Newton's Minions

Chunking, Reading, Video Games, and Physics

noreply@blogger.com (Tatnall Physics) — Thu, 28 Feb 2013 17:13:00 +0000

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

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

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

This applies to just about every human endeavor.

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

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

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

If you work example problems or the class does them together, with you writing, make this part of the process really explicit, and make it happen before you do anything else. Don't start writing your IF chart or conservation equation and then off-handedly say "well, there's no friction, so we'll use CopM, right?". Do it every time.
Give students - early and often - chances to get it wrong. It's easy to fall into the trap of only giving practice and assessment problems using the concept du jour, but it hobbles them later. Ever have great unit assessments and terrible comprehensive exams? This'll do it. This opportunity is why I went back to a CVPM CAPM BFPM UFPM sequence (instead of CVPM BFPM CAPM UFPM) - it gives students (in the second unit) a chance to differentiate between models. I really like to introduce models in pairs and emphasize that: CVPM vs. CAPM, BFPM vs. UFPM, pTM vs. CopM, ETM vs. CoEM. Having choices to make between just two competing models is a good stepping-stone to the bigger choices when all of the model are in play, and if you don't emphasize it when the choice is easy, then they won't be able to do it suddenly later. This part can easily get lost in the planning. I do a good job of using 'older' concepts when they apply in the new context, but I need to give more practice and assessment of those skills just for their own sakes later in the term.
Make articulating model choice a part of assessment - consistently.

Incomplete Mastery (conscious competence):

When students don't fully master a skill (or don't practice it periodically after mastering it), they have loose ends. Maybe they don't even have that - maybe that can do it accurately, but they just have to think it through and put a lot of effort into it to get it right. That doesn't only take time, but it takes mental effort, which is a finite resource. This goes back to some of the things in the posts about fluency here and here and here.

This comes up a lot with skills that are used often, like symbolic algebra, trig (breaking vectors into components and the reverse), graph-making, unit conversions and prefixes, etc.
It derails the more important thought processes that we're trying to get to - it's that mental energy allowance, in addition to the time issue, for assessments.
It builds a poor foundation for later concepts. In math and physics, everything (should) build on what came before. Having middling understanding of something means that whatever application or extension comes next already starts out on shaky ground.

Both of these cut down on the level of complexity of situations that students can analyze: they need to be able to quick dissect the situation into models (maybe several different time intervals with differing models) and then have the fluency to apply those models accurately. That's a tall order, and they can't do it if their brains are exploding trying to remember some details of each skill or concept simultaneously. The ballistic pendulum's a great one to work on with this: you have at least three different sets of models applying to different time intervals over the course of the motion, and we all-too-often blow past that determination step. The same goes for the Atwood machine. Once you're through introducing mechanics, have students model it with forces/kinematics, momentum/impulse, and energy/work. It's a brain-buster for them trying to determine why the force exerted upward by the pulley on the string DQs conservation of momentum but not conservation of energy.

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

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

Musical Instrument Project

noreply@blogger.com (Tatnall Physics) — Wed, 27 Feb 2013 14:21:00 +0000

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

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

During the course of the project, each instrument is revised a lot; some completely change and some need model tweaks - using the end correction, sometimes the tension/wavespeed relationship or Helmholtz resonators (none of which they didn't know about before this). It's a great chance to really experience that prototype/revision cycle.

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

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

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

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

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

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

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

PVC Clarinet - This one wasn't really a clarinet, since it used buzzing, but the first design involved a reed. I had a couple of groups use reeds successfully last year, but none stuck with it this year. This was the first instrument that I've had with a reasonable implementation of holes to change the pitch. The timbre gets crazy after several are uncovered, but it does a reasonably good job of producing an intelligible pitch.

Batterie De L'eau (water drums) - this one also went through several revisions. By the end, they used a small strip of paper across a plastic container filled partially with water. By using the end correction, the contained resonated to selectively amplify the desired frequencies from the noise of the paper strip. It's a noisy sound, but the pitch is clearly audible. Video

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

Practice: Art and Physics

noreply@blogger.com (Tatnall Physics) — Tue, 19 Feb 2013 14:32:00 +0000

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

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

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

My first attempt at a face, back in the summer:

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

How Much Information Is Too Much?

noreply@blogger.com (Tatnall Physics) — Sun, 10 Feb 2013 22:15:00 +0000

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

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

The scariest interpretation: "Can I just ignore this now?"
"Should I bother to reassess this individually, or will it happen anyway without me scheduling and taking an individual reassessment?"
Another cynical one: "At what point should I actually try to learn this?"
"I'd like to plan my limited number of reassessment days (remember that we're within a couple of weeks of the end of the term, and they can only reassess one std/day, only on M, W, F) - do I need to use those for a different standard, and pick this one up on one of yours?"

