24 August 2010

Mail Time: Pretests and the level of physics you teach

Jason Buell is a middle school teacher in San Jose, California.  He commented on a previous post about pretests.  I totally neglected to follow up.  Why?  Choose one:

(A) Because I've been in eight different cities this summer for various lengths of time and with various levels of internet access;

(B) I'm a negligent dork.

Whatever the reason,* Jason's query deserves a response.  He said:
* "B!B!B!B!" shouts Burrito Girl from the other room

"What do you think about the value of a pre-test with regards to a student observing their own progress? We're going to pre-test this year with that purpose. Curious on your opinion."

Preface my response with the fact that we teach very different populations. You're teaching a general-population middle school, according to your google profile; I'm teaching junior and senior boys at an independent school, where we don't have the top 5% or the bottom 30% of the students you will teach.

For MY CLASSES, I don't at all believe in the pretest for self-evaluation... for several reasons.

(1) Students aren't really supposed to know much about physics coming in. We all know that they will have serious misconceptions.  So, a pretest exposing those misconceptions will produce astoundingly poor performance, almost like saying "look how dumb you are now!" I think that sets up serious hostility, where students are likely to dig their heels in to prove me wrong rather than to go with the flow of the course.

(2) I think the better way for students to observe their progress is simply to talk to their peers.. This happens naturally. You expose a misconception to the class, and the students themselves tend to become uncomfortable when a peer makes that error in conversation or on homework problems. That's when they say, "look how much I've learned."

(3) While I do agree that it is important for students to see how much they've learned and to be proud of their progress, I don't believe such progress can be properly "measured" by a pre- and post- test. You give tests already. If these are authentic, then they should serve this purpose of demonstrating progress. There's no need to rub the students' nose in the fact that they didn't know anything coming in to the course... they weren't supposed to!

(4) If nothing else, a pretest wastes a class early in the year when you have the students' maximum attention due to the novelty of school. I prefer to use that time to show demonstrations.

Now, the biggest difference in our classes is the level. My students are adult-like. I carefully distance myself from many of the "educational methods" that they have been exposed to in middle school or elementary school, because 16-18 year olds rebel automatically if they perceive that I'm treating them like kids. I would worry that a pre-test might be perceived as a cute little technique that I learned in ed-school, that might be prefaced by "Now, Boys and Girls..." That's a disaster when dealing with 16-18 year old boys.

You're teaching co-ed middle school. I don't know enough about how to teach that level. It might be that kids that age NEED the rub-your-nose-in-it "you don't know nothin' about physics yet, but I'll help you figure it out!" that a pretest might provide. They might need more than just a midterm exam to show them how far they've come in their knowledge. They might need more concrete goals than I provide, and a pretest might fill that need.

So my answer to your comment, Jason, where you asked for my opinion of a pretest for the purpose of student self-evaluation, boils down to my throwing the question back at you. Having heard my thoughts based on teaching upper-level high school boys, what is YOUR opinion of how a pretest would work or not work at the middle school level? You are more likely the expert in this situation, and I'd love to hear your answer.

23 August 2010

Mail Time: First test in AP physics B

Michael Gray teaches in Georgia, where school starts the first week of August.  I guess they figure that since they have to run the air conditioning 11 months a year anyway, they might as well start school early.  He writes:

I have gone through Equilibrium and Free Body Diagrams, Torque and 1-Dimensional Kinematics with my AP Physics B students. I want to give them a test this Wednesday. I was thinking of giving them ~15min of multiple choice and 25-30min of Free Response in our 50min period. Does this sound like a good plan? Or would you do all MC or all FR for each test?

Also, should I let them use the formula sheet? When are they allowed to use calculator?
Michael attended my AP Summer Institute at Kennesaw State University a month or so ago.  He knows my general advice to AP teachers -- give all tests in authentic AP style, even using authentic questions from past exams where possible.  I'd say the same thing to all those who teach toward a high-stakes, cumulative exam, such as the Regents, IB, or whatever.  Classroom tests should be identical in form, content, and degree-of-difficulty to the final exam.
Second question first:  The AP exam allows the "constant sheet" for both multiple choice and free response sections.  AP allows a calculator and formula sheet for the free response only.  Therefore, I always do the same on my classroom tests.
Getting the mix of free response and multiple choice right is difficult.  Michael's difficulty is that he has only 50 minute periods every day.  I have an 85-minute lab period once a week, meaning that I can give a nearly half-length AP exam with both kinds of questions in that time.  (The actual AP exam is 180 minutes.)  It's trickier with the short periods. 
Later in the year, I might give a full 50 minute multiple choice test, knowing that my next test a few weeks later would be 50 minutes, all free response.  But on the first test, I think it's important for the students to get the feel for both types of questions, and to have the opportunity to show their knowledge on as many types of questions as possible.
The AP free response rule-of-thumb is one minute per point, or thereabouts. And, AP multiple choice is designed with 70 questions in 90 minutes.  The multiple choice and free response are weighted equally, since students spend the same amount of time on each.  Whatever option Michael chooses for his tests, I encourage him to stick to these time and score frames.  AP students need to get used to the time allotted for the exam.

