Capstone 1 Unveiled! Comments Wanted!

The first capstone draft is out!

Alex has done some analysis of the Osmos video game - his capstone paper draft is linked here.  Take a look, let him know what you think.  After revision, this will be posted at capstonelearning.org , a capstone aggregation site so cutting-edge that there hasn't even been a post yet!

Post-Game Analysis, Part 1

I've been following John Burk's and Frank Noschese's ideas about "post-game analysis" (that's what you do after an assessment).  Too often, we just move on like nothing happened, and so the students do as well.  Unfortunately, asking "are there any questions?" and doing a few solutions on the board yourself has several problems: you're probably only addressing a small proportion of the kids at any given time (so they tune out), you're doing the work, while they're passively receiving (that didn't work for them the first time!), and it can take forever.

It also happens on the next class day, which can be as much as three days away, with our every-other-day schedule here.

There are also the traditional problems about feedback from me - many don't read it (hopefully fewer than before I started really talking about mindset and normalizing mistakes often), it takes a long time for me to write, and I might end up writing less than I'd like because of the time demand and effort required.

Here's a big one: my feedback, even if it's as long and detailed as I'd write in the ideal world where I have only one student (and 15 free periods and a boat), is based on what I think your issues are, based on what you wrote, which may not bear much relation to what you're actually thinking!  After three days, do you even remember what you were thinking?

I gave the immediate post-game feedback a try this week, on our first assessment for graphical models of constant-acceleration motion.  It was basic stuff - using slopes and areas to go from one type of motion graph to another, but there are lots of little places to not have it go quite right.  The kids did well overall, but most people had one or more little issues with the execution.

After they finished the assessment, they went to one of the three keys that I had made (these took a little while, because I was super-explicit about every piece of physics and logic) and used a green colored pencil to write down what they were trying to do and what they should've been doing for any places that they had mistakes (well, that was the goal - most did pretty well!).  Only they know what's going on in their heads, and they won't remember later, so this seems like a great opportunity to capitalize on their attention and motivation, and to let them write comments that are the most helpful to themselves, instead of me guessing what they were thinking/what they need to hear.

Here are a couple of terrific examples of post-game work from a student.  Notice how I don't really have much to say, because she has done all of her own 'fixing'!

I'm going to ask them today to give me some feedback on how well this worked for them.  I'm thinking that I'll do this with the first assessment or two for each standard, as a way to get their early mistakes and misconceptions dealt with more quickly.

Fluency = Awesomeness

Another term for the unconscious competence that we've been talking about (here and here) in class is fluency.  In language, fluency is about being able to do a lot of the lower-level skills (pronunciation, grammar, vocabulary) automatically: you're only focusing on the content - on the meaning.

That's the goal is math and science, too.  Too often kids get stuck on and obsessed with the tools (prefixes, scientific notation, algebra, trig, calculus, definitions, moles) and miss the forest for the trees.  Having to spend a lot of mental energy on those things also means that you simply don't have the stamina to get to the end of something with a lot of sub-parts, because the sub-parts require too much effort (because you can't do them fluently!).

We worked at this fiendish challenge problem from The Physics Teacher today. 

Mainly, I wanted to illustrate the concept of looking at different cases or regions within the problem.  Here, we had to consider cases in which neither block slipped, only the bigger block slipped, or only the smaller block slipped.  Cases in which both blocks slip are ruled out by the ribbon's masslessness (think about it - it's a little subtle!).

We went through what the accelerations of each slipping block and non-slipping block (+ribbon) would be in each of the three cases, as well as what the static friction force on each non-slipping block would be in each case.  If a scenario is impossible, you'll get an impossible result from the comparison of the net force required for the acceleration indicated and the acceleration that the static friction /gravity can provide.

It looked something like this:

That's quite a bit of algebra, but... how long did it take us to come up with these functions for all of these different cases? 10 minutes, maybe!