Much like Star Trek movies, two and four are good and one and three aren't. I might be overly optimistic, but I think that, for most of the kids that have asked me (thinking of the individual kids that have asked me), it really isn't a diabolical or cynical question, but one about time management.

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

Python, Ramps, and Energy

noreply@blogger.com (Tatnall Physics) — Sun, 10 Feb 2013 21:17:00 +0000

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

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

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

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

Correct physics
Constant speed
Constant x-dimension speed, constant y-dimension speed while on the ramps (tie)
Accelerate down the ramp and up the ramp, but back to ball 1's speed on both of the flats
Accelerate down the ramp and up the ramp (but too much, so that the balls end up tied)

The videos are here (not in that order :) - A B C D E

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

The Innovation Game

noreply@blogger.com (Tatnall Physics) — Thu, 07 Feb 2013 13:16:00 +0000

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

The highlights:

Every month, one teacher leads a session in which he or she introduces an innovative technique that he or she has found successful in the classroom
During the following month, everyone else will try out that technique at least once
An online forum will be set up - as soon as you try the technique, you report to the forum, and discussion ensues
A free wrap-up lunch occurs a week or so before the next session, to discuss further, celebrate successes and failures, and to build collegiality

It's still in the planning process, but there are a good half-dozen teachers on board, and we're looking forward to starting soon! Comments and suggestions welcome!

EduCon 2.5, Day 3

noreply@blogger.com (Tatnall Physics) — Sun, 27 Jan 2013 21:02:00 +0000

I skipped the panel on "What Does the Entrepreneurial Spirit Mean for Schools?". Entrepreneurship has been a big focus of the conference, but it doesn't really resonate with me. It could be a private/public disconnect, but I don't see entrepreneurship as the big thing lacking from education.

My first conversation today was with some kids from SLA. Since the school's completely project-based and standards-based, I asked some kids about homework when I overheard them talking about it. Where does homework fit into the grade? It doesn't. Does that mean that they don't do it? No. SLA does a great job of making homework worth doing and with bringing kids into the process, so that they actually want to do the homework, knowing that it will help them along the way towards becoming proficient with the core goals of the courses. Having ownership of the process a little bit - there are decisions to be made about where to spend the majority of your time, when more practice is needed and when it isn't, etc. - is really important in there process of making kids able to manage their own learning, which they will definitely need to do in college and for the rest of their lives. Even without a stick or carrot of a grade, kids can see the value of work outside of class, but it does take some concerted effort and dialogue about it.

My first scheduled conversation today was "Structuring Inquiry," with Chris Lehmann (head of SLA).
The conversation will continue later at #educoninquiry

First focus: how do we set the conditions for inquiry?

Small group discussion: what do we mean when we say 'inquiry'?

Ideas from the group and from the large group discussion following:

