27 February 2010

What I've been working on...

Busy, busy time here at Woodberry.  We're approaching trimester exams; today was the last day of class before exam week.  Sunday is "consultation day," during which teachers will be in their classroom all afternoon.

My general (non-AP) physics class follows approximately the AP physics B curriculum... except that we spend from September through February on mechanics only.  The upcoming exam in that class will consist of seven problems, each one based on an authentic AP physics B problem from the last 20 years. 

I've spent the week creating new exam preparation exercises, especially for general physics.  I wrote some new exam-style questions based on AP problems; I followed these up with quizzes, and then multiple choice review exercises with the "clickers," a.k.a. classroom response system.

Things are still too hectic for now to post specifics -- baseball tryouts concluded yesterday, and I'm way behind on my grading.  But next week I will be able to start posting again.  I think these clicker review exercises will be well worth a look.


P.S. In case you're confused, the picture is of Woodberry Forest baseball captain and soon-to-be Georgia Tech Yellow Jacket Paul Kronenfeld.  And yes, Mr. Kronenfeld IS in fact a physics student.

19 February 2010

Writing out the Lenz's Law problem solving process

I think I've done a reasonable job over the years teaching Lenz's Law for the direction of an induced current -- my approach is detailed in this post.  The next obstacle to my students' understanding is to remember and internalize the problem solving process.  This time of year, we've just finished electricity AND magnetism -- it's tough enough to get the class to remember the difference between electric and magnetic fields, let alone the difference between the THREE right hand rules for magnetism and how each one works.

Because the use of Lenz's Law seems so easy on the surface, and because you usually have a 50-50 shot of getting the right direction for an induced current, students tend to give short shrift to using the law correctly.  They don't write out their reasoning, and so they lose opportunities to cement confusing ideas like the difference between magnetic flux and magnetic field. 

I'm going to try something a bit different this year.  On Monday, when I introduce Lenz's Law, I'm going to write out each step in the process on the board, in longhand.  When I assign Lenz's Law problems, then, I am going to require everyone to write out the steps as their solution.  In the past, I've begged, pleaded, and cajoled the class to explain their reasoning.  Well, I'm gonna try modeling the reasoning I want to see, hoping that I get better retention.

Below is an example problem from Serwaybased on the diagram at the top of the page.  I've typed in the template that I want students to use:  they write out the phrases, and fill in the blanks.  This template works with virtually any Lenz's Law problem.

A rectangular loop is placed near a long wire carrying a current I¸ as shown above. The current I is decreasing. What is the direction of the current in the resistor?  Write out the Lenz's law problem solving process:

(1) The direction of the magnetic field is _____________. I know this because___.

(2) The magnetic flux is (increasing / decreasing). I know this because ____.

(3) So I point my right thumb ____________ toward (increasing / decreasing) flux, which means the current flows _______________.

18 February 2010

New lab: resistance of a mystery resistor

My AP labs generally follow a predictable pattern:  We take a large set of data, make a graph that's curved, manipulate the graph's axes to form a straight-line, and then use the slope of that line to determine some value associated with the experiment.  AP exam questions frequently follow this same approach.

For example, my first experiment of the year asks students to attach a cart to a spring scale, then to put the cart on an incline.  We measure the force parallel to the incline plane that holds up the cart; we plot that force as a function of the angle of the incline, giving a curve.  Next, we plot the force we measured vs. the sine of the incline angle; this gives a straight line.  Students show that the slope of the line is equal to the weight of the cart, and they divide this weight by g to find the cart's mass.

This process goes on again and again -- make a straight line, and relate the slope to a constant quantity.  I know I'm doing my job when students start to groan about going through the same process again and again.

BUT:  The slope of a stright-line graph isn't always the most meaningful of that line's attributes.  Many folks were shocked in 2007 when problem 6 (check out the link, page 11) required the use not of the slope, but of the y-intercept of an experimental graph.  The problem involved use of the thin lens equation, 1/f = 1/di + 1/do.  The y-axis was 1/di, the x-axis was 1/do, so the y-intercept became the recipricol of the lens's focal length.

I do that experiment in the spring.  But I want to give the class some experience with using the y-intercept of an experimental graph now, and we haven't dealt with lenses yet. I've used the pressure in a static column equation, P=Po + ρgh before -- use a vernier probe to measure the absolute pressure in a water-filled container as a function of depth.  The slope of the pressure - depth graph is ρg, while the y-intercept is the surface pressure Po.  This year, for a variety of reasons, I wanted an experiment less reliant on computer data collection and more complex in its analysis.

The equivalent resistance of parallel resistors is given by 1/Req = 1/R1 + 1/R2.  Huh... This equation  is quite similar in mathematical form to the thin lens equation.  I have the equipment to measure the equivalent resistance of a parallel combination (i.e. an ohmmeter); I have several "variable resistance boxes," pictured above, which allow the resistance to be varied through a very wide range.  So why not use this equation as my "y-intercept training?"

