Monday, December 31, 2012

Using Google Docs for Labs

I have a couple of labs that I have flipped the data collection process for, and done more of the analysis in class. There are advantages and disadvantages here:


  • Less time taken in class for data collection, more time for data analysis
  • Everyone gets to make the measurement, instead of some students sitting on the sidelines
  • More data possible, as we can bin the data sets for big group analysis
It's this last one that has the most impact on whether I do the data collection like this or not; if we need a lot of data, it's boring and cumbersome for each group to do it and not as easy to share as it should be within the classroom.

Some disadvantages:
  • The collection process has to be simple and cookbook enough for students to be able to do it independently, with essentially no equipment (simulations and videos are good)
  • There's not any tinkering with the setup or designing the experiment
  • It's not appropriate for introducing a completely new paradigm - not at all
  • Students can't/don't easily ask questions, so you can get some junk data if you're not careful with the design and instructions
With those caveats, there are some cases in which I've found it quite useful:

Experiment 1: Period Measurement Techniques
Students did the experiment here.

The goal was to look at the effects of different measurement techniques on the period value - not just the mean, but the width of the distribution. I use this to introduce the concept of distribution width, too.

I put columns into the Google spreadsheet to calculate the period for each method and then paste the data into Excel, where I graph the normal distribution derived from each data set and graph them on common axes:

There's not much choice about this one - you need a big data set, and this is the easiest way to collect and analyze it that I've come up with.

This requires some manual cutting/pasting, etc., but the next one's nice and automatic:

Experiment 2: Resonance
I'm doing this one during the upcoming unit; I haven't done it before, but I think that it's relatively foolproof.

Students did the experiment here, which uses an applet dealing with the amplitude of a driven string. We're getting at the idea that a system will respond with a big amplitude only when it's driven at or near one of its natural frequencies (the frequencies of the allowable standing waves, in this case). This is a great intro to musical instruments: the buzzing of a mouthpiece or reed isn't really producing a single pitch, but a wide spectrum of noise, of which only the instrument's natural frequencies resonate and are heard.

This one is much cleaner with the data analysis. I used Python and GoogleCL to download the Google doc data, sort it, and graph it automatically.

The code looks like this:

And the output looks like this (fake data that I used to test it):

I do these infrequently (about once per term), but it can be a big help. I also wouldn't do them in any sort of context that required big paradigm-building, etc. They're straightforward cases where I need a lot of data, where that data can be collected over the internet or at home, and where the experiment's straightforward enough and involves an established setup or concept that I can trust them to give me accurate data.

Tuesday, December 25, 2012

Sharing Whiteboards

What to do with student whiteboards? Pick a great one and share it with the school! Here's a display case that I had Operations build to show off whiteboards outside my room:

Some Capstones

A few capstones from the AP class in the first term. I wasn't super-happy with the management of these - not enough revision and discussion - but there were certainly some good ones in there. Here's a smattering of the final reports. Some include VPython programs which are pretty neat, too.

  • A capstone where a student writes a VPython program to prove that the freefall time for any tunnel through the Earth (along a chord) is the same
  • A capstone where a student write s a VPython program to verify the time for the freefall through the center of the Earth (comparing to the solution for the SHM diff. eq.)
  • A capstone where a student calculates the through-the-Earth times for different planets/objects (that was a popular topic this year)
  • A capstone where a student analyzes a clip from Toy Story, where the slinky dog dives down, changes mass, and spring back up
  • A capstone where a student builds a tricord instrument, predicts the correct mass to tune the string to a chord, and tests the predictions
There were several others, and this is just a selection. There were also lots of cool ideas that fell by the wayside for expediency, which is something that I'd like to avoid happening in the future. Some cool ideas about programming a simulation of the view of the Venus transit from Earth (I couldn't quite get this one to work myself, but it was an awesome idea), simulating the Home Alone bucket swing and crash (this one's totally doable), and a few other really neat ideas unfortunately were lost along the way. Oh, well - two more tries left this year. Lots more good ones to come, I'm sure!

