Speed of Sound

OK, so we're finally there in AP - the speed of sound calculation. Matter and Interactions makes a hand-waving argument based on dimensional analysis to get the longitudinal speed of sound from the interatomic bond length and spring constant and the atomic mass. That's fine, but I wanted to get to the real derivation, which involves a very interesting couple of linear approximations and some possibly bogus calculus, but it's doable.  The transverse one is basically the same story.

It's more guided and less inquiry, but it's a tough bit of stuff. I'm OK with there being less discovery here, because it's going to be a gigantically powerful result - predicting the frequency of a sound using the molar mass, density and Young's modulus? Awesome.

We're applying both of the expressions today in lab.  I'm spitballing the work flow here:

• Wave intro, animations, etc. Define wavelength, frequency, v relationship by analogy to traffic
• Longitudinal wave derivation:
• With known molar mass, modulus, and density, they determine k, d, the atomic mass, and v (using the dimensional analysis result)
• The real derivation - super-guided by me
• Demo singing rod, have them calculate its frequency
• Sing, record, FFT
• Party
• Transverse wave derivation:
• Animations - difference between longitudinal and transverse
• Derivation
• Give them sample of wire - they determine the tension needed to have the sound be an octave below a resonance box (128 Hz); help them with the standing wave's length
• Use force wire strung between two poles (one with a force probe on it) to measure tension. Other end of wire is still on the spool, which is on the rod. Kids twist spool so that the sound is in tune; reveal tension (or vice versa?)
• Party

The setup with the spool (yellow string added so that you can see the path of the wire):

Here's my drawing of the whole process:

Illuminations for Models

In the packets that I make for each unit (generally broken up by physical model), I include a little illumination-esque drawing, using the model's abbreviation as a backdrop to illustrate situations where the model applies. It's fun, and hopefully a kid sees something at some point on one that makes something click.

I'm drawing them (since BFPM) with SMART Notebook and my tablet PC (ThinkPad X220). I've finally found a use for Notebook!

Feel free to use them (with attribution and an email :) if you like them.

These are the ones that I have for the first term:

Physics and Honors Physics:
CVPM (Constant Velocity Particle Model (or Motion, as you prefer))

CAPM (Constant Acceleration Particle Model)

Honors Physics:
BFPM (Balanced Force Particle Model)

UFPM (Unbalanced Force Particle Model)

Physics:

OPM (Oscillating Particle Model)

Yellow to Green

My grading scheme this year for AP Physics (C: Mechanics) has, so far, worked out the best that I've had for that course. My physics/honors physics scheme involves (basically) one or two standards per model, so the standards are fairly coarse. The problems are easy (enough) to generate, and reassessment at more frequent intervals is good for reinforcement, practice, and experience for those first-time learners. Applying that to the AP course in the past has been problematic, given the headaches of senior scheduling and senior motivation. It's also another group of reassessments for me to prepare, schedule, and grade. I posted about this before, but I've made a few tweaks and it's started to actually get used.

Here's my scheme this year:

• The standards are more grainy (see the list here), compared to honors physics (here)
• There are (generally) two assessments per unit in class
• There's one reassessment available per unit, covering the whole unit
• I made a chart showing the acceptable evidence for each standard. Typically, it'll be two strong showings in assessments/reassessments for that standard or one strong showing and several out-of-class successes (problems) or a capstone or several out-of-class successes and a capstone
• Everyone's required to do at least one capstone per term, even if you rocked all of your assessments
• Students submit this slip when they have some evidence to show for a standard.  There may be some revision needed before it's accepted.

The extra outside effort needed to find and do problems and/or capstones motivates them to do good work on assessments, without me needing to wade through another sea of reassessments.  The capstones are my favorite part, and they're coming up with some great ones (more on those as they mature).  Overall, I'm liking the balance between giving them flexibility with their busy senior lives, keeping them accountable, and respecting the fact that, even though there aren't so many grades 'in the book' right now, they're still working.

Today's a big day, because the first student went from yellow (NY: "not yet") to green (P: "Proficient").  Many more to come of those, as well.

Balanced and Unbalanced Forces

We're starting forces tomorrow in Honors Physics, after having done 1D CVPM and CAPM motion (both algebraically and graphically).  In general, I'm pleased with how quickly and deeply they've picked up these concepts and how well they're already starting to tie them together.

I'm doing a new version of the lab that I call "Balanced/Unbalanced." Last year, I did a hoverpuck thing similar to Kelly's, but I wanted to try something a little different this year. I'm trying to surprise them a bit out of the gate and get them to reference data to (probably) disprove their own predictions - we'll see if they see what's there or what they want to see:

I'm setting up Atwood machines from my ceiling mounting rack, with about 130 g of mass on one side and a force probe on the other side:

The students will observe the motion of the force probe and its reading in several situations, including:

• at rest (130 g of mass balances the probe nicely)
• moving upward (still 130 g)
• moving downward (still 130 g)
• moving downward (70 g on the other side)
• moving upward (190 g on the other side)
• moving upward (70 g on the other side)

In each case, they'll note the reading on the force probe (some surprises there, for sure), draw a well-scaled force diagram, and determine what type of motion model describes the motion. The desired UFPM/CAPM (or at least not CPVM) and BFPM/CVPM connection should come quickly, but I'm hoping that the second, third, and sixth cases are very stark messages about the difference between net force direction and motion direction. 