Encouraged curiosity
cycle of 'wonder, experiment, learn'
Empowering students to actually determine things for themselves, not having them dependent on authority (books, internet, teacher) to answer/model
Leveraging student curiosity
Balancing student interests vs. teacher guidance
80/20 'tinker time', a la Google employees - somebody said yesterday that there's a school doing this for both students and faculty
How do you assess inquiry?
Does there have to be _one answer? Someone chimes in that the word 'question' is loaded, in that it implies an answer exists. Problem/dilemma/etc. instead?
Inquiry based on confusion vs. inquiry based on wanting to understand something at an even deeper level
Recursive process: prototyping and revision!
Actually taking part in the types of thought practiced by historians, mathematicians, scientists, etc., instead of learning about what they do. This is a big modeling advantage - doing science vs. hearing about science
Inquiry means living in an uncomfortable place where the issues are real and difficult and the answers aren't simple
Kids don't always know how to ask good questions, because schools often teach them not too. It's important for schools to teach the process of inquiry, even more than content
SLA's framework: Inquiry, Research, Collaboration, Presentation, Reflection; this is for classes, professional development, etc. - he says that it's an interesting way to make debates and discussions less rigid and more flexible
When it's going right, the students and teacher are on the same journey. There is a lot to be said for taking some time to explore something that the teacher doesn't know about, so that you can be an example of real inquiry
Doing it from the top-down is difficult, but when kids get hooked on it, they might start to demand it from the bottom up.
Demonstrating the value of inquiry can be an issue in a test-obsessed public school situation, but it's important to fight that fight
There's an innate tension between AP curricula (many of them, at least) and inquiry. It's important to be "one school" - to be philosophically consistent in every aspect of the school
"If you want easy, put the desks in rows. If you want meaningful, there are things that you'll have to grapple with."
Tension between messy and neat and tidy - inquiry's a bit messy by design, but didactic instruction is a false efficiency
Inquiry can be equalizing - weaker students can be better risk-takers in lots of situations
Inquiry builds community
Inquiry vs. recipe-based instruction is the important part - project-based classes aren't the magic bullet if they're not applied well
Scaffolding's important, and it's the art of the process. Inquiry isn't the same as turning kids loose to find their bliss and drinking some coffee. It's a lot of work and it'll probably look different every time
Links: bit.ly/RamiEnglish11_Sept and bit.ly/SLASFP1213
Scaffolds: giving enough to prime the pump without being prescriptive
Here's a telling thing: there are over a hundred teachers in here, hotly debating inquiry and being very high-level in their animated discussions. A student just spoke up and gave her perspective, totally without prompting and totally confidently.
Inquiry makes more difficult: covering content, planning, and assessment
His view: you can't really get an objective measure of what kids know - certainly not test scores. He also sees grades as mixing up effort ("because sweat matters") and achievement, as opposed to a traditional SBG view of having removing everything but achievement from the grade
When you go to a school where there are lots of folks doing inquiry, blogging, etc., things change a bit - you're not the only show in town anymore, but you're in a space where colleagues understand the demands of flexibility, innovation, engagement, etc.
What do college students say after leaving SLA? These kids get engaged with professors (even ones that are traditional), do better with research, assignments, and tests in college. His argument is that the classrooms in colleges are traditional, but the tasks that they're asked to do aren't, so that this training transfers well
Being the only person in the building do it: benefit from uniqueness, scaffold to take kids from the ground floor up towards more open inquiry over the course of the year, focus on pieces of inquiry at a time (play the JV game before the varsity game)
People use the tests, college, etc. as excuses not to start doing inquiry, but is the traditional approach really working now? Is it producing what we really want in kids?
Algebra II is the most difficult year to do authentic inquiry/projects, but earlier grades (especially elementary) are the easiest and most profitable places to do it.
Final really big question: what else will change if your pedagogy becomes inquiry-driven? Example: discipline (you just taught the students how to question :) )
Related question to ask: what's the worst-case scenario of your best idea/intention?
bit.ly/SLACapstone

Next session: "Where Are All of the Beautiful Learning Spaces?" with Jennifer Chan (@jennzia), and Andrew Campbell (@acampbell99)

Some high-level talk about what spaces say to us, implications of structures ("All visitors must report to site office"), and what the spaces say ("don't run, think, learn, yell").

Their tumblr: http://beautifullearningspaces.tumblr.com/

Some discussion questions:

What qualities would make a learning space a 'must see' destination?
Does the current learning space you use reflect and support your pedagogy?
What are the tensions between your ideals and cultural/social expectations?

I'm more conscious of the fact that other folks are more focused on architectural details of spaces than I am. In my lab renovation, I wanted to focus on function: no fixed furniture, whiteboards, etc., but there's more there, too. I'd love for all of my walls to be whiteboards, or even all of the halls! My focus, though, is on what these things do to the learning process.

Interesting discussion here about security and the unintended bad consequences from trying to fortify and protect schools: "let's stop pretending that our students are any more in danger at school than at the bus stop, in the store, on the playground, etc."

Next session: "Honoring our Learning Philosophy Through our Learning Reports: Is it About Learning and Progress or is it About Grades?" with Megan Howard (@mwhoward) and Jill Gough (@jgough)

We're introducing ourselves - there's a senior here from a different Philly high school. I don't think that I've seen a student attending an ed conference before...

