Newton's Minions

Review!

noreply@blogger.com (Tatnall Physics) — Tue, 28 Feb 2012 14:44:00 +0000

The physics classes made some review boards for the midterm exam, splitting into groups, with each pair or trio working on one standard. Some are great, some are good; all should be helpful in the review process, so here they are, physics-nauts!

FFT

Beats

Oscillations: Period and frequency

Interference and Reflection

Standing Waves

Timbre

Causes of Oscillation

Amplitude

Wave Descriptions

Resonance

2 Source Interference (they ran out of time on this one)

This is a good day

noreply@blogger.com (Tatnall Physics) — Thu, 16 Feb 2012 02:44:00 +0000

OK, it's nearing the end of the term. For you SBG superstars out there, it probably means that you're busy with reassessing kids like I am. Here's one story that made it worth it today:

A student was reassessing on gravitation. It's a difficult, abstract, and unfamiliar topic, so I'm glad that they get a chance to work on it and take another crack. She was down to the end, but couldn't get a part of a problem dealing with the surface gravity on some other planet - she had determined the freefall acceleration, but couldn't remember the kinematics toolkit (she knew that it applied, though, which is great). She confirmed that the kinematics part was separate from the gravitation part, and I thought she'd hand in the towel then.

Instead, she worked some more, and then came back and said... "I just solved it with graphs instead."

That's the best thing that I ever heard.

Winter Meeting: Tuesday Afternoon

noreply@blogger.com (Tatnall Physics) — Tue, 07 Feb 2012 22:28:00 +0000

I saw Kip Thorne's plenary session on black holes and gravitational waves - very interesting. I didn't blog it because I needed all of my faculties to follow his tensor analogies. :) The sensitivity of LIGO detectors (around 10^-16 cm) is about 10,000 times smaller than the width of a nucleus - that distance change over the distance of 4 km beam paths!

There's a post earlier about my talk, which was just after lunch.

Following that, I went into "Effective Practices in the Instructional Laboratory"

Slipping Spheres and Sliding Blocks: The "Role" of Kinetic Friction

This session is mostly about the race of a sphere and block down a ramp
It begins with a multivariate analysis of the parameters of the problems and how they affect the outcome of the race (low angles: ball, high angles: block)
They go through the experimental setup for determining the motion data and friction coefficients
There are some interesting (though small) changes to the friction coefficient - the sphere's decreased and the block's increased as the acceleration (in a half-Atwood system) increased
They're the same material (wood), but the shapes might be an issue
Nothing really here about using this in education, but it's a possible place for the AP class to investigate

Teaching Optics in the Introductory Mechanics Laboratory

Labs tied to the course could become demos that don't engage the students and have them focus on too many components (apparatus, design, analysis, etc.)
Instead, these folks keep the concepts pretty much the same during the term for the lab work, and don't progress with the material (kinematics and forces in first term, DC circuits in the second - which is in lieu of class instruction!)
Intertwining of lab and class exposure causes analysis issue on how effective each component is
They're using optics in the 1st term to free up time for other stuff in the 2nd term, and they never teach it in class then
Optics labs: wrote and reviewed lab papers, did point and extended objects, refraction, beakers, lenses, not really any mirrors, modeling images
Removed the mechanics labs during lab session, did some quick mechanics lab investigations in class instead (focusing on error analysis, etc.)
Optics Concept Assessment pre-/post-test
Students did as well on optics as students with more "rigorous" in-class experience
FCI/FMCE gains were somewhat lower than in previous years, but he doesn't think that it was necessarily caused by the labs' removal
Giving it 8 months later, students had basically forgotten their optics knowledge, but they have no previous tests to compare to
Contact: masters@ipfw.edu

Assessing Student Learning of Error Propagation in the Undergraduate Lab

Pre-/post-survey of error propagation using calculus method: addition adds direct uncertainty in quadrature, multiplication adds fractional uncertainties in quadrature
HW from Taylor's An Introduction of Error Analysis
TA didn't lecture during lab, so HW was never discussed as a whole
Think-Pair-Share was used a bit
There was a gain: 5/25 to 9/25 for one question, 5/25 to 15/25 for the other (significant gain)
They classified the wrong responses: direct/fractional issues, typos, multiplying uncertainties, assuming dependence (adding uncertainty)
The 2nd time, everyone at least tried it
The pre-test was after a first semester though, so... yikes. It's only a bit less scary after the 2nd term
Contact: barker@nscl.msu.edu

I stayed for a couple of other talks here, but got tired of typing. :)

It has been a great Winter Meeting - thanks to all of the great speakers and the organizers! After grabbing a bite, I'll head to the airport and back to the land of no palm trees.

The Physics of Osmos: AAPT Winter Meeting Presentation

noreply@blogger.com (Tatnall Physics) — Tue, 07 Feb 2012 20:44:00 +0000

Here's the video presentation from the AAPT Winter Meeting. Sorry, but there's no audio here - this is the video that played as I gave the talk, but it speaks for itself in some ways. I'd love to add more, but my schedule says that it probably won't happen!

The image should link to a public file in my SugarSync account - please let me know if you can't access it!

Winter Meeting: Tuesday Morning

noreply@blogger.com (Tatnall Physics) — Tue, 07 Feb 2012 19:04:00 +0000

Just one session in the 8 am block, then to breakfast and practicing my presentation!

It's a good one, though, a 30 minute session in the "Using the Riches of Astronomy to Teach Physics":

Using Black Holes and Extrasolar Planets to Teach Kepler's Laws (and more!)

They're certainly popular topics, and can help kids get into several basic physics topics
Kepler Mission: looking for transits around other stars using super-precise photometry
Neat - data shows six different planets around a single star
There's a Lego Orrery that they're using to simulate it (kepler.nasa.gov/education) approx. $100 cost
Vernier light sensor, lamp, planets, calipers (one broken bulb from clamping calipers :) ), light baffles also needed with multiple setups
They have TA introduce the idea - going from the data and getting students to figure out why the light dips seems a better tack
Questions that they have them explore: How does the % of light blocked depend on size of planet (prop. reasoning and scaling argument), orbital distance effect (you'll be getting into apparent/angular size here, which doesn't matter in the normal scale, but matters here)
Neat light curve from three-planet system
Orrery seems to not give correct orbital periods (qualitatively OK, though)
They have one group design for another group (and predict the resulting light curve), and the other group has to figure it out only from the data; I like that bit
At that point, they start getting tricky: moons, rings, off-axis transits
Kids like it - duh! :) It looks fun, for sure.
Next activity: about the supermassive black hole at the center of the Milky Way
Uses data from the UCLA data on Saggitarius A
That's a sweet animation - I want it!
Students get ta plot of the paths, without context - students figure out that they're orbiting something, figuring out that it has lots of mass -> black hole
I guess that I'd tell kids that they're stars, then let them reason down that they're orbiting something much more massive (since that object doesn't seem to move), and get to BH that way
The plot is angular, so they need the distance to the galactic center (8kPc) - that might be tricky for my kids
We don't know the constant for ellipses in our honors class, so calculating mass would be difficult
The orbits are inclined, so there's that - this is getting complex quickly
Some student report: "We didn't think that astronomers actually had to use equations in real astronomy" - interesting: why do we teach them? To punish the students, I guess...
This is recent science, and the same science that "real scientists" are working on now, rather than long-settled questions
Neat: you can sometimes see the little bump from reflected light as a planet's about to go behind the star - apparently, the loss of that reflection's called a secondary eclipse
Contact: seth.hornstein@colorado.edu

Winter Meeting: Monday Night

noreply@blogger.com (Tatnall Physics) — Tue, 07 Feb 2012 03:47:00 +0000

Here's an interesting one - an hour on the AP Physics B Course and Exam redesign (about time!):

