As I've gotten more into using blogs and twitter as a teacher, I find that they are both such an amazing learning tool for me. This post will make a lot more sense if you read Kelly O'Shea's blog on LOL Diagrams. As you can see by the comments I made I was taught a slightly different way of making LOL Diagrams in my modeling workshop (See here).
For the following problem:
Here's how I would use LOL's to solve it. I would first state what objects are in my system (in this case, the spring, the cart, the earth, and the track). I would then draw the following LOL diagram.
As you can see, the "L's" are exactly the same, however in Kelly's format, you show the objects in the system versus those out of the system. In this style you show the flow of energy as you move from the initial state (in this case, the energy stored in the compressed spring) to the final state (the cart moving at the top of the loop).
Kelly later gives an example of what the LOL would look like if you do not include the spring within your system. Here's my take:
Since the spring is no longer part of the system, some "outside object" is doing work on the system. Also, since the spring is outside the system, it doesn't matter if it's a spring or a rocket or anything else, "something" is providing work to increase the energy of the system. The way my thermo teacher in college summarized it, if you care what did the work, include it in your system, but then it's not work.
{If that doesn't make sense, if the source of "work" is the spring, then you would call it elastic potential energy or spring energy. If it were a rocket, you would call it chemical potential energy. etc.}
If we go back and include the spring, but also include friction. Then your LOL diagram would look like this:
As I mentioned in my comment to Kelly's post, I think either method could work. To me, this method makes more sense given the "O" in between the "L's" since it shows how you are getting from the initial to the final state. I think if you are using Kelly's method, the "O" should go before the first "L".
I'll be the first to admit that I'm learning a lot more from her blog, then I've even thought of sharing on this one. Just wanted to try to show what I was trying to say. I'd love to hear from other experience modelers as to which style they use.
Now that I'm able to blog again, one thing that has been taxing my thoughts is my school's ongoing switch to the "Common Core."
{A little background} My school has always (at least as long as I've been here) had learning objectives for each class. Since we are a private Catholic School, we've had the freedom to set our own objectives (in collaboration with the other Catholic HS in our diocese). Although we used the state and national standards as a point of comparison, we were free to write our own objectives for the course. The good thing about this was the freedom to mold the course the way we as teachers wanted it to be. The downside was that we had to meet every five years to edit and revise those standards. Over the last year or so, our diocese has decided to adopt the Common Core standards as they emerge and be in compliance (if that's the right phrase) within the next 2 or 3 years.
So where does "School of Rock" come in? One, it's an awesome movie, so why shouldn't it be there. Two, I think the chorus of the song can be slightly modified to explain some of our struggles with adopting the common core. I think you have to live the "Common Core" before you can teach the "Common Core." What I mean by that is, most teachers fall into the trap of teaching how they were taught. I reading the various posts on education reform, most teachers would agree that there's always some new thing that comes out. By the time you fully switch to it, the new flavor of the month comes around and now you are to switch the that new thing.
As I interact with teachers, I think they see this switch to "Common Core" as just one of those new flavors of the month. They see a new set of standards, not a new mentality for teaching. To me, the shift of the "Common Core" is about changing the dynamics of the classroom. No longer is my job to be the "Sage on the Stage," but rather the "Guide on the Side." (Sorry, I forgot from whom I stole that, but it's definitely not mine).
Since "all" of us have had teachers that were the "Sage on the Stage," they see this new change as just changing what they teach, not how they teach. As I've gotten more involved in the Modeling, I am beginning to appreciate, what I see, as the true changes for "Common Core." After going to the modeling workshop last summer, I was able to be a student in a class where the teacher didn't "teach" us anything, but rather created activities, and guided us through them.
I remember talking with some of the other "students" the first few days about our frustration with the fact that they weren't teaching us the "Modeling Method." After we got into the 2nd unit, it dawned on me, that the only way to truly teach by experience, one must first learn through experience. I think that is truly the "Ah Hah" moment that teachers talk about after going to one of these workshops. It finally clicks that true teaching is in creating the experience and knowing where the tough spots are, not how many cool facts you can tell your students.
You've go to learn "Common Core," before you can teach "Common Core."