We took 15 minutes to go around and look at different report cards from four independent lower schools and to leave Post-it note comments. Some interesting things:

One of these is 20 pages long, another 11, the others 3 and 5 pages long.
I really liked one in which students each wrote comments/reflections for each subject. What would that moment be like when you have to write "I didn't really try this term in Spanish, so I struggled"? I think that it would be a good one.
The shorter comments with denser displays seemed to communicate more than the super-verbose ones, which tended to have lots of boiler-plate

Great discussion here on grading and reporting - sorry - I didn't write much down!

The discussion continues on #RCSatl !

The conference that sounds like a monster truck rally (EduCon - Sunday, Sunday, Sunday!) comes to a close. Good conversations and good times - don't come if you're not into participating!

EduCon 2.5 - Day 2

noreply@blogger.com (Tatnall Physics) — Sat, 26 Jan 2013 21:27:00 +0000

My first conversation: "A New Vision for Mathematics in High Schools," with (Mike Thayer) @grblxt

The premise is that the algebra 1-geometry-algebra 2-precal-calculus sequence is broken and doesn't work for him. Interesting bits:

we teach things in algebra 1 (like rational functions with factorable denominators) to kids in 7th or 8th grade in algebra 1 that weren't part of algebra 1 for most of history.
He has a book (missed the author) with 'everything that you need to know about trig, algebra, and geometry - it's 119 pages long.
His challenge - assuming competency with fractions, decimals, etc. - can we do all of that stuff in a 100 hour course? This is a course that covers the essentials of algebra 1, geometry, algebra 2. There's less material included in that than in the three courses currently, but what would there need to be?

Now... we discuss...

Some ideas from the group about things that can be thrown away:

"most of geometry" - angle theorems, centroids, etc. The idea of proof is important, but does the two-column regime actually communicate that? Do students come out of geometry able to prove things?
half angle/double angle/trig identities
vocabulary - associative, commutative, etc.
matrices

Our group's "keepers" (partial list - didn't get to completion):

Right-triangle trig
Modeling: choosing appropriate algebraic models for data, using graphical and algebraic representations together, applying and interpreting the models
Understanding equations as relationships: create, manipulate, and solve single equations and systems of equations

Presenter's proposal: a one-year intensive experience in abstract math, with topics left out of this course taught in the subjects in which it's applied (exponential growth in bio, etc.). His big idea is that we've divorced math so much from the applications that it's not effectively transferrable to other courses.

Discussion following that:

One report of collaboration of science and math teachers just on aligning vocabulary had a big effect on this transferability.
Can't we just teach multiplication and exponents conceptually, so that it's not a set of rules, but just a consequence of the concept? Presenter reports his district teaching exponents in alg. 1 and alg. 2; you can't tell which kids had it the first time around - it was divorced from use and totally forgotten. They were rules, but when kids understand that it's repeated multiplication, kids don't need the rules, and can actually use them.
What if we co-taught these bits in other courses? That's a scheduling nightmare, but we could be the resource for kids and teachers.
Shoving kids through this content is counter-productive: it's painful for all involved, doesn't help kids later, and takes time away from really understanding
The assessments are part of the problem: what do they assess, and is it what we really value?
A year of mathematical thinking (content fairly unimportant, context important) is a popular notion here
Dan Meyer and 101qs.com came up; the issue here is that these are overwhelmingly proportional reasoning problems, so it's not a solution for everything, but it can suck kids in.
A great point that it doesn't have to be about being 'real world,' but 'interesting' is great too
Awesome point that we need to be careful not to teach students that math problems are things with unambiguous answers that can be solved in 10 minutes.
Does mathematical thinking have to only involve doing mathematics? Can it be done by making these, in a hands-on way? If we reinforce mathematical reasoning tacitly, won't that make the pencil and paper stuff easier and more meaningful?

Some slides from a Standards-Based Grading conversation in a different session: http://www.slideshare.net/lpahomov/educon-2013

Now I'm in "Qualitative Formative Assessment: Letting the Learning Environment Dictate the Tools", with Reshan Richards (@reshanrichards).

We start with an odd activity:

Draw a creature that's half-perro, hal-canard that is sitting near an iconic Philly landmark while contemplating the area of a circle. Provide a grammatically correct sentence as a caption. Stand up and stretch.

