Thursday, March 31, 2011

Chains of Reasoning: Static Electricity #2

Ahh, Volta's Hail. It's my favorite static electricity demo. It really has it all: conduction, polarization, charge induction, attraction and repulsion, grounding...

If you're not familiar with it, here's the setup (image from

The top plate is put in contact with a Van de Graaff generator, and the conductive pith balls are resting on the bottom plate.  After that?

Let's warm up first, just like my kids did last week.  They broke into groups and each tried to come to agreement on one of the conceptual questions from the text (Giancoli) that I had given them for homework.  In the past, I have given these short shrift, but they can be a valuable part of your teaching arsenal, if you let them be.  I do clicker questions and conceptual ranking tasks in class, but I had always shrugged them off for HW before.  Anyway, this warmup worked really well for one section, and really well for two groups in the next section, but the other groups hadn't done their homework, and...  well, you know how well that goes.

The questions (paraphrased) and the whiteboard solutions:
  • If a plastic ruler is rubbed with cloth, it can pick up small pieces of paper.  Explain why, and why this doesn't work as well on a humid day.

  • What balances the repulsive force between the leaves of a charged electroscope?

  • Explain why clothes that have just come out of the dryer can sometimes stick to you.

  • When a charged plastic ruler picks up small pieces of paper, occasionally one will stick to the ruler and then quickly jump away.  Why?

The honors classes haven't done as many reasoning chains, and the results are certainly mixed here.  There are all the classics: the insufficiently justified, the over-written, the under-written, etc.  Some of these are about communication and learning what's really telling the story, and some represent holes in the conceptual understanding ("But I know the answer!" We all know that having the answer doesn't necessarily mean having the understanding.  They haven't all gotten the message, but we're getting there.)

The chains that we did last class and the conceptual homework have, however, delivered far greater understanding than what I've done in the past.  All of that demonstration, lecture, etc. gave them the sense that they knew what was going on, but...  this year, they're so much stronger with their conceptual understanding.

The difference really became apparent when we went to Volta's hail.  I laid out the scenario: the materials that the apparatus is made from, what I'm going to do, etc., but did not demonstrate and did not tell them what would happen or indulge their questions.  Get in groups, get on that whiteboard, and figure it out.  This part of the cycle I've done before (at least two years).  It's always a colossal bust.  Almost no groups figure out the complex set of things that are going to happen. 

This year, though... all of the groups eventually "got it," only about half went significantly down a blind alley (and they only needed a small prompting question from me to get them back on track), and they really discussed the concepts like folks that knew what they were talking about... ...because they did!

Here are a few of their whiteboards.  It was great seeing them move from their gut reactions (usually just that the pith balls would move up to the top plate) on to making a complete and correct prediction.  It's especially awesome that their understanding and reasoning process was able to overcome their initial guesses without any intervention from me at all!

These aren't bad at all, and I think that most of the omissions here are communication-oriented rather than about gaps in understanding.  Here's a fuller chain:
I will, though, give a video of the demo in action.  If you don't use it in class, I'd consider it, because it's really slick and is one of the few really active electrostatics demos.

Tuesday, March 29, 2011

Oh, the barbell

Last week, we tackled this excellent "Figuring Physics" problem by Hewitt (as posted in TPT):
I love this problem - it helps students differentiate between translational and rotational motion.

It's also a great example of a chain of reasoning that's not too difficult to lay out, but which has a critical choice to be made right at the beginning. This choice bifurcates the reasoning tree into "the real answer" and "bizarro world".  One's true, the other's the opposite, and... it all relies on getting one little piece correct.  Here are the dueling trees:

Now it's time to make the call: is the bottom of the bar moving forwards or backwards relative to the track?

If it wasn't moving at all - like it wasn't as the dumbbell rolled at the beginning, and like it won't be after the friction sets the rotation "right" again - then the bar would be rolling without slipping, which is a super-important concept for students to have a handle on.

The most amazing thing about rolling without slipping is that the total velocity of the contact point of the wheel is zero!  Here's a great picture of a wheel that's rolling without slipping, taken by Archan Baldev Luhar of Medfield High School, for the AAPT Photo Contest (any Tatnall students interested?!):

Great photo!  The v due to the rotation is the same as the translational v, but in different directions at the top and the bottom (and zero in the middle).  Excuse my lame graphic:

This means that the top moves at 2v, the hub at v, and the bottom doesn't move at all!

This is an excellent entryway into how friction works with wheels, both static and kinetic.  The direction of the static friction on a wheel can be hard for students to get, but it's just resisting the potential slippage of the tire (just like static friction always does), so you just need to figure out how the wheel would slip if there weren't any friction, and the static friction force is the opposite direction.  Neat, but a bit beside the point.

