Thursday, February 28, 2013

Chunking, Reading, Video Games, and Physics

"Chunking" is what the brain folks call it when you group information into larger (relatively automated)... well... chunks. The idea is that, by doing this, you're reducing the amount of information processing that you have to do on a moment-by-moment basis.

It's really important in reading: if you were sounding out every word, could you read Moby Dick? Definitely not, and not just because it'd take forever. The larger chunks are that you can process with relatively little effort, the more mental energy that you have to make connections between them and do other higher-order thinking.

It's also important in both reading and writing music. Why do musicians practice scales so much? part of it is so that you can think "that run is in F minor: Ab up to G down to F," instead of "OMG: Ab Bb C D E F G F Eb Db C Bb Ab G F". When you do that, you can play it faster, think about your rhythm, tone, balance, blend, and intonation, and do all of the other things that make it music and not just notes. When you're composing, if you have to think about voice leading, scales and modes, rhythms, instrument ranges, counterpoint, etc. very consciously, then you have no mental energy left for the big picture - theme, development, form, etc.

This applies to just about every human endeavor.

In physics and math, students can get lost in the trees and miss the forest very easily. There are at least two prominent forms that this takes:

Completely missing the point of the problem: 
Students sometimes do a ton of work, but using tools that don't apply to the problem. If they're not consciously looking at the situation, evaluating which models do and don't apply ("OK, there's a net external force from the rope pulling the box, so momentum isn't conserved and the rope is adding energy to the box-system, so it's not conserved, but it's not accelerating in the vertical dimension, so the forces are balanced and it's in constant v motion in that dimension, but the forces are unbalanced in the x-dimension, but the pull force isn't constant, so I can't use the constant acceleration kinematics that I know."), then sometimes they'll go completely off track.

This model determination is something that we have to foster in students. Some ways to start doing this:

  • If you work example problems or the class does them together, with you writing, make this part of the process really explicit, and make it happen before you do anything else. Don't start writing your IF chart or conservation equation and then off-handedly say "well, there's no friction, so we'll use CopM, right?". Do it every time.
  • Give students - early and often - chances to get it wrong. It's easy to fall into the trap of only giving practice and assessment problems using the concept du jour, but it hobbles them later. Ever have great unit assessments and terrible comprehensive exams? This'll do it. This opportunity is why I went back to a CVPM CAPM BFPM UFPM sequence (instead of CVPM BFPM CAPM UFPM) - it gives students (in the second unit) a chance to differentiate between models. I really like to introduce models in pairs and emphasize that: CVPM vs. CAPM, BFPM vs. UFPM, pTM vs. CopM, ETM vs. CoEM. Having choices to make between just two competing models is a good stepping-stone to the bigger choices when all of the model are in play, and if you don't emphasize it when the choice is easy, then they won't be able to do it suddenly later. This part can easily get lost in the planning. I do a good job of using 'older' concepts when they apply in the new context, but I need to give more practice and assessment of those skills just for their own sakes later in the term.
  • Make articulating model choice a part of assessment - consistently.
Incomplete Mastery (conscious competence):
When students don't fully master a skill (or don't practice it periodically after mastering it), they have loose ends. Maybe they don't even have that - maybe that can do it accurately, but they just have to think it through and put a lot of effort into it to get it right. That doesn't only take time, but it takes mental effort, which is a finite resource. This goes back to some of the things in the posts about fluency here and here and here.
  • This comes up a lot with skills that are used often, like symbolic algebra, trig (breaking vectors into components and the reverse), graph-making, unit conversions and prefixes, etc. 
  • It derails the more important thought processes that we're trying to get to - it's that mental energy allowance, in addition to the time issue, for assessments.
  • It builds a poor foundation for later concepts. In math and physics, everything (should) build on what came before. Having middling understanding of something means that whatever application or extension comes next already starts out on shaky ground.
Both of these cut down on the level of complexity of situations that students can analyze: they need to be able to quick dissect the situation into models (maybe several different time intervals with differing models) and then have the fluency to apply those models accurately. That's a tall order, and they can't do it if their brains are exploding trying to remember some details of each skill or concept simultaneously. The ballistic pendulum's a great one to work on with this: you have at least three different sets of models applying to different time intervals over the course of the motion, and we all-too-often blow past that determination step. The same goes for the Atwood machine. Once you're through introducing mechanics, have students model it with forces/kinematics, momentum/impulse, and energy/work. It's a brain-buster for them trying to determine why the force exerted upward by the pulley on the string DQs conservation of momentum but not conservation of energy.