He's the creator of the Explain Everything app, and he is looking at making assessment a bit more dynamic, including screencasts.

He has some issues with flipped classes, as they're just time-shifted lecture. Yup, that's true! Also, issues with a paradigm that means that you know exactly what page you'll be on 8 months from now - is it student-centered, in that case?

I'm hearing lots of stories of technology purchased and deployed with little support and buy-in. Lecture/demo as a training method for faculty isn't good, just like it doesn't work well for students.

Each table asked a question, shared them via Google Doc, and re-organized based on interest. I'm in this one: "How do we not put the (laptop) cart before the horse? Adding gadgets without motivation/need/understanding/purpose - it doesn’t help. How do we add technology in a way that positively impacts student learning, and doesn’t just look shiny?

There were lots of observations about top-down tech decisions being problematic, and one good story about an increasing training web of folks that help each other, all the way down to the kids. Training and support really takes more effort/money than buying the darn things.

The discussions that I was involved in diverged pretty widely from the topic here, which is too bad, but they were good in their own right.

EduCon 2.5, Day 1

noreply@blogger.com (Tatnall Physics) — Fri, 25 Jan 2013 18:44:00 +0000

I'm attending EduCon this weekend; I left school just before lunch on Friday to come down to visit the Science Leadership Academy in Philadelphia, which is hosting the conference. This is a public magnet school which is both standards-based and project-based. It's really fascinating to see these kids getting deeply into projects. Some observations:

First class: Advanced Engineering. They're working on their big projects of the term - I saw robots, water filtration by organisms, and a few other things. The most striking bit of that was when the teacher explained to us that, because of the recent budget cuts (40% over the last two years), the entire school's supply budget (paper, pens, toner, lab supplies, etc.) for the year is $200. No wonder they're all raising funds during the conference: kids are selling pretzels, shirts, etc. I'm going to lose some money today.
Second class: History (of some sort). They're role-playing reactions to The Declaration of the Rights of Man and of the Citizen from nobles, Haitians, commoners, etc.
Third class: Algebra II. I'm not sure how the project-based part was playing out here. They were figuring out various things about parabolas from the equation, in a fairly participatory but mostly traditional setting. I didn't get to see too much of this one.
Fourth class: Statistics (I think). They're programming here, debugging and sharing their projects, written using Processing. This one was a game with a player running from ghosts, which will slow the player down if they catch the player. I'm less confident that I'm in statistics now. The schedule says that comp. science engineering and stat meet in the same room with the same teacher at the same time. Interesting!

Visiting another school is a great thing to do - we're all busy, but it's really invigorating, especially when it's a vibrant place like SLA. The students and teachers that I've met have been passionate and curious. What else can you ask for in a learning community?

Pick a Fight!

noreply@blogger.com (Tatnall Physics) — Mon, 14 Jan 2013 17:22:00 +0000

Well, not really, but maybe a "physics fight"...

We had a friendly competition with a neighboring school today and Friday via Skype:

Each school checked out a clip of "Despicable Me" this week (about four minutes, dealing with the rocket trip to the moon, the shrinking of the moon, and the trip back) and was challenged to model, debunk, predict, verify, etc. whatever they could. My class spent 90 minutes on this, and I think that the other school did about the same.
I didn't give them any help or direction, except for telling the name of some new concept that they wanted, so that they could effectively index/Google on their own (terminal velocity, energy-mass equivalence, and shear strength came up)
Each problem was whiteboarded, and we took pictures of the boards (some of theirs had nice electronic presentations, though).
Today we Skyped and took turns: 10 minutes of presentation followed by 7 minutes of questions.

It's not really a competition, but it's fun to frame it that way, since they're used to having long-standing rivalries in sports against local schools.

The investigations were fun, and it was great for the students to interact with each other from afar. We're also planning to trade some screencasts with intentional mistakes in them.

If you want to interject a little more fun into the WCYDWT?/whiteboarding/Mythbusting/modeling paradigm, maybe you should pick a 'fight' with a nearby school!