Well, of course the NRC accused AP Physics B of being a mile wide and an inch deep - it's the poster child for it!
That seems to have been a trigger for similar redesigns of other AP courses
Interesting, but not really surprising, bar graph of the results of surveys of colleges about coverage of topics in different semesters
Good seven big ideas of physics: don't have time to get them down, but... Systems have properties, interactions are forces, waves mediate p and E exchange, math is useful for describing nature, didn't get the rest
Tradeoff: reduced credit for students scoring well on the B exam if it's split, but increased access (especially given that they always recommended B being a second year course)
I might like this...
It might not align well with some state graduation requirements (like California)
They're promising a detailed curriculum framework, including boundaries and depth
Adding inquiry and conceptual reasoning
Proposed release date: Fall 2014
Nice question: "I was at one of these meetings two years ago, and I saw a similar talk, that said that it would be coming out in two years."
They're saying that having B1 (mechanics) as a first course would prepare students to do well with both parts of AP C in a second year. The idea of having an option for the B1 kids to take a second year (particularly those without the calculus prereq.) of physics is good, though I don't have a free prep to teach it!
Now we're talking about the curriculum
They're saying that the curriculum isn't a sequence or a pacing guide, but instead a framing of the seven big ideas
Each big idea has some 'enduring understandings' subordinate to it
Below that, there's 'essential knowledge' (more than just facts, allegedly) and 'science practices: inquiry and reasoning'
Below that, nougat
A second shot at Big Ideas: "Objects and systems have properties such as mass and charge. Systems may have internal structure," "Fields existing in space can be used to explain interactions," "that force/interaction one", "missed one", ""Changes that occur as a reult of interactions are constrained by conservation laws," "Waves can transfer E and p from one location to another without the permanent transfer of mass and serve as a math. model for the desc. of other phenomena," "The math. of probability can be used to describe the behavior of complex systems and to interpret the..." Sorry - I type too slowly
The division here lends itself pretty well to SBG
The "science practices" are being shared among different AP science courses - that'll help out our benchmarking!
Some examples: models/representations, math, questioning, plan and implement data collection, three or four more; they says that they're available on the AP site, since they're common to all courses
Each of those comes with several skills used to demonstrate the desired practice
Essential knowledge and science practices are alleged to collide inelastically and usefully to the teacher to become learning objectives
They've promised that there are no required labs about 6 times
An unfortunate example of one of the Essential Knowledge items: "A force exerted on an object is always due to the interaction of that object with another object." Will there be a list of underlying assumptions, since there's a big one behind that statement?
Rotation being added (angular kinematics and momentum, torque without angular acceleration)
For some reason... intro circuits is in the AP 1 course.
It's starting to look a bit more packed now: kinematics, dynamics, p, E, oscillations, waves and sound, rotation, statics, electric circuits
C courses left untouched (at this point)
Symbolic problem-solving, lab and analytical skills, experimental design, more reasoning questions, deeper conceptual questions, error analysis, much more writing to justify understanding: changes to the exam
Overall, it seems like a good pitch. We'll see how it plays out (can you tell that I'm skeptical of the College Board? :)
Afterwards, a good story when talking to the presenter about the (grossly disfunctional) AP audit process: one of the teachers that wrote one of the sample syllabi on the site (which I basically had to copy to get them to accept my audit proposal) had her syllabus rejected. :)

Winter Meeting: Monday Afternoon - Popular Media and Online Courses

noreply@blogger.com (Tatnall Physics) — Mon, 06 Feb 2012 22:17:00 +0000

After some In-N-Out Burger goodness, we're back to "How I Use Popular Media in Teaching Physics"

I've seen more people with tablet computers (not 'toy' tablets, but actual PCs) than I have since I taught at an all-tablet school! I love my Lenovo tablet!

Angry Bird Physics

Rhett Allain!
This vehicle for engagement and analysis has been pretty well-covered (certainly very well by Rhett himself) in the blogs and even mainstream media, but I wanted to get it straight from the horse's mouth :)
A little Tracker analysis - I love using the quadratic fit rather than even the v vs t slope - kids often think that you can get the v directly from the video, not even knowing that there's an error-inducing difference quotient in there
The split blue birds have a total mass 45 times the mass of a single blue bird?!
The yellow bird analysis (what happens when you tap?) is a decent entry-way into designing an experiment that will need revision (it's not immediately clear what's going on and how to analysis the data), but it would really take a long time to collect all of that data, and I can see that many students would be disillusioned by that
The white bird egg dropping seems not only to use non-real physics (no problem), but it seems to reinforce some pernicious misconceptions (the egg always falls straight down, momentum's not conserved even in a conceptual way, etc.). This may do more damage than it's worth, considering that students usually remember the first thing they see/hear, and that we've previously set up a few examples to illustrate that the physics is (sometimes, at least) good in this game
Good point that this requires indirect techniques, which is very indicative of science - we can't just weigh the rock, but have to come up with a way to get at what we want by measuring what we're able to measure
Contact:

Next, I slide over to the "Online Physics Courses: Technology, Assessment, and Experiences" session:

Transforming Physics Curriculum by Teaching Physics Online

First point: online learning needs to be personal - tailored to the student, flexible, etc.
Star Trek IV clip!
Interesting: he's not afraid of making a statement. So far, he's said that electronic books, regular books, and clickers are a dead end
Biggest point is that changing the content isn't the answer - it's about how the content is taught
The classroom needs to be a safe space where students can learn and discuss without the fear of punitive grading - sounds like SBG to me!
His vision seems to be about social media more than anything else
OK, here it is: the social homework project
It's supposed to enable students to collaborate on their physics HW and to learn from each other. There are peer-review, group solving, and discussion capabilities for rich-context problems, and they write problems and questions for other groups as well
It looks like a Facebook app/group for collaboration, basically. Everything seems to be in an early form yet
A questioner brings up a common issue with discussion forums: frequently, a well-meaning student will "give away" the solution - this requires management and acculturation
Contact: hlousek@csulb.edu

Particle Physics Online

This is about a CSU-wide online course in particle physics (senior undergraduate level)
They used Elluminate, with downloaded equation packet, live lecture with video camera with some whiteboard space.
They scanned and sent in HW, he sent back scores only
Tests were given live, by local faculty as proctors
Could any research-inspired methods be incorporated here? Is that less important as the audience is winnowed down to upper UG physics majors and grad students?
Contact: pbsiegel@csupomona.edu

Online and Blended Climate Change Courses for Educators from AMNH

This is about some courses developed in partnership with the American Museum of Natural History and NASA
They aren't inquiry courses, but say that they try to model it
They're using a stripped-down and more accessible version of the global climate model
Good lessons here about bringing together model, theory, observation, causality, etc.
rsteiner@amnh.org

Tabletop Kits Help Students Grasp Concepts in Light

These kits are designed for students taking distance (or face-to-face) courses as a relatively simple way to get hands-on intuition about light
There's color mixing, diffraction spectra (glasses), some LEDs to demo things
Neat experiment using two LEDs to simulate amber light - very different spectra
Spectra about CFL backlit monitors
Apertures to develop the ray model of light - good conceptual question about a hole at the end of a hallway
Pupil aperture size/power
Point vs. extended sources through apertures, also with shadows
Neat question giving two point sources, location of shadow components on screen - where's the shadow-caster?
Ray tracing to determine image location with flat, curved (cylindrical) mirrors
Photoelectric-type effect: UV making paper glow green, red light won't
Peacock feather for iridescence
Increases engagement, but doesn't always transfer - more mental-model creation needed in structure of investigations
millspaj@ipfw.edu

We'll be back after dinner!