Here's a video game analogy: if physics is like Mega Man (or a million other games), then the tools (graphs, IF charts, LOL diagrams, FBDs, etc.) that we learn are like the weapons that you get when you conquer a level. Didn't beat Fire Man? Then you don't get to use Fire Storm. (OK, I had to look that up - high school was a long time ago. Also, feel free to update with more relevant video game references. :) This is another way to help kids chunk in their physics analysis - those kinematics toolkit equations might be handy, but they only apply in certain situations, and if determining which models apply isn't part of their process from the beginning, they'll be trying to use them later, when the acceleration's not constant.

One more thing: don't keep understanding about the learning process to yourself - talk about it with your kids, and often! Many students think that they know how they learn best, but they frequently fool themselves into thinking that something's solid when it really isn't. If you can convince, cajole, exemplify, and otherwise harp on meta-cognition consistently, then you can change how some students learn. Once they really can evaluate for themselves whether their mental models are solid, the subject material's beside the point.

Wednesday, February 27, 2013

Musical Instrument Project

Of all of the projects I've done with my physics class, this is the only one that has consistently come out great. There are often high levels of achievement and a comparatively low risk of incomplete or far below-average projects. Managing these types of projects often means being pulled several ways at once, and the squeaky wheels can sometimes get the grease - it's a difficult balancing act, so look out for that. One thing that has helped this (and my honors physics independent project) has been to spread out the work days. Instead of four consecutive days, breaking those up into pairs or singles separated by other work (especially review activities) can help any groups that don't have an idea or are otherwise behind and increase the overall quality of the projects.

The task here was to create a musical instrument which is in tune with the rest of the musical world (providing evidence of that), can play a short but recognizable tune, and describing the timbre and standing wave properties by graphs and diagrams. At the end, the groups present their instruments and their mini-posters.

During the course of the project, each instrument is revised a lot; some completely change and some need model tweaks - using the end correction, sometimes the tension/wavespeed relationship or Helmholtz resonators (none of which they knew about before this). It's a great chance to really experience that prototype/revision cycle.

Here are some of the projects, and links to the recordings:

  • Capped tube marimba - this is an instrument made of PVC tubes, played with a mallet on the caps. Video

  •  PVC pan flute: this is really more of a PVC bugle assembly, made from five pipes played by one player. This had a really interesting behavior in that it behaved both like it had open ends and one closed end. Video

  •  PVC trumpets - similar to the one above, but played with teamwork. Some evidence of that dual behavior is seen here as well. Video

  •  Uketair - it's always difficult to build a string instrument. This group did a good job of building a resonating box, using shaved golf tees for stable tuning pegs, and making a bridge from a bolt. The fishing line strings stretch too much after tensioning, which makes it really difficult to keep in tune, but the principle's there. Video

  • Tuning fork resonators: these were custom-cut tubes that amplified the sounds of tuning forks. Even at that, they weren't super-loud, so they recorded the sounds and arranged the song in Garage Band. Video

  • Leg Marimba - this one was going to be a Blue Man Group PVC and paddle instrument, but the paddles didn't work too well, so they revised to using their hands and then (in a stroke of genius) to their legs. Video

  •  PVC Clarinet - This one wasn't really a clarinet, since it used buzzing, but the first design involved a reed. I had a couple of groups use reeds successfully last year, but none stuck with it this year. This was the first instrument that I've had with a reasonable implementation of holes to change the pitch. The timbre gets crazy after several are uncovered, but it does a reasonably good job of producing an intelligible pitch.
  • Batterie De L'eau (water drums) - this one also went through several revisions. By the end, they used a small strip of paper across a plastic container filled partially with water. By using the end correction, the contained resonated to selectively amplify the desired frequencies from the noise of the paper strip. It's a noisy sound, but the pitch is clearly audible. Video

  •  Pan Flute - this one's a PVC pan flute proper. The end correction proved a little trickier in here (I think that the face near the end affects the dynamics a bit, reducing that effective length), but worked out well overall. Video

Tuesday, February 19, 2013

Practice: Art and Physics

I took a drawing class last summer - the first time that I had any instruction to speak of in art. I did this partially for pragmatic purposes (diagrams in class, etc.) and partly for enjoyment. I wasn't great at the beginning, and I still am not great, but I'm so much better now than when I began. I'm also much better than I thought that I could be at drawing. I thought that I knew what types of drawing I would be good at and what types I wouldn't be good at, but both of those estimations were off of the mark.

