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30 April 2014

Mail Time: Will calculators and equation sheets be available on the new AP Physics 1 and 2 exams?

Ryan Mitchell writes in:

Hi Greg... Question about the new courses: My understanding is students will be allowed to use the equations and constants/conversions sheets on both MC and free response sections of the AP1 and 2 exams…

That is correct.  Calculators, too, will be allowed on both sections.

 No more memorization of equations. Is that correct?

Well, I'd personally go the other way... with so much less material, and so much less emphasis on calculation, I will have a heightened expectation that my students know fundamental relationships cold.  A smart student who hunts and pecks equations can get a 3 on the AP Physics B exam; such a student will definitely, without question earn a 1 on the new exams.  

My own preference would have been for the College Board to eliminate the equation sheet and calculator entirely.  But they (quite reasonably) want calculator access, even if students only need it three times on the whole exam; and once calculators are allowed, they want to provide the equation sheet so students who program their calculators won't have an "advantage."  I don't agree that a programmed calculator is an advantage, though... I think it's a disadvantage, because such a student will tend to rely on formulas and numbers rather than on reasoning, understanding, and verbal communication.  

The new 5 Steps book (available end of June) has an entire chapter devoted to these sorts of issues.  I think that success on the AP Physics 1 exam will be in inverse proportion to the number of times a student grabs his or her calculator.

Good luck...


25 April 2014

A spring that's both stretchable and compressible

At the recent AP Physics consultant powwow, I heard great ideas from about twenty really good physics teachers.  At one point we discussed all the many investigations that can be done with just a class set of springs and masses.  But which springs do you want?

The PASCO equal length spring set is great, if expensive.  It requires using heavy (500 g or more) masses; but the advantages are the equal length, durability, and the clearly stated spring constants.  The PASCO dynamics track spring set is my preference for most student experimental work, due to its utility with smaller (~100-200 g) masses.

The main disadvantage of these spring sets is that they do not compress -- they only stretch.  In their resting state, the coils touch.  It's often tough to demonstrate or show experimentally that Hooke's law (F = kx) is valid for both stretching and compressing.

A fellow consultant -- I forget who, but it might well have been Miami's own David Jones -- suggested purchasing springs from McMaster-Carr.  In particular, he suggested the spring pictured above.  It has a spring constant of 1.9 pounds per inch; a moment's googling makes that 330 N/m, or much stiffer than most of the other classroom springs I own.  But I've always wanted a compressible spring, and this one fits the bill.  I don't doubt that one could scour the McMaster-Carr catalog to find a compressible spring with a smaller spring constant -- if you find one you like, please let me know.

The best part about this spring is the price -- $6.50 for a pack of 12, plus shipping.  I bought a pack for each of our physics teachers as a gift.  Most people want chocolates, flowers, or the like as gifts... me, I'm happy with a bag o' springs.

15 April 2014

AP Physics 1 and 2: What raw score will be necessary to earn a 5? (Update July 2015, see comments)

Okay, that's the question of the year for 2014-15.  For decades, the raw score to AP score conversion on the Physics B exam has been relatively consistent -- in the neighborhood of 65% for a 5, 50% for a 4, 35% for a 3, 25% for a 2.  I've used those cutoffs in my own class on each of my monthly tests.  Sure enough, students who consistently earn what I call "5s" on my in-class tests tend to earn 5s on the actual AP exam.  

But what's going to happen on the new AP Physics 1 exam?  The style and structure of the Physics 1 exam is substantially different from that of the Physics B exam.  We have no word from anyone at ETS or the College Board about how the score cutoffs might look.   

The actual score cutoffs will be set by a complex data mining process involving statistical wizards at ETS and a committee -- not the test development committee, a different committee -- of high school and college physics teachers.  A College Board representative described the process briefly to the consultants at our weekend meeting.  I didn't quite follow all the details.  Suffice it to say, it's a statistically rigorous process, but one that can't be gamed or anticipated.  We will not know anything real until the summer of 2015, after the first exam adminstration.

So how should an AP Physics 1 teacher set expectations in class this year?  That's going to require a significant amount of guesswork.  We teachers have only a few data points to guide us.  