Winter Meeting: Monday Morning - DIY Tech, PER, Physics in Animation

noreply@blogger.com (Tatnall Physics) — Mon, 06 Feb 2012 19:24:00 +0000

After a very welcoming "First Timers" breakfast, I made my way to the "DIY Technology for the Physics Classroom" session, where I saw three talks.

General observations (going into my thinking process about my talk tomorrow):

There are kind of a lot of folks at each talk
10 minutes, especially compared to the usual 95 minutes that I get in class, is not a lot
I hope that the contrast for the Osmos clips is good in these bright rooms
It would be nice to include some expanded references to the Osmos talk for reference. I'll see if I have time today to get that done!

IPAL: In-class Polling for All Learners

Bill has developed some open-source polling software that can be used with any web-enabled device - no clickers required
The Moodle or stand-alone modules can import ComPADRE or other established question sets, so you have something to start with at least!
Bill Junkins is happy to help you out with this: junkinwf@eckerd.edu

Using Your Classroom Projector to Demonstrate Some Properties of Light:

Wow: DLP projector technology seems to be overly complex, but very neat: strobe light + rotating color wheel + tons of tiny individually-aimable mirrors!
The LCD projector's dichroic combiner cube looks like a good total internal reflection demo/application for class
Using holographic diffraction grating glasses (cheap!), which are 500 line/mm diffraction gratings, looking at vertical lines through the projector is a neat demo n color mixing, and also showed that we didn't have an incandescent bulb in the projector
Using a polarizer, you can show that the projector's green light is polarized perpendicularly to the red and blue!
For more info: ottinger@missouriwestern.edu

Build your own electric field demonstrator

This is supposed to be a simpler demo than the "grass seeds in mineral oil" demo
This demo uses lettuce seeds instead (more arrow-like) and vegetable oil instead, with a VdG to set it up, along with a hangar, styrofoam cups (to stand-off the hanger between the vdG and petri dish. Put paper under dish for camera mounted above, use fluorescent tube to bleed off charge
It should spark between the wires, and the seeds will move quite a bit
He showed videos of monopole source, dipole, parallel plates, absence of field inside a conductor (my favorite)
For more info: james@physicsvideos.net

After this, I went to the "PER: Investigating Classroom Strategies" session:

Getting the Word Out: Effective Communication of PER Study Results

This is about not original research, but best communicating the results to others; she's a science journalist as well, so uses lessons from that field
The fundamental disconnect between being aware of data and an actual change in behavior is really analogous to the whole "book learning" issues for students and, apparently, for teachers taking PER results seriously - many teachers know about it, but still continue to lecture
I want to DL this one to share.
The information-laden approach that we try to use to advocate for research-based instruction is just as big a problem as trying to do it with students
"The deficit model assumes that the public are empty vessels waited to be filled with science knowledge, upon which they will rationally act" (OK, I typed it quickly - maybe not a quote)
Unfortunately, initial emotional appeals, etc. with some data as support are more effective than a data-driven approach
Be upfront about the challenges of implementation - many try reformed strategies, only to drop them after a term or so
Contact: stephanie@sciencegeekgirl.com

The Challenges of Assessing Teaching Effectiveness: Strategies for PER to Influence Practice

Importance is for quality assurance (from the institutional side) and for personal teaching reflection and modification
Aligning the assessment instruments for those purposes (and aligning them to PER) is important
This alignment isn't usually present, though: lots of reliance on student evaluations and other poor measures by institutions. External measures, like the US News rankings, are super-terrible
The heavy use of student evaluations makes folks nervous to change things for fear of lower evaluations (even if the measures of learning increase!)
We need more and better-publicized research-based assessments
PER is good as the lesson/course level: was the lesson/course successful? It doesn't have as much for program-level assessments, but there's starting to be focus on this at a political level, so we need to catch up
Measuring progression of reasoning skills and conceptual understanding of specific concepts across a program are easier; we don't have much for problem-solving skills yet - what would that look like?
Contact: charles.henderson@wmich.edu

Variance and Variables: The Analysis of Pre-test Results from Thousands of Students

It must be nice to have a gigantic data set (like several introductory courses in a large college)!
We're comparing pre- and post-test data
First question: are they normally distributed? Normal quantile plot
...or binomially distributed? (as if they were draw from a population of students giving random correct/incorrect answers) Nice presentation - there was probably the biggest binomial-gaussian distribution comparison graphical analysis audience laugh ever heard.
Amount of prior instruction: ANOVA analysis showing differences between no instruction, some instruction, and all instruction; not much difference in many cases
Open question: why are some questions binomially distributed and others not?
Contact: pheron@uw.edu

Designing Research-based Instruction in a Large Lecture Course Without Recitations

Intro calculus-based college course: 4 lectures, no recitations or TAs, lab not run by teacher
HW assignments online, most tests multiple-choice
In such a traditional, inflexible environment, how can we use PER?
Prelectures/checkpoints (multimedia, animations, etc.): works better than text reading, students like them
LON-CAPA and some turned-in work (mostly on form)
You-tube videos of worked problems - takes that out of classroom
<10 minutes of actual lecture
3-8 daily voting questions, using colored cards instead of clickers
Important strategies: leaving the stage, answering questions, monitoring student discussions
FMCE gains weren't super-duper, but the checkpoints and cards helped somewhat
Some research cited on "high structure" classrooms, and how that helps at-risk students
Nice distinction: urban, rural, and... frontier - he does teach in North Dakota. Nice graphic on >50% of the counties in ND which have <= 6 people per square mile!
Warren.Christensen@ndsu.edu

Learning Integration in Physics Using Debate Problems and Multimodal Communication

Looking at center-of-mass determination
Conceptual intro to continuous distributions: here's the discrete definition, which is the continuous definition? (poll question)
After that's done, how do you determine if they really have it? A couple of diagrammatic methods shown, ask them to derive the integral def'n from the discrete (hard), ask them to apply the integral equation (not the same as understanding what it means), have them use multiple representations (diagrams, etc.) - best!
1. Group discussion; 2. Groups present to each other; 3. Recorded presentations shared between sections
They assessed individual student presentations with Smartpens, so you have to paper and the student's narration
Another example question: I for rod; determine integral expression for rod around parallel axis
Result - lots of students think that 'd' in an integral means 'change', and maybe this is the first static integral they've ever seen!
vonkorff@phys.ksu.edu

The next place I went was to a talk given by Ron Henderson (physics PhD, Princeton, formerley worked at Cal Tech) on how waves are encoded in animation. Ron's a DreamWorks animator.