The reason is fluency.  These kids would've taken forever to get these out last year, and would've made a lot of wrong turns and not noticed for a while, because they were still stuck with partial fluency on some of the skills needed to write these equations.  By my estimation, these are the skills that the kids had to be fluent with to model these three situations so quickly:

• Identification of forces (normal, mg, kinetic and static friction)
• Identification of acceleration direction and which accelerations will be equal to which others
• Trig and vector components
• Rotation of axes
• Defining positive in a consistent way for both blocks
• Newton's 2nd law
• Requirements for static friction to be in effect
• Symbolic algebra
• Relationships between the friction coefficients
• Inequalities

Sure, you can explain this problem from the ground up to your mother (well, maybe yours is good at physics: how about mine?), but what if you also have to explain all of those ideas?  It's just a losing battle. 

After all, no composer can write an opera if they have to do "Every Good Boy Does Fine" to know what the notes are!

Another Reason for Reassessment

In a recent post, I talked a bit about this continuum of understanding/stages of learning:

• Unconscious Incompetence
• Conscious Incompetence
• Conscious Competence
• Unconscious Competence

One big reason that you want to get to UC is that you'll be building skills on top of earlier skills; if you're wrestling with motion (CVPM, CAPM), it'll be difficult for you to confront a situation where you're not interested in the motion, but with things that change the motion (forces, momentum, and energy analysis all presuppose a real fluency with motion!), you'll be stuck spending a lot of effort in the wrong place.  Imagine how difficult it'd be to make sense of Killer Angels if you had to sound out every word.  The more that you can 'automate' skills, the more mental effort you'll have left to deal with the newest skills.  This can really derail a physics student!

Another importance reason for getting to the fluency and automaticity of the unconscious competence stage of learning is retention.  Not only is it easier to apply a skill which you have mastered to the point of not needing to consciously think through it, but you'll also retain that understanding longer.

When you really know something, it sticks with you for a long time.  Cramming, on the other hand, might (probably not in physics!) get you to conscious competence, but that level of understanding isn't nearly as stable.  At that point in the learning process, you know quite a bit and can do quite a bit, but you don't have the perspective to put all of the pieces together.  It's not until you can do problems in multiple ways, explain where things come from, and what other phenomena they influence that you're really there.

I think that it's all of those connections that help you retain this level of mastery over a loner period of time.  A strand here or there may break, but if everything's interconnected in your mental model, then there are more strands to help to hold it up, and you have a basis for reconstructing that lost knowledge for yourself.

If you've struggled to gain even a minimal level of competence (consciously incompetent), then your understanding is fragmented enough that it will be all be gone in a matter of a few days or weeks, and you'll be back where you started.

After all of the hard work that you put in to understand a subject, it's wasteful to let it slip away!  If you're not mastering the material when the big assessment/test rolls around, it's crucial for you to address that right away, because the situation will only get worse.

The lower your level of understanding is, the faster it erodes.

Apart from concern for grades or concern for building later knowledge on a firmer foundation, it's vitally important to do some work to maintain or increase your understanding as a defensive measure against losing what knowledge you already have!

Capstone Proposals: Feedback wanted!

The AP Physics class is working on their first set of capstone project proposals.  These are more independent explorations that show a student's ability to synthesize concepts, formulate questions, and apply physics in "real world" scenarios.  The final product will be narrative summaries of the design, results, and interpretation; we'll post those for feedback and revision as well.

Here's where you come in: these are draft proposals, and need feedback.  There are great ideas here, but they need focus, specificity, and a devil's advocate about measurement and design issues.  Comment early, comment often!

The draft proposals, in no particular order:

• Kati:
• Will hitting a field hockey ball with no follow through affect the motion? Will how far I follow through affect the motion of the ball? Will the ball accelerate more? I plan to test the velocity of the ball with and without a follow through. Then see if there is a greater acceleration with more follow through.   
• http://www.youtube.com/watch?v=3uoWvI9hS84 
• the first swing in this video is what I will do but I will not be in motion.

• Alex C:
• My capstone will be analyzing the physics of the computer game Osmos.  In this game, a mass accelerates by 'shooting' part of its mass in the opposite direction.  I am going to analyze whether these separations agree with the conservation of momentum.  I will also being seeing if they do this in one, two, or three dimensions.