Modelers: how do you develop 1/2mv^2 from lab? how do you develop mgh from lab?
At the modeling workshop this summer, we did exactly that, however, instead of just rehashing that post, (you can read it here), I figure I would tell you how I tweaked the experiment for my AP class.
Since my AP-B class is a second year class, my students already have a working idea of the relationships (as time goes in and I fully switch to modeling, they should know the models) from the first year. So instead of using the labs as a discovery of the relationships, I like to have some challenge in the lab in which the students have to predict something using their data.
Here's the setup:
Equipment
vernier cart
vernier track
vernier spring launcher
motion detector attached to track opposite the launcher
Set up the track at an angle (ie - place a book under one end of the track)
Using LoggerPro and the motion detector, pull the cart back to compress the spring and let go. Stop the detector after the cart has reached it's highest point on the track.
The Analysis:
Have LoggerPro display a position vs time and a velocity vs time graph. From the velocity vs time graph, highlight the data, and use the "Statistics" function. The minimum value will be the compression ($\Delta x$), and the max value will be the maximum displacement ($d_{max}$). Highlight the data from the velocity vs time graph, and the maximum value is the maximum velocity ($v_{max}$).
(Note- if you want to do so, you can have the kids look at what position the max speed occurs (x=0)
Repeat the procedure several times, recording $\Delta x$, $v_{max}$, and $d_{max}$ into a second data set. Plot $d_{max}$ vs $\Delta x$. Have the students linearize this first graph, and they should see that $d_{max}$ is proportional to $\left( \Delta x \right)^2$. Now plot $v_{max}$ vs $\Delta x$, lead student to plot $\left( \Delta x \right)^2$ on the x axis, since that will allow this graph to relate to $d_{max}$. They should find that they need to plot $v_{max}^2$ on the y axis.
(If you want to take it a step further and include the masses to fully develop conservation of energy, go for it. As I said, my kids already knew those relationships from last year)
So here was my twist, how do you relate the maximum displacement to the vertical height? Since my students knew the energy relationships, I had them use their data and trigonometry to calculate the angle of the track. Just to give you heads up, here is what they should get...
From trigonometry, you know:
$h_{max}=d_{max}sin \theta$
And since mass is used for both kinetic and gravitation energy, you can rewrite the energy conservation as:
I then measured the angle of the track using a level app in my iPhone to compare the actual angle to the one predicted by the groups. The app I has was able to measure to the tenth of a degree. Most groups were able to get within $0.5^o$ of the value measured on my iPhone.
(I can't believe it's really over!)
Jon
mentioned that he does this unit a little differently, in that he has
his students provide the definition of momentum on the Unit VIII test.
At the start of class he shows that list to the students. What he has
found is that most have a very good concept of momentum. He said the
modeling unit focuses more on changes in momentum (which tends to have
more errors). Usually from their definitions, he can lead them to the
equation for momentum:
$\large \vec{p} = m\vec{v}$
or
$\large \Delta \vec{p} = m \Delta \vec{v}$
He said he also makes sure that they know that the units are $\left(kg \cdot m/s\right)$. After being part of the Global Physics Department Meetings, Andy Rundquist,
aka superfly, mentioned that he calls this "derived" unit a pom
(particle of momentum), others at the meeting, name it after one of the
students. Jon mentioned that he names it after the first student that
asks what is that unit called.
Next, Jon and Chris
showed us the beginnings of collisions. They attached a force probe to a
ring stand at the end of a track. They replaced the hook with a rubber
bumper, and then had the extended spring end of the cart collide with
the rubber bumper. At the other end of the track they had a motion
detector hooked up. After zeroing and making sure that all probes were
defined in the right direction, they had them collide. On the projected
screen, they had a plot of $F$ vs $t$ for the force probe data and a
plot of $v$ vs $t$ for the motion detector.
They used
the stats function on the $v$ vs $t$ plot to find the cart's velocity
before and after the collision (max and min values), and they multiplied
these by the mass of the cart. (using the equations from the beginning
of the unit $\large \vec{p} = m\vec{v}$.