Homework Worth Doing

I posted a few weeks ago about motivating kids to do homework by making it worth doing. That's a pretty heavy gauntlet to throw down, and I did have at least one Twitter response calling me on that. I don't claim to always have the right answer to this, but there are a few things that can take us in the direction of kid-obvious worth, I think:

  • The most obvious kind is practice. This is an easy type of HW to give, but the tricky part is making kids see that they need it. Assessments should be framed as an opportunity for the students to find out what they need to work on - as formative, rather than summative, and HW is then the second step in a lot of cases. This is a difficult thing to do, and it requires a lot of frank talking with students in class, particularly at the beginning. I get better at selling this every year, but you'll never have every kid on board. Those kids that you can't ever get probably weren't getting much out of "completing" mandatory HW anyway.
  • Deeper applications of concepts that you already know can work, but they can be difficult to pull off. Because of their nature, lots of kids are going to miss a subtle concept in there, and you'll have a few successful solutions waiting around for everyone to catch up in class. Depending on the kids and the culture, you may have a large percentage shut down and come in with something blank. It takes good scaffolding for these, and I'd use them sparingly - this is exactly the sort of thing that class is good for.
  • Simulations or calculations can take some of the time-consuming, but not super-difficult bits of lab work outside of class. If kids are following up on a collision lab by calculating the center of mass velocity or change in kinetic energy for each system, that's something pretty easy for them to do, and they won't mind doing it (because it's not mentally taxing), but it'll save you class time. If they're at the point where they're pretty comfortable modeling, you can give them a simulation and have them model the relationship. I do this with universal gravitation (since we can't do the experiment in class anyway) and sometimes with circular motion, depending on how I'm feeling about experimental setup. At this point in the year (early second trimester), they're mostly ready to do that - certainly the design, data-taking, and graphical modeling, and most can do the algebraic modeling as well. We can then wrap up the relationship together and have a good discussion when they're 'fresh,' rather than after they've spent an hour taking data and running fits, etc.
  • Another useful kind is new explorations. If they're framed well and have a low barrier to entry, they can be really productive. The first one where some kids obviously didn't do it should bring some helpful peer pressure as well. If you have one where nearly everybody doesn't do it and there's a frustrating day, that's a good candid conversation to have with them (and to remind them of the next time).
In this last vein, I have an example, using this gravity simulator (I just got sidetracked for 10 minutes playing with it while finding the link):

This is basically a way to get the conversation started on elliptical orbits, while reviewing a bit about circular orbits and Newton's laws. The kids come in with all sorts of observations and ideas, and it is a great springboard into the topic. If you do this in class, you end up having to curtail their investigation in the hopes of getting the discussion started, which isn't super fun for anybody. 

Not every assignment worth doing looks like this, but it's a way to start to think about meaningful HW outside of class that isn't practice on old topics. 

Thursday, November 22, 2012

Newton's 2nd Lab

I thought that I had posted about this apparatus before, but I guess that I hadn't, so here goes:

I've tried several setups through the years for students to model Newton's 2nd law. Qualitatively (balanced vs. unbalanced, direction on "unbalance" is the same as the direction of acceleration) getting the concept should come first - I have a previous post on that here, but when it comes time for modeling acceleration's dependence on force and mass, the setup can be tricky. Some that I've tried and/or seen:

  • Pulling a cart with springs, measuring acceleration with a motion detector; it involves a lot of performance (keeping the spring stretch constant) time and practice that I'd rather have them spend on the analysis, especially with my small number of class days
  • Half Atwood machine: you can easily vary the hanging mass to change the force exerted on the cart, but you can't equate the hanging weight to the tension, and you can't solve for it unless you know N's 2nd already. You can change the mass of the cart, but then you're changing the tension.
  • Half Atwood machine, analyzed as one system: it's procedurally easier, but mystifying for students. Looking at the whole system means that your vector directions will have to be changed because of the pulley, which seems mysterious to students that haven't done that much force analysis. Keeping the weight of the hanging mass constant while adding mass to the cart is easy, but then they really need to record the total mass of the system, which is a bit conceptually tricky so early on. Keeping the total mass of the system constant when you are changing the hanging mass is similarly black-box for them at this point. It's an elegant setup from our point of view, but doesn't ultimately make much sense to most of them at this point in their physics careers
Here's what I used this year:

