


26 September 2013

Mail Time -- Why is my algebra-based textbook using calculus?!?

One of my summer institute participants wrote in the other day with a question that I've been asked in similar
from this is NOT calculus!
form many, many times...

I discovered this morning that the textbook we have for the course, College Physics [by Serway and Vuille] has calculus-based content for 2D motion. I have resorted to using the textbook I have for general Physics, Physics: Principles and Problems by Glencoe, as an alternative for this section of material. Have any of you run into a similar issue or have any suggestions for other ways to communicate the necessary material at an AP level? I'm just wondering for this particular section, and if I run into a similar issue again down the road with content (since we're teaching algebra-based Physics).

Yeah, this is why I hate the standard-fare textbooks, written by Ph.D. physicists for Ph.D. physicists.  It's NOT calculus, even though it looks like it on first glance.  My correspondent pointed me to the section describing instantaneous velocity.  Serway uses a full page of equations, many of which look exactly alike to the untutored eye,* to make the simplest of conceptual points.

* My eye is tutored, but the 17 or 19 year old reading this text is not.  First rule of writing: know your audience.

The page in question uses mathematical notation that says the limit of a distance divided by a time as time goes to zero is the definition of instantaneous velocity.  Well, the eleventh grade student came to class angry: "We just started taking limits last week in my calculus class.  I've never seen this sort of thing before, and I don't understand it yet.  I thought you said we don't need calculus for this class!  How am I supposed to understand it?"

First, the general issue about algebra-based physics, calculus, and resources:  If students read texts or online information, they will often -- too often -- see mathematical explanations that resemble calculus.  See the picture above, which is using five rectangles to approximate the area under a curve.  "That's calculus, I know it!" says the novice.  Well, it's not.  The area of a rectangle is base times height -- that's 6th grade math, not calculus.  Even in algebra-based physics, we have to compare the slopes and areas of curved graphs... and you can expect someone to indignantly holler "Calculus!" when you draw the slope of a tangent line.  What "algebra-based" means is that we don't ever have to evaluate an integral or derivative of a function to make a numerical calculation or derivation -- it doesn't mean that we never look at curved graphs.

One of our tasks as a teacher of first-year physicists is to help them simplify tough ideas.  That means steering them away from poorly-written or misleading sources.  That means explaining in words, and minimizing mathematics.  A diligent but frustrated student must understand that yeah, the textbook is ridiculously confusing, but that doesn't mean you can get angry -- you simply have to find a different way to understand the topic.

Finally, the specific issue of Serway's presentation of instantaneous velocity:  All this math is just telling you that (1.) velocity is distance traveled per second, and (2.) "instantaneous" velocity means the velocity RIGHT NOW.  Distance divided by time is, generally, velocity.  If you use data over an hour, you get the average velocity for that hour.  But if you don't look at an hour, or a second, but at a fraction of a second, then you're looking at instantaneous velocity.  Serway is doing his highfalutin' physics professor best to say just that, but in mathematics.  I wish he'd speak English.


19 September 2013

Foucault Pendulum -- Latitude of a Google Doodle

On Wednesday, the Google Doodle showed a working Foucault Pendulum simulation.  As it happens, my research students are in the opening stages of a deep investigation of the Foucault in preparation for the US Invitational Young Physicists Tournament.    We are tasked with building a Foucault, using it to determine our latitude, and then conducting the error analysis to define the precision of the measurement.

What a useful coincidence... I added the question to my research students' quiz: "Determine the latitude portrayed by the Google Doodle."

The equation for the precession per day of a Foucault pendulum is 360 degrees times the sine of the latitude.  Solving, then, the latitude is the inverse sine of the precession per day divided by 360 degrees.*  We need to find the precession rate from the simulation.

*Explaining the geometry and conceptual physics behind this equation will be part of each research team's presentation at the tournament, of course.