Jon then
walked/guided us through the derivation of Newton's second law to show
the relationship between Impulse (J) and Momentum
$F = ma$
$\large a = \frac{\Delta v}{\Delta t}$
$\large F = m \frac{\Delta v}{\Delta t}$
$F \Delta t = m \Delta v$
Jon
then asked, "What is $p\Delta v$, to which we all replied momentum. He
said, well we call $F\Delta t$ Impulse. He then asked, "What changes a
velocity?" To which we replied, "A force." He followed with, "What
changes momentum?" We answered, "Impulse." {If only all education was
to people who already knew the material!}
Since the
impulse changes the momentum, the magnitude of the change in momentum
should be equal to the impulse. Since impulse it force times time, we
can find that quantity as the area under the $F$ vs $t$ plot. Jon used
the integration tool in LoggerPro, and amazingly enough, the value
"matched" the change in momentum calculated from the $v$ vs $t$ plot.
We
agreed that #7 has some issues in that, for a rocket to go anywhere, it
must lose mass. Since we aren't given that information, it technically
can't be solved. However, Jon mentioned that we often start with
idealized situations, and then add complexity. We also agreed that most
of our students wouldn't know this anyway.
As we came back from lunch, we watch the PSSC video on Frames of Reference:
After that video, Jon and Chris showed us a cool video for E&M:
They
next had a "student" come to the front of the room and sit on a stool,
which was on a turntable. They put a tennis ball in each of the
student's hands, and started gave the student a spin. While spinning
the student was told to release the ball so that it his a certain
target.
Jon then thanked the student, removed the stool
and got up onto the turntable himself. He then had Chris throw a
bowling ball to him. After getting help to stop spinning, he threw the
ball back to Chris.
From there, we moved into the actual paradigm lab. We had a track with 2 carts. Most groups had a small picket fence/flag
to insert into the top of the carts. Other groups just used a bent
index card. They also had two ringstands, each with a photogate
attached.
Chris and Jon showed us several ways that the
carts could combine, and we as a class agreed on 7 combinations we
would study in our 7 groups.
1 stationary cart, 1 moving with it's spring plunger extended (between the two carts)
Both carts moving towards each other, one with plunger extended
One car moving towards the other, colliding with velcro between making carts stick
1 moving cart, with magnetic repulsion causing the "collision"
Varying the mass of one cart, 1 cart moving w/ plunger out
varying mass of cart with both carts moving w/ plunger out
Both carts moving with velcro collision
From there we quickly ran through the pertinent parts of the paradigm lab discussion: What can we measure? Purpose:
To
determine the graphical and mathematical relationships that exists
between the total momentum of the system before and after a collision.
Right
at the end of the day, Jon showed us a few more demonstrations. First
he hung a electrical tape "nest" from the ceiling. Here are pictures:
Inside that cradle he placed a raw egg. He set the length of the string to stop just before the floor, seen here:
Then,
while standing on a stool, said to the students, think of this as you
driving the car one day. You happen to come around a bend in the road,
texting away, and a tree decides to move itself into the road. What
happens if you are properly belted? With that, he dropped the egg.
Since it's in the nest, it bounces like a bungee jumper. In his class,
he then pulls another raw egg out of his pocket and says, this is what
happens if you forget about your seat belt {drops egg -> splat!}.
Any questions?
Hey then gets 2 students to help him
with his next demonstration. He has one student help him hold a cotton
table cloth as seen here:
If
you look carefully, you'll notice that they make a slight lip at the
bottom of the sheet. As the egg hits the sheet, they rotate it to
horizontal, so that the egg won't roll off. Here's an action shot of
the egg hitting the sheet {quite impressive given that I was using an
iPhone if I do say so myself}:
Lastly,
Jon took out a tennis ball and the bowling ball (David recommended
using a basketball to avoid damaging the floor, however, they didn't
have an inflated one handy). Drop both from the same height, and you
see that both return to about the same height. Then, stack the tennis
ball on top of the bowling ball and drop. One word, Awesome! Here are
some pictures:
After
that, FIU PER asked us to go into the hallway for a practice poster
presentation of the research before they head off to the AAPT national
meeting in a few weeks. The couple things that jumped out to me {yes
I'm probably butchering their edu-jargon terms, but I'll give you the
basic idea}:
To great strategies for modeling are seeding and passive direction
seeding: give one of the groups (especially struggling groups) an
important insight, so they have a key ingredient to share during the
board meeting.
passive direction: as the teacher, don't be inside the circle
(sitting w/students) if they don't need you. Allow them to take
ownership of the meeting. During the group work, determine where the
misconceptions and errors are. Let the groups work them out, only step
in if they are floundering or off task.