Here are our whiteboards, from both sections that participated:

An analysis of the speed of the spaceship (not surprisingly, too fast for reality), using the altitudes of different parts of the atmosphere for reference:

An analysis of the mass of the shrunken moon, assuming that its density stayed the same:

...using that mass, the freefall acceleration and very-low-orbit speed for the tiny moon:

Assuming that all of that missing mass was converted into energy, the ridiculously large amount that there would be:

An analysis of how the now-tiny moon would basically eliminate tides:

This class assumed that the moon's mass would stay the same, rather than its density. A proof that this would do nothing to the tides:

Assuming CAPM speeding up and slowing down, the acceleration of the spaceship and the resulting huge forces on Gru, if he is going to make it to the dance recital:

The freefall acceleration on the surface of the tiny moon:

Trying to determine Gru's speed when he hits the shrunken moon (it shrinks to be at its center of mass, so he's one moon-radius away, and then he freefalls towards it); CAPM is used, with the acknowledgment that it's not appropriate.

Assuming that he hits the moon and stops in a short distance (stomach compression), the huge normal force that would be exerted on him by the moon when he hits it:

A comparison of the pressure exerted by that huge force and the shear strength of bone, showing just how easily that moon would cut a hole straight through him (and then he'd continue past it, slowing down as he moves, then back again, in an oscillation with the moon passing through the same hole over and over... OK, physics isn't pretty).

Physics Jeopardy

noreply@blogger.com (Tatnall Physics) — Fri, 11 Jan 2013 16:58:00 +0000

As part of a little mid-year reflection on the force and motion models that we've developed over the first third-ish of the year, Honors Physics students developed a series of Physics Jeopardy answers and questions.

Our format:

'Answers' (the clues) are motion graphs or net force equations
'Questions' (what the players are supposed to determine from the answers) are diagrams of the situation being modeled

The idea is to encourage a closer connection among three of the representations that are most common - diagrams, graphs, and equations. By going 'backwards,' students have a lot of detective work to do, which really makes them think about which physical statements or results are consequences of which models.

Here's our set of answers and questions:

Using Google Docs for Labs

noreply@blogger.com (Tatnall Physics) — Mon, 31 Dec 2012 17:38:00 +0000

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

Advantages:

Less time taken in class for data collection, more time for data analysis
Everyone gets to make the measurement, instead of some students sitting on the sidelines
More data possible, as we can bin the data sets for big group analysis

It's this last one that has the most impact on whether I do the data collection like this or not; if we need a lot of data, it's boring and cumbersome for each group to do it and not as easy to share as it should be within the classroom.

Some disadvantages:

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

With those caveats, there are some cases in which I've found it quite useful:

Experiment 1: Period Measurement Techniques

Students did the experiment here.

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

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

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

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

Experiment 2: Resonance

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

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

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

The code looks like this:

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

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

Sharing Whiteboards

noreply@blogger.com (Tatnall Physics) — Wed, 26 Dec 2012 02:18:00 +0000

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

Some Capstones

noreply@blogger.com (Tatnall Physics) — Wed, 26 Dec 2012 02:12:00 +0000

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

A capstone where a student writes a VPython program to prove that the freefall time for any tunnel through the Earth (along a chord) is the same
A capstone where a student write s a VPython program to verify the time for the freefall through the center of the Earth (comparing to the solution for the SHM diff. eq.)
A capstone where a student calculates the through-the-Earth times for different planets/objects (that was a popular topic this year)
A capstone where a student analyzes a clip from Toy Story, where the slinky dog dives down, changes mass, and spring back up
A capstone where a student builds a tricord instrument, predicts the correct mass to tune the string to a chord, and tests the predictions

There were several others, and this is just a selection. There were also lots of cool ideas that fell by the wayside for expediency, which is something that I'd like to avoid happening in the future. Some cool ideas about programming a simulation of the view of the Venus transit from Earth (I couldn't quite get this one to work myself, but it was an awesome idea), simulating the Home Alone bucket swing and crash (this one's totally doable), and a few other really neat ideas unfortunately were lost along the way. Oh, well - two more tries left this year. Lots more good ones to come, I'm sure!