22,000 Intel Xeon cores, 120 TB or storage, 120,000 frames, >1 billion files for a single DreamWorks movie - yikes.
The animation rig for a single character in one of these movies can have up to 10,000 controls - lots of strings for a puppet to have
200-800,000 hairs for a rendered cat, like Puss in Boots. ...then you have to make the hair go around the belt, etc.
Goose feathers: 'grown' via algorithm along equipotential lines, in order to minimize collisions between them (just like real goose feathers, approximately). So there.
Volumetric modeling of clouds for high-res 3D models, like in the Jack and the Beanstalk bit
34% Bachelor's, 40% Masters, 20% PhD among R and D engineering staff; degrees most common in CS, Engineering, graphics, match, physics (4%), in that order
Premise: non-physical motion is distracting to audiences. Why don't they hate Star Wars then? :) It all really depends on knowing what your audience knows and doesn't know!
A good way to plan out a complex endeavor: they look at each movie and ask themselves: "what do we want to go after that we haven't gone after before?" You can't reinvent every wheel every time. Pick your battles.
Breakdown of man-hours for effects for Puss in Boot (in order): clouds, dust, destruction, water, splashes, tornado, beanstalk
Their destruction model includes: explosive, primary debris (moment of inertia, spin simulation here!), secondary debris, dust source, fluid simulation, and visual development; fracture analysis, particle dynamics, rigid body dynamics, and fluid simulation are the primary models for destruction animation
Their model selection is artist-driven, so multiple approaches/representations are very important for them
There's a nice explicit balance between physical law (simulation) and computability (using simplified models). This is a good thing to emphasize with students: we understand the approximations and simplifications that we use (and why!), but we can usually do a better job of getting students involved in that process!
Incompressible Euler equations sued for tornado simulation; apparently a common model for fluids in animation. They're controlling a buoyancy term, a dissipation term, and a third term.
The complex behavior of the tornado comes from solving the equation for lots of little boxes - the coupling between the boxes creates the complexity.
They let the artists control divergence terms to make it look how they want it. They add obstacles to respond to the artist requests to "make it more turbulent"
They warp the physical simulation onto a controlled skeleton to compromise between the desired physical and un-physical parts of the animations
Great question from the crowd - "there's lots of physics going into making the animations look great - is there a lot of biology going into the beanstalk animation (and others)?" Answer: "no." There are skeletons, etc. but skin and such are algorithmic at this point (designed to "look right", rather than physical simulations).
This was pretty awesome. The 45 minutes flew by - I could stand another couple of hours of this!

...off to In-N-Out Burger!

California ho!

noreply@blogger.com (Tatnall Physics) — Sun, 05 Feb 2012 01:01:00 +0000

So... anyone going to the AAPT Winter Meeting? I'm leaving early in the morning tomorrow, and I'll be able to catch some of Sunday, all of Monday, and most of Tuesday. I'm looking forward to a bunch of new ideas and sharing with other physics teachers.

If you're there and you're looking for something to do, why not drop by EH01 at 1:15 on Tuesday to see my "Physics of Osmos" talk? I'll look at how the video game can be used to supplement or replace some traditional demonstrations, can help build intuition about orbital mechanics, and can be the springboard for sooooo many independent modeling projects!

Here's to a smooth travel week, and to Wednesday, when I'll be getting into Philly at 6 am and going straight to school to teach (fun!).

See you there!

That was a moment.

noreply@blogger.com (Tatnall Physics) — Wed, 25 Jan 2012 21:28:00 +0000

There was a seemingly small, but actually big moment in honors physics today. We putting our newly-developed model of universal gravitation through its paces, and started by looking at the Sun-Earth system. After listing all of the stuff that we knew about the system (discussing fusion vs. combustion a bit, too), making a conscious decision to model the Earth's orbit as circular, and asking what we could figure out next, we decided to determine the Earth-Sun distance, given the Sun's mass. It went the other way historically, I think, but this was good for our purposes.

The free-body diagrams started, followed by Fnets, and - before long - came the question/confused utterance (from a few sources in each section):

"There's a force acting on the Sun... ...and only one... ...but isn't it sitting still?"

The discussion afterwards about Newton's 2nd, approximations, etc. that got the problem train a'rolling is much less interesting than the train of thought that led to the question.

I made a big deal of it, because it was a big deal. There was confusion because worlds were colliding - students have "known" for most of their lives that the Sun sits still and the Earth orbits it. They have only recently begun to wrestle with the realities of Newton's laws, and, despite our best intentions and efforts, students can keep those two worlds mostly separate, mentally. There's the "real world" and the "physics class world." This is exactly what Eric Mazur is talking about.

Today, though, the confusion indicated that the two understandings weren't separate - they were both in there, trying to edge each other out of the ol' brain pan. Having a gut reaction like that, seeing that it doesn't make sense for a single force to be acting on an object if that object's not accelerating, and not being willing/able to just push the "physics class understanding" to the side is exactly what my goal is for my students.

What a great present for a Wednesday!

More software advice...

noreply@blogger.com (Tatnall Physics) — Wed, 25 Jan 2012 13:38:00 +0000

I got such a great response last time I asked for a referral to graph-creation software (yeah OmniGraphSketcher!), that I thought that I'd throw out another request.

Does anyone have a good piece of software for storing and sorting test/quiz/assessment questions and assembling them into finished printable assessments? I'd definitely need something that has easy image support, and an efficient way to organize all of the questions by topic/level/etc. Something that allows editing of the text parts would also be helpful. If it could store solutions as well, even better. I'm assuming that I'll put my standard rubrics in as questions that I can group on the last page, but a more native support would be awesome too. Oh, and I like to put graph paper behind each question.

That's not too much to ask, is it? :)

A Great Thursday Morning: Time with Eric Mazur

noreply@blogger.com (Tatnall Physics) — Thu, 19 Jan 2012 17:15:00 +0000

Today I traveled to Malvern Prep School to attend a workshop on technology in education with physics ed superstar Eric Mazur.

If you haven't seen this - whether you're a student or teacher - I'd certainly advise that you watch - even the first 20 minutes gets you the idea:

I'll record some of the content and reflections on it, mostly for my own benefit!

He's using a web applet that his company developed, mostly for word clouds (so far). There are valid criticisms of word clouds, but the first big idea is about learning through doing, not through being told. Check. We also have some mini-clickers that we'll be using later. They seem to have all of the capabilities of the first-generation Senteo/SmartResponse clickers. They're branded "Response Card." They're smaller and look cheaper, but their webiste doesn't give prices. Perhaps a more cost-effective way to clickify a larger school?
It looks like we're getting a recap of the deprecation of "sage on the stage" teaching (direct instruction, lecture, etc.) from the famous video above. It's like going to a concert - I'm comparing the little deviations from the recording I've seen so many times! :) He must have said this sooooo many times. All good points, for sure.
I also love that his spiel includes a discussion about how evaluation results from students are generally not correlated with how much students have learned. Instead, high marks are usually associated with ease of the class, average grades, or how much they "like" the teacher. Here's what appears to be a good summary of some of these issues. I wasn't successful in finding the paper that I was looking for that showed that students that reported "liking" the teacher tended to rate the teacher highly on even objective matters like the teacher starting and ending class on time, and vice versa.
It only took 19 minutes for the "flipped classroom" to be brought up. I have some axes to grind there. How'd we get to the point where learning on your own outside the class is the "flipped" way? I seem to remember being held responsible for learning at least the basics of the material before class, with class being for application, extension, and higher-level connections. Still not a bad concept.
I sum it up like this (it's something that I try to keep in mind always): lecture is about the transfer of information, but "active engagement" (modeling, inquiry, peer instruction, whatever your route is) is about the construction of understanding.
About 20 minutes into the recap of "Confessions," I'm ready for some new material (it's really really important material - watch "Confessions" if you haven't! It's just that I have seen it two dozen times. :).
Learning certainly is about being able to use that understanding in a new context. That's why you always get problems that are totally new to you on those pesky physics tests!
29 minutes in - now we're talking about the FCI. Uh oh, no new material coming for next next 15 minutes, I'll wager.
Wow - that's a Father Guido Sarducci clip. Nice.
Now we're into Peer Instruction - 44 minutes in.
I wish that it weren't such a pain to write new clicker questions. The questions aren't as much the hassle as using Notebook software is. I have not found Notebook to be robust enough or quick enough to use to supplant OneNote and other software that I use in class. Maybe I'll devote the summer to increasing my cache of clicker questions.
He's absolutely right that it's painful to give up your well-designed lectures and the thrill of a slick derivation on the board. To do so in exchange for students (initially, at least) being less enamored of your teaching is even worse. To see increased understanding on the FCI and other tests makes up for it.
Peer instruction demo: 10 seconds lecture on thermal expansion, followed by the hole-in-the-plate problem [I saw that one coming!]. We answered using his Learning Catalytics web software, discussed, and people could change their answers. 23% initially correct, 33% after discussion. Well, pobody's nerfect. PI definitely depends on a higher proportion of initially correct answers than 23%. You're supposed to pair yourself with someone with a different answer. Not all of those will result in conversion of an incorrect answer to a correct one, and many folks out there were missing someone with a correct answer. He did a good job of stressing that the mental model is the important part, and the answer is secondary - if you're not keeping in mind the overriding condition that the metal atoms all push away from each other when the metal's heated, but try to generalize surface observations, you're toast on this one. I wish that I'd been a part of a conversation (or listened to one) between novices here.
Interesting that he just pointed folks to his "Confessions" on Youtube. They'll find it familiar!
75 minutes in: Peer Instruction 2.0.
He's looking at features of his site (a bit of a commercial, really), and how they're improvements on traditional clickers. One helpful bit is that they can be used with any device, and don't require the capital investment of clickers. The big issue for me is how the responses are collated and presented, so that you can make some sense of the answers in the moment. Without that, it would be pretty weak.