I had two recommendations for Michael, neither of which is ideal with his short periods, but either of which will work.  For that first test, he might give an entire half-length AP over two days.  For example, Thursday's class would be 45 minutes, 35 multiple choice questions.  Then on Friday he would give 45 points worth of free response in that class period.  The sections would be combined into one test, graded on the AP scale.
The other possibility if he prefers a single test day is to give, say, 15 minutes for 12 multiple choice questions; then 2 or 3 free response questions equalling 30 points.  In this case, the multiple choice would be weighted to be 1/3 of the total test grade, because students spent only 1/3 of the test time on multiple choice.
Good luck to Michael, and to all who are trying to design AP-style tests.  It took me hours and hours my first year teaching to write my tests.  Of course, that was in the days before easy PDF scanning.  I had to recreate every diagram in microsoft draw 1.01.  Nowadays, we have authentic old tests available in microsoft word format, and I just cut and paste.  Plus, a diagram can be inserted in less than a minute by scanning, copying, and pasting.  I think I started teaching 15 years too early.

16 August 2010

Bat Physics

Burrito Girl (my wife and sidekick) and I are vacationing in Estes Park, Colorado right now.  Last night we attended a Rocky Mountain National Park ranger talk entitled "Superheroes of the Night."  Bats, owls, mountain lions, and coyotes were dubbed "superheroes" for their unhuman physical adaptations.

The main purpose of the evening was to help the young NachoBoy earn his Junior Ranger badge.  He certainly enjoyed the talk, as one of his regular activities lately has been leanring to differentiate between the hoots of various owl species.

From a physics perspective, the owls piqued my interest.  Their ears are not aligned in the same vertical plane.  An owl's right ear is above the eye socket; the left ear is near chin level.  How does this help the owl survive?  An owl hunts from the branches of a tree, but is searching for prey on the ground.  The time delay of a sound hitting each ear can help the owl pinpoint the location of the animal.  People have pretty good directional sense about sound as well, but only in a horizontal plane around our head; the owl's ear position is well adapted to their sort of dive-bomb hunting.

Owls were fun, but bats... well, bats brought out the paper and pencil for a quick calculation.  And I'm still confused by this one, so help me out if you can.

Bats navigate and hunt principally using echolocation, i.e. sonar.  The park ranger last night described an experiment in which batologists* strung wire "less than the thickness of a piece of paper" around a darkened room.  A multitude of flying insects and bats were released in this room.  The wires were monitored to note each time that a bat collided with a wire.

*Or whatever they're called

What happened?  The bats ate all the insects, but never once touched a wire.  Conclusion:  Bats have pretty awesome sonar skills.

Here's where I brought out the paper-and-pen.  For the bat's sonar waves to reflect off of the paper-thin wires, the sonar wavelength has to be on the order of the wire thickness.  That's about 1/10 of a mm, or 10-4 m.  The speed of sound is 340 m/s, or about 102 m.  Therefore, the frequency of the bat sonar has to be v/λ = 106 Hz.  That's better known as 1 MHz, well above the ~50 kHz limit to human hearing.

I made a quick check on the reasonability of my calculation by asking the bat-savvy ranger if he had ever heard the bat's echolocation.  He said no -- he confirmed that the sound must be above the audible range, but he did not know the precise frequency.

A more involved internet search found this excellent discussion of the physics and biology of bat radar.  It states that the bat-recepticles are fine tuned to detect 60.0-61.5 kHz.  Bats use a wider range of outgoing frequencies, because then they will be able to detect the doppler-shifted return wave.  (Cool non-AP physics problem:  Calculate a reasonable range for outgoing bat frequencies for a reasonable range of insect speeds, such that the doppler-shifted return pulse will be in the 60.0 kHz range.)

But this fact contradicts my original calculation.  The wavelength of a bat's radar is (340 m/s)/(60,000 Hz) = 5 mm or so.  How, then, can the bat accurately detect something 50 times smaller, like a paper-width wire?