Homework Worth Doing

noreply@blogger.com (Tatnall Physics) — Wed, 26 Dec 2012 02:00:00 +0000

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

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

In this last vein, I have an example, using this gravity simulator (I just got sidetracked for 10 minutes playing with it while finding the link):

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

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

Newton's 2nd Lab

noreply@blogger.com (Tatnall Physics) — Thu, 22 Nov 2012 15:59:00 +0000

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

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

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

Here's what I used this year:

Half Atwood machine, with a force sensor screwed to the cart (the string's tied to the sensor). A motion detector helps them find acceleration (from the slope of the v vs t graph):

The system being analyzed here is just the cart. The force probe measures the tension directly, so no complex analysis or tricky conceptual arguments need to be made. About halfway through, it's good to stop them and ask them to compare the hanging weight to the tension force reading and to explain the discrepancy conceptually.
Varying the force exerted on the cart just means varying the hanging mass, and varying the mass of the cart is simple, too - no mysteriously motivate shuffle of masses back and forth. The experimental design is completely transparent to them.
You might want to have them split into two factions: some groups investigate how acceleration varies with force and others investigate the dependence on cart mass. They then present whiteboards and the class can determine the combined model from the two partial models. Don't underestimate the reasoning leading from the two individual models to the combined model.

Everything seemed to go quite smoothly (that last conversation's still a bit difficult - I need a better angle on that, because it happens frequently), and my students this year have become stronger conceptually and computationally than with the setups that I've tried in the past, while moving at a faster pace. This one seemed to work quite well.

Spring Wave Speed Lab

noreply@blogger.com (Tatnall Physics) — Tue, 20 Nov 2012 19:24:00 +0000

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

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

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

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

The whiteboards:

Question Boards and Answer Boards

noreply@blogger.com (Tatnall Physics) — Tue, 20 Nov 2012 18:00:00 +0000

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

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

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

Here's an example:

Collision!

noreply@blogger.com (Tatnall Physics) — Thu, 15 Nov 2012 12:22:00 +0000

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

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

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

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

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

Success!

Whiteboards:

A Practicum I Can Believe In

noreply@blogger.com (Tatnall Physics) — Mon, 05 Nov 2012 19:01:00 +0000

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

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

Another benefit is that I can put together a robust practicum that uses both CAPM and OPM:

On the day, I will set up a ramp of unknown length. There will be a pendulum at the end, oscillating perpendicular to the track.
I will let them observe the pendulum in motion.
I will demonstrate for them, three times, the cart starting at rest at the top and traveling freely to the bottom. I will tell them the length of the track.
I will assign each group a number of oscillations - the pendulum must complete this number of oscillations between the time the cart is released and the time that the cart gets to the end, and the pendulum must collide with the cart as it reaches the end
They need to have a procedure ready to determine how far up the track the cart needs to be released in order for these things to happen.

I let them work for a couple of days in groups, with a pendulum and a 1.2 m cart track. They need to develop and test their method so that it can work in any situation that I give them.

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

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

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

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

Nonuniform Circular Motion

noreply@blogger.com (Tatnall Physics) — Fri, 02 Nov 2012 19:18:00 +0000

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

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

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

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

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

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

Comparing Springs

noreply@blogger.com (Tatnall Physics) — Fri, 19 Oct 2012 13:24:00 +0000

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

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

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

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

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

from visual import *

scene.height=600
scene.width=600
scene.scale=(.6,.6,.6)
scene.center=(0,-.7,0)

# scales
Fscale = .1
vscale =.4

# objects
roof1=box(width=3,height=.05,depth=3,color=color.white,pos=(-.5,0,0))
roof2=box(width=3,height=.05,depth=3,color=color.white,pos=(.5,0,0))

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

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

#forcevec=arrow(pos=ball.pos, color=color.red,shaftwidth=.05)

# physical constants
k = 20
restlength = 1
mass1=.6
mass2=.6

deltat=.001
t=0

while 5 <= 10:
rate(300)

# forces
gravity1=vector(0,0*mass1,0)
springforce1 = -k * (mag(spring1.axis)-restlength) * spring1.axis / mag(spring1.axis)
netforce1 = gravity1 + springforce1

gravity2=vector(0,0*mass2,0)
springforce2 = -k * (mag(spring2.axis)-restlength) * spring2.axis / mag(spring2.axis)
netforce2 = gravity2 + springforce2

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

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

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

#forcevec.pos = ball.pos
#forcevec.axis = Fscale*netforce

spring1.axis=(ball1.pos-roof1.pos)
spring2.axis=(ball2.pos-roof2.pos)

# time update
t = t + deltat

Speed of Sound

noreply@blogger.com (Tatnall Physics) — Fri, 19 Oct 2012 13:09:00 +0000

OK, so we're finally there in AP - the speed of sound calculation. Matter and Interactions makes a hand-waving argument based on dimensional analysis to get the longitudinal speed of sound from the interatomic bond length and spring constant and the atomic mass. That's fine, but I wanted to get to the real derivation, which involves a very interesting couple of linear approximations and some possibly bogus calculus, but it's doable. The transverse one is basically the same story.