• Alex K:
• In the 2007 X-Games, skateboarder Jake Brown was launched 50 feet into the air, lost his skateboard in flight, and consequently slammed onto the flat of the ramp. I want to calculate the acceleration of his head in order for it to come to rest. From the various videos, I know the maximum height in which he reaches, and I can find his velocity. I can therefore find his velocity just before contact.
• To find his velocity, logger pro will be used. Using toolbox equations I can calculate his final velocity just before he hits the ground. I can then model his (non-constant) acceleration using logger and find a function of the acceleration of his head.
• MEDIA:  http://www.youtube.com/watch?v=CTeXKHkNqgk

• Mike:
• I have two ideas for capstones. One is to determine how far down the pellet from my air rifle will drop when aiming for a target that is 100m away, then use this data to determine how much higher above the target I would have to aim when the scope is calibrated for 30m to hit a target is 100m away. 
• Second is to determine which of my kicks a roundhouse, side, front, axe, back, jumping roundhouse, jumping side, jumping front, or jumping back kick exerts the most force. I would determine this by taking the average force between 3 of the same type of kick on a punching bag. 
• I would appreciate your feedback.

• Toru:
• In an iphone app called “Tiny Tower”, there exists a ridiculous elevator. This “Infini-Lift Lightspeed”  elevator has an extreme acceleration rate that can injure the rider when it tries to stop. I will find the acceleration value and the force on the rider by scaling this app to the real world. With the newly found, I will find the movement of the rider when the elevator comes to a complete stop.
• The link to the video that shows how fast the elevator moves 
• http://www.youtube.com/watch?v=-AL6GIIthYU

• Cam:
• For my capstone project, I will build a roller coaster on Roller Coaster Tycoon, and graph the acceleration and position of the rollercoaster based on the velocity which is given.  I would build a simple wooden roller coaster that consists of a chain hill that goes into a steep drop, goes up a steep hill, takes a 180 degree turn and go back down the steep hill, go up 2-3 smaller steep hills based on how long the chain lift is.  The coaster will then take one last 180 degree turn and then head straight into the station.  With knowing the acceleration and velocity of the roller coaster, I will try to determine how long the roller coaster is by using kinematic equations to find the delta X of the roller coaster.  I will be able to check my answer by looking at the data page of the roller coaster, which lists the ride length among other things.

• Brandon:
• The defensive lineman hits an average joe. The footage I will be using is on the link below between time 4:26 and 4:36. I will be calculating the direction and the size of the force needed to make that hit happen. The average joe is 5' 6'' 160lbs. and the 6'5'' 360lbs. And also what the force is on him has he hits the ground. 
• http://www.youtube.com/watch?v=2QOEIQ3_Kuo&feature=related

• Kawala:
• 
  Question: To test the roller coaster slows down when passing the second hill than passing the first hill, which obeys the principle of conservation of energy.
• Physical principle: Conservation of Energy. The car has initial kinetic energy when it starts so that it can go up the first hill. Then the potential energy turns to kinetic energy as the car goes down the hill. The further it goes, the more energy is transformed. The car has the maximum velocity at the bottom of the hill. As it goes up the second hill, the kinetic energy turns back into potential energy so that the car slows down. This also proves that the second hill of is designed to be lower than the first hill. The car cannot reach the same height as the first time because the energy is decreased due to the friction.
• How to approach: From the video I found, I can scale and use the logger pro to determine the velocity at different points. Also, the formula of the conservation of energy and kinematic equations can help to find some of the variables. Derivatives and Integrals might be necessary
• Quantities: Initial velocity, final velocity, the radius of the loop, the mass of the car, g

A Great Discussion and a lot of Abbreviations

First: honors physics had the best discussion today.  We went through some graphs, practicing whether they told us about a CVPM (constant v) motion, a CAPM (constant a) motion, or neither.  It's pretty early practice in our CAPM unit, so we're just learning the ropes of what each graph says about the motion.  This was our set of graphs (thanks to Minds On Physics and Kelly O'Shea):

We've done some modeling of carts on ramps, finding functions for the final velocity as a function of delta t and seeing the shape of x vs t), so that was their background with accelerated motion (that, and the curve in our error analysis of... well, I'll save that post for another day).  Everything was smooth sailing until one unlucky soul got graph H. 