Here, we're looking at kinetic friction.  What's happening is that either the bar of the dumbbell is rotating too fast for the translational speed (which means that the bottom is moving backwards, relative to the track) or that the bar is rotating too slowly for the translational speed (which means that the bottom of the bar is moving forwards relative to the track).  It starts with the "correct" rotational speed, but that's the speed for the larger radius of the weight, not for the bar.

This brings us back to the question at hand, the choice that will send us down one path or the other (BTW, our dueling trees did narrow it down to a choice between C and D, so we already know more than we did at the beginning!), the measurement that creates two parallel bits of the multiverse, etc.

Is the bar rotating too fast or too slowly for the translational speed?

How fast does something rotate if it's rolling without slipping?  The rotational speed must be (you might have to click through to the post to read the LaTeX if you're on a reader):

We can easily determine the rotational speeds that the barbell already has and that it'll need to roll without slipping when the bar is on the track:

Here, r is the bar's radius and R is the larger radius of the weights.

It's easy to compare them with my favorite tool, the ratio:

If the needed angular velocity of the bar is greater than it currently has as it rolls on the weights,  we can say that the bar is rotating too slowly when it hits the track.  This means that the bottom of the bar is moving forwards (the forwards translational velocity is not canceled by the "rotational part" of the velocity), which puts us on tree #2!

As von Braun tells us, one experiment is worth a thousand expert opinions, so... (click through for video)

 The reason that I make a big deal about experiment here is that we all talked our way through the long chains of reasoning, and were smugly satisfied that the first chain was correct.  Sometimes, it really does pay to write a little something down.

In particular, it really helps to write things down when there's a symmetrical comparison to be made - it's really easy to get things backwards!

The reason that I bring up the experiment being worth so much is that the kids (bless their hearts) recognized that they hadn't quite wrapped their heads around the situation, and leapt to "let's do it!"  A quick field trip to the fitness room while others set up the track, and we were off.

The explanation came quickly, and the understanding was much more solid (and correct!).

Doing is learning.

Oh yeah - it works backwards, too: now the bar speeds up and the rotation slows! (click through for video):

Monday, March 28, 2011

Estimation Nation

So, it's the day before spring break.  As if that weren't motivation enough (for the students) to not move on with content, there were lots of kids missing and this was an orphaned 'A day' (we're on an A/B schedule, and I have one section of physics and one of honors physics on each of the days, so I have to be careful about missed days in order to keep them together).

So... let's do something fun! (as usual), but non-content oriented (not as usual).  Let's do...

Fermi problems!

Here are the ground rules:
  1. No calculators, long division, or long multiplication: stick to 1 or 2 sig figs (maybe the only time I say those dreaded words all year!) and concentrate on getting the right power of ten for the answer
  2. No research: you know more than you think you do, and you can figure things out from distantly related facts (remember all of those chains of reasoning that we've been doing?!).  Anything else?  Intelligent estimation.
I presented a big set of questions, and students, in groups, chose a question and dove in.  In the past, I have given everybody one question or assigned each group one question, but I thought that this was more in line with the WCYDWT? spirit that we've been going with this year.

Here's the list of questions (many creditable to Maryland's list), along with student solutions.  Many of the reasoning chains are pretty well-communicated, which is great.  Some haven't gotten there yet, but we're working on it.
  • How many piano tuners are there in NYC?
  • How many hairs are there on your head?
  • How many pencils would it take to circle the equator?

  • What's "your share" of the land area of the Earth?
  • How much (per hour) will you pay for classes in college?

  • How many drops of water are there in the Great Lakes?
  • How many blades of grass are there in a typical lawn?
  • If you remove all of the string from all of the tennis rackets in the US, how far could it stretch?
  • How heavy is the rain that falls on the school's roof during a big storm?
  • How many hours would you have to work (at minimum wage) to pay "your share" of the national debt?
  • If the whole US were a pool, how deep would it be when filled with all of the milk consumed in the US in a year?
  • How many flat tires are there right now in the US?
  • How long would it take you to reshelve every book in the library?
  • Could we build a pipe organ in the classroom that covers the whole range of human hearing?
I thought that it was interesting to look at which ones were popular and which weren't.  Mostly, students stuck to things close to their experience and/or in their personal interest (pencils, tuition cost).  These are also very concrete ideas - easy to get a handle on for students.  At least we have a consensus that it'd take some number in the low hundreds of millions of pencils to circle the equator!  You can rest well during spring break now, secure in that knowledge.