One of my students sent a rather tetchy response, complaining that he'd have to sit there for most of an hour just to watch how long it takes for a peg to be knocked down.  Some cursory exploration finds a cheat:  look in the lower right corner at the clock face.  Click on the clock.  A slider appears, allowing you to fast-forward time.*

*A second slider allows you to adjust latitude.  I'm doing everything here for the default latitude when I just click on the doodle link.

I set the slider to 12:00, and fast-forwarded until all pegs were knocked down.  At 6:25 PM by the clock, the last peg was still standing; at 6:40 PM, the last peg had fallen.  This means that the pendulum rotates 180 degrees in somewhere between 18.42 hours and 18.67 hours.  Pro-rating this rotation rate, this works out to between 276 and 280 degrees per day.

Now plug into the relevant equation: the latitude of this pendulum is between 40.0 and 40.7 degrees.

Reader help, please:  I anticipated that the simulation either (a) used the geo-located latitude of the computer accessing the doodle, or (b) used a default latitude with some special meaning, such as Google's Mountain View, CA headquarters.  Oops.  I am located at Woodberry Forest, VA, 37 degrees north latitude; Mountain View is also 37 degrees north latitude.  Any clue where this Foucault is supposed to be?  (Or, alternately, any corrections to my calculations?)

And, if you'd like to participate in our tournament, solve three of these four problems and come to San Jose, CA on Jan. 31, 2014.  I'll be happy to help you out with both the physics and the attendance logistics.

12 September 2013

Ray optics simulation

Screen shot is from the Phet site at the linked refraction demo.

Before I start talking about an awesome simulation, hear the standard disclaimer:  Online simulations are in no way a substitute for live quantitative demonstrations.  

That said, online simulations, if they're programmed correctly, can be extraordinarily useful: for making quick "measurements," for showing experiments and regimes within an experiment for which you don't have the equipment, for student use at home... As long as you are not trying to replace live equipment with a computer, simulations are wonderful resources.

The Phet interactive simulation site is one of the traditional favorites of physics teachers.  These have been maintained and developed over time by pros.  Note that they are free (with donations accepted), and that they require Java.

Today my conceptual class used a laser and a fish tank to make measurements of incident, reflected, and refracted angles.  Homework questions will ask qualitatively about which way light bends at various interfaces, about comparing angles, about how these angles change in different situations.  

My colleague Alex Tisch whipped out this phet simulation which runs exactly the same way as my in-class live demonstration.  It even comes with a protractor that you have to place properly to measure angles.  I particularly love the option of a "mystery material" for which you have to use the protractor to figure out the index of refraction.*

* In Regents or AP physics, I'd have students use Snell's law to determine the mystery index of refraction.  For conceptual, I could ask students to rank materials by their n, or to compare the material's index of refraction to that of water, say.

I'm not actually using this for any sort of official assignment, at least for now.  Rather, I just put a link on the class folder, and offered extra credit to anyone who actually downloads and plays with the simulation tonight.  If nothing else, I might use it myself in creating a problem -- a screen shot provides me a diagram from which I can ask virtually anything.  Alex did the live demonstration, then used the simulation to make many quick measurements without having to turn out the lights, click erasers to visualize the laser, draw the rays on the glass, etc.  

Thanks for the link, Alex!


09 September 2013

Take a picture of every demo and lab

Folks, I've been asked for years:  "Do you have a list of all of the quantitative demonstrations and lab setups that you do?"  I've never actually compiled such a list.  I just create on the fly, usually.  A quantitative demonstration is merely an end-of-chapter problem scaled such that the answer can be tested with available equipment during class.  Each year, I look in the equipment closet, set something up, and go with it.  I *like* the improvisational elements this approach brings to my classes.  Just as I don't want my students to think of laboratory as an object lesson in instruction-following, I don't want to fall into the trap of making physics teaching a strict note-following process, either.

That said, I often want to remember things year-to-year, and I often want to communicate to others what I'm doing.  I've never been organized enough to write down details of my demonstrations.  I've documented many demos on this blog with a photograph and description; but taking and uploading each photo, and then writing the description, has been a time consuming process.