The guy had a third term he dropped, but I don't remember it.
Basically he talked about learning what the students were doing, and
planning you questions while they are working. Give the class a chance
to ask them, and add them in as necessary.
Another poster talked about one powerful benefit of whiteboarding,
namely that it allows students to interconnect with their peers, which
improves their sense of belonging. This improved attitude they have
shown, had increased retention rates in the subject at the college
level. They speculate it would have an even more profound at the HS
level.
A third poster described how modeling allows for personal (mastery) interactions and more importantly "vicarious" interactions
Their research has shown this is especially important for female students' success in physics.
After finishing my work, I multi-tasked by looking at my twitter feed. John Burk (@occam98) asked a great question while at a new teacher mentoring workshop:
To which I replied the concerns parents express with not "teaching" their child. I've been using a lab based program (CPO Physics),
and I'm guessing modeling teachers have similar issues. I know I
always have to go in to the idea that my job isn't to tell the answer,
but to find the best way to help their child learn the concept. John
replied that there is a lot of talk about this very issue in the
modeling listserve. For those that are thinking of moving into
modeling, make sure you give a little thought to the question, "What is
your job as a teacher?" Is it to make sure you tell all the facts you
expect the students to know, or is it to create an environment in which
they can best learn your subject? Personally, I hate when teachers talk
about "covering" material. I'll get off my soapbox now.
We next went about whiteboarding our results to the worksheets.
Notes from board meeting
Some
of the problems need to be modernized, not sure if students would know
what a "Geo" is, Cooper Mini or Smart Car might be better names for the
small car.
wkst 2 #7 needs to be cleaned up, give students names to avoid "former/latter" terminology
Lab Practicum
(def: looking for 1 final result not collection of data, using skills in the lab to now test the model)
Set
up 2 carts 1 with known mass and 1 with unknown mass (tape masses to
cart so they can't be seen and can't slide around) "stuck" together.
Use conservation of momentum to determine unknown cart's mass- contest for either grade or some other prize
What worked?
Egg seat belt demo
All the other demos from Jon
Designation of tasks in labs
changing collision scenarios for each group
PSSC Frame of Reference Video
Having a practicum
Jon breaks his class into 4 groups - all members must know how to do it
Quiz the next day (small part of grade), only selects 1 persons quiz from each group for group grade
Quiz is practicum calculations with slightly different numbers
Fixes freeloaders
The practicum is a means of measuring mass without the needing gravity
What didn't work?
Re-word questions Worksheet 2 #7&8
Re-think rocket question Worksheet 1 #7
To finish the day, we took the FCI as a Post-Test, then worked
on some surveys for FIU. With that, warm up the bus, it's been a
pleasure:
Jon started today by giving a brief demo. He had a rubber stopper
tied with a string attached to a hanging mass. In between the two was a
plastic tube (think very sturdy straw), which he held in his hand. He
asked us where he would need to release the ball in order to hit a
certain object. He then asked where he would need to release it to hit a
different object, in a different part of the room. He then
socratically questioned us to say that the speed of the rotating stopper
was constant, but the velocity was continuously changing.
He then asked us, what causes a change in velocity? (answer: unbalanced force)
What direction must the force be? (answer: towards the center*)
What direction is the acceleration? (answer: towards the center)
*Chris
showed us a demo we can do if the class doesn't agree that the
force/acceleration is towards the center. He grabbed the bowling ball
(yes, the bowling ball, again) and a broom, and asked one of the
students to make the ball move in a circle. She first started out
inside the circle of the ball and was constantly pulling the ball
towards herself. Chris then had her stand outside the circle and put a
cup as a reference point for the center of the circle. She again had to
constantly push the ball towards the cup.