Half Atwood machine, with a force sensor screwed to the cart (the string's tied to the sensor). A motion detector helps them find acceleration (from the slope of the v vs t graph):
  • The system being analyzed here is just the cart. The force probe measures the tension directly, so no complex analysis or tricky conceptual arguments need to be made. About halfway through, it's good to stop them and ask them to compare the hanging weight to the tension force reading and to explain the discrepancy conceptually.
  • Varying the force exerted on the cart just means varying the hanging mass, and varying the mass of the cart is simple, too - no mysteriously motivate shuffle of masses back and forth. The experimental design is completely transparent to them.
  • You might want to have them split into two factions: some groups investigate how acceleration varies with force and others investigate the dependence on cart mass. They then present whiteboards and the class can determine the combined model from the two partial models. Don't underestimate the reasoning leading from the two individual models to the combined model.
Everything seemed to go quite smoothly (that last conversation's still a bit difficult - I need a better angle on that, because it happens frequently), and my students this year have become stronger conceptually and computationally than with the setups that I've tried in the past, while moving at a faster pace. This one seemed to work quite well.

Tuesday, November 20, 2012

Spring Wave Speed Lab

My first lab with the spring wave speed used to be a prescribed method of stretching the spring, then keeping the length the same, but not using all of the spring, using the unstretched spring amount as a stand-in for tension, etc. ... It became more about direction-following and less about understanding than I wanted, and I had to dismiss the possibilities of amplitude, etc. affecting the wave speed. At the end of it all, they still didn't have the main idea (that wave speed only depends on properties of the medium) in mind very well.

I've gone to a more open-ended WCYDWT-style lab:
"Here's a slinky: look at these cool wave pulses. What do you think might affect their speeds?"

Take down the list dutifully - this year's ideas:
First section:
- Spring tension
- Amplitude
- Carpet vs. tile floor
- Horizontal vs. vertical pulses
Second section:
- Spring stretch
- Amplitude
- Frequency (this was a fun one to test. There was a metronome involved, and it was tricky to measure the speeds of the lower frequency waves, but it was a good experience for the hearty)

They did a much better job of experimental design, whiteboarding, and presentation than in the past. I'm still having to answer too many questions/guide Socratically too much about what should be on the axes and what the order of the axes should be, but the Honors classes are much better in that regard. Time will hopefully improve this situation for both. Everybody's getting the experience of designing and analyzing, and of calculating the wave speed, too, regardless of their question.

The whiteboards:

Question Boards and Answer Boards

I've been taking pictures of student whiteboards for a while, uploading them to our online classroom on our school's website. When the problems are different, they can be a source of extra practice (complete with solutions) for students.

When the framework is WCYDWT (What can you do with this?), the problems are definitely all different, because they're generated by the students. Today, I had them shoot a launcher straight up in the air, and then they had to develop and answer a question when the launcher was at some other angle. They determined the initial velocity from the first shot, and then came up with a variety of other scenarios for the 2D shot, including simple range equation angle and distance determinations, all of the way up to firing a ball into a moving CVPM buggy.

I structured the whiteboard sharing a little differently this time, though. I had each group write up a nice solution on their big whiteboard, just like normal, but I also had them use a small whiteboard.  On the small whiteboard, they made clear what their question was and included only raw data. This is the "question" board, and the big one is the "answer" board. This makes the process of using these as practice problems more practical and more like "flying solo."

Here's an example:

Thursday, November 15, 2012


Today was the day for the collision practicum! I set up the air track, cart, and pendulum like this:

I released the cart from the top - 4.8 meters away - and they could time how long the trip took (3 trials).  I also let the pendulum swing for a while, and they could measure whatever they liked. I assigned each group a number of cycles which the pendulum must go through from the time when they release the cart until the cart reaches the bottom of the ramp. They must calculate the location at which the cart must be placed in order to make that happen. There's a piece of magnetic track from my son's train set that makes noise when the magnet attached to the bottom of the pendulum swings just above it - this signals success.

My tests before school were all very successful, so I was hopeful before class about their success.