The next time we do Fermi problems, I'll force some engagement with some of these that just seem impossible to them (until they dig in), like the drops of water in the Great Lakes, the number of piano tuners, or (my personal favorite) the amount of water flowing through the Mississippi River in a year.

    Wednesday, March 23, 2011

    The Fine Line

    Teaching is a series of balancing acts - a net of fine lines that you don't want to cross, like a Socratic Tholian web.

    Here's one related to SBG:
    • What's the balance point between an ethos of "ongoing assessment," where students are psyched about having their "grade" increase as they attain more and more mastery of the material, and an environment where they feel like "every time I ask a question, my 'grade' goes down!"?
    On the pro-assessment side, I want to have a record of growth in each standard over time.  Later applications will (hopefully) be more successful than later ones, and showing the growth in understanding (or lack thereof) is one of the important factors that make SBG so great.

    I record scores each week (I track them on a sheet, enter the scores at the end of the week, and that goes into the graph - here's a post explaining the current system of SBG that I'm using, and here are some better examples of tracking sheets and some of the graphical summary sheets that the students get).  Unfortunately, here aren't that many weeks that I'll be guaranteed assessments on any given standard, so I do want a score on that first shaky-legged-foal week.  I'll probably only get three or four scores for lots of the standards (maybe fewer!), which isn't as many as I'd like, but it's a lot better than two or three.

    I also like the idea that they need to always be "on": that really knowing something means that you know it.  You can bet that none of those fantasy football-playing guys and gals that I have would let someone talk about an awesome play on 5th down that they saw last night, but they often don't have the same awareness of physical concepts.  They should.  That's what knowing means, and it's what I want for them.

    On the con side, I have actually heard the feared "Big Brother's watching" response from a few kids.  One of our first models was of the awesome WCYDWT: Tricycle Race video.  Students posed questions and dove in to start answering them.  Stuff was going swimmingly - maybe a week in, and they're already rocking independent exploration.   

    Here's the rub: I'm taking some notes on their modeling skills, units, algebra, kinematic issues, etc.  It's pretty low-key, and most students ignore me (except when I'm asking them something or they're asking me something).  One young lady asks about something (I don't remember what), I answer with a question (probably, knowing me), and a few minutes of appropriate confusion ensues.  I'm nearby as they work it out and get back on track.  I make a note, and here comes the reaction:

    "Wait, every time we ask you a question our grade goes down?"

     That's the sort of thing that garners attention, and it was one of those moments where kids' impressions of you, SBG, and physics are cemented (physics? that's silly!  Don't let my little puppet show represent Archimedes, Einstein, and everything in between!). 

    My spin (and intent) was to communicate that they haven't quite caught on to how SBG works yet: sure, having a pretty large misconception about physics means that this standard score won't be as high as if you didn't have it, but it's a heckuva lot higher than if you didn't work out.  That, however, is a secondary issue about interpreting this bit of "grading." Here's the main event:

    Nothing that you do today is set in stone.  As long as you understand more tomorrow than you understand today, you don't have anything to worry about as far as your grade goes. 

    I tried to make it clear that I want their grades to represent what they know or can do right now - nothing more and nothing less.  What that means for "the grade," be that an upward trend or a downward one, well...  that's up to them.

      Wednesday, March 16, 2011

      Chains of Reasoning: Static Electricity #1

      In the past, I've been guilty of blowing through the whole charge transfer/induced charge/polarization thing in a day, and not coming back to it well until the test.  That's sort of how we're trained, though, isn't it?  If there aren't any numbers, then it's "easy." 

      Of course, it's not true, and spending some time thinking about the concepts just on their own merits is vitally important to make sure all of those numbers go together well when you get there (assuming that you're writing good problems in the first place, that kids can't just see through and that actually require understanding!).  I'm hoping for some much better RC circuit understanding later. *crosses fingers*

      So we started today, talking about protons, electrons, Ben Franklin being a jerk, polarization, induced charge, etc.  The big addition is some time for them to construct a reasoning chain about what happens to a negatively charged electroscope when you bring a positively charged object nearby, and the same for a negatively charged object.

      The electroscope itself is awesome: there's conduction, repulsion, the opportunity to talk about polarization (bring a rubbed balloon near it, but don't actually transfer any charge) and induced charge (same, but touch the leaves with your finger briefly, then remove the balloon).

      Here, though, we charged it with the balloon and thought about what'd happen when you bring a negative charge nearby:

      ...and a positive charge nearby:

      These are the first explicit reasoning chains that we've done with honors physics, so we'll see how it goes tomorrow, when we go after Volta's Hail storm.