Long answer, short answer, etc. - semantic analysis is mentioned, but he doesn't go into much depth. All I really see is the word cloud tangibly at this point, which isn't super useful for me in particular.
There's a neat vector-drawing capability - you can put up a drawing and ask students to draw a direction, and then see all of the responses collated very quickly on top of each other. Nice feature - I like this one.
Graph sketching works like this, too. Awesome.
Text can be highlighted (highlit?), too, with a "heat map" of what students identified as important.
You can select a region on an image, too
You can key the input devices at the beginning of the session to where they're sitting in the room - where are the right/wrong answers coming from? The system can also track those trends historically. If one student has correct answers, but keeps being dissuaded or keeps not being able to persuade his/her partner, then you can track that. That's great, but tracking seems like more work than almost anybody has time to do.
Overall, the system seems to have a lot of promise. It's still in beta, so it's free for now. Who knows what it'll cost when they start charging for it, though? I'd guess that it'd be much less than buying even one set of clickers.

After a bagel break, we're back. Me: 2, bagels: 0 for the day.
From some of the questions submitted to Mazur during the break, it looks like all of that time spent on interactive engagement and the failure of lecture in the first half didn't get everyone on board: "How do you balance time between the peer instruction discussion and covering material?" That presupposes exactly the normal lecture paradigm and that students learn what the teacher says - they learn what they construct for themselves, instead. Me rushing through a few more things doesn't mean that they learn a few more things, only that I've said a few more things. His results show increased performance even on problem-solving when using PI, even though they don't do any problem-solving in class! This isn't an addition - it's a substitution (at least a partial one) for the lecture/problem-solving paradigm.
Now we're back into more on Peer Instruction. I like that he's being explicit about using data from students (clickers, etc.) to shape how the class evolves. He's also talking about 30-70% initially correct being a 'sweet spot' for PI, but having plans for the other cases!
PI Trial #2: some buoyancy questions - rock in a boat, then remove the rock - what happens to the water level?; also rock in a boat, then rock goes to the bottom of the pool - what happens to the water level? [I thought that it would be the box at the bottom of the pool question, which is also great] The starting percentage for the first was more in the wheelhouse for PI, but the second went only from 17% to around 35%, similar to the first. There wasn't much instruction before or during, so it's no big deal, but Mazur did report that "physics instructors average around 30% on the first time," which seems to me to be at least as big of a problem as what we're doing pedagogically. How does our system let you get to be a physics teacher while missing lots of fundamental conceptual understanding? (It's not just this question that I'm reacting to - I've heard this type of setup a lot, mostly as an argument about how important it is for us to teach conceptual understanding.) It's a rhetorical question - certainly there are many factors that press folks into service as physics teachers against their training, etc., but getting successfully through a physics degree program without wide-ranging conceptual understanding ought to be not possible.
PI Trial #3: this one was more in the ethics arena (about retouching photos and how much is too much), with Mazur demonstrating how PI can be used in non-technical fields as a framer and catalyst of discussion (I suppose that's why Mazur calls his company Learning Catalytics).
He has only addressed a couple of the audience-submitted questions, but promises that his post-docs will answer them all and email them to us. That should be an interesting document; I'll add it to the post when I receive it, or make a new post, depending on the time delay.
His presentation of results is a good model - he shows the axes first, discusses what they mean and what information is being presented in what way, and then adds the data. That's a great way to present graphs.
A bit now about non-tech methods to do the same polling (fingers against the chest here) - the key's the engagement, not the tech that makes it happen.
Ending with a bit about resistance from students - the initial drop in performance/confidence upon changing methods. This is very similar to my post about the transition from unconscious incompetence to conscious incompetence, which is unfortunately the only way to get to any level of competence. This is a big one. You have to stick to your guns, and acculturate students towards the idea that making mistakes is the most important part of learning - they're not to be feared! We have to run towards the gunfire. For teachers, that also means the much less fun gunfire from students and parents when they see something new, when they have difficulty for the first time (because they're reasoning much more heavily for the first time), when their grades have no "fluff" to boost them to compensate for lack of understanding, etc. Hold the line - it's only about learning. Learning can be measured. That evidence is what you can use to confront these concerns (and the only thing that really verifies whether what you're doing is working, no matter what you're doing!), but you have to personally argue and really believe that you can change how somebody thinks about learning and how well they can learn.
While talking for a while in the lobby afterward, we were the only two left and then got a little chat with Mazur and a handshake! :)

Congratulations Alex!

noreply@blogger.com (Tatnall Physics) — Wed, 04 Jan 2012 19:38:00 +0000

Alex Christofferson made a video of his "Physics of Osmos" capstone project results to submit to the Physics of Osmos Contest, hosted by Hemisphere Games and featuring a $500 Amazon gift card for the winner.

He did a great job analyzing the conservation (and non-conservation) of momentum in the game, and of finding out that the mass of the motes is depicted by their area (rather then by their volume or length).

For his excellent work, Alex has won first prize in the competition! Great job, Alex!

Quick Labs: AP Physics/Energy

noreply@blogger.com (Tatnall Physics) — Sat, 17 Dec 2011 20:49:00 +0000

The AP Physics class did a bang-up job on some quick labs about energy on Friday - just a mere 3 days before winter break! All three projects showed terrific use of revision of their prototype experiments, as well.

The premise of the quick lab is to design, carry out, analyze, and present an experiment during a single 90-minute class period. Presentations should be a single whiteboard.