Part of my thinking here is that students can doubt their reasoning a lot. Even if they go through what we'd understand as a very convincing linear argument, that's not always enough to convince them in their guts. Not being able to see force magnitudes (exactly) using the hoverpuck seemed to play into that a bit for my kids last year - there was this mysterious realm of stuff going on that we weren't measuring and, even though we had a good story about what was going on, who knows if there wasn't other stuff happening that they didn't know about - what if I was lying? What if their information was bad? What if their reasoning was wrong? All of that was a possibility, if they haven't really bought into, you know, how science works (and the fact that it works). This computer, though, it wouldn't lie to them (well, that seems to be how they think).

We'll see.

M and I: Chapters 1 and 2

I'm not a big fan of how Matter and Interactions introduces some algorithms upfront, well before their application, like looking at calculating relativistic momentum and breaking changes in momentum into parallel and perpendicular components before even broaching the momentum principle, but I can reorder a bit with no harm; my first set of assessments will group chapters 1 and 2 into a single unit, anyway.

They can also undercut my affinity for symbolic algebra, but I think that we'll be able to press ahead ok symbolically, for the most part.

Here's a progression of whiteboard problems that they did on the second day of school; they read about both relativistic momentum and the momentum principle the night before. They were familiar (though not by name) with the momentum principle already, having done a lot with both Newton's 2nd and impulse last year.

• Projectile motion: given the initial velocity (speed and angle), use the momentum principle (not kinematic equations!) to find the velocity of the particle after some amount of time.
• Projectile motion: use the position update formula to determine the location of the projectile at that time (quickie review of average velocity, including vector form now - hey, we're actually using average v for something!). This is great - two dimensions, no waiting (and no toolkit equations)!
• Space shuttle: if it used its maneuvering thrusters to fly towards Proxima Centauri, what would the issues be? Fuel consumption's a huge one, but let's pretend that it's not, and that the shuttle's mass stays constant (removing this assumption would be a great place to start a capstone!), and that it can get away from Earth easily enough. Using some nominal mass value and the real thrust of the maneuvering thrusters, how fast would it be going after, say, 15 years (using the momentum principle)?  It's going to take a while to get there, after all! Answer: more than the speed of light.  That's a problem. Now we look at the model that we use, and how the p and v grow with time (use program referenced in earlier post). What really happens, though is this (use relativistic def'n with the program). The momentum principle's always true - it's that def'n of p that was wrong.
• OK: how fast will it be going, then after 15 years?
• How far will have gone? Oops - that's too far. 
• Unfortunately, we can't solve analytically for how long it'll take, because of p's complex dependence on v. Time for a program! We sketched it out in pseudocode together, and they finished it in class or for HW.

This Year's Marshmallow Challenge

I always start off the year by doing (never by talking about the syllabus!).  We start with the Marshmallow Challenge, where the students try to build the tallest structure made of 20 sticks of spaghetti, one meter of tape, and one meter of string, to support a marshmallow as high off the ground as possible.

The TED talk accompanying it is great, and it's a great intro to standards-based grading.  What happened to those creative kindergarteners that were unafraid to fail and benefitted from their own mistakes to turn them into disaffected failure-shy business school grads? Well, school, mostly. The combination of high stakes (grades that are indelible) and low skills (what learner doesn't have low skills at the beginning?) creates all kinds of damaging behavior in the long-term (poor retention, little conceptual understanding, focus on "the answer," cheating, cramming) in the service of short-term gains, because those short-term gains are incentivized and they don't yet have the tools to earn them legitimately.

Anyway, this year I had 6 of 16 teams end with intact structures. The two tallest, both at 60 cm are below.

Last year's post

PS: I do allow them to use guy wires, but only connected to the table. Is that cheating? I dunno, but that's what I do.

Assessment Strategy for AP C

I'm running my AP C: Mechanics course a bit differently this year. Most notably, I'm using Matter and Interactions as the curriculum, which takes some major head-wrapping. I've done as much of that as I can before actually seeing students in the course. Frank Noschese, Mark Hammond, and I came up with standards and aligned old AP problems to chapters in M and I this summer, but the grainier nature of those standards presented me an assessment scheme challenge. Usually, my standards are much bigger, translating to fewer per term, and I only allow one standard to be reassessed per day (and only on M, W, and F, after registering via Google doc). Those standards, for fall and winter, look like this.

The AP standards look like this, with chapters 1-5 in the fall term, 6-10 in the winter, 11 in the spring (with some mechanism for including previous term standards that I haven't devised yet).

I was toying with some more project/portfolio-based assessment for this course, especially after I saw success with limited screencast reassessment at the end of last year).

What I'm going with is a combination of in-class and out-of-class assessment, which I'll put under the umbrella of 'portfolios.' Basically, there are a lot of ways that you can prove to me that you have nailed a standard (and it's your responsibility to make that case to me for each standard):

• Show me how well you did on in-class assessments that covered that standard and/or reassessments (I'm only preparing one or maybe two per unit)
• Show me how you applied this understanding to an in-depth analysis ('capstones')
• Show me a lot of problem-solving from the text (M and I's problems are generally pretty robust and most are not the kind of sterilized problem that you see in Giancoli, Walker, etc.)
• Ideally: all three.

I need a mechanism to make sure that not everybody's just doing problems, with all of the potential issues (ethics and others) that that entails. Maybe I'll make a tally sheet for them, so that they have to color-code the methods that they used, so they (and I) can see at a glance how they met the standard. I'd like to make sure that they do at least three capstones per term, as well.

I'm thinking about a binary scale (Yes, Not Yet) and a 50 + 50*(% of standards met) algorithm.

Thoguht?