything.  After all, anyone with a brain could figure out that each of the three main topics from the last marking period would be on the test; and that a cumulative exam requires at least one problem dealing with the first part of the course (mechanics).  But this list does encourage the students to practice problems from each of the four topics before the exam.  They come in to the exam far more confident knowing that "#2 is the optics question."

For the actual year-end FINAL exam, I go one step further, especially because I have not been able to review in class regularly (due to senior-junior issues -- see this post).  I hand out part (a) of each of the four problems!    Now, not only does the class know that problem 3 is about circuits, they know that part (a) is asking them to draw a circuit digram based on a sketch of four wired light bulbs.  They know that the mechanics question involves a spring pushing a mass off of a table, and that they must start by figuring out the time for the mass to hit the floor.

Of course, each question on the exam will consist of parts (a) through (c) or even (f).  It is the job of the student to be prepared for whatever further questions I choose to ask about the physical situation.  But figuring out what kinds of questions can be asked is itself a physics skill!  I am *pleased* when a group of students figures out that they'll likely be asked to calculate the current through and voltage across each light bulb.  It is wonderful when the students suggest to each other than they might have to solve for the distance the spring compresses.  That's how real physics works... not just solving the well-posed problem, but determining in the first place what problems are interesting and solvable.

I'd encourage folks to try this approach to exam review, and to tell me how it went.  If you come to one of my summer institutes, I will be happy even to give you a copy of my handouts and my exam itself for you to use in future years.

GCJ 

Elevator question #1: Forces on the student

The poll question to the right asks only for the downward forces acting on the student.  For the purposes of our discussion, let's first consider ALL forces acting on the student.

It is important to focus only on the forces acting directly on the student himself.  Forces that act on the elevator, on the scale, or on the building are utterly irrelevant to this question. 

So, we begin with earth's gravity.  We know the earth applies a downward force on the student.  That downward force is generally called the student's weight.

Since there are no electric or magnetic fields here (and, if you're really going to be a lawyer about it, since we're not dealing directly with a nucleus), any other forces on the student require contact with the student.  What else is touching the student?  Only the platform scale.  And since he's standing on the scale, that scale must push upward. 

What about the "normal force?"  A normal force is defined as the contact force of a surface pushing perpendicular to that surface.  Because the scale provides a surface for the student to stand on, the upward force of a platform scale *is* a normal force... on a free body diagram, a label of "Fn" or "N" rather than "Fscale" would be completely correct.  Just recognize that when we apply Newton's second law, whatever value we find for the normal force is the reading on the scale.

What about the force of the student pushing down on the scale?  Well, that force certainly exists... but that force does not act on the student.  In order for Newton's Laws to work, we must consider only the forces that act ON the student, not forces exterted BY him.

What about the force of the cable attached to the elevator, or the elevator's weight?  Isn't the entire elevator accelerating, not just the person?  Yes... but we must choose a single object for the purpose of using Newton's second law.  Had we chosen the entire elevator with the person inside, then there would be an upward tension from the cable, and a downward weight.  But we were asked about forces acting on the person, not the elevator. Newton's second law applies just fine to the person alone, even though the elevator exists. 

And as for the "force of motion" or the "force of acceleration"... these things do not exist. A force must be attributed to some agent pushing or pulling, either through contact or through a gravitational (or electric or magnetic) field.  Sure, forces can cause acceleration, but the "force of acceleration" is not a meaningful or correct phrase.

Next, I'm going to ask about the MOTION of the elevator... stay tuned.

Final Exams in mixed 11th-12th grade courses, or in AP

Most high school courses end with a final exam.  The exam can be a wonderfully positive culminating experience, showing students how much they've learned over the past year.  In my athleticly-oriented mind, the final exam serves the same purpose as the state track meet -- it's what you've been aiming toward in all the year's preparation, and win or lose, it tells you where you stand.

Various situations and school policies can eliminate the effectiveness of the exam as "culminating experience." 

Most obviously, in an AP course, the AP exam itself is the culmination of the course.  If you are required to give your own final to an AP class, you're going to face a tough audience.