The experiments:
Alex, Alex, Brandon

They took video of basketball shots, from launch to floor, and used video analysis to determine how much energy the net (all were 'swishes,' of course) took from the ball as it went through.
Revisions: initially using the first two points of the video to determine the launch velocity gave unrealistically high results, so they changed that part of the analysis to use kinematics to analyze the change in horizontal and vertical position and time taken (all easily measured from the video) from launch to goal in order to find the launch velocity.
The boards (yes, they cheated and used two!):

Kawala and Kati

They slid a small whiteboard eraser down a ramp, after which it plunged to the floor. To determine the coefficient of kinetic friction between the ramp and the block, they used the fall distance and how far away the eraser landed from the table, along with the ramp length and angle. This required marrying kinematics, conservation of energy, and the work-energy theorem, and 2.5 gallons of algebra.
Revisions: they used two different 'floors' to take data, having the eraser hit the actual floor in one trial and hit a crate sitting on the floor in another trial. The advantage of this is that we can find errors by looking at the trend in the data as the height of the floor is varied. This is a great check that nothing unexpected is going on, and it was a good thing, because the first value was reasonable, but there were a few little errors to be uncovered. The coefficients came out negative when the height was changed, so it gave a prompt to find the issues, and now they're confident in these numbers!
The boards (also two!):

Cam, Mike, and Toru:

These guys took some high-speed video as well, analyzing the heights of a bouncing ping-pong ball. In addition to modeling the height of the ball as a function of bounce (and making a slick argument that the exponential function implies a constant-percentage loss of energy (rather than a constant amount of energy lost), they used Logger Pro to graph the gravitational PE, kinetic energy, and total energy as a function of time, showing the expected constant total energy during each flight (well, a slight decline due to air resistance), with "steps down" in total energy following each bounce.
Revisions: after considering the parallax issue with measuring the height of the bouncing ball moving in front of a meter stick (especially with the camera mounted to a tripod), they instead dropped the ball next to the meter stick, eliminating the point-of-view issue.
The board:

Why We Run Towards the Gunfire

noreply@blogger.com (Tatnall Physics) — Tue, 13 Dec 2011 19:10:00 +0000

We had some scheduling issues last week in physics with visitors, so I made an in-class assessment a take-home assessment. One great thing about SBG is that there's really no point to cheating on such an assessment, so I think that I'm still getting a good picture of where they are.

On this question, they were (in general) in the weeds:

" Two radio towers 30 km apart transmit synchronized 240 kHz signals. If a car equipped with a radio receiver tuned to the transmission frequency drives directly from one tower to the other, what will the receiver hear? Explain; a diagram would help! Radio signals are light waves that travel 300,000,000 meters per second.

What would the signal be like at a point along the drive that is 8750 meters from the first tower

How would the driving experience change if the radios’ frequencies were changed to 300 kHz?"

We've done some work with 2-source interference, from looking at the "overlapping ripples" diagrams to doing some predictions of frequency from two interfering sound waves given the locations of some points of constructive and destructive interference in the room.

This is the same concept, but a different-looking context, and that's where kids that haven't quite figured out the whole axiomatic reasoning thing have difficulty - yes it looks different, but we can still use the same principles to make predictions about what happens.

In particular, the big message for 2-source interference is that, even though both waves start in phase, they may not be in phase when they reach you, if you're different distances from the two sources. The difference in travel distance determines the phases of the waves and whether they'll interfere constructively or destructively. [This type of relationship is familiar: rates (relatives of differences) are famously difficult for students to intuitively grasp - see calculus!]

Back to the story, though:

I collected the assessments at the beginning of class and then posted this problem via projector. I set the online stopwatch to five minutes and told them to come up with something coherent in their whiteboarding groups. There was a good discussion after that, and we made a lot of good connections.

...before that, though, there was an audible groan when I posted the problem.

Why? It's a hard problem! They've already wrestled with it for some period of time, felt anxiety that they were adrift about (da-dum!) an assessment problem, and here I was bringing it up again.

Here's the thing, though: you don't learn anything by running away from those difficult problems - you have to figure them out so that you can use that understanding in the future. Denial is death in problem-solving.

Soldiers and police officers are incredible because they run towards gunfire, while the rest of us run away. There's an anxiety-filled and dangerous situation, but they do the harder thing and confront it directly.

In physics (or learning in general), we have to run towards the gunfire too - you have to seek out and fix those misconceptions and misunderstandings. It's anxiety-filled, too, but one student yesterday noticed a crucial difference between the two situations, when SBG is used: for us, the wounds aren't permanent.

Not Proficient? No problem - wrestle with the problem, come back, and then you'll be whole again. Using traditional grading that students are accustomed to, I totally understand why they get gunshy, even at the level of course selection. Reminding them that this is a safer space for making mistakes has to be a constant occurrence because of that ingrained anxiety, but it's well worth the effort.

One of my favorite demos

noreply@blogger.com (Tatnall Physics) — Wed, 07 Dec 2011 20:35:00 +0000

I love the demonstration of two-source interference of sound waves - two speakers and a sine wave generator is all it takes to get one of those moments that kids remember for a long while after the course is over (now, if we can just get them to remember why it happens!).

The echoes in my lab aren't too bad, and we can actually map an interference pattern reasonably well, in large areas. At some point, I'd like to try this in a big space and have them mark nodes (quiet points) and antinodes (loud points) with cones or something, and see if we can recreate the classic illustration.

In the meantime, we mapped out a few points that were relatively easily found:

At this point, we already knew all about order lines and how these loud and soft points came to be; we had analyzed a diagram of the interfering waves, determined where constructive and destructive interference were happening, and noticed the pattern in the 'lines' of nodes and antinodes (and even brought those shapes back to the base definition of a hyperbola!).

This was their first chance to apply that to a live problem: what's the frequency of that annoying hum that I'm playing through the speakers, anyway? Are these measurements all that we need to determine that? After all, there's nothing about time here at all, so determining the frequency seems daunting at first.

"What order line is that first soft point on?" is the real catalyzing question that I ask the groups a few minutes into their whiteboarding, if they haven't figured out how to apply the two-source model yet.

From there, there are a few steps of reasoning, some triangle manipulation, and some unit conversions needed. The triangles and unit conversions shouldn't be an issue at this point, though they still are for some that haven't reached an unconscious competence level. These assumed skills can really derail you. Especially if a problem is already difficult enough to tax your faculties to the max to begin with, adding a protracted wrestle with a unit conversion or diagramming effectively is likely to push your brain into a useless fried state (like okra).

Once we've connected that the order number is important, that connects to something about the distances from the speakers to the point, so we need to find those distances, using the Pythagorean theorem:

OK, great, but what does the order number tell us? This is a place where the sound is quiet because there's destructive interference, which happens because the waves travel different distances to get here. The waves began synchronized, but since they've traveled different distances, they're at different points in their oscillation between high and low pressure (they're out of phase). At this place, the wave from the left speaker has traveled half of a wavelength further than the wave from the right speaker (that's the .5 in the order number!). Now we know two different ways to write the difference in travel distances:

Now that we know the wavelength, we're all set:

That's quiet a chain of thought there - let's trace the inferences that you have to make to solve this problem:

That's quite a set of inferences and observations, each necessary to solve the problem. This number of inferences and observations is necessary for many problems that students try to solve, but we don't often think about the chain of logic so literally. A great deal goes on behind the scenes... or doesn't. Note too that there's knowledge from previous courses, previous terms and units of this course, and the current situation, but that it all has to fit together; this doesn't happen if students view understanding as disposable. That sort of mindset is like tying your leg to a tree and trying to go for a run - no matter what direction you go, you can only go so far.

I think that, if students can get comfortable spelling out their reasoning like this, then they can get better at making a linear argument, which is what all problem-solving is - each step must be supported by knowledge or information and must lead to the next step. Scatter-shot thinking is rampant, and it does not help problem-solving. Perhaps conscious effort on constructing a "chain of reasoning" can help a student be able to do this type of thinking unconsciously, too!

SBG: Changes for the Winter Term

noreply@blogger.com (Tatnall Physics) — Tue, 29 Nov 2011 13:05:00 +0000

An informational post, mostly for the benefit of students in my courses:

This winter, we'll be implementing a few changes in our standards-based grading system, in order to streamline the reassessment system and reflect the larger number of standards assessed in the second term.