The transfer to physics learning (or any other learning) is real:

  • Even if you're not good at something, you can improve dramatically through intentional practice and engagement with feedback. The 'intentional' and 'engagement' parts are really important.
  • You can't be sure about what your 'talents' are before putting in work. We're obviously not all going to be Paganini, but we could all improve a great deal by practicing the violin purposefully over the course of a long time period.
  • Consistent practice over time is better than fits and spurts of intense work. I haven't practiced a lot, but I'm now doing an open figure drawing session twice per month. I could get better faster by practicing more often, but doing the time that I am doing all at once and then stopping for a year wouldn't be as productive as spreading it out.
My first attempt at a face, back in the summer:

My most recent face, from yesterday: It's not the best face ever drawn, but it's a ton better than I even thought that I could do!

Sunday, February 10, 2013

How Much Information Is Too Much?

We're getting near the end of the term, and there's a characteristic increase in the rate of reassessments. Some of this is just natural: there are more standards in play, and the standards introduced later in the term all must be reassessed in a shorter window than the earlier terms. Also, those standards are assessed fewer times by me, so some students that might've worked it out on another in-class assessment need to do it individually. Of course, there are also students putting things off until later in the term. Some of that, though, is also benign - there are a lot of papers/tests/projects/reports/HW due (with a capital 'D') in other classes, so, if they can still demonstrate that proficiency, but later in the term, that's just a good time-management decision. There will always be some students that procrastinate, too.

Here's a question that I've fielded a good number of times over the past three years that I've been using SBG: "will this standard be on a future assessment this term?" I've never quite known what to think about that. Several possible scenarios come to mind, some troubling and others perfectly reasonable:

  • The scariest interpretation: "Can I just ignore this now?"
  • "Should I bother to reassess this individually, or will it happen anyway without me scheduling and taking an individual reassessment?"
  • Another cynical one: "At what point should I actually try to learn this?" 
  • "I'd like to plan my limited number of reassessment days (remember that we're within a couple of weeks of the end of the term, and they can only reassess one std/day, only on M, W, F) - do I need to use those for a different standard, and pick this one up on one of yours?"
Much like Star Trek movies, two and four are good and one and three aren't. I might be overly optimistic, but I think that, for most of the kids that have asked me (thinking of the individual kids that have asked me), it really isn't a diabolical or cynical question, but one about time management.

I'd like to hear your thoughts: how much information should students have about upcoming assessments? I sometimes list the standards that will be the primary focus (no promises about anything else that might come along with those) on the calendar. Is that beneficial for time-strapped students trying to best plan how to demonstrate as many proficiencies as possible or does it support mercenary rating-collectors (points-collectors for a new age)?

Python, Ramps, and Energy

We're early in energy in Honors Physics, and I went looking for an applet that I used last year with some animations of ramp races - you know, the flat one and the down-an-up one: which ball wins the race? which ball gets to the end at a higher speed?

Anyway, I couldn't really find it, but I did stumble upon the dissertation of Thomas Thaden, which was related to this sort of thing, and which has a big series of possible outcomes of the race. They're small Quicktime videos and I didn't think that they were big enough or clear enough for what I wanted to do, so I wrote a simulation in VPython.

I think that this is much more interesting than what I was planning to do, which was to just have them predict, argue, and then see the results (peer instruction-esque). Instead, I'll have them check out five different possibilities, poll them, have discussion, and see what kind of consensus comes. Maybe there won't be one, but we'll be defining the gravitational PE that day, based on our lab from the previous day (maybe more on that in another post, if I have time), so that could help.  I'm torn about whether to do that first or second, but maybe second is the way to go.

Anyway, the five models in the simulations for the down-and-up track are:

  • Correct physics
  • Constant speed
  • Constant x-dimension speed, constant y-dimension speed while on the ramps (tie)
  • Accelerate down the ramp and up the ramp, but back to ball 1's speed on both of the flats
  • Accelerate down the ramp and up the ramp (but too much, so that the balls end up tied)
The videos are here (not in that order :) - A B C D E 

Let me know if you're interested in the VPython script! Edit: Python script is available here. Let me know if you find it useful! There's a bug in there that causes odd behavior with some ramp configurations. Let me know if you find it!

Thursday, February 7, 2013

The Innovation Game

Our esteemed Latin teacher Charles came up with a great idea - "The Innovation Game." The purpose is to create a community of innovation and to start conversations about new things in education, connect to each other as teachers more, provide an easy way to put new techniques into action and a safe space to succeed or fail, and to generally spark more discussion around education.

The highlights:
  • Every month, one teacher leads a session in which he or she introduces an innovative technique that he or she has found successful in the classroom
  • During the following month, everyone else will try out that technique at least once
  • An online forum will be set up - as soon as you try the technique, you report to the forum, and discussion ensues
  • A free wrap-up lunch occurs a week or so before the next session, to discuss further, celebrate successes and failures, and to build collegiality
It's still in the planning process, but there are a good half-dozen teachers on board, and we're looking forward to starting soon! Comments and suggestions welcome!