I had each group write up a whiteboard that just needed data plugged in, and we began the data-taking with about 30 minutes left in class.

In the first class, almost all of the runs looked extremely close, but we couldn't get the sensor to trip - downer. :(  In the second class, I adjusted the sensor setup, and two out of four were successful. One of the others had a good method, but was just a touch off in execution and/or measurement.



Monday, November 5, 2012

A Practicum I Can Believe In

I've had some difficulty coming up with a good end-of-term practicum for the physics class for a while. This year, we put motion up front (CVPM and CAPM, all graphical analysis) and then went into oscillations (this used to be our first topic).  In oscillations, I've traditionally looked at period/frequency and amplitude, oscillation graphs, using proportional reasoning to solve problems, and qualitative restoring/driving/damping forces.  Proportional reasoning is something that this crew needs to work on in practice, so much of the year is topics that yield to it fairly well.

There have been several benefits to changing the order, though:
- the oscillation graph analysis seems to come just after they cover it in Pre-Calculus, so that saves me a lot of headache
- I can add motion analysis (where's the acceleration the highest?, find the max v from the position graph, etc.) that I couldn't do before
- the reasoning goes down better after they've done a lot of it in CVPM and CAPM, even though it should've been better to start with the easier reasoning here. It probably has something to do with their familiarity with speed vs. their unfamiliarity with period

Another benefit is that I can put together a robust practicum that uses both CAPM and OPM:
  • On the day, I will set up a ramp of unknown length.  There will be a pendulum at the end, oscillating perpendicular to the track.
  • I will let them observe the pendulum in motion.
  • I will demonstrate for them, three times, the cart starting at rest at the top and traveling freely to the bottom.  I will tell them the length of the track.
  • I will assign each group a number of oscillations - the pendulum must complete this number of oscillations between the time the cart is released and the time that the cart gets to the end, and the pendulum must collide with the cart as it reaches the end
  • They need to have a procedure ready to determine how far up the track the cart needs to be released in order for these things to happen.
I let them work for a couple of days in groups, with a pendulum and a 1.2 m cart track. They need to develop and test their method so that it can work in any situation that I give them. 

I give them a packet with several pages: one for outlining a plan of attack (which they need to revise, if that plan changes), and several pages for completing each sub-task. Identifying that they need to determine how long the cart will have to travel, and that they need to measure the period of the pendulum and use the given number of cycles to find that time, is one example of a sub-task here. 

Students tend to be bad at laying out an abstract 'path' through a problem, especially if there's unknown information there. It's a tricky issue to tackle, but requiring these kinds of tasks of the students is certainly part of the equation. It's basically the same thing that I'm trying to address with the chains of reasoning exercises.

I laid out that structure on the first day, and students jumped into the problem at different spots, and most figured out a couple of sub-tasks at least.  There was a lot of average velocity vs. final velocity confusion, as is typical for these students.  On the second day, I had them start by writing out a list of the sub-tasks that they had identified - this is the "flow" of problem-solving that I'm trying to help them with. Most were good at this point, even though most groups hadn't figured out how to accomplish all of the sub-tasks yet. Here are the summary boards: interestingly, the first section was able to parse the task very well, but the second section had a great deal of difficulty understanding what the task was, which numbers were measurements and which were calculations, which variables explicitly affect their calculations (and should be measured, like the amount of time for the cart to go down the track) and which implicitly affected it (like the angle of the ramp, which affects the acceleration, but which doesn't appear in their calculations).

For the practicum itself, I'm using my 5 meter (!) air track :)

Friday, November 2, 2012

Nonuniform Circular Motion

I was trying to create a non-uniform circular motion experiment this summer, but I was barking up the wrong tree.  I thought about swinging a ball in a circle at constant speed and have students derive the tension as a function of time or angle - measuring it with a force sensor - but you have to mess with the pivot point of the string (in a really interesting way) to make the ball move like that. Also - that's not non-uniform CM anyway! I then tried (at Physics Teacher Camp) to put a horizontal pole through the force sensor's mounting point and let a weight swing on a string - nonuniform CM was good, but the non-zero mass of the sensor ended up being a huge issue, and the tension was hardly ever parallel to the sensor's axis.