Reassessment requests must be made through this Google form: Reassessment Form.
- The reassessments, at least at the beginning of the term, will be given on Mondays, Wednesdays, and Fridays (let me know if there's a scheduling issue for you)
- You need to complete the reassessment form by the previous M, W, or F; for example, if you'd like to reassess Monday, you need to complete the form by the previous Friday.
- The form asks about the preparation that you have done in order to earn reassessment. Corrections are, as always a minimum, and you need to bring the written work that you have done to prepare for the reassessment.
The grading scale for standards will be a little more detailed this term, adding 'half levels' between NP and De and between De and P, in order to have the grade give a finer level of detail about your understanding.
- A: Advanced
- Pr: Proficient
- P-: Proficient Minus
- De: Developing
- D-: Developing Minus
- NP: Not Proficient
As there are more standards this term, a single NP will only limit your overall grade to a maximum of C+, rather than C-. Any scores below P will still limit your grade to a maximum of A-.

For full details, check the SBG page on wikiphys.

Capstone 1: Final Paper

noreply@blogger.com (Tatnall Physics) — Sun, 20 Nov 2011 23:48:00 +0000

Alex has finished our first capstone of the year. This is also the first post for CapstoneLearning.org; great analysis, Alex!

Abstract:

In this paper I explore the physics of the computer game Osmos. It was my goal to see how accurately Newton’s laws applied to this game. I captured video of the game and used Logger Pro to analyze the physics of how an object propels itself by expelling some of its mass in the opposite direction. I discovered that impacts between random objects have perfect conservation of energy; when the main mass controlled the player moves conservation is not conserved. In that situation, the player is given approximately four to five times the amount of energy dictated by Newton’s laws to make the game easier.

Full paper linked here.

Three Representations

noreply@blogger.com (Tatnall Physics) — Thu, 17 Nov 2011 01:07:00 +0000

Today the honors physics classes took their first crack at connecting three of the four representations of interactions: system schemas, free-body diagrams, and motion graphs (v vs. t in particular here). Along with net force equations, these will be the basis of most of the rest of the year!

We had some great whiteboard meetings as we split into five groups to construct our representations and then made sure that all of each group's representations agreed in each situation. This is good practice for looking at your own work - multiple representations not only give you multiple avenues to attack a problem, but also let you check yourself!

I encouraged them not to write these down on the sheets that I gave them with the setups, so that they can use them as independent practice later, checking back to the whiteboards for verification afterwards.

For each situation, the students evaluated each representation while the box was at rest, being pushed (and speeding up), and after it is released (after having been pushed).

The four situations were:
A rubber-bottomed cardboard box with a block inside it, on a rough floor.

A cardboard box with a block inside it, on a rough floor.

A cardboard box with a block inside it, on a smooth floor.

A cardboard box with a block inside it, on a perfectly frictionless floor.

A follow-up task for my students:

Draw v vs. t graphs for each of these four situations on the same set of axes, assuming boxes of equal weight and push forces of equal and constant size. Here's a template, along with a color-code, ready for magic markers!

Along the way, we had a great discussion about what happens to our system schema if we split the box and the block inside it (leading us to our first encounter with static friction!), and about what we can't tell about the motion from free-body diagrams (like... the direction of the motion!).

Thanks to Kelly for the great springboard to this one!

Capstone Project 2 - Comments Wanted!

noreply@blogger.com (Tatnall Physics) — Sat, 12 Nov 2011 12:33:00 +0000

Kawala has submitted her draft of a capstone project on roller coasters.

The draft is available here, and she'd love your thoughts!

How Good Is That Number?

noreply@blogger.com (Tatnall Physics) — Fri, 04 Nov 2011 17:38:00 +0000

When we calculate anything, we're always modeling - we're making assumptions and approximations, and our measurements are always inherently uncertain to some degree. Our calculation must therefore be viewed with an understanding of its limitations and biases (not the colloquial term implying that there was an agenda, but rather any sort of consistent skew to the results due to some physical mechanism that wasn't accounted for).

One experiment that we did to determine the speed of sound a few days ago is a great case study for talking about error analysis.

The Goal: We were trying to determine the speed of sound in air.

The Setup: Students spread out across a large field, at known distances from a student with a baseball bat and ball. The student tossed the ball into the air and hit it.

The Measurement: Students started their watches when they saw the ball hit the bat and stopped them when they heard the impact - the travel time delay and the distance can then be used to determine the speed of sound.

Sources of Error: Again, there's a difference between everyday use of 'error' and scientific use; we don't mean 'mistakes' - if you made a mistake, then you need to fix it. We're talking about consequences of our modeling assumptions and unavoidable measurement uncertainty.

In this experiment, two big sources jump out at us, and illustrate very nicely the two main forms of experimental error that students are likely to encounter:

Timer error - every time you start and stop the watch, there's some uncertainty in that measured time interval. You could have started or stopped a little too late or early, and it's impossible to tell which happened in any given measurement, just based on that one time. This is a random error source, because it could make your measurement either too high or too low; it generally serves to scatter your data - some points are a little high and some a little low, but the trend is unaffected.
Reaction time - this one's more subtle here, and a diagram really helps to illustrate its presence in this case:

The subtle part is is the difference between the two events. We saw the impact coming - he tossed the ball into the air, and we could anticipate the impact, so the beginning of the time interval came as absolutely no surprise to us. The end of the interval, however, was subject to our reflexes; you can't hear the ball until the sound gets to you, so there's no way to anticipate the moment at which you should stop your watch. This tells us that the measured time intervals will all be too long - that's a systematic error source, because it skews all of our data in the same direction, and has an effect on our average value.

Effects of the error sources: This is the most important part of the error analysis, because it gives us information on how we should trust our final calculated value. In this case, we should expect our calculated speed to be lower than the true value. We could quantify how much longer, but that's a bit deeper than I'm interested in going with this physics class. If we can qualitatively analyze the effects of error sources, then I'll be thrilled!

The reaction time issue will cause our times to be uniformly too long, which will cause the speeds to be too low. This is a systematic effect, and we should expect the average value to be lower than the true speed of sound.
The timer error will scatter our values, but not affect the average value; some will be too high (because the times were too low) and some too low (because the times were too high), but there's no effect on the average speed.

Now This Is a Great Design

noreply@blogger.com (Tatnall Physics) — Fri, 04 Nov 2011 17:14:00 +0000

I usually begin our discussion of waves by tasking the students to design an experiment (as a class) to measure the speed of sound in air. It's a backdoor way into experimental design, error analysis, and rate analysis, rather than really particularly wave-focused. There are a variety of factors that make this difficult, not the least of which are the high speed of the wave (necessitating large distances) and the issue with measuring an event at a distance (made necessary by the large distance).

One of the slickest ways to get around this is by synchronizing watches, spreading out over a distance, and stopping the watches as each person hears a lour sound. The differences between positions of the timers and the differences in times can be used to determine the speed - most easily by fitting a line to the position vs. time data, where the slope will give the speed, magically using all of the data in a single calculation!

A very creative design this year came from a couple of groups, actually:

Stand some distance away from a wall
Clap

... I've heard this one before, up to this point. Generally, the problem comes when students try to measure the delay of that echo, which is really short.

Clap again, when you hear the first echo
Repeat, repeat, repeat...
By counting claps and timing, say, 50 of them, determine the travel time for each echo.

That's a slick design, and applies some of the good measurement techniques that we've learned to apply to timing oscillations - nice work! It takes a few cycles to get your clapping tempo to match the travel period, but after you're synched up, you can take data on this pretty easily.

Our data:

Average time of 13.43 seconds for 50 clap cycles (51 total claps!)
Distance from the wall: 42.8 meters

There's an easy mistake to be made in the analysis, which a diagram will sort out:

The distance traveled during the time between claps is twice our measured distance; you have to make sure that the time and distance that you use to calculate the speed are for the same motion!

With an average travel time of .2686 seconds, and a distance traveled of 85.6 meters, our calculated speed of sound is... 319 meters per second! That's pretty good for a really low-tech method, I'd say.

