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 

BOUX day

Every baseball announcer has a catch phrase; similarly, every physics teacher has some personal or instructional quirk that identifies and (hopefully) endears him or her to the class.

My own catch phrase is “BOUX!” This comes from an old Dave Barry column, in which he describes the difference between New York Mets fans (who say “Boo! You stupid bum!”) and Montreal Expos fans (who say “Boux! Voux dumme bumme!”) Or something like that.

Throughout the year, I write “Boux!” on papers that demonstrate major fundamental errors. For example, saying that a box must move to the right because it experiences a net force to the right – Boux! Saying that the acceleration of a ball is zero at the peak of its flight because its velocity is zero – Boux!

On the last day of class, I open a blank page in Microsoft word with the word “Boux!” at the top. The class is encouraged to shout out mistakes they might make that would earn a “Boux!”. This exercise serves several purposes. It is cathartic, in that the class sees that EVERYONE, even the smartest student, has at one time or another earned a boux. Furthermore, as students begin to think about the three hour exam coming up on Monday, they remind themselves of mistakes that they can easily avoid. My hope is that if someone begins, say, to use conservation of kinetic energy in a collision problem, that person might stop himself, saying “oh, wait, Mr. Jacobs would sure say “Boux!” to that, ha ha.”

The whole exercise is generally lighthearted and fun… and it produces an interesting study guide. Here’s a list of the class’s “Boux!” list from last year. Enjoy! And good luck on Monday.

1. Adding electric fields without considering direction

2. Putting centripetal force on a FBD

3. Mg always points down, not at an angle

4. Acceleration does not equal zero at the top of a ball’s flight

5. Units (or numerical values) on variable problems; no units on a numerical problem.

6. Adding voltages with directions

7. Putting a sign on the charge when calculating electric field

8. Using a point charge equation when a field was produced by the Almighty Bob

9. Putting anything other than a force on a FBD

10. One rope = one tension (Jacobs Law of tensions)

11. Object distances are never negative

12. Assuming equilibrium for an Fnet problem when a is not zero

13. Mixing up sin and cos when breaking vectors into components

14. Putting both components and a force itself on a FBD

15. Leaving a free response problem completely blank

16. Saying F=ma when only FNET = ma

17. Setting a random voltage = IR

18. Assuming that if heat is added, temperature goes up

19. Assuming KE is conserved in a collision

20. Using left hand for a right hand rule

21. Drawing rays that refract through a mirror or that reflect off of a lens

22. Using kinematics when acceleration is not constant.

23. Fishing for equations

24. Putting acceleration anywhere but toward the center in circular motion

25. A normal force does NOT necessarily equal mg!

26. Putting Fn not perpendicular to the surface

27. Measuring an optics angle not from the normal

GCJ

AP exam review: 2004 B1, Roller Coaster

It's time for that final AP exam review. Today's post gives a multiple choice review exercise based on an old AP exam question; tomorrow I'll describe my final classday activity.

As I've discussed before, just doing an AP practice problem does not provide sufficient review. Practice problems must be followed up somehow. Usually I have students do corrections on what they missed. But for a fun change of pace in the spring, I get out my classroom response system (my "clickers") and run a little contest for extra credit.

Before I go on, please note that (a) this contest works just fine without "clickers" -- just have the groups write their answer really big on a piece of paper and hold it over their heads. And, (b) this type of review is not confined to AP physics. AP questions can be carefully selected, or edited, for use with your general high school physics class. You can use this as final exam review.

How the contest works

This contest is based on problem 1 from the 2004 AP physics exam. For lawyerly reasons I can't post the actual question here, but you can get it via this link: http://apcentral.collegeboard.com/apc/members/exam/exam_questions/2007.html#name04

First, I have the students do this problem to the best of their ability on their own. This usually means as a quiz.

Next, I use http://random.org/ to divide the class into teams of two. Each team gets one clicker

Now, I ask the multilpe choice questions that you see below. I ask them one at a time, giving at least 60 seconds for the teams to discuss the correct answers. After the 60 seconds, I collect responses, and then go over the correct answer

Scoring: Each team gets one point for the correct answer, and one more point for each group who doesn't get it right. There are a bazillion ways to score a contest like this... I've found that this particular scoring makes students less willing just to listen to the smartest students without thinking for themselves. I get good arguments amongst the class, which is what I'm after.