Some schools exempt students with an A average from exams; others exempt seniors but require juniors in the same class to take the exam.  Any time only part of a class is preparing for a high-stakes exam, a class management nightmare can ensue: the exempt elite, who don't want to be in class on a beautiful day in May or June, either directly or indirectly distract and frustrate the unexempt plebes who must buckle down to study.  What to do?

I certainly don't have all the answers.  All I can do is relay ideas I and others have spawned in order to deal with unusual exam situations.  Here we go:

* While it's tough for an AP teacher to give an exam, and it's tough to exempt just a few students, the combination of policies can work well in an AP course.  Imagine that students with an A average in AP are exempt from a school-administered final exam, but those below an A are not exempt.  Well, give an AP-style final, and tell students you'll bump their grade up a full letter if they perform on the final.  (That is, a student with a year-long B can have an A for the year if he gets a 5 on the exam.)  Since these are AP students and already more academically serious than most, a few might be inspired to show that they know their physics.  And since physics understanding tends to coalesce after seeing the same topics multiple times, it might be that many of the B students have truly improved their understanding to the A level. 

* When only a select few have to take the exam, make the exam as transparent as possible in order to focus and minimize study time.  My general-physics juniors have to take a final exam.  The exam matters to them, becuase their grade is still meaningful, and many can improve their overall course standing with a good performance.  Yet, I can't prepare them in class like I want to, because my seniors would tune out and become difficult.  So, we end the year building an AM radio -- fun for all.  But I still help the juniors prepare...

I construct the exam from modified AP questions.  My general class is used to this format.  In the second half of the year, I began advertising the topic of each problem before a test -- that helped focus their study.  For this final exam, though, I actually publish the stem itself of each question.  Meaning, I don't just say "problem one is about Newton's Laws" or even "problem one has a sled on a slope."  I paste the diagram, the description of the situation, and part (a) into a file that I give to the class. 

I look at this like a history teacher who advertises some possible essay questions before the exam.  Will I (or the history teacher) get a true, valid sense of the students' abilities to remember and synthesize everything from the entire course?  No.  But I'll get more and better studying for the specific topics on the test than I would otherwise.  And for a mixed junior-senior class in the spring, that's good enough for me.

* And what about the juniors in AP physics to whom I'm required to give a final?  Those who are entering my research course for next year are already working on USIYPT projects. Their exam will be a 5-minute powerpoint based on their preliminary research.  Those who are NOT going into the research course get to take the general physics final exam.  I put it to them as a way for them to help me out -- "The exam will include some questions I've never asked before, and I want to see if they're good and valid questions.  By including some AP students, I'll get a sense of whether the question is clear, whether it asks what I mean to ask."  My AP juniors are happy with this approach -- they don't need to study, and they know they're helping out the school's physics program.  They still may think of the exam as kind of busy work, but they're okay with that.

Other suggestions or ideas?  Post a comment or email me at greg_jacobs@woodberry.org.

Recruiting techniques for next year

The AP exam has been over for a few days.  AP students are either working on USAYPT research projects, or are doing busywork that I'd otherwise have to do -- printing out old AP exam solutions, organizing and labeling my cabinets, cleaning my office, creating the wall of 5s, and so on.  General physics students work at their own pace on a circuits lab; next week, after our final test, they will solder together an AM radio kit.  We're all coasting into the end of the year.  That's not to say that learning isn't happening.  It's just that we've worked our butts off since September, and now it's time to relax the daily regimen of quizzes and problem sets and take in a different, more laid back style of physics.

Not coincidentally, this is the time of year when students are asked to choose their classes for next year.  I think I've done a good job at Woodberry of encouraging more than just the smartest few to take AP physics.  That said, I know there are still folks out there who would enjoy the course, but who are scared.

I have to remember that, even though I've been at the same school for ten years, even though it's well established here that physics is fun and rewarding, it's still a BIG step for a guy without 800 SATs to sign up for AP physics.  My students are advised by a wide variety of folks, including parents and other teachers, whose 1970s-era experience is that physics is a too-hard subject reserved for übernerds.  How do I break down this misconception?

