Sunday, September 9, 2012

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.

Thursday, September 6, 2012

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.

Monday, September 3, 2012

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.