Clearly I'm not understanding something.  Can anyone out there explain?  If so, then I've got an excellent discussion for this year's waves unit.  Perhaps we can bring in a bat for demonstration purposes.


(P.S. -- The picture at the top of the post is of a bat drinking.  Bats can't land to drink, because their gliding wings don't allow them to take off from the ground.  Airspeed velocity and such.  So they glide across standing water, lapping the water up with their tongues.  Awesome.)

12 August 2010

Mail Time: So How *DO* You Cover Measurement and Sig Figs, If Not On the First Day?

The blog's newest follower Evan Willkomm writes in with the natural follow-up question to my post about the first day of school:

I'm a newer teacher and I'm still working to come up with a strong curriculum for general physics.  For the first two years of my teaching, I taught measurement, significant figures, and sig fig math in the first unit of the year.  This decision was made simply by opening the text that I inherited from the teacher before me and presenting the material linearly, starting with chapter 1.  After reading through some of your blog posts, I've found that you hit the ground running and introduce forces and equilibrium to your AP students and position-time graphs for general physics - all on the first day.  I'd really appreciate your thoughts on whether I should continue to include those topics or not.  How do you address sig fig math? 

Hi, Evan... good to hear from you. You're right that, at any level, one of the fundamental secrets to physics teaching is to "hit the ground running" with real experimental physics. At Woodberry, we take this approach at all levels, including AP B, AP C, regular, and conceptual.

Measurement, sig figs, and the scientific method are actually quite deep concepts. They, and abstract unit conversion mathematics, are generally taught in every science course, starting even in 6th or 7th grade -- and yet, many if not most students will graduate high school with only the most tenuous grasp of such things. Sure, I can spend a week at the start of school on these issues, but without context, I will be just as unsuccessful as a host of prior teachers. (Trust me. I've tried.)

I would suggest that all of the above ideas are best learned through the use of numerous unannounced "teaching moments." For example, on the first day of AP, we predict the reading on a spring scale to be 2.3 N. Before we look at what the scale actually reads, I ask the class how close we have to be in order to call ourselves correct. Since the scale itself has markers only ever 0.2 N, we agree that we're happy with an answer between 2.1 N and 2.5 N -- that is, +/- 0.2 N.

Or, in general physics, I might calculate the slope of a cart's constant-speed position-time graph, and ask how far we expect the same cart to travel in 3 seconds. Once again, the question of "how close is correct" will arise. This time, we might suggest that our reaction time places this time measurement within only about 0.2 or 0.3 s, so I'm happy with an answer that's within 6-10%.

In regular and AP physics lab, we're regularly calculating percent differences between two different measurements, such as a speed measurement with the slope of a crudely made position-time graph and a speed measurement with a sonic motion detector. Throughout the year everyone sees that a measurement to within 5-10% is pretty solid. Then when we're calculating answers to book or test problems, we can use that ingrained knowledge: "You haven't measured anything in lab to better than 5% accuracy all year, and yet you're telling me that the mass of the sample is 1.32452 kg? A 10% difference would be 1.45something kg... in other words, those last digits are utterly meaningless."

And finally, students get the message of "I took two points off for writing every digit on your calculator."

Do my students truly, deeply understand significant figures and measurement uncertainty after my class? Probably not. My hope is that some folks get it, and that at minimum everyone understands the fact that a fourth significant digit is very often utterly ridiculous.

But that's not the right question to ask. The right question is, do my students understand significant figures and measurement uncertainty any worse because I don't go over them at the beginning of the year?

Answer: My students understand these things AS WELL OR (USUALLY) BETTER by covering them in context rather than by covering them in isolation at the beginning of the year.

And FAR MORE IMPORTANTLY: Without question, my students display a more positive attitude toward physics, and they have a better understanding of the purpose of physics as a discipline, than when I started the year with a measurement and math unit. My class sees on day one that this isn't just another math course. They see ideas and experiments presented in a way that is completely new to them; they aren't bored, they don't think of my class as a repetition of anything in their previous schooling. Physics is about predicting and measuring how the natural world works. My class knows that within 30 minutes of the first day of school.


[P.S. for a more rigorous treatment of these issues from an Education Professor's perspective, check out Arnold Aron's classic text, *Teaching Introductory Physics."  His findings agree 100% with mine.]

06 August 2010

Thickness of Gray vs. Brown Hair

In my AP physics institutes, I show the classic demonstration in which we measure the thickness of a hair via diffraction.  I hold the hair in front of a green laser, and project the resulting diffration pattern on the white board.  We measure the distance x between dark fringes. 