      We did, BTW, make the simplifying assumption for our drawings that all of the charges are mobile (protons and electrons alike).  No, it's not true, but it's the assumption that we make for circuits anyway, and we do talk about it a bit.  There's an animation that does a good job of showing what happens when you keep track of all of the charges and don't let the protons move, though.  This would be a bear to draw, and I'm always worried about losing the physics in the laborious process of drawing, writing, building, etc.  Let's keep it simple for now.

      Of course, there were the obligatory hair vs. Van de Graaff pictures:

      ...and Hugh's really bad at picking things up (image links to video):

      Tuesday, March 15, 2011

      Chains of Reasoning: Doppler Effect

      The students are getting better at reasoning chains, even as the problems get harder!  That's the good news.

      Here's the prompt that they worked with last class.  This. is. a. hard. one.

       ...and not just because the time scale on the second pressure vs. time graph is jerky (I'll blame a previous colleague, who put that graph together :) ).

      Now, with these problems that I've been posting (here and here, so far), I am giving the students a whiteboard, and they're working in groups.  The Coke/Sprite problem was non-curricular, and we were just working with a cool question and looking at reasoning.  The Sand/Standing Wave problem was from the just-passed winter final, but I gave it in a stripped-down form, including the given information, but no sub-questions - just the ultimate conclusion that I meant to get them to/ meant them to get to.  The same thing is happening here, so don't think that I throw them into the deep end with this problem on the test (though, that's the ultimate goal, isn't it?).  I'll talk more about scaffolding during tests in an upcoming post.

      Here's my reasoning chain (tree?):

      Even though there is a lot of reasoning to be done here, the biggest hurdle by far is the step with the star: the relationship between the Doppler frequency shift and the beat frequency.  I gave two different ways that students came up with to reason through this: the left-most one is more mathematical and formal, and the second is more of a conceptual argument.  I didn't include the third argument: a graphical one.  This one's pretty slick, and was relatively common, though some students still don't believe in the power of diagrams (grrr)!

      I love this explanation - it totally encapsulates both of the reasoning boxes that I used in my diagram!

      The student chains are all improved from the first two, though many still eschew getting into the nitty-gritty of the reason that the beat frequency is twice the Doppler shift.  They figure out (by hook or by crook) the answer, and it's the answer that that captivates them, when it should be the concept and the structure of the argument.  Some are really starting to roll with this, though!

      The real story:

      Who cares what this answer was?  You'll never see this problem again!  Understanding the principles that we used and how to structure the argument let you solve the next problem!

      No fancy math required; accurate thinking essential.

      Monday, March 14, 2011

      Tipping Cars

      AP Physics rocked a Fermi problem this week on the wind speed required to tip over a car!

      Standards - How Many?

      How many standards per term/unit/whatever is too many? ...too few?  I've landed at around 25 per term (trimester) this year.  For AP, I go with about 5 per unit, with 6 or 7 units total.  The AP standards stay the same throughout the year, since the year leads up to the AP exam.

      Too many standards means that it's difficult to assess them all enough to show any sort of progress during the term and/or year.

      Too few risks having not enough resolution to pinpoint student difficulties.  This makes it hard for students to identify where they need work, and for me to identify where to reassess an individual and how to steer the course.  If you start thinking about the extreme case of this problem - only 1 standard, called "physics" - then you see just how poorly a "regular" grade communicates!

      Friday, March 11, 2011

      Chains of Reasoning: Sand and SW

      I'm trying to directly, explicitly work on students in physics reasoning well.  By "well," I mean that they can construct a linear path of inference from known information to the conclusion.

      They think that this is easy, and that they're just "not showing" some steps that they did in their heads, but... about two-thirds of their initial answers are wrong!

      Here was the prompt:

      This is the best of the student work; I was surprised at the amount of difficulty that many of the groups had here.  Many thought that they were just not writing down some steps, but when I made them do it, there were gaps in their logic.  Filling in the gaps led to the correct answer!

      My main message:

      Science isn't about 'knowing;' it's about being able to figure out something that you don't know!  If you can't reason, then you're not doing science.

      The biggest resistance is from the 'memorizers,' and why not?  It has worked for most of them before.

      Here's about what I'm looking for - the student group above did a pretty good job of it, but many groups weren't quite able to get to here:

      One thing that made it trickier for them was that this isn't really the totality of the situation.  If I really went through everything, it might look more like this:
      The reasoning process isn't linear - there are branches, dead-ends, parallel tracks, islands that don't connect, etc.  It's a central skill to be able to prune that tree - to figure out what inferences and facts are relevant, and how they connect to form a complete argument. 

      How do we teach that?  Well, that's the trick, isn't it?  I think that being forced to explicitly write it out can help model the processes will push them in the direction of logical progression of thought when they don't write it down, but I'm open to suggestions!