23 December 2010

The pejoritive connotation of the word "homework"

Bad dog from discoveryeducation.com

What does the typical American think of upon hearing the word "homework?"  While I have no psychomological evidence of this, I suspect that the word is generally considered to be synonymous with "rote drill," and has a profoundly negative connotation.  On one hand, this is silly -- homework in any subject does not have to consist merely of rote drill. 

(What's wrong with rote drill, anyway?  I don't see the National Association of Music Educators campaigning to stop making violinists learn their scales; I don't see the National Association of Football Coaches minimizing the importance of conditioning, blocking, and tackling drills.  Done properly, and with the correctly limited scope, rote drill at any level of any subject is an important part of learning.  Anyway.  Ahem.)

Physics homework in particular does not, or at least should not, generally consist of rote drill.  Homework problems are used for practice, sure, but students are practicing the skills of creative problem solving, they're practicing to eliminate their crazy misconceptions, they're practicing their ability to explain concepts with reference to a relevant equation... Doing the homework, and moreover doing homework problems seriously and carefully and correctly, is an integral part of learning physics.

Nevertheless, students do not always take homework seriously.  In some upper level physics classes in particular, these very smart students say, I don't need to practice, I can just perform on the test.  (Then they perform poorly on the test because they didn't practice, and they say physics is just too hard.)  How do we get students to pay attention to homework?

Well, it starts (but does not end) with the homework grade.  I put a score on homework problems every night or two.  This score explicitly counts for 30% of students' course grade.  Of course, even with that explicit carrot, my lower level students do not pay appropriate attention to the homework.  They turn in hastily done crap, then just sigh when they see that their answer was wrong.  It never occurs to them to check BEFORE class whether their answers were correct; it never occurs to them that it would be a good idea to understand WHY their answers were wrong.  So the grade itself is a necessary but not sufficient motivator.

At a Virginia AP physics workshop, a teacher reported that he was forbidden by his administration from counting homework more than a token amount toward the course grade.  While I stared open-mouthed in a state of flabbergastation, others chimed in that they were under the same restriction.  But one clever physics teacher in my workshop had a solution...

I don't call my assignments "homework" precisely to avoid the negative connotation.  I use the phrase "problem sets" or "nightly problems," and I regularly make the comparison to the English essay -- I'm asking for the equivalent of a couple of well-written paragraphs every night in an English class.  The woman in my workshop took my phrasing and analogy a step further.

"Just call the homework an 'assessment'," she said.  "English teachers are allowed to count a series of take-home writing assignments as equivalent to a test.  So, we do the same thing.  These problem sets are the precise equivalent to a writing assignment, so they will be counted just as the English department counts them." 

And perhaps that trick might help the students as well as satisfy the clueless administrator.  If a student hears "this counts as a test," his effort seems to double.  I've noticed that students will repeatedly make the same kinds of mistakes on homework problems, but if they get the same exact question wrong on a "quiz" in class, suddenly they start remembering.

Why does the psychology of "homework" seem to work against the legitimate goals of nightly assignments?  I don't pretend to know.  All I can do is make the observation, and then use the observation to the benefit of my class and my students.


22 December 2010

Quiz -- elecric fields introduction

Electric Field Pic from thefullwiki.org

I introduce electric fields in an unusual way, one that's not consistent with any textbook. 

Most textbooks start with Coulomb's law for the force between two point charges.  Then, eventually, they define the electric field as the force per unit charge on a "test charge" in the field.  This is of course correct, and consistent with the way many seasoned PhD physicists think of the electric field.  Try explaining this to a 17 year old in his first physics class, though -- you might as well try to explain the infield fly rule to someone who's never seen baseball.*

* The infield fly rule is a closed book to many actual baseball players and coaches, too -- trust me, I'm an umpire.

I've found much more success presenting the concept of the electric FIELD as primary.  We begin with a full day's class on nothing but F=qE and the definition of the electric field.  And F=qE essentially *is* that definition.  F=qE gives the magnitude of the force on a charged particle in an electric field.  This force is in the same direction of the electric field for a positive charge; the force is opposite the electric field for negative charges.

Those ideas seem so, so basic... but it takes nearly a week of practicing before my students figure this out.  What do they do wrong?  Everything. 

* Label a point in space "point P," and say explicitly "There is nothing at point P but empty space, but the electric field at point P is 200 N/C to the right."  Then ask a student point blank:  "Is there a charge at point P?"  "Is point P positive or negative?"  "What is the force on point P?"  Merely getting folks to agree that a position in space does not have mass or charge, and cannot experience a force, is a MAJOR challenge.

* Now, put an electron at point P.  Verify with the class that an electron has a negative charge.  Ask about the direction of the electrical force on the electron.  Half the class will get this wrong... even though you just told them the rule about charges and electric fields!  Try it.  This is more complicated than you might think.