After a bit of fumbling to an answer, I opened it up.  They were all opened up for questions, but this was the one the everyone was unsure of.  After a few minutes of half answers followed by examining of my face for feedback (that wasn't forthcoming), they really engaged with each other.  Discussions are really easy to have between each kid individually and the teacher, but it's difficult to get them to discuss with each other, particularly when the topic's not subjective.  The biggest key is for me to shut up.  It's hard to do, but a little patience will see them start to really turn their brains on. There's a correct answer here, but what is it?  The tipping point here is when they start actually listening to each other - you know you're there when they analyze the consequences of someone else's argument, and it's a beautiful thing.

     But isn't it easier if I just confirm/deny their answers, and let everyone know what the correct response is?

It depends on what you mean by easier.  Easier for me? Yes. Quicker? Yes. More comfortable for them? Yes.  Better for them to learn how to reason through an unfamiliar situation? No.  Better for them to build a mental model of the process?  Not even close.

Atul Gawande (I'm linking to John Burk here, because that's where I heard of him) has this thing about stages that learners go through: he identifies them as Unconscious Incompetence, Conscious Incompetence, Conscious Competence, and Unconscious Competence (there's a great scene from Waiting for Guffman on this topic...).  I'd sum those up as:

UI: Clueless - doesn't know what the game is

CI: Knows the game, can't play it well

CC: Can do it, but have to think about it

UC: No sweat - like second-nature

The trick about this progression (well, there are two, but the second one I'm saving for another day!) is the frustration and self-confidence swings during this journey.  I made this graph to sum it up:

 

• The understanding increases as you move from level to level, but you'll always have plateaus that you'll have to break through.
• Your confidence really takes a hit as you figure out what you don't know (conscious incompetence), rebounds, and then goes off the charts as you really figure it out.  This is one way to get a handle on where you are on the chart: if you have apprehension, you're not at UC (but you might be at UI!)
• The frustration of going from unconscious incompetence to conscious incompetence can be brutal.  You have started to learn how little you know, and the hill can seem steep.  This, however, is the only way through to competence of any sort.  Ignoring this (by having passive study or avoidance) does not fix the problem.  There's some frustration in clearing the last hurdle, but much less, because your confidence is bolstered by having competence in the material already.

There's a connection that I make here to that study (which I still can't find) about preparing for an exam by passive study or a period of time, cramming, and taking a test.  The test-takers were best prepared (now they really know what they do and don't know), but least confident. That confidence can be a bit of false internal feedback.  You have to be aware of it, push through it, and know that good times are on the other side. 

I see a lot of skills that should be UC for students (like algebra, graphing, writing) take the forefront as points of difficulty; maybe they studied to become consciously competent for a test a few years ago, but that's not enough when you're trying to build on those skills.  You need to be able to do them without thought or hesitation - you need to be unconsciously competent.

Maximization and an Awesome Connection

Last week, AP Physics took kinematics to the max (or min).  The prompt for the day:

     Pick a situation and maximize (or minimize) something related to a motion.

In a few small groups, everyone ended up landing on trying to find the angle that maximizes projectile range down (or up) a hill.  This is a fun problem, and really tests the algebra/bookkeeping skills.

This is also a good chance to test out not one but two cool applications of the quadratic formula.  You have a couple of equations that are quadratic not in theta but in the tangent of theta!

Getting all of the way down to the end requires some slick tricks like that, but also a great deal of discipline and the ability to work quickly but very accurately.  Thinking back to my undergrad physics courses oh-so-long ago, I remember that being an under-advertised but very important skill.  The whole idea of junior-level mechanics and E&M and certainly of undergraduate quantum mechanics seems to be to exhaust all of the problems that can be done analytically, which means that they get... ahem... robust, in terms of the algebra.