Today, my colleague Curtis offered an elementary yet elegant observation about documenting his demonstrations.  He was frustrated because he didn't remember the experiment that we ran on the first day of conceptual physics last year, even though we had done it in detail last year, even though I described it to him again.  However, when I went into my classroom and actually set up the experiment for him, he instantly knew what to do.

This year, then, he took a picture of the setup with his phone; he emailed the picture to himself, and saved it in a file marked "lesson plans."  

See, I hate the term "lesson plan."  It implies that I should have pages of notes explaining what I'm doing in each portion of my class.  Well, I did have such notes the first couple of years I taught.  Now, though, I just set up a demo and improvise.  I don't need no stinkin' "lesson plan" -- The photo BY ITSELF is sufficient for reminding me what I did last year, for communicating to colleagues, and even perhaps for reminding students about setups.  Curtis even suggested using the photo as the basis for a lab quiz:  "Here's the setup from yesterday's demonstration.  Explain how to use the equipment present to measure angles of incidence and reflection."

My pledge for the next couple of years is to remember to take as many pictures of lab setups as I can.  This year I'll work on conceptual; next year will be AP Physics 1.  Hopefully I can compile a big file of picture after picture so that when other teachers ask for a list of demonstrations, I can forward these files.

And yes, I am aware that to folks who are more tech savvy and/or about a decade younger than I, this post must sound like "oh, it's good to have a collection of books, but they're especially useful if you take the books down occasionally and read them."  :-)


02 September 2013

Mail Time! Some quick questions about AP Physics

It's that crazy-arse time of the year, at which point I look at the calendar and say, "Oy, my next day without an obligation is the Wednesday before Thanksgiving."  So in honor of the start of school, here are a few quick questions from readers with quick answers.

From Joseph: 

Hi Greg. I was examining some of the grading done on the AP as well as how you graded some of your tests. I ... saw that you adjust the multiple choice scores slightly. The example I'm looking at says you multiplied the MC score by 1.304 after rounding then added that to the total FR points for the RAW AP score. Why did you adjust the MC? Does your strategy vary test to test? 

Hey, Joseph.  Both sections should be weighted to one minute per point.  Since on that test I gave 23 questions in 30 minutes, I multiplied the mc score by 30/23 to add to the free response.

From Youri, who has two questions:

1. I can't remember but on the AP do they go by significant figures or by given answer to 3 decimal places?? Can you clarify that for me.

Use 2 or 3 sig figs.  Not worth throwing a fit over with the students, though, compared to the other classic battles like using units or describing a solution thoroughly.

2. Do you have any cool demos I can do for kinematics, using a pasco track, carts, I have a fan for the cart, a labquest, a motion detector a force sensor...basically what you told me to get. I want to do a demo but I am not really sure what would be the most appropriate and useful to the kids???

Use the fan cart on the track with the motion detector and do qualitative and quantitative demos.  Like, what will the x-t or v-t graph of this motion look like?  Can someone make the cart create this graph?  What initial velocity will get the cart to stop at the top of this inclined track (given the cart's acceleration)?   Or, just what is the cart's acceleration given the v-t graph?  All sorts of fun stuff.  Choose an end-of-chapter problem, and scale it to a cart on a track.

From Jessica:

Random question. I have a student who is solving force problems with tangents instead of sines and cosines to break forces into components and determine magnitudes of force components. His math works. But I rarely see tangents show up on rubrics. Does it matter? As long as his math is sound? Or will it lose him points to not show force components in sines and cosines? 

Hey, Jessica!  His approach is fine, as long as the physics is correct.  Nonstandard but correct and clear approaches always earn full credit.  (As I sometimes say rather cheekily, that's why the College Board hires physicists to grade the exam rather than lawyers.  The rubrics are meant to be interpreted intelligently, not inflexibly.)

Good luck to all this year... please email questions as you have them.