The first set of data is the previous years' physics B and C exams.  The physics B exam changed significantly in its emphasis in the mid 1990s; yet the cutoff for a 5 remained around 60-65%.  Physics C contains two completely different courses and exams.  Physics C mechanics cutoffs in the 1980s and 1990s were about 10% higher than the E&M cutoffs; since the mechanics exam added more experimental and conceptual questions, and since it placed more emphasis on calculus-based problems in the free response problems, that gap has lowered to essentially nothing in the last two released exams.  On either exam, you now need in the neighborhood of 53-58% to earn a 5.

The AP Physics exams have changed gradually and organically through the years, but the redesign to the new AP Physics 1 and 2 courses will be seismic and unprecedented. 

Um, wait... not unprecedented.  The College Board did a similar redesign of the AP Biology course for the 2013 exam; and of the AP Chemistry course for the 2014 exam.  The 2013 AP Bio exam has been administered and scored.  While biology is a completely different animal from physics, perhaps we can draw some lessons in how the cutoff scores changed from 2012 to 2013.

In 2012 (before the redesign), the score cutoffs for AP Bio were:
5 73%
4 63%
3 55%
2 46%

In 2013 (on the redesigned test), the score cutoffs for AP Bio were:
5 77%
4 62%
3 45%
2 25%

Now that I've seen these, I better understand what bio teachers have told me about the new test.  They say (and the College Board confirms) that far fewer students earned 5s on the new exam, far fewer students earned 1s, but more people scored in the middle of the distribution.  That could be a result of the new style and content on the exam, but it could also -- and in my mind, more likely -- merely be a consequence of the higher cutoff score for a 5 and the way, way lower cutoff score for a 2.  We'll see in August whether the AP Chemistry redesign produces a similar scrunching of the bell curve.

To summarize:  Physics B cutoffs have been consistent over decades.  Physics C cutoffs recently have been consistently a bit lower than physics B cutoffs.  The redesigned AP Bio test raised a wee bit the cutoff for a 5, but substantially lowered the cutoff for a 2.

What should you do?  What am I going to do?

Not sure yet.  My gut is still telling me to stick to my current cutoffs for the first year, because these will be close enough.  I do like using cutoff scores that are easy for students to remember: 65%, 50%, 35%, and 25% are nice round numbers. I'll let you know if I end up changing my approach.  

12 April 2014

Multiple choice question: "evaluating claims" about impulse

John and Bob, both of mass 70 kg, each drop on to a scale from the same height. Which of the following explains why they both experience the same impulse in the collision? 
(A) Both start at zero speed before they jump, and both end at zero speed after they jump, so both change momentum by the same amount. 
(B) Both have the same mass, so both experience the same force; both were in the air for the same time; and impulse is force times time. 
(C) Conservation of momentum says that the change in one object’s momentum is the same as the change in another object’s momentum in a collision. 
(D) Since they dropped from the same height, they each have the same speed before hitting the scale; they both come to rest after hitting the scale; since their mass is also the same, they change their momentum by the same amount during the collision.

A good number of questions for the new AP Physics 1 and 2 exams will ask students to evaluate claims, to identify features of correct and incorrect physics reasoning.  Above is a question in the style of an AP Physics 1 multiple choice question.  But where did I get the idea for it?  And how do I use it in my class, other than just asking it on a test?

I've had my class do this "bent legs/straight legs" problem in several different incarnations.  You might know it as the airbag problem, or the catcher's mitt problem... when something comes to rest, it experiences less force when the time of collision increases.  This can be understood through kinematics and Newton's second law, or through the impulse-momentum theorem.  I prefer to use the latter approach, particularly when we're studying impulse and momentum.

In class, I walk students through the bent legs/straight legs problem in stages.  The first stage question is, "Which of the variables in J = Ft is the same no matter how your legs bend?"  That's a tough one in the first couple days of studying impulse... 

The most common incorrect answer is "Force is the same either way" with some spewed non-physics baloney.  My response is to ask them to jump off a 10-foot wall and to land with straight legs.  "No, that would hurt," they say.  "No it won't!  You said that the force on your legs is the same however you land!"  But this is a mistake stemming from of a lack of understanding the problem, or of laziness of thought.  Since no real physics is involved, this is not a true physics misconception.  

The misconceptions come when they try to justify why the impulse is the same in both the bent leg and straight leg case.  Consider each of the three incorrect choices (A), (B), and (C) in the problem above.