One group finished quickly enough to test their prediction with a ball launcher and looooooong ramp:

The prediction worked like a charm, and the ball's maximum range occurred at the predicted launch angle.  They made some pencil marks (did you guys erase those?!) on the track, and here was where it got real.

Even though the maximum range did occur at the predicted angle, they noticed that the range didn't change much even with what seemed to be a relatively large angle change.  It decreased, just not as much as they had expected.  On one side of the optimum angle, the range changed very little for up to 10 or 15 degrees of angle change; on the other side, it was significantly more sensitive.

This observation led to a couple of great revelations (without any input from me):

• This tells us a good bit about the shape of the function.  On one side, the function slopes away from the maximum relatively slowly, but falls off much more quickly on the other side
• This is, 100%, the "algebraic test" for extrema!  OK, we may have made that name up, but it's the process where, instead of taking a second derivative to test the type of extremum you've found, you test a value to the left and one to the right.  This test works well if the derivative's complex.  Visually, this is it, in the flesh!

That connection - the idea that we can just see what some arcane mathematical procedure is about by doing an experiment - is fantastic.  I'd love to take credit for having designed the whole situation to force that epiphany, but it just happened.  That makes it even better!

Let me tell you about units...

Sometimes students think that units are for me.  I get all excited about them writing down and checking their units.  "It's a chance to catch your mistakes," I say.  "It's a chance to really know what the units in the answer are," I say. "It can tell you how to do the problem!" I exclaim.  "Come out to the coast, we'll get together, have a few laughs," I say (wait, that wasn't me).

Anyway, the students that see it, buy it, or try it... succeed.  Those that refuse... generally struggle (certainly, they struggle more than they need to).

I get that you might (should?) need more than my word to buy into something.  That's where the logical argument and all of the times that we've seen it work in HW and class should come in.  If that didn't do it for you, then how about this?

On our first assessment covering amplitude of oscillations, I asked this question, after showing a video of a lab cart oscillating with the help of two horizontal springs.  They had already determined the amplitude at my request, and had stopwatches available.

     "How far would the cart travel in a year, if its amplitude remained constant?"

Yes, it's not terribly 'real world,' because the cart certainly won't go that long, with all of those juicy damping forces around.  That's OK - we're just stretching our legs a bit.

What I like about this is that it connects period/frequency and amplitude.  That, and we'd never done anything like it before.  There's always something new on a physics test, but you can apply old concepts to figure it out.  That's just... how physics works.  If you're waiting for me to list all of the "types of problems," then you'll be waiting a long time.  The concepts that we apply to this multitude?  Well, you can list that pretty easily (it's the list of standards for the term!).

Anyway, here's where the units hit the road.  Folks that have taken my advice and really gotten into checking their units had a real advantage:

     Not only did unit-checkers get all of the more familiar applications of T, f, and A correct, they also all got this entirely new question correct!

Yeah, all of them.  Here's a chart showing how folks that check their units did on the question, as opposed to those that didn't:

I'm not really sure how to say it more clearly than that.

Pull-back cars redux

Here's another report from our investigation of pull-back cars:

How does the launch speed vary with ramp angle? - Cam, Mike, Toru  

The Goal:   The goal of our lab was to find the launch speed off a ramp in terms of the ramp angle. 

How'd You Do It?  We kept the distance of travel on the ramp and the distance we pulled back the car a constant. This way we could keep the function with only two variables, θ and ∆x. To get the maximum results we made the distance of travel where the car reaches near maximum speed while the car is still accelerating. This distance was found using Logger Pro. In order to give a bigger range of ∆x's, we put the ramp up on a higher location. The bigger range reduced the possible errors that could affect the calculations for the launch speed. 

What Happened?  We concluded through our experiment that in actuality any inclined angle in which the toy car has to exert a force up the slope, has a negative effect on the car's total distance traveled due to a decrease in velocity when leaving the ramp. So in the case of toy cars, the lower the angle, the farther the toy car will travel as long as the starting point is elevated above the measuring distance.