Post-game Reassessment: Instant Feedback

noreply@blogger.com (Tatnall Physics) — Thu, 03 Nov 2011 11:41:00 +0000

A few days ago, I posted about our first use of Frank Noschese's system for instant post-assessment feedback. The highlights:

After finishing the assessment, students go (with paper in hand, but not pencil) to one of the exhaustively completed keys around the room
Students pick up a green pencil and mark on their papers: what they were thinking while doing any analysis that came out incorrect, what they can do better next time, and even alternate ideas for analysis if theirs was already correct, but not the same method(s) that I used
Students hand in the paper to me, I grade them, record the grades and feedback, and return them as usual

From my point of view, students are looking at their own work right in the moment, so they have immediate buy-in and a fresh memory of what they were thinking while doing the problem, so it's much easier for them to identify their errors in thinking (rather than their errors in doing) than it is for me to try to guess what they were thinking, given only what they did. Writing their own feedback also helps them have automatically meaningful input for future reference. I add in anything that I think that they're still missing, but they're doing most of the work here - as it should be! Learning, unfortunately (for efficiency, fortunately for fun!), isn't something that anyone can do for someone else.

Well, those were my thoughts and hopes. The next class, I asked students to give me some of their feedback, to see if they saw it as I did. From their papers on assessment day, I saw a surprising depth of self-reflection and it seemed (from my POV) to be successful. From their point of view:

"I thought it helped me to understand problems/errors I made while the problem was still fresh in my mind. It was Good + Useful!"
"I thought what we did helped a lot because it showed me what I need to work on for the test."
"I think the green pencil was helpful because it allowed me to learn from my mistakes."
"It helped me understand some of it, but it was a little difficult to know if I would get partial credit, like with tangent lines, but it did help me understand what went wrong" The small wrinkle that they were drawing tangent lines by hand to determine velocity from a curved position graph meant that some students had difficulty judging what was close enough. The partial credit thing is really ingrained in them - focus on the learning, not the points!
"Good, so you know right away what you did wrong and fix it."
"Was not helpful because I did not understand what to do."
"This method was kind of helpful because it forced me to look at my mistakes but sometimes I don't know what my mistakes were."
"I liked it because it helped me learn what I did wrong."
"I liked the idea. My thought process was fresh in my mind."
"Now I know what I was thinking on the test. This is positive so I realize what I was thinking during the test."
"I liked it! It helped, I think, and I could see my mistake as soon as it happened and know where I went wrong."
"For the first side the numbers were slightly different but the method was the same, so it confirmed my procedure. The other side showed how I messed up the equation slightly."
"I liked doing the green pencil because it was right after the assessment so I knew what I was thinking while taking the assessment."
"I thought that going back and making corrections on the assessment immediately after taking it was very helpful. I could figure out what I did wrong and then use the corrected version to look over and study from. Also, I know what types of mistakes I made, so I know what to watch out for in the future."
"I liked it. It was good to see my mistakes right after."
"I liked the idea a lot, but it didn't really help me since I had the answers right."
"It helped me learn what I did wrong to see the work."
"It helped me pinpoint what I needed to work on."
"It helped. When I got my quiz back, I recognized what I was thinking when I took it."
"I think it was nice because I could look at the correct answer and see why it was wrong instead of you just declaring it was wrong and not showing us exactly."
"It was hard to tell exactly what you did wrong or if you needed more information than you had." My key was very verbose - some kids did ask if they needed to show all of the work that I did.
"It was good feedback."

Habits of Great Problem-Solvers

noreply@blogger.com (Tatnall Physics) — Tue, 01 Nov 2011 18:23:00 +0000

We're wrapping up CAPM (constant acceleration motion) in honors physics, and one of the biggest ideas is determining the direction of an object's acceleration. It's very important once we start moving into force analysis, because it tells you about how the forces acting on an object are related, and sometimes tells you the direction of a force that you couldn't determine any other way (static friction, I'm looking at you!).

We took a second to stop and collect our list of ways to determine the acceleration of an object:

From the x vs. t graph: is the slope increasing or decreasing? You have to be careful here to differentiate between getting steeper vs. flatter (which tells you about speed) and whether the value of the slope is increasing or decreasing (going from a zero slope to a negative slope is decreasing).
From the v vs. t graph: is the slope positive or negative? There's your acceleration sign direction, too.
From a diagram: is the object speeding up or slowing down, and what direction is it moving? The combination of the acceleration and velocity directions determines whether something's speeding up or slowing down, so you can work backwards to find the acceleration direction from the directions and relative sizes of the initial and final velocities. If you know that it's moving left and speeding up, you know that the acceleration's left as well. If it's moving left and slowing down, then the acceleration is in the direction opposite the velocity (so a is to the right, in this case).
From the x vs t graph: is the graph concave up or down? That is, does it open upward or downward? Positive accelerations have concave up position graphs.

We applied this to an easy example using a ramp and a Pasco Visual Accelerometer. These are pretty neat little boxes that produce a green arrow or a red arrow to one side or the other, based one the direction in which it is accelerating. For some reason, kids will believe that little computer box with all of their hearts.

The second challenge was a little tougher: I roll a cart up the hill with the visual accelerometer on it, and let it go up to the top and then come back down. I asked the students to predict the direction (or directions) of the acceleration, and to defend their answers with at least two pieces of evidence (they have four possible lines of inquiry from our four methods above!).

This is one that always has the potential to stump my students. Detaching the directions of velocity and acceleration (indeed, differentiating that velocity and acceleration are actually two different things!) can be tough, as can detaching speed from velocity.

Which direction is it moving? You can't tell by this acceleration reading!

They did very well with it, though, with most groups coming to the correct answer rather quickly and confidently. A big part of this seemed to be their use of these multiple lines of evidence to back up their decisions. Every approach that you take to a problem will give you an answer. Whether that answer's worth much? It's hard to say, if that's all you have to go off of. If you can attack the problem from multiple directions, then you can really have some confidence in it.

I definitely had groups draw iffy motion graphs during this. Most groups, however, as they used the diagrams and graphs to try to come to the same answer over and over again, noticed when one representation gave a different answer than the others, and were able to flip that velocity graph or look at the starting position more carefully.

This is what great problem-solvers do - they use multiple avenues to address a problem, letting the results of each one inform the others. It's not really a linear process, but an attack from multiple angles, until you break through, and then a mopping-up of all of those open threads, in order to make sure that everything line up as it should.

Once again, we see that:

Great problem solvers don't always get it right the first time - they just catch their own mistakes, so that the first answer that you see from them is right.

This idea about the non-linearity of problem solving doesn't just apply to problem-solving, though: the whole web of knowledge in your head really is a web. If you only connect each piece of knowledge to the next in a single chain or ladder, then it's difficult to tell when a thread breaks. After all, you'll always get an answer.

If, however, each piece is connected to many others, then one strand breaking isn't an issue, because you have several other ways to make that connection. This is really the secret of complex problem-solving, and pretty much the definition of knowing something cold (unconscious competence!).

Here's a web that I threw together for my knowledge connecting the kinematic quantities:

The most fundamental thing that makes my understanding deeper than the honors students' understanding at the moment is that I just know some more connections than they do (so far). Making this web as rich as possible is really your job as a learner. When teachers bemoan "surface understanding," cramming, and answer-hunting, it boils down to a difference in the process for a student - that student's goal directly impacts the level of understanding that he/she'll get out of the course.

So, how about it? Are you trying to get someone to tell you "the path to the answer," or are you building your own sprawling web of highways?

Capstone 1 Unveiled! Comments Wanted!

noreply@blogger.com (Tatnall Physics) — Sat, 29 Oct 2011 00:08:00 +0000

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!