This year in particular I'm at an advantage because I coached sophomore-level football in 2008.  The sophomores on my team are now the rising seniors signing up for my class -- and a LOT of them are signing up.  I noticed a similar effect in 2005 when I had coached sophomore-level baseball for a few years.  Involvement outside the science department broke down some preconceptions, and established my credentials as NOT a complete übernerd.

All that said, the biggest intimidation factor keeping the enrollment numbers down in upper level physics is the perceived mathematical nature of physics.  Bad physics teaching -- to which the parents and advisors of many students were subjected -- can make physics into a playground for the mathematical showoff.  Overly mathematical physics teaching can not only make the majority of a class unsuccessful at physics, it can develop true hatred of the subject.

So, what do I do when a student asks about taking AP physics B?

I do ask what math course he's taking.  If the answer is honors *anything*, whether honors algebra II or AP calculus BC, I tell him he's ready for AP physics.  If his math is not on an honors track, I explain the scope of the two nightly problems:  how students are required to communicate in detail the steps toward the solution, and to take up a full page per problem in making that communication. 

Then, for either the honors or not-honors math student, I ask the following questions.

1.  Can you solve this system of equations for x and y?

          3x - y = 5

          2x + y = 3

2.  Can you find the length of the side labeled x in this triangle?

Most of the students I talk to nearly laugh... they say "of course I can," or simply, "yes."  I don't make them actually solve; I just want them to tell me that they CAN find a solution. 

I then explain that they have just seen the deepest math that they will see all year in AP physics.  It's amazing how students who had approached me trepidatiously walk away from our discussion with confident body language. 

Convincing even one rising senior that he can, in fact, handle the AP physics course can have deep resonance within the class.  That one senior will encourage his friends to sign up, or at least to talk to me, so I can have the same conversation.  The end result is a well-subscribed AP course, and, hopefully, a significant number of students passing the exam next year... when the recruiting process starts all over again.

GCJ
 

What is conserved in a collision?

First of all, consider what the word "conserved" means.  A quantity is conserved if its total value does not changed.  For example, in a chemical reaction, mass is a conserved quantity -- though one reactant might seem to disappear, if we carefully trap all the reaction's products, we find that the total mass before and after the reaction is the same. 

Momentum is conserved in ALL collisions.  (This means that the TOTAL momentum, including all objects, is the same before and after the collision. 

Velocity and force are not conserved quantities in anything that I am aware of.

Kinetic energy is usually NOT conserved.  Only in the special case of an "elastic" collision is KE conserved.  In an elastic collision, the objects must bounce off each other.  However, the converse is not true:  the fact that objects bounce off of one another does NOT mean that the collision must be elastic.

A frequently asked AP-style question (as on 2008 B1) gives details about the collision, and then asks whether the collision was elastic.  Usually the solution entails using conservation of MOMENTUM to find the velocity of each object after the collision, then calculating total kinetic energy before and after the collision for the comparison.

Department of Blatant Advertising: 5 Steps to a 5 and other books

I'll get back to real physics teaching ideas shortly.  With the AP exam coming up Monday, I thought I'd share with you the best prep book on the market, the one I authored, the 5 Steps to a 5: AP Physics B &C. It's not a textbook:  it's designed to be read by students, not referenced by physics professors.  If you don't have one, now's the time to get it for weekend review.  If you come to one of my Summer Institutes, I'll sign your copy!  (Also, I might have some available free to teachers at my Summer Institutes... stay tuned.)

If you have children, nieces, nephews, cousins, or siblings, or friends between the ages of about 6 and 12, you should buy them the Everything Kids Football Book and the Everything Kids Baseball Book as a present.

Another book project is in the works -- more information to come eventually.

GCJ

The Wiggles, and video astronomy

Time for some silliness.

As of a few years ago, one of my favorite trivia questions was "Name the Australian entertainer(s) with the highest gross income."  Answer:  The Wiggles.

The Wiggles, an insidious children's band, sing cheery songs in the style of Barney, but without the excuse of being a big purple dinosaur.  Each "Wiggle" dresses in the same color, whether he's wearing pajamas or Star Trek-style fashions.  My wife and sidekick, Burrito Girl, used to debate with her fellow moms which Wiggle was the hottest.  The Wiggles were inflicted upon me when my kid was about two, and I liked them -- they didn't make me throw up as much as, say, Mr. Rogers or Max & Ruby.