(A) Some correctly use the fact that impulse is change in momentum.  Problem is, they consider the change in momentum from when they begin their fall to when they finish the jump.  No!  The equation J = Ft should be used in a collision:   J is the change in momentum from the collision's start to the collision's end.  Sure, they dropped from rest to the ground before the collision, but that doesn't mean that the momentum immediately before collision is zero.

(B) Others try to use J = Ft to explain why the impulse remains the same.  Again, they conflate the collision with the time in the air before the collision.  The time of the fall is the same no matter how students land; the force of the earth on John and Bob is the same while they are in the air, because they have the same weight.  That means that the impulse on John and Bob is the same while they are in the air.  But the question asks about impulse in the collision.

(C) Aargh!  Conservation of momentum states that two objects have the same TOTAL momentum before and after they collide with each other.  John and Bob are not colliding with each other, they're colliding with the Earth in separate collisions.  Conservation of momentum means that any momentum lost by John in the collision is picked up by the Earth.  That doesn't help compare the impulse on John and Bob.

I gave this question on a test; most of my class got it right, because we had gone through this reasoning enough in class.  Those who got it wrong were asked to write a correction.  Most just restated the correct choice (D) in their own words.  I told them that's not good enough -- they had to explain why the answer they originally chose was incorrect.  

So much of good physics teaching is about picking at every detail of a problem until students can not only come to the correct answer, but until they can articulate every bit of reasoning that goes into the solution.  And so much of the new AP Physics exams will be questions requiring just this sort of articulation.  You want to write a good AP Physics 1 question asking for an evaluation of a claim?  Write down three incorrect student responses on a conceptual homework problem, add in the correct response, and voila: Physics 1 multiple choice question.

03 April 2014

Landing knees-bent or knees-locked -- use a video

One of my impulse-momentum theorem exercises is to predict which applies more force to a person: jumping off a chair and landing knees-bent, or jumping off the chair and landing knees-locked.  Each student makes and justifies the prediction, then jumps onto a force place to experimentally verify the prediction.

To guide the students through the prediction, I start by asking which variable in the impulse-momentum theorem is the same for both cases.  That's actually a tough one.  Even though I've already explained that the point of the exercise is to determine which case delivers more force, a bunch of students tell me the force term is the same for each.*

* My response is to ask them to keep their legs locked as they jump off an 8-foot high fence.  After all, the force on your legs should be the same either way... [student retreats sheepishly]

The more common and more understandable mistake is for students to tell me that the time of collision is the same.  Usually, this stems from a misconception of what the t term in J=Ft means -- they correctly state that the time for the person to fall from the chair to the force plate is the same regardless of how the person lands. Sure... but the t term isn't just any old time, t represents the time of the collision.  Anything that happens before the collision isn't exactly relevant to the impulse-momentum theorem.

But I do have a number of students who consider the collision, and state to me earnestly that they believe that the time of collision doesn't change either way -- it's the same surface, the same person, the same speed before collision.  I need to address this incorrect reasoning without appealing to my authority as teacher.

We recently downloaded the "Coach's Eye" app on some ipads, and we had used this app in class a while back.  So I asked a couple students who were struggling with the time of collision issue to make two videos of Trevor jumping onto the force plate -- one with knees-bent, one with knees-locked.  They managed to record these videos in about three minutes.  (Wow, I love modern technology.)

The app allowed me to run the video frame-by-frame with a stopwatch superimposed.   All the rest of the day, whenever a student struggled with the idea that the knees-bent case resulted in a longer collision time, I showed him the video.  I had him advance the frames to show that the knees-locked Trevor took about 0.10 s to land, and the knees-bent Trevor took more like 0.40 s to land.  That ended the argument about whether the time of collision was or wasn't the same... then I could visually show the instants before and after collision to help the students understand why the impulse -- i.e. the momentum change -- must be the same for both Trevors. 

01 April 2014

Daily quiz about momentum concepts -- why I asked each question

Each day in 9th grade physics we begin with an 8-12 question quiz.  I usually write these the night before -- I wait until I've had all my classes and graded all the problem sets before I decide what needs to go on the quiz.  Sure, sometimes I'll reuse questions from previous years.  But many of the questions are invented on the spot.  They're targeted to bust a misconception, to make a point about a common mistake on a problem set, or to reinforce a discussion from class.

Below are the ten questions from tomorrow's quiz.  I'll explain what led me to ask each one...