Here are the questions I ask:

1. At which labeled point does the car attain its maximum speed?
(A) I
(B) II
(C) III
(D) IV
(E) V

2. To calculate the value of the car’s maximum speed, do we use kinematic equations (vf = vo + at and so on) or conservation of energy?
(A) Kinematics must be used
(B) Conservation of energy must be used
(C) Either kinematics or energy conservation may be used
(D) Neither kinematics nor energy conservation will produce a solution

3. What general formula for potential energy do we use here?
(A) mgh
(B) ½mv²
(C) ½kx²
(D) qV
(E) (3/2)nRT

4. What general formula for kinetic energy do we use here?
(A) mgh
(B) ½mv²
(C) ½kx²
(D) qV
(E) (3/2)nRT

5. To calculate the speed at point B, which of the following formulas is correct?
(A) mg(90 m) + 0 = 0 + ½mvB²
(B) mg(50 m) + 0 = 0 + ½mvB²
(C) mg(40 m) + 0 = 0 + ½mvB²
(D) mg(30 m) + 0 = 0 + ½mvB²
(E) mg(20 m) + 0 = 0 + ½mvB²



Which of the following free body diagrams correctly represents the forces acting on the car when it is upside down at point P?
(A) A
(B) B
(C) C
(D) D
(E) E

What is the weight of the car?
(A) 700 N
(B) 7000 N
(C) 700 kg
(D) 7000 kg

What is the magnitude of the NET force on the car?
(A) mg
(B) Fn
(C) Fn – mg
(D) Fn + mg

What is the magnitude of the car’s acceleration?
(A) 0 m/s²
(B) 28 m/s²
(C)[(28 m/s)² / (20 m)]
(D) 10 m/s²

What is the direction of the car’s acceleration?
(A) Down
(B) Up
(C) Left
(D) Right

Imagine changing the (still frictionless) track such that point B is still 50 m off of the ground at the top of a circular loop, but the circular loop has only a 15 m radius. What happens to the speed of the car at point B?
(A) It is smaller than before
(B) It is larger than before
(C) It is the same as before

Consider the same track with NON-negligible friction. What is true about the speed at point B now?
(A) It is smaller than 28 m/s.
(B) It is larger than 28 m/s.
(C) It is still 28 m/s.

How could we adjust the track with NON-negligible friction so that its speed at point B is the same as we calculated previously?
(A) Make the radius of the circle smaller
(B) Make the radius of the circle bigger
(C) Make point B closer to the ground
(D) Make point B higher off the ground

Fundamentals quiz based on the 2008 AP Physics B exam

This time of year, many of us who teach AP Physics are giving last year's free response as a practice test. Great... but don't stop there. Make your students correct what they got wrong.

Below is a "fundamentals quiz" based on the 2008 free response exam. I can't post the original questions due to copyright issues, but you can find them here:

http://apcentral.collegeboard.com/apc/public/repository/ap08_physics_b_frq.pdf

After my class took this test, and after they did corrections, I designed this quiz. All of the quiz questions speak to raw recall issues -- no problem solving, just general facts and techniques that must be memorized. Try this!


(a) Two blocks collide and bounce off one another. What quantities are definitely conserved? Circle all that apply.

Kinetic energy momentum velocity force

(b) What does it mean for a quantity to be conserved?

(c) Define an elastic collision.


2.
(a) When a problem involves two interacting objects, how many free body diagrams must be drawn in order to use Fnet = ma?

(b) When a problem involves a changing net force, kinematics cannot be used. What do you use instead?

(c) Which of the following expressions represents the net force on the right-hand block on the flat surface above? Choose one and explain

o 4.0 N - Fspring
o 4.0 N
o Fspring
o Zero

(d) The blocks in the diagram above move with constant acceleration. Are they in equilibrium? Explain.