The thickness of the hair d is given by the equation x = mλL/d, where m = 1 (because we measured between two fringes, not across several of them), λ is the wavelength of the laser, and L is the distance to the screen.

The thickness of every hair I've ever measured has been between 10 μm and 100 μm.  Though I've had students investigate, we've never found any significant and consistent difference in thickness between different colored hair, between boys' and girls' hair, or between "thick" and "thin" hair.  Perceived "thick" hair has the same diameter as anyone else's hair, it must just lie together differently so that the distance between hairs is larger.

At my Manhattan College institute, I asked for a volunteer hair for this demonstration.  I looked around the room and saw virtually everyone with either bald heads or extra-short, nearly shaved, haircuts.  Fortunately, Manhattan College alumna Regina Verdeschi shook out her hair clip to reveal a deep brown mane that hung halfway down her back. 

Regina asked, "Do you want a brown hair, or a gray hair?"  I froze for a moment.  For one thing, no student of mine has EVER asked that question.  But more to the point, with my wife Burrito Girl that's a trick question to which I know the answer:  "Brown, of course, because you don't have any gray hair."  (This will be the correct answer even in 20 years when her hair is deepest silver.)

Even though Regina is emphatically NOT Burrito Girl, I still gave the appropriate answer: "Brown, please.  I didn't notice any gray hair."  I've been trained well, I guess.  We measured the thickness of Regina's brown hair to be about 50 μm.

When I described my history of 10-100 μm hair thicknesses in every color and gender, Regina spoke up again.  "What about gray hair?  It's noticably thicker.  That's why I asked."  She proceeded to pull one of her few gray hairs and hand it to me.  She was right that the hair felt noticeably thicker. 

At this point, the entire class was clamoring for a second measurement.  We projected the diffraction pattern and saw immediately that the fringes were considerably closer together.  The calculation suggested that Regina's gray hair was about 75 μm thick, or 30% thicker than her brown hair.

While I will not be able to repeat this experiment in my class of 16-18 year old boys, some of whom are balding but none of whom is going gray, I would be interested in feedback from the audience.  Measure one of your colleagues' gray hairs.  Tell me your results.  *Is* gray hair generally thicker than not-gray hair?  I'd do the experiment myself, but neither I nor Burrito Girl has access to the necessary materials.


05 August 2010

RC, RL, and LC circuits -- a teaching tool

Most general-level physics class teach DC circuits with resistors.  Equipment for this unit is easy to find and use -- Radio Shack, Harbor Freight, or any online electronics wholesaler can sell you meters, resistors, breadboards, light bulbs, and power supplies.

Some advanced courses, including AP physics B, teach DC circuits with capacitors, as well as the "after a long time" behavior of an RC [resistor-capacitor] circuit.  The best demonstration tool I've found for this unit is the 1 farad capacitors available from science supply stores.  Why 1 F, which is prohibitively large for any useful application?  Simply because the class can do quick Q=CV calculations in their heads during my demonstrations.  If I have students work with capacitors in a laboratory setting, I buy some cheap capacitors from Radio Shack.

Some very advanced courses aimed at future scientists, including AP physics C, teach DC circuits with resistors, capacitors, and inductors, including the time dependant behavior.  RC and RL [the "L" indicates the presence of an inductor] circuits reach a maximum or minimum voltage exponentially; the voltage of an LC  or RLC circuit oscillates.  Teaching the mathematics of exponential decay and the meaning of the "time constant" is a tough challenge.  But so is demonstrating the behavior of these circuits.

Showing the time-dependent behavior of an RC circuit can be straightforward -- hook the 1 F capacitor in series with a battery and a variable resistor box.  The time constant (equal to RC) can be varied by adjusting the value of the resistor.  Measure the voltage across the capacitor or resistor with a Vernier voltage probe and Logger Pro software.  You can show the variation of voltage as a function of time, which generally matches theory quite precisely.  Add a Vernier current probe, and you can make even more graphs.

When I started teaching the behavior of an inductor in a circuit, I gave up on cheap equipment; I just bought a PASCO RLC demonstration device, shown in the picture above.  This card has easy connections to several resistors, several capacitors... and an 8 mH inductor!  Now, an 8 mH inductor gives RL circuit time constants on the order of milliseconds.  But that's okay -- the voltage probe can be set to take data 1000 or even 10000 times per second, as long as you only take data for a second or two.  You zoom in on the voltage-vs.-time graph, and voila, you see the correct exponential behavior.