It's more guided and less inquiry, but it's a tough bit of stuff. I'm OK with there being less discovery here, because it's going to be a gigantically powerful result - predicting the frequency of a sound using the molar mass, density and Young's modulus? Awesome.

We're applying both of the expressions today in lab. I'm spitballing the work flow here:

Wave intro, animations, etc. Define wavelength, frequency, v relationship by analogy to traffic
Longitudinal wave derivation:

With known molar mass, modulus, and density, they determine k, d, the atomic mass, and v (using the dimensional analysis result)
The real derivation - super-guided by me
Demo singing rod, have them calculate its frequency
Sing, record, FFT
Party

Transverse wave derivation:

Animations - difference between longitudinal and transverse
Derivation
Give them sample of wire - they determine the tension needed to have the sound be an octave below a resonance box (128 Hz); help them with the standing wave's length
Use force wire strung between two poles (one with a force probe on it) to measure tension. Other end of wire is still on the spool, which is on the rod. Kids twist spool so that the sound is in tune; reveal tension (or vice versa?)
Party

The setup with the spool (yellow string added so that you can see the path of the wire):

Here's my drawing of the whole process:

Illuminations for Models

noreply@blogger.com (Tatnall Physics) — Wed, 17 Oct 2012 15:38:00 +0000

In the packets that I make for each unit (generally broken up by physical model), I include a little illumination-esque drawing, using the model's abbreviation as a backdrop to illustrate situations where the model applies. It's fun, and hopefully a kid sees something at some point on one that makes something click.

I'm drawing them (since BFPM) with SMART Notebook and my tablet PC (ThinkPad X220). I've finally found a use for Notebook!

Feel free to use them (with attribution and an email :) if you like them.

These are the ones that I have for the first term:

Physics and Honors Physics:
CVPM (Constant Velocity Particle Model (or Motion, as you prefer))

CAPM (Constant Acceleration Particle Model)

Honors Physics:
BFPM (Balanced Force Particle Model)

UFPM (Unbalanced Force Particle Model)

Physics:

OPM (Oscillating Particle Model)

Yellow to Green

noreply@blogger.com (Tatnall Physics) — Mon, 15 Oct 2012 19:35:00 +0000

My grading scheme this year for AP Physics (C: Mechanics) has, so far, worked out the best that I've had for that course. My physics/honors physics scheme involves (basically) one or two standards per model, so the standards are fairly coarse. The problems are easy (enough) to generate, and reassessment at more frequent intervals is good for reinforcement, practice, and experience for those first-time learners. Applying that to the AP course in the past has been problematic, given the headaches of senior scheduling and senior motivation. It's also another group of reassessments for me to prepare, schedule, and grade. I posted about this before, but I've made a few tweaks and it's started to actually get used.

Here's my scheme this year:

The standards are more grainy (see the list here), compared to honors physics (here)
There are (generally) two assessments per unit in class
There's one reassessment available per unit, covering the whole unit
I made a chart showing the acceptable evidence for each standard. Typically, it'll be two strong showings in assessments/reassessments for that standard or one strong showing and several out-of-class successes (problems) or a capstone or several out-of-class successes and a capstone
Everyone's required to do at least one capstone per term, even if you rocked all of your assessments
Students submit this slip when they have some evidence to show for a standard. There may be some revision needed before it's accepted.

The extra outside effort needed to find and do problems and/or capstones motivates them to do good work on assessments, without me needing to wade through another sea of reassessments. The capstones are my favorite part, and they're coming up with some great ones (more on those as they mature). Overall, I'm liking the balance between giving them flexibility with their busy senior lives, keeping them accountable, and respecting the fact that, even though there aren't so many grades 'in the book' right now, they're still working.

Today's a big day, because the first student went from yellow (NY: "not yet") to green (P: "Proficient"). Many more to come of those, as well.