3. There are three right hand rules for magnetism. State the equation associated with each, and what quantity the right hand rule is used to find.

EQUATION This RHR finds the direction of what quantity?
RHR #1
RHR #2
RHR #3

4. (a) A ball is launched at a 30o angle with a 15 m/s horizontal velocity. What is the initial speed of the ball?

(b) What is the speed of the ball at the peak of the ball’s flight?


(c) When is the equation P = Po + ρgh valid?

(d) Where is the pressure in this fluid stream largest? Choose one.
0 at the peak of the flight
0 at the fountain’s opening
0 when the water hits the table
0 none of the above, the pressure is the same everywhere

5. Consider the first law of thermodynamics.
(a) What does the variable W mean? How do you find it from a PV diagram?
(b) What does the variable Q mean? How do you find it from a PV diagram?
(c) What does the variable ΔU mean? How do you find it from a PV diagram?

6. (a) What kind of mirror(s) can produce either a real OR virtual image?
(b) What kind of mirror(s) can produce a reduced image?
(c) What kind of mirror has a positive focal length?

7. Which equation below can be used to calculate the kinetic energy of an electron? Explain briefly why the choice you eliminated is incorrect.

E = ½mv²
E = pc

Revealing test question topics

My AP class is ready to take the 2008 -- that is, last year's -- actual free response exam. We've been in real review mode for less than a week. That means that I've covered every possible topic on the exam, but the students are by no means confident yet. Everyone seems a bit overwhelmed by the sheer amount of material they need to know. That's okay, for now. In a month, after lots of targeted practice, they'll be fine.

Normally, when my students ask me what's on a test, I say "everything." Physics is a cumulative subject -- principles from earlier in the year, like force and energy, show up in every subtopic as overriding themes. But philosophically, I don't think I can say I've taught anyone physics if I give them license to forget anything that we covered more than a month ago.

A funny story that came out of my cumulative testing: one year a very bright student just wouldn't let this subject die. Chat kept asking me, "what exactly do we have to know?" He was concerned because a quiz had required the class to know that the period of the earth's rotation was 24 hours, a fact that -- gasp! -- I had not covered in class. "Do we have to know random stuff like that for the test?" He asked. I said yes. "How obscure is the information we have to know? You wouldn't ask us about, say, the gross national product of Tanzania, right?" I basically ignored that question. On the next day's quiz, everyone else got a set of straightforward multiple choice questions, while Chat's paper said, simply, "What is the gross national product of Tanzania?" He laughed with me, but I would have given him full credit had he answered the question correctly.)

A few years ago I took an idea from my history department colleagues. They occasionally distribute a list of possible essay questions before a test, and then use one of the possible questions verbatim on the actual test. The idea is, students will too often throw up their hands in despair if they are faced with studying for a broad spectrum test. But, if they have something concrete to prepare, they do much more work ahead of time, and that preparation is productive.

Now, I'm not going to give my test problems out ahead of time -- that would defeat the purpose of testing. Instead, in general physics I began announcing the general topic of each question. Even if all 7 questions covered every possible topic, the class felt better knowing exactly which question would cover which topic. They prepared in an organized manner. They entered the test with confidence, and performed well.

I state the topic of each question for every general physics test beginning with the first trimester exam. Of course, I have to be very careful not to fall into the trap of revealing too much. I do not not NOT want to be that teacher who says stuff like "I'd really suggest studying the coefficient of friction when a 20 kg sled comes to rest over a distance of 50 meters, hint hint hint. That might show up on the test." The test must be a fair evaluation of what the class knows and doesn't know. I don't believe I'm giving away anything by stating, for example, that they'll see a collision problem -- they should have been able to guess that themselves!

I've never given out the topics of AP problems, reasoning that the class doesn't get such a benefit on the May exam. But, for the first time this week, I tried announcing topics. The picture at the top of the post shows my whiteboard from this morning, when I foreshadowed the 2008 AP Physics B free response. I could feel some of the students' tension evaporating while I wrote -- "Ah, so I don't have to study circuits, they won't be there. Thank goodness." I was careful to point out that they will, in fact, be expected to understand topics that aren't covered this time; but we'll work on those things later. For now, my class is spending the evening watching basketball and reviewing just these seven topics. We'll see how they do tomorrow.