On today's problem set, I asked: "Momentum is conserved in a collision.  So, how is it possible for a cart to collide with another cart and change its speed without changing its mass, too?"  A whole bunch of folks gave answers that implied that speed was conserved in a collision.  Others missed the point of the question entirely.  So the first few questions on today's quiz are targeted toward understanding the conservation principle, that a single object can change momentum, but the total momentum must remain the same.

1.      True or false: In a collision, the total momentum of two objects is conserved.  My students all know this, virtually everyone will get this right; but they don't read carefully.  I think they skim over the "total momentum" part, and read, "In a collision, blah blah blah conserved."  Hence the next few questions.

2.      True or false: In a collision, the total mass of two objects is conserved.  This one is a "synthesis" question rather than a "recall" question.  These other true-false questions can be answered with straightforward reference to facts I've handed out on a fact sheet or to discussions we've had in class.  However, I've never explicitly discussed conservation of mass.  Here I'm asking the students to apply their understanding of the word "conserved" to a different situation.  I don't expect more than half the class to get this right.  Why do I ask, then?  The discussion of the general principle of a conservation law will be effective in the context of this quiz question.  If I would instead say, "listen up while I talk about conservation laws," no one would pay attention.

3.      True or false: In a collision between two objects, any speed lost by one object must be gained by the other.  I have discussed how a consequence of the conservation of momentum in a collision is that both carts change their momentum by the same amount.  As with question 1, I don't believe my students are reading or listening carefully:  I think they are internalizing "anything lost by one is gained by the other."  I'm checking in several different ways whether they recall that momentum, not speed, is conserved.

4.      True or false: In a collision, the total speed of two objects is conserved.  Same as #3, just with different language.

5.      True or false: In a collision between two objects, any momentum lost by one object must be gained by the other.  This is the alternate statement of momentum conservation that I've discussed repeatedly.  Although this is a straightforward statement, recognizing it as true requires two minor steps of reasoning:  (1) recognition that this is a restatement of "total momentum does not change in a collision" and then (2) recognition that it is total momentum, not speed, that remains unchanged.

6.      True or false: In a collision between two objects, the amount of impulse on one object is the same as on the second object.  And now I've added a third step from the reasoning in the previous question:  Impulse is change in momentum, so this statement is a restatement of #5.

7.   A 2 kg ball slows down from 3 m/s to 2 m/s.  Calculate the impulse on the ball.  When I give this quiz, we will have studied collisions for more than a week, but impulse for only a day.  I know the students are still struggling with the idea of calculating a change in an object's momentum.  They tend to simply calculate a momentum, and call it "impulse."  Or, they subtract one object's momentum from another object's momentum and call that "impulse."  I want to guide them to the habit of calculating a single object's initial momentum, its final momentum, and then subtracting to find the momentum change.

8.      True or false: two identical objects that fall from the same height must experience the same force during the collision with the ground.  Word for word what someone told me today on an in-class lab problem.  The counterexample is to ask a student to jump from his desk with and without bending his knees.  Since he didn't hurt himself with bent knees, if this statement were true he should be able to land stiff-legged without damage.

9.      True or false: two identical objects that each collide with the ground for the same amount of time must experience the same force in the collision.  Also word for word from a student.  By this rationale, since a belly-flop onto a gym mat from six inches is safe, a belly-flop onto a gym mat from the roof should be equally safe.
10.  A 4 kg object is moving 2 m/s when it collides with the ground, stopping after 0.05 s.  Calculate the impulse experienced by the object in the collision with the ground.  My students know that impulse is both change in momentum and force times time.  The misconception here is that the "force" in the impulse-momentum theorem is just the weight of the object.  No!  The relevant force is the contact force between colliding objects.  I know darned well that half the class will see the time interval, and grasp at straws to find a force: "Oh, 4 kg has a force of 40 N," they'll say.  I'm using this problem to make the point that they can't make up forces.  Rather, if J=Ft isn't useful, use impulse = change in momentum.

I'll give the class four minutes to do these ten questions; then I'll have them grade someone else's paper while I explain the answers.  I doubt more than one student in each section gets all of them right.  So what.  This quiz, like all daily quizzes, isn't really, actually an evaluative quiz.  Rather, it's a means for getting my students to articulate what they think about momentum concepts, so that a discussion about those concepts is meaningful, in-context, and memorable.  While I can't guarantee that this quiz will lead to perfect understanding of momentum concepts, I can guarantee that going over this quiz is substantially more effective than a lecture or a reading.