Monthly Archives: June 2011

FIU Modeling Workshop – Day 3

We started today by finishing our whiteboard discussion for our constant velocity lab (buggy lab).  As mentioned the previous post, Jon and Chris recommended to not worry about which variable was on a given axis (just make sure they had thought it through and had a reason).  However, they said as the whiteboard session is winding down, begin to force the discussion (with Socratic questions) to which graph ($d$ vs $t$ or $t$ vs $d$) gives more meaningful information (answer: $d$ vs $t$ since the slope is speed/velocity).  They also mentioned to direct the students to think about position and time interval rather than distance and elapsed time, as the former will help with the distinction of speed and velocity (which haven’t been resolved as yet), and the concept of acceleration.

They also reminded us, that at this point in the year, the students “know” LoggerPro and scientific techniques learned in the first unit.  The supposedly know what slope means (but in reality they know how to calculate it, not what it means).

One important line of questioning to pose to the students is, “What does the slope of the $x$ vs $t$ graph represent?”

Slope is defined in algebra classes as the change in $y$ divided by the change in $x$.

$ \large m= \frac{\Delta y}{\Delta x}$

Since the $y$-axis of a $x$ vs $t$ graph represents position, a change in position relative to a change in time, the slope represents the average speed over the elapsed time

$\large \overline{v}= \frac{\Delta x}{\Delta t}$
Since $\Delta x$ is a distance, it would have units $ \textit m$.  $\Delta t$ is an elapsed time, so it would have units $\textit s$. Thus the slope of the x vs t graph should have units $\textit m/s$, which is consistent with the units for speed.  {Thanks Global Physics Department for introducing me to LaTex!}
Next on the agenda was using LoggerPro to create a $v$ vs $t$ graph for our data.  After which, we used the integral function to find the area under the “curve.”  Again, we discussed the meaning of this area.  From math, we know:
$area=(base)(height)$
Since the base is time, $t$, and the height is velocity/speed, $v$, we can show that the area is displacement/distance.  In looking at my notes, one thing that I’ll get clarification on, is when due we, the teacher, distinguish between speed/velocity and distance/displacement during this process.  Have we gotten to that point, and I forgot to note it, or are we not to that stage in the cycle. 
Next on the agenda, we were asked to work on Unit II worksheets One & Two.  Each group was again  asked to present one part of this assignment on a whiteboard.  A few comments to note:
  1. Jon mention that before beginning these experiments, he has the lab groups perform a vernier experiment using motion detectors and labquest mini interfaces to match their motion to given position vs time and velocity vs time graphs. (I mentioned that I do the same activity as a competition between lab groups, which I find gets the kids very excited.  I’ll probably write about my “Physics Olympics” at some point in the near future.)
  2. On wkst 1, question 2a, ask the group “How do you know they are the same?”  Meaning, get them to discover how the could determine the scales were the same given the limited information.
  3. On wkst 1, question 2d, ask the group “Can two of your members enact the motion depicted in the graph?”
  4. On wkst 2, question 6&7, use Socratic questioning to lead students to drawing dashed vertical lines at the points of discontinuity.  Someone asked about including open and closed dots to show where the object was at the point of discontinuity.  Chris answered that we don’t know, nor do you need to get into that level of sophistication.

We ended the day by discussing the last tool in the modeling arsenal, Motion Maps:


The above examples show two different maps (the first above the red line, the second is below).  Some key features of the map are: the position vector, which shows the origin (X) and the direction of positive motion; the dot (which I couldn’t get to work as a small dot); the arrow on the dot, which represents the velocity of the object at that location and time.

That’s where we ended today.



		
Advertisements

FIU Modeling Workshop – Day 2

To start of today, we finished up the “Board Meeting” with the groups that studied length vs period.  For physics teachers, this is obviously the group that was able to show an actual correlation.  One of the most interesting parts of the discussion, to me, was when Jon and Chris recommended not worrying about linearization yet.  They told us to now worry about that battle, as it will come up as you move into the next phase of the cycle.  Just let the kids use LoggerPro to get the mathematical relationship.  They did recommend spending some time to discuss whether or not the data should go through the origin.  In the course of that discussion then mentioned what they called the “5% Rule” which basically states that if the y-intercept is less than 5% of the biggest measured value in the data for the y axis, assume that it goes through the origin.

After we finished that discussion, we then moved into the next phase of the modeling cycle in which we worked on linearizing data using LoggerPro.  The worksheet had 6 data sets (we had version 3 of this worksheet, I’ll add that link if I find it), and we had to plot the data and determine how to manipulate the data to create a linear graph that went through the origin.  Jon and Chris mention that they only used the first four problems (which I think are the 4 in version 2) with their classes as they have found that they are sufficient to get the students acclimated to the process. Jon and Chris did recommend to have the students write the regressed equation rather than the proportion shown (ie: equation with slope and y-intercept, not y is proportional to 1/x).

After we had linearized the data, each group was assigned a different problem to put on a whiteboard to share with the cohort.  Again, we were able to get a greater feel for how the whiteboarding process works, and able to ask questions as to how to moderate, when to step in and when to let the conversation go.

After a brief break, we then moved on to discuss our HW from the previous night.  To do that, each group was assigned a different section of the reading and asked to provide a synopsis on a whiteboard.  To sum up, we had a very lengthy discussion on the discrepancy between what a teacher thinks he/she is teaching and what the student is learning.  I didn’t bring it up, but this made me thing of Frank Noschese’s blog on Pseudoteaching. In our discussion, we talked about how as we, as teachers, think we are helping our students understand a concept through example problems, our students, for the most part, are fixating on the equations produced.  The problem with that is students mistakenly think they can apply the derived equation to any problem dealing with the same concept.  I alluded to Rhett Allain’s post by describing an “ABC Gum Rule.”  (I didn’t really have a name for this concept until I read Rhett’s post, but I would always tell my kids that they had to always start from the basic equations, they could not ever start with derived equations.  Thanks Rhett!)  The rule, as I pointed out, is that you never want to eat Already Been Chewed Gum, rather, you always want a new piece.  Same thing for physics, you should always start a problem from the beginning, not an equation that was made for some other situation (which may or not be the same).

After that, Jon and Chris asked for feedback as to how we thought the first unit went.  It’s amazing how well these modeling people all act as I remember Frank Noschese blogging about getting feedback from students more often than just the end of the year (read the post here).

They asked what worked and what didn’t?  To the first we said, we liked learning: how to use LoggerPro (especially for linearization), the linearization summary sheet, breaking up the pendulum lab to finish the lab in less time (made groups take more ownership of work since others were depending on them to get it right), and using inductive reasoning to determine relationship instead of the teacher just telling “us” the answer.  What we didn’t like: some wanted more explicit explanation of the relationships between independent and dependent variables (hopefully I’m remembering that correctly), and some wanted the workshop to move a little faster (I think she was referring to limiting some of the discussion, but Chris rephrased it as getting started quicker/more punctual coming out of breaks.  I’m not sure which was what she meant).

From there were moved onto Unit II: Constant Velocity Particle Model
Using battery-powered buggies rolling across the table, we again worked through, What do you observe, What do can you measure, and what can you manipulate.  After going through this, we again developed our purpose (Chris led us to the procedure with Socratic dialogue) after starting with Jon’s beginning statement (To determine the graphical and mathematical relationship between).  From there we were each given buggies (each a constant speed buggy, but each group’s buggy traveled at a different speed), meter sticks and stopwatches (masking tape was also present if we wanted it).  The day drew to a close as most of the groups were finished plotting the data in  LoggerPro, and 3 groups shared their results on their whiteboards.  


I’m guessing we