GCJ

Collaboration rules for AP problems assigned for homework

This time of year especially, I like to assign AP questions as homework. But when I do, the collaboration rules change.

Up until now, I've asked students merely to approach the problem individually, spending at least 5 minutes and showing me some kind of reasonable start. After that, collaboration is freely allowed and encouraged. I award full credit for a correct answer whether or not the individual work was on target.

Early in the year, I'm happy if someone merely copies the question and the diagram on his own; at least he's thought about the problem, and has context for the subsequent discussion with his friends. After a couple of months, I insist on a bit more... I start taking off unless the student does SOMETHING on his own, even if he's wrong.

Now, though, my students know how to learn physics. They no longer should be hesitant to approach a problem. Furthermore, an AP free response question always has several distinct parts -- if part (c) is hard, they should still be able to get full credit for parts (a), (b), and (d). Now is the time to practice this kind of approach to AP questions.

Throughout the school year, I nudge my class gradually toward becoming more independent physics students. Now it's time to take the final step. Many will be surprised how well they do on their own after relying on friends' input for much of the year. Others will expose blatant gaps in their knowledge; but they'll be forced to confront their lack of understanding, giving them incentive to figure out what they don't know.

Instructions for AP problems assigned as homework:

* Do the ENTIRE PROBLEM on your own before seeking assistance. Do NOT discuss the problem at all until you are completely finished. This should take no more than 15 minutes.

* If you make any changes, these must be in a DIFFERENT COLOR of ink or pencil. Cross out (do not erase) your original wrong work.

* You will earn full credit for your final answers, unless you fail to follow these collaboration rules.

GCJ

Teaching AP Physics? Then give AP tests.

People consider the AP physics exam difficult. Of course, “difficult” is a relative term. Difficult compared to what?

Usually students mean that the AP exam is tough compared with the tests they are used to taking in high-level math and science courses. The College Board agrees:

“Since the complete exams are intended to provide the maximum information about differences in student achievement in physics, students may find them more difficult than many classroom exams.” [p. 16, College Board’s AP Physics Course Description.]

A school’s grading scale usually requires a score of 90% or more to earn an A, and 80% or more to get a B. This requirement should not be onerous on tests that require simple recall. However, the AP exam demands so much more than merely recalling physics facts. On-the-spot problem solving is a far more involved skill than memorization is. Thus, on the AP-1 exam, 70% or so of the available points equates to a top score of 5; the average score nationally is below 50%. No wonder students think the exam hard – in their minds, even the very best students barely managed to earn a D.

Now, most physics teachers recognize the need to prepare their students for the rigorous nature of the AP exam. In April, they give their students practice exams. I submit, though, that giving normal, classroom-style tests all year followed by practice AP exams in April is a recipe for failure.

Imagine a college football team who plays a ten game season. The first nine games are against division-3 doormats, and the team goes 9-0. But, the last game of the year is at the university of Florida, a team sending half of its seniors to the NFL.

How should the coach get the team ready for the Florida game? Perhaps he arranges a scrimmage against Ohio State the week before. Is that going to be enough preparation?

Or, are the players going to be so intimidated at the vastly higher level of physical play that they hang their heads and give up the first time something goes wrong, that they begin to expect failure?

I submit that the only possible way this coach might have a prayer of beating Florida in week 10 is to schedule similar teams all year – even if the team’s overall record goes from 9-0 to 5-4. If the goal is to win the big game, the team must prepare for the big game from the start of the season, not just a week or two ahead of time.

Students who go through the school year from August to March getting 95% on their classroom tests have been conditioned as to what to expect on a physics test. Then, when they take an authentic practice AP exam in April, they are thrown for a loop. Even if they are capable of getting the 70% necessary for a top score, they may well hang their heads and give up 30 minutes in when they recognize that they aren’t performing nearly as well as they had on their classroom tests.