Anyway.

I recall watching a Wiggles song and noting some strange astronomy.  After much searching, and with the help of my friend Matt who was forced to watch WAY more Wiggles than I was, we found the relevant youtube clip.  Below is today's assignment for my regular physics class:

1. Watch the youtube video above. (Don’t like it? Think it’s silly? Then be extra careful about birth control.)

(a) Based on how the “sun” moves, I know which hemisphere this action is supposed to occur within. How? Be sure to explain thoroughly.

(b) Assume this action took place on March 21. Estimate the latitude of the meadow in the video. Justify your answer thoroughly.

(The answer to part (a):  The cardboard sun appears to move across the sky from right to left.  That's what caused me trouble the first time I watched this clip with Milo all those years ago.  In Australia, in the southern hemisphere, the sun rises in the east, but at noon is to the NORTH.  Therefore, the sun appears to move right to left, unlike here where it moves left to right.)

(For part (b), the sun never gets more than about 20 degrees above the horizon, which implies that this video is taken at 70 degrees south latitude.  That seems unrealistic for Australia -- no parts of that contintent are within the antarctic circle -- so I'll chalk this up to the Wiggles' propmasters' poor astronomical precision.  Nevertheless, they got the sun to move in the correct direction, so kudos to them.)

GCJ

Is your class sick of seeing you? Put them in charge!

In my AP sections, we've been in review mode for a while.  Typically, we do a couple of free response questions each night for homework.  In class we take a quiz, go over the quiz, and go over the homework.  I try to spice things up with clicker exercises, a physics walk, and other special events.  Nevertheless, especially now that ALL of my students' AP classes are pushing hard toward next week's exams, my students' focus is flagging.

For today's class, I put my students in charge.  That got their attention.

At the beginning of last week, an informal survey indicated that people wanted to review circuits, and especially capacitors in circuits.  On Wednesday, I asked the class to vote in secret ballot for the classmate they'd prefer to lead a discussion of these topics.  On Wednesday night, I asked the leading vote-getters (two classmates tied in one section) if they would be willing to lead the class on Monday.  They all agreed.

For Monday, then, I distributed the homework assignment, which was two resistor-capacitor circuit problems from old AP exams.  I wrote a multiple choice quiz based on one of the problems.  I forwarded an advance copy of the quiz to the student leaders, along with the rubric to the AP problems, a few hours before class.

It was important that I not be in attendance.  If I had been there, the temptation for all would be to defer to mefor an explanation.  (And I would be tempted to give said explanation.)  Without me, the class worked through the issues together. 

How did I arrange not to be there?  In past years, I arranged this class for a day when I had to be out of town for one reason or another.  This year, I just traded classes with a colleague, so I taught conceptual physics today while he sat in the back of my class.  I instructed him NOT to participate, other than to maintain order or focus if necessary.  (In four years of doing this exercise, I've never had a colleague report that he had to step in to maintain order.  I think my class is so happy to be doing something unusual without me there that they are extra-careful to show respect to the appointed class leader.)

Student response has generally been fabulous.  "I figured out circuits after the homework and today's class," Kevin told me this morning. 

A couple of hints in case you try this exercise:

* Don't warn the class ahead of time that they will be able to vote for a student to lead the class.  There would be politicing, blocks of votes, hurt feelings, and general mayhem.  Just suddenly distribute ballots and ask for an immediate vote.

* It's better to use a colleague than a "substitute teacher" for this lesson.  Since the faculty member who sat in the back of the room is a member of the science department, the students all knew that I would get a clear report of what went on.  And so, they took the review seriously.  There was no baggage associated with a substitute who may or may not have any interest in what went on.

* This takes a LOT of preparation on the teacher's part.  I had to have the homework and quiz prepared well ahead of time, I had to be sure that answers were available to the student leaders, I had to follow up with my colleague, and, today, anyway, I had to prepare and teach my colleague's class.  The student-run class does not save time.  It's just something fun to do as spring rolls along.