I took a bunch of resistors in the 5-100 kΩ range, put them on breadboards, and called them the "mystery resistors."  I showed the class how to put the variable resistance boxes in parallel with the mystery resistors, and how to measure the equivalent resistance with the meter.  I initially asked them to graph the equivalent resistance as a function of the box resistance -- this gave a curve. 

Next, I asked them to plot 1/Req on the vertical axis, and the recipricol of the box resistance on the horizontal axis.  This produced a line.  Of course, everyone knew by now to draw a best-fit line; but most folks reflexively took the slope of that line.  It was only after I made them identify the y-axis, x-axis, slope, and intercept using the equation of a line (y =mx +b) that they recognized to use the y-intercept -- the inverse of the y-intercept is the resistance of the mystery resistor.

I will scan in some sample data below, once some folks turn in their labs.  It didn't occur to me until later, and it never occurred to any student that I know of, that the original Req vs. Rbox graph could be used directly to find the mystery resistance:  draw the assymptote as the box resistance gets very large... then read off the vertical axis to get the mystery resistor.  You can tell everyone WHY that works in the comments; I might ask that question as a quiz someday.


12 February 2010

How and why to use the equation sheet

I gave a free repsonse test today.  The first problem was 1993 B2, about the electric field and potential due to point charges.  This is the easiest of such problems, I think, in the AP physics B annals.  The second problem was 2007 B2, a ranking task about circuits; this one makes my "top 5 AP physics problems of all time" list.  (That's a list I should publish some time on this blog.)  I haven't graded the third one yet, the easy 1998 problem with standing waves on a string. 

In those first two problems, at least seven off my 23 students used an incorrect equation.  Why is that so annoying?  Because the AP free response section, as well as today's test, provides an equation sheet!

Below is a note I wrote to the class's email folder.  I publish it here because I think it gives good advice about how to use the equation sheet, and perhaps implies the fundamental reason that the sheet is provided in the first place.

Look. You've got to memorize equations. We all know that. So, then, why do you even have an equation sheet?

The novice or dumb physics student hunts and pecks through the sheet. "The problem asked for a charge on the capacitor, and I know charge is Q. So, let's look for an equation with a Q in it. Here's one! ΔU = Q + W! Now I just need to plug in something or other for U and W." I know that youall aren't doing that, and I'm glad. (You would be shocked how many people are just this silly.)

However: You should never use an incorrect equation on a free response test! You've got the equation sheet right there. You should use it any time you're unsure of the exact form of an equation: "Huh, is it Q=CV, or C=QV? I don't remember. Let me look that up real quick." Or, "Is electric potential kQ/d, or d squared? I don't remember for sure, I should check."

Of course, I want you to know these things by heart. But when you know you're unsure, when you know you might have a brain fart under pressure, just use the sheet. That's what it's for.


10 February 2010

In prase of Giambattista's multiple choice questions

People ask me about textbooks a lot.  I don't have a favorite.  I've tried several, but I've never been truly happy with any of them -- most are too detailed for the novice, even though they serve as reasonable references once students have experience.

Lately, it seems that all the textbooks are trying to advertise their usefulness for test preparation, which is silly -- if it's a good textbook, then it will be useful in preparing for good test.  Period.  But someone is insisting that texts add test prep gimmicks, sometimes via online resources, more often by merely adding a section of multiple choice questions.

Be careful with these multiple choice questions.  Most are LOUSY.  Serway, for example, has taken a bunch of plug-and-chug problems and made them into "multiple choice" items; no, that's not what a multiple choice question is about.  They and other texts also ask questions that are so involved that they are not answerable in a minute or two -- EVERY multiple choice available requires an average of, at most, a couple of minutes per item.

The best multiple choice questions that I personally have seen in a standard textbook are in the Giambattista, Richardson, and Richardson text.  This one was recommended to my by Martha Lietz, a colleague from the AP reading who teaches outside of Chicago.  Giambattista has a reasonable grasp of the purpose and scope of a multiple choice item.  Take a look at these, from the second edition, that I adapted for a recent quiz:

23. An organ pipe is closed at one end. Which sketch is NOT a possible standing wave pattern for this pipe?

24. Which sketch shows the lowest frequency standing wave for an organ pipe closed at one end?

Now, I know that these would be back-to-back problems on an extensive exam, and I know that many exams use five rather than four choices.  Who cares.  The thrust of these problems is good.  The first tests whether the student recognizes that a closed pipe includes an antinode at one end and a node at the other; the other simply tests visually the student's ability to apply v=λf based on a picture of the wave.

Giambattista has more good multiple choice questions, of course, and a few bad ones as well.  But if you're looking for a good source, get yourself a copy of this book.