This week, I figured it out: the sensor is the ball. I attached a string to a rotary motion sensor (so that I could determine the angle and angular v as a function of time) and hung the force probe from it.

Puling it back and letting it swing, I got a good data set, even though I couldn't effectively zero the rotary motion sensor for some unknown reason.

Students then looked at the forces acting on the probe at some arbitrary angle and derived the tension as a function of angle and angular velocity.

To get the model to work without the rotary motion sensor being zeroed, I added an offset to the formula when I created a calculated column in Logger Pro. Once I did that, we could compare the graphs of actual tension (red) and predicted tension (pink):

There's an interesting time offset that I haven't explained yet: ideas?

Friday, October 19, 2012

Comparing Springs

We went through simple harmonic motion derivations two days ago in AP. Writing the second-order diff eq. was easy for them, but it was the first one that they've solved, so we had a nice long guess-and-check for possible solutions. Ultimately, it was pretty clear to them how to take that trig function and get what they needed from it, but the process of using that diff. eq. solution as a model to solve similar ones (especially the hanging spring) was more difficult for them. I don't have any awesome inspirations on teaching that, but looking at a few other situations (two springs, etc.) helped quite a bit, and I assigned the "fall through the Earth" problem last night, which is a great application of SHM.

The point here, though, is to talk about some of the realizations about SHM that they had, and how Python helped that happen. They don't do oscillations in their first course, so this is the first that they've seen it in a physics context. The idea of amplitude independence is always tricky for students, so I just let them make a prediction about what would happen to the period of a spring when I changed the mass, or the spring constant, the amplitude, or g.

It's easy enough to see those results by looking at the derived period function, but it was always difficult to demonstrate some of those things cleanly - springs wobble, students imagine slightly different periods, they can't tell exactly what the amplitude or equilibrium point are (and damping doesn't help), I can't turn off gravity, etc.

I modified our second programming assignment of the year to have two springs instead of one, and demonstrated all of those cases very easily. Because they know how the program works (they basically wrote it), there's more faith in it (well, not faith, since it's based on reason, but they put more stock in it), and it's much easier to see.  The springs will oscillate perfectly forever and I can listen more to the discussion than worry about restarting the springs all the time.

Here's the script - use with attribution and an email:

from visual import *


# scales
Fscale = .1
vscale =.4

# objects

ball1=sphere(radius=.1,, pos=(-.5,-.5,0), velocity=vector(0,0,0))
ball2=sphere(radius=.1,, pos=(.5,-.7,0), velocity=vector(0,0,0))
#ballvvec=arrow(pos=ball.pos,, axis=vscale*ball.velocity,shaftwidth=.05)

spring1 = helix(pos = roof1.pos, coils=15, axis=(ball1.pos-roof1.pos),radius=.1)
spring2 = helix(pos = roof2.pos, coils=15, axis=(ball2.pos-roof2.pos),radius=.1)


# physical constants
k = 20
restlength = 1


while 5 <= 10:

    # forces
    springforce1 = -k * (mag(spring1.axis)-restlength) * spring1.axis / mag(spring1.axis)
    netforce1 = gravity1 + springforce1

    springforce2 = -k * (mag(spring2.axis)-restlength) * spring2.axis / mag(spring2.axis)
    netforce2 = gravity2 + springforce2

    # v and r update
    ball1.velocity = ball1.velocity + netforce1 * deltat / mass1
    ball1.pos = ball1.pos + ball1.velocity * deltat

    ball2.velocity = ball2.velocity + netforce2 * deltat / mass2
    ball2.pos = ball2.pos + ball2.velocity * deltat

    # vector and graphical updates
    #ballvvec.pos = ball.pos
    #ballvvec.axis = vscale*ball.velocity
    #forcevec.pos = ball.pos
    #forcevec.axis = Fscale*netforce


    # time update
    t = t + deltat


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:

Wednesday, October 17, 2012

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)

OPM (Oscillating Particle Model)

Monday, October 15, 2012

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.

Monday, October 8, 2012

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.

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.