From there, Jon led us to derive an equation for the average speed of an object in circular motion:
From there, we walked through the tradition questions for paradigm labs:
What do you notice?
What can you measure?
What can you manipulate?
Then Jon helped us to create the purpose:
To
determine the graphical and mathematical relationships that exist
between the speed of the stopper and the amount of mass hanging on the
string.
{We did not study the mass rotating, however you could
have part of the class investigating this, and the radius if you want to
"kick it up a notch" - Bam!}
We found that this lab was very tricky and had lots of error. A couple points to minimize the error:
Have the lab members keep one job: timer, recorder, twirler
Make marks on the string to help see where it needs to be to keep a constant radius
This is huge!
Possibly use a force sensor held against the table.
Possibly use video analysis to determine the actual radius
as the ball drops, the length of the string is no longer the true radius
cut a slit in a tennis ball and squeeze over stopper to make a more visible point.
We also discussed what to do if a group has "bad" results.
We agreed that early in the year, make sure you are doing a thorough
job of checking the groups while they are experimenting to avoid this.
However, as the groups get comfortable with the whiteboarding process,
letting mistakes slide into the meeting can make it more interesting.
Think through when you want to call on those groups. We also agreed
that we need to remind students that the data measured isn't wrong, the
procedure to keep multiple variables may have been insufficient, but the
data is the data. Encourage the students to discuss the subtleties of
their procedures to determine where groups differed. If the class is
getting bogged down, don't be afraid to say, "Let's come back to this
after all the groups have presented."
If the
students didn't already, have them create graphs of $F_{hanger}$ vs
$v^2$ instead of $m_{hanger}$ vs $v^2$. When they do so, ask what the
slope represents. If they aren't sure, ask what the units of the slope
are (kg/m). Since the slope is constant, what mass and distance are
staying constant? To which, they should reply the mass of the stopper
and the radius of the circle. From there you should be able to derive
the centripetal force equation:
$\large F_c = \frac {m v^2}{r}$
When we came back from lunch, Jon again attempted to shoot his ping pong launcher. See the results in this blog post.
A couple great ideas from one of our cohort to help students "see" circular motion:
Cut a wedge out of a disposable pie pan, then roll the ball roulette style
ball will come out in a straight line
Have student's run down multiple flights of stairs as fast as they can
may need to make this a "mental" experiment not an actual one.
ask students what they must do to turn from one flight to the next while at a landing
Before the workshop started today, I
saw a very cool video on youtube that I'll show, just because I thought
it needs to be seen:
We
started to day whiteboarding our summaries of Arons' Chapter 5. For
those that haven't read it, it's a fantastic book with sharp insight
into the shortcomings of teaching physics. It's written at a very high
level, but once you get used to it, it has a lot to tell you about how
you should be teaching physics.
From there we finished up Unit VIII What worked?
We liked the demo with making the bowling ball move in a circle
Especially the person outside the circle
Getting insight into what to do (and what not to do) during a lab
once members determine the job they can do, stick with it
POGIL
Student discussions help them get understanding as to what lab was showing
The idea that data isn't wrong, the method of isolating variables may not be sufficient
The fact that we (the students) are always finding the graphical and mathematical relationships
once you get the hang of it, you know what to do when the models get more difficult
new lab, same analysis
What didn't work?
Teacher notes require editing/more detail on graphs
Centripetal force lab
Notes:
Even though we knew what the outcome should be, struggling through labs is very helpful
For labs that fail (class completely lost), come back as a teach demo and explain how you are doing the experiment differently
demo vs lab less time if you don't have it (due to lost period of failed lab)
If you have problem students or limited supplies, split the class
and have half do the lab and the other half work on problems &
switch part way through.
Use record player and put a thin piece of wood (less than 1x4)
across the deck, have students measure coefficient of sliding friction
$\mu_{k}$, and predict what is the greatest radius to place the penny
such that it won't slip. (Find $\mu_{k}$ from maximum angle with no
slip).
vernier has a lab for accelerometer and turntable
difficult to due with calculators, not too bad with computers
Would be nice to see a paradigm lab for universal gravity
One member mentioned that this graphical analysis is very important
as the next generation standards will implement a lot more graphical
analysis.