* No matter what you do, students will be confused about negative signs.  I tell them again and again: IGNORE NEGATIVE SIGNS when dealing with electric fields.  Neither a field or a force can be intrinsically negative.  Use F=qE to determine the amount of a force or field; then use the rule about negative charges to determine a relevant direction.

* The electric field does not determine the direction of a charge's MOVEMENT.  This is a holdover misconception from mechanics -- force and velocity are independent of one another. 

So on the first night of electric field study, I break my rule about assigning only two AP-level problems per night.  Instead, I assign six plug-and-chug F=qE problems.  All I'm looking for are the basics -- can students state magnitudes and directions of electric fields and forces.  See, that's more than half the battle in electrostatics.  If we can bust these misconceptions, then perhaps the ideas of parallel plates and point charges won't be so impossible.

Below is the quiz I gave after this first night of homework.  You might think this is "too easy" for an AP class -- but no, it's actually on or above their level after the first night of electrostatics.  And, I could give this at the end of the year, and I would not expect anything close to perfection from a class of students who will mostly earn 5s.  Electrostatics is HARD and ABSTRACT.  Anything we can do to simplify, we should do.


1. An electric field points right. What is the direction of the electric force on a +3μC charge in this field?

(A) positive
(B) negative
(C) Left
(D) Right
(E) None of the above, the force is zero.

2. An electric field points north. What is the direction of the electric force on an electron in this field?
(A) North
(B) South
(C) positive
(D) negative
(E) None of the above, the force is zero.

3. A 500 N/C electric field points left. What is the electric force on a -2 μC charge in this field?
(A) 1000 μN
(B) 1000 μN left
(C) 1000 μN right
(D) -1000 μN
(E) Zero

Questions 4-5: An electric field points to the right. An electron enters this field while moving to the right.

4. Which way is this electron moving immediately after entering the electric field?
(A) right
(B) left
(C) positive
(D) negative
(E) nowhere, the electron is not moving

5. Which way is this electron forced when it enters the electric field?
(A) right
(B) left
(C) positive
(D) negative
(E) nowhere, the electron is not forced

Questions 6-8: The charge on an electron is 1.6 x 10-19 C; the mass of a proton is 1.7 x 10-27 kg. A proton is placed in an upward electric field of 200 N/C.

6. What is the direction of the electric force on the proton?
(A) Up
(B) Down
(C) Positive
(D) Negative
(E) None of the above, the force on the proton is zero.

7. Which is bigger, the electric force or the gravitational force on the proton?
(A) The electric force
(B) The gravitational force
(C) The electric and gravitational forces are about the same.

8. How many times bigger is the bigger force?
(A) 109 times
(B) 106 times
(C) 103 times
(D) 100 times

21 December 2010

Mail Time: Waves and sound on the AP physics B exam

Paul Dugas, of Woodbridge, VA, writes:

I was wondering about the waves and sound portion of the AP B curriculum.  The description is very short.  In looking at some past AP questions, there are some detailed sound interference pattern questions and sound intensity as a function of time.  The equations for intensity do not appear on the equation sheet AP gives to students.  Do you teach these concepts and, if so, how much time do you spend on them?

Certainly the double slit diffraction pattern for light, sound, and even subatomic particles has appeared on numerous exams. Students are expected to understand qualitatively how the intensity of a sound or light beam will vary on a screen when the wave is passed through a single slit, double slit, or diffraction grating. For the double slit / diffraction grating, they must be able to make the quantitative prediction of the location of the bright and dark spots.
I don't remember what intensity "as a function of time" question there might have been. 
The relevant principles here deal with light or sound intensity as a function of space.  And we don't have specific equations for a continuous I(x) function, but we know the locations of the bright and dark spots.  So we can fill in the blanks, knowing that a single or double slit diffraction pattern changes intensity gradually, while a diffraction grating produces sharp bright spots.

13 December 2010

Two-cart elastic collision -- how to measure the speed of both carts

I've taught conservation of momentum with the same set of quantitative demonstrations for years. I get two carts and a motion detector, make the carts collide, and predict speeds of the carts before or after the collision. Pretty basic, without much room for creativity. Until today, that is.