The solution, I believe, is to give AP-level tests right from the start of the year. Pick out authentic questions that cover the topics you have studied in class. Make the students work at the pace necessary for the real AP exam – approximately 1:20 per multiple choice question for physics C (1:50 per question physics 1), one minute per point for physics C free response (2 minutes per point for Physics 1). Then, grade the test on the AP scale! Somehow, whether it be through a curve or (as I prefer) by earning back points with test corrections, make sure that 70% or so converts to an A, 55% or so to a B, and so on based on the scoring from a released exam.

[Edit in 2016: Nothing wrong with giving items from the old physics B tests early in the year, and then moving the focus steadily from problem solving to explaining by integrating more and more physics 1 items.  Either way, you're using authentic AP items with available, external rubrics, on which 90% is essentially unattainable.)

Sure, you’ll get complaints before and after that first test. Everyone will come out thinking they failed, thinking they’ve never seen a test that hard. But, when they see their actual grade, when they get a chance to correct their mistakes and earn credit for those corrections, when they recognize that they are NOT going to fail the exam, they’ll relax. About halfway through the year, AP-style testing will become routine.

The proof is in the pudding. I don’t have geniuses in my class by any stretch. Yet, on the AP-style trimester exam consisting entirely of authentic questions from previous APs, 17 of my 25 students earned 5s, and everyone got 3 or above. They’ll do even better in May. I am thoroughly convinced that my class’s success is not as much due to my teaching skill as to the fact that I make them comfortable with the level and style of the exam throughout the year. Try it. It works.

GCJ

The Jacobs Crusade – NO QUESTIONS DURING A TEST!!!

I refuse to answer questions during a quiz, test, or exam.

Why am I so cruel, you ask? Or, at least, students, parents, and colleagues ask. Thing is, by mid year, no one complains about the “no question” rule. And my colleagues are occasionally envious.

I want to know what my students can do on their own. Daily interaction and coursework provides plenty of opportunities for students to talk to me and to each other, to figure out how to approach the types of problems the class covers. The purpose of a test is for my students and me to see how successful they have been in learning the material. And I can’t effectively evaluate my students or my teaching unless I get an authentic account of each student’s ability.

Think about what kinds of questions students tend to ask during a test…

-- “What is this question asking for? How do you want me to answer?”

This student may be truly confused by the wording of the question; or, the student could be stuck and hoping for a hint. Either way, this is an inappropriate question. I make sure that homework problems are worded in the same style as test problems, so that there should be no surprises on the test. Homework is the time to learn vocabulary, and to get in tune with “what the problem wants you to do.” And if the student is stuck, well, then the test has served its purpose – it’s exposed a portion of the course that the student does not understand yet.

Besides, how am I supposed to answer this? Tell him to read the question again? Or, am I supposed to just solve the problem for him? I don’t think so.


-- “You didn’t give us enough information to solve this problem.”

Well over 90% of the time when this question comes up, the test problem is just fine… it’s that the student is approaching the problem incorrectly. For example, in a conservation of energy problem, the mass term often cancels; an object’s mass is not a necessary piece of information. Recognizing that the mass cancels is a physics skill, one that I often test. But if students are allowed to ask why I didn’t give them the mass, then part of the purpose of the test problem is eliminated!

So what about that rare instance when you should have given an object’s mass, but didn’t? Shouldn’t people be able to ask about that?

No.

Before the first test of the year, I prepare my classes for just this kind of situation. I tell them that if they think I screwed up by not giving them critical information, then they should tell me so in writing on the test… then they should continue solving the problem by making up a reasonable value. There’s nothing wrong with someone writing, “You didn’t tell us the mass of the roller coaster! So, I’m going to pretend it’s 500 kg.” This student will be in good shape… even if he was supposed to solve for the mass some other way, he can still get partial credit for finishing the problem. And, if I truly screwed up, then he’s demonstrated enough knowledge to earn full credit. Most importantly, he hasn’t distracted the entire class with his question.

-- “You made a typo here. You said, ‘find the nass of the roller coaster.’ Did you mean ‘find the mass of the roller coaster?’ ”

This sort of question makes me livid. Do you want me to take off every time your writing is unclear, or every time you make a minor grammatical error? You distracted the entire class for the express purpose of saying, in effect, “Na na na na boo, boo, teacher screwed up!”

Once again, pre-test preparation can prevent this sort of one-upsmanship. Make it clear from day one that you don’t mind any sort of WRITTEN comment on the test. If a student wants to write how awful a question is, or to criticize my spelling or syntax, more power to him, as long as he does it in writing. In fact, I often give long, detailed, polite responses to reasonable criticisms written on a test.

Most importantly, of course, if the student happens to be right about a poorly worded or ambiguous question, I’ve got to be fair in my grading. Once in a long while I just throw out a part of a question, or give a huge variety of answers full credit, because I realize later that the problem wasn’t good to begin with.

In fact, just today someone told me (after the test was over) that multiple choice question #18 included two identical answer choices. It turned out that those choices were wrong, so no one cares. But if the identical choices had been correct, I would have at least counted either choice right, and possibly thrown out the entire question because of the confusion my mistake caused.

But no one asked during the test. All of my students got 120 minutes of silence in which to do their work. I got some grading done. This time of year, if I’ve done my job right, a trained orangutan could administer my tests. And that, I think, is the way things should be in high school.

Where do you find good multiple choice questions?

Yesterday I described my nefarious scheme for getting students to study for the trimester exam by means of a multiple choice extra credit exercise. I also indicated that the multiple choice portion of the AP trimester exam will include 23 multiple choice questions. During the trimester, I give multiple choice quizzes two-three times a week. And you will find out soon that, next month, my AP class will be plowing through many, many multiple choice exercises in preparation for the May AP exam.

You will find that I BELIEVE in the utility of a well-constructed multiple choice item to evaluate students’ understanding of physics concepts, and to help students confront their own misconceptions. Sure, many physics skills are better tested with free response items; I willingly concede that if the majority of your assessment is done with multiple choice, you get a biased account of a student’s physics ability. Too often, though, teachers and administrators dismiss multiple choice merely as the first and last resort of a lazy instructor.

Such is the pejorative connotation of multiple choice that when I was the first Woodberry teacher to acquire a scantron machine, I hid it in my office in order to avoid the inevitable soapboxing from my colleagues outside the science department. The machine is still in my office… but after eight years it’s become an open secret. At exam time I willingly help out the rebels from humanities departments who sneak down to use the machine.

Now, don’t think that I’m encouraging slack teaching. In order to be useful, a multiple choice question must be well-constructed. Writing good items is not a trivial exercise, as I’ve discovered numerous times. Not much is more embarrassing than going over a quiz in which the correct answer doesn’t appear in the choices, or in which the answers are not clearly different from one another. Initially, the front-end work necessary in finding or writing multiple choice questions cancels out the back-end work saved by grading via scantron machine.

(As an aside, my English department colleague El Molé invented the principle of conservation of exam workload – in writing an exam either you have to spend enormous time writing multiple choice or grading essays. The total time spent on the exam process is conserved regardless of how the exam is structured.)

Perhaps I’ve convinced you of the utility of multiple choice. Multiple choice practice might be useful and wonderful, but this post begs an obvious question – where in the heck do you find enough good multiple choice items for use in your class?

That’s a tough one, but I have a few suggestions. First of all, get good at evaluating the quality of an item. When you assign a question on a test or quiz, rewrite it immediately or throw it out if it didn’t work quite the way you thought. When you happen to see a good question somewhere, write it down before you forget.

The best source of multiple choice items is the College Board itself. A number of full-length AP exams have been released. Go attend an AP physics workshop, contact an AP physics consultant, or go to collegeboard.com and look for released exams. (Neither I nor anyone else is allowed to post content directly from an AP exam, as that would infringe on the AP program’s copyright and a plague of lawyers would descend upon me.) The College Board also writes the SAT II physics test, which consists of well-written and vetted multiple choice questions. Take a look at a sample test and use some of those problems.

I do not recommend most commercial AP or SAT II preparation books. It’s rather pathetic how out of touch most of these books are with the level or content of the exams, or sometimes even with what physics is all about. Similarly, I strongly recommend against fly-by-night companies such as the ubiquitous “D&L marketing” who send flyers peddling AP physics multiple choice tests.

Two books, though, are in fact useful. One is my own, 5 Steps to a 5: AP Physics B & C by Greg Jacobs and Josh Schulman. Yeah, I had better recommend my own book. One other good source is the older book published by Kaplan, written by Connie Wells and Hugh Henderson. Connie and Hugh are both AP readers, both former members of the Test Development Committee (the group that writes the AP test each year), and both should be on any list of the top 10 physics teachers in the USA. It’s worth finding a copy of the Henderson/Wells book – the newer Kaplan book has different authors, and I have not evaluated its quality.

Each year the American Association of Physics Teachers sponsors the Physics Bowl, a 40-question multiple choice contest. Old tests from 1994-2000 can be found at the PSRC website. Some questions are good, some aren’t, some won’t cover the topics you want; but one way or the other, Physics Bowl questions are an awesome resource.

The AAPT sells CDs of Physics Bowl tests and solutions from 2001-2007. They also sell a couple of other multiple choice tests on CD. These are worth the money.

If you’re looking for below-AP level multiple choice, a terrific source is the National Science League. Their contest is rather silly – my top 10 students in AP physics would have no excuse not to get a perfect score. But for my GENERAL physics class, the NSL test provides solid review questions. I’ve been buying this contest each year for a decade now, and so I have a large bank of basic questions for lower-level students.

Got a good source for multiple choice questions? Post a comment.

GCJ

Preparing for the Trimester Exam

It’s nearly trimester exam time! In AP physics, my 2-hour trimester exam will consist of 23 multiple choice questions in 30 minutes, followed by a full-length 90-minute free response section consisting of authentic AP exam questions. The general physics exam is an eight question free response test designed to be 2 hours long (but I allow three hours for everyone). The exams will, of course, cover everything we have discussed all year.

(Students always wonder if the exam will be cumulative… why wouldn’t it be? Why did I bother to teach back in October if you’re just allowed to forget what I taught you? Are you saying that the material I taught isn’t worth remembering? And in AP physics, the May AP exam is cumulative, so I would be doing you a disservice if every test were not cumulative. Now quit asking silly questions.)

With the exam upcoming, prepare for a series of posts about exams. Today, I discuss exam “review.”

I refuse to enter into conversations about what specifically will be on the exam, or to run a “review session.” If I’ve been doing my job, and if students have been paying attention, then exam preparation should be nothing special. Daily homework, quizzes, and discussion are exam review.

Woodberry holds a “consultation day” before each exam period, during which teachers hold court in their classrooms, and students can visit whomever they want to ask questions. I don’t want consultation day to degenerate into “so, want to tell me what’s on the exam?” But I want to encourage my students to stop by. I dangle bait for my class in the form of extra credit.

Yesterday I distributed a sheet with 20-30 multiple choice questions (a different sheet to AP physics and general physics, of course). The extra credit assignment is to do these questions if they were a test – no books, notes, or collaboration. Then, on Sunday’s consultation day, they can come to my classroom to scan their answer sheet. Showing up on Sunday is the first requirement for extra credit.

The second requirement is corrections. For each question they missed, they must explain how to get the correct answer. Corrections must be done on the sheet displayed to the right. (I hope the quality is good enough to read... if you want a ms word version of the sheet, email me.) The standard of evidence for the correction is high – if they don’t thoroughly convince me that they understand the problem, they don’t get credit. The corrections are not due until next Thursday’s exam; but, since collaboration is allowed and encouraged on the corrections, most students stick around on consultation day because so many folks are around to discuss the problems and to help each other out.

Students appreciate my approach, and not just because they get extra credit. Think about how your students will prepare for a physics exam. OCD-style students might think that they must study for hours… and those hours are too often unproductive. Lazy students might not normally prepare at all. But the extra credit multiple choice assignment helps both of these student phenotypes. The exercise helps the OCD folks focus their studying, so that either (a) the questions they missed inform them about what topics need special attention, or (b) they feel like they’ve studied, and so they don’t waste any more time preparing for the exam. As for the lazy folks, the extra credit might well lure them into doing something when they might otherwise have done nothing.

If nothing else, just getting my students physically in my and each others’ presence is a productive exercise, because conversations invariable turn to physics. Extra credit can be an amazing attractor. (I note that food often works as well. First trimester consultation day is well known as Nacho Day in the physics classroom. I sometimes wonder whether the ample supply of official Nacho Man Nachos or the extra credit does a better job of bringing in the sheaves.)

GCJ

(Picture at the top courtesy of falconsscience.wordpress.com.)

Know your fundamentals

Pitchers and catchers have reported to spring training. Woo-hoo! Spring is just around the corner, as is spring break here at Woodberry. My family will be heading to Jupiter, Florida, where the St. Louis Cardinals hold their camp. The Nachoboy, my almost-six-year-old, has decided that he is a Cardinals fan, mainly because he could recognize the bird on their uniform since he was about two.

What will the Cardinals be doing in Jupiter, and what relevance does that have to a physics blog?

The Cardinals will be drilling their fundamentals – pitchers covering first base, ground balls to the infield, cutoff throws from the outfield, and so on. You know, the same things that the middle school baseball team works on at practice. Sure, the Cardinals are professionals, and are some of the best ballplayers in the world. Yet, they still work hard on their fundamentals.*

Advanced physics students may not think they need to drill physics fundamentals, but they often do. Simple recall of equations, units, and definitions can lead to stronger test scores. Drill must be handled carefully, though. On one hand, advanced students will turn off instantly if they feel they are being made to do “busy work.” On the other, less-than-advanced students must not be made to think that success in memorizing formulas is equivalent to success in truly learning physics.

The balance I have struck is never to include recall-style questions on homework assignments, but to give regular “fundamentals quizzes” in class. These recall quizzes are weighted heavily in the students’ grades; I also give rewards such as pieces of candy or exemption from future work to those who do well on fundamentals quizzes.

Since my AP class is preparing for their trimester exam next week, I thought it a good time to hit the fundamentals quizzes hard. The 45-minute lab portion of today’s class was devoted to fundamentals. I had four 10-question quizzes prepared. Everyone took the first quiz; the students traded and graded. (I certainly did not provide a key… they had to look up and/or argue about anything they weren’t sure of.) Anyone who got 9/10 or better could leave.** Everyone else got to take the second quiz, and so on and so forth.

As it turned out, 4 of 15 students got to leave early. Everyone else got the benefit of taking four different fundamentals quizzes. I have no doubt that these folks are much better prepared now for next week’s exam.

Below is a typical fundamentals quiz, for which I allot 5-7 minutes. In a future post I’ll make some suggestions about how to write your own fundamentals quiz.

* And, some would say professional ballplayers should work even harder on fundamentals, especially if they’ve ever watched the Cincinnati Reds defense.

** Leaving early from lab is a major perk, one that has not yet been extended to anyone in the class this year.

1. Two masses are connected by a string over a pulley. How many free body diagrams do you make?



2. A car smashes into a tree. The driver of the car is not held in place by a seat belt or any other restraining device. Just after impact but before the driver hits any part of the car:
(a) How do you know the driver’s velocity?

(b) How do you know the driver’s acceleration?


3. A block of mass m slides down an incline of angle θ . What is the component of the block’s weight parallel to the incline?

4. Write the ideal gas law. What are the standard units that should be plugged in for the P term?

5. Which of the following quantities is always conserved in a collision? Circle all that apply.

Velocity
momentum
acceleration
kinetic energy


6.
(a) Where is the velocity of an oscillating mass on a spring largest? Circle one.

At the equilibrium point
at the maximum displacement
(neither of these)

(b) Where is the acceleration of an oscillating mass on a spring largest? Circle one.

At the equilibrium point
at the maximum displacement
(neither of these)

7. A wire carries a current I to the left. What is the direction of the magnetic field at point P?

P.


I

8. What is the equation for the magnitude of the magnetic field produced by a wire?

9. What is the equation for the magnitude of the magnetic force on a wire?