The first collision problem I attempt is very straightforward.  Take a look at the setup in the picture to the right.  I keep the red cart at rest, and send the heavier blue cart toward the red cart.  A velcro strip on the carts causes them to stick together after the collision.  The motion detector measures the speed of the blue cart before and after the collision.  I tell the class what the motion detector said the blue cart's initial speed was; we predict the speed of the combined carts after the collision.  Generally we get this prediction correct within 5-10%.
In the next collision, I push the blue cart toward the stationary red cart without the velcro, so that the carts bounce off one another.  Again the motion detector records the speed of the blue cart before and after the collision; we predict the speed of the red cart after collision.  Problem is, how should I measure the speed of the red cart to verify my prediction?  I pose that question to the class.
Most quickly understand why the single motion detector can only read the blue cart's speed.  The detector can't "see through" the blue cart. 
The solution suggested by a majority of students is to place a second motion detector on the left side of the track to track the red cart.  And I've tried that before.  But I've never gotten two facing detectors to work properly -- I think the sound waves interfere, causing nonsense results.  (Anyone else have any thoughts on this issue?)
What I've always ended up doing -- until today, anyway -- is to have students measure the time between the collision and when the red cart hits the end of the track, 100 cm away.  Since the track is level, the speed of the red cart is 100 cm divided by the time the students measure.  This works, but stopwatch measurement uncertainty causes this to be accurate only to about 20-30%, if that.
In today's class, junior Will Choate made the suggestion that I've missed for the last 15 years:  "Can you pick up the blue cart after the collision?  Then the detector can read the red cart."  That's IT!
So, I collided the carts.  After the collision, I gave the detector a brief moment to read the blue cart's speed, then I picked up the blue cart.  Sure enough, the velocity time graph showed the initial speed of the blue cart (47cm/s); the final speed of the blue cart (31 cm/s); a bunch of nonsense where my hand briefly got in the way; and the final speed of the red cart (80 cm/s).  We used conservation of momentum to predict that the red cart should have been moving 84 cm/s, within 5% of the measured speed.
The class was pleased with Mr. Choate for his creativity, and because he earned a TWO Reese's Cup reward.  I think much of the applause and congratulations was kissing up to Mr. Choate in case he felt inclined to give away his candy, but nevertheless.

07 December 2010

Quantitative demonstration -- Bernoulli's equation

Photo of my class by Frederic Lamontagne
A straightforward problem with Bernoulli's equation leads to a fun and dramatic demonstration, along with a fascinating discussion of the meaning of "negligible" and some use of the continuity equation.  Here we go...

I start with an empty tennis ball container.  With a pocket knife, I poke a small (<1 cm diameter) hole near the bottom of the container.  I show the class the container, and explain:  I'm going to cover the hole, and fill to the top with water.  The water clearly will shoot out of the hole.  What will the speed of this water jet be?

The class understands that a flowing fluid problem requires Bernoulli's equation.  So we write the equation:

P1 + rgy1 + ½rv12 =  P2 + rgy2 + ½rv22

Consider point 1 to be the top of the water, and point 2 to be as the water exits the container.  We want to find v2.  Let's see what terms can be cancelled or set to zero.

The water at the surface and at the exit is exposed to the atmosphere.  Any time a liquid, flowing or not, is exposed to the atmosphere, its pressure is atmospheric.  So the P terms cancel.

We can always take the lower y position to zero in Bernoulli or conservation of energy problems.  So get rid of the y2 term. 

Now we have a class discussion / argument.  Is the speed of the water at the top zero?  Certainly not.  But the water at the top is moving very slowly relative to the jet at the bottom.  So let's try setting that v2 to zero, and see what happens.

We measure the distance from the hole to the top of the container to be about 15 cm.  Solving Bernoulli's equation, we find the speed at the position of the hole to be 1.7 m/s.  Awesome!

But this is a quantitative demonstration.  We don't just solve the problem... we have to verify the answer.  How?  I can't just put a Vernier motion detector on the water jet.  The class brainstorms for a bit, and comes up with a great approach:  treat the water jet as a projectile.  Given the jet's initial horizontal speed of 1.7 m/s, we should be able to predict how far the jet will travel horizontally before hitting the ground.

What a great way to reinforce projectile motion problems, which we covered two months ago!  The horizontal acceleration is zero, the vertical acceleration is 10 m/s2, the vertical initial velocity is zero (because the jet comes out of the tennis ball container horizontally).  I place a large beaker on the ground to catch the stream of water; we measure the vertical distance from the top of the beaker to the hole in the container for use in the projectile problem.

When all is said and done, we calculated a 65 cm horizontal distance for the jet to travel.  While I filled up the container (and kept my finger carefully over the hole!), the students measured 65 cm along the ground and placed the large beaker at the correct spot.  I released the water....

... and the jet landed right in the beaker.  Physics works.

FOLLOW UP:  We all saw obviously that the speed of the water at the top was NOT zero.  But our prediction of a 1.7 m/s speed was accurate!  What's up?

We go back through the problem, this time not assuming that the speed at the top v1 is zero.  Instead, we use the continuity principle ( A1v1 = A2v2 ) to get another equation relating the speeds at top and bottom.  We can solve the two-variable system for the speed at the bottom.  We need to measure the cross-sectional area of the hole, and the area of the tennis ball can.  We find that the can has a diameter of about 7 cm, while the hole only is 1 cm wide.  Therefore the area of the can is 49 times that of the hole.  We resolve for the speed... and find that we still get 1.7 m/s.  Any difference would be in a later, very insignificant digit.  So, the speed of the water at the top is negligible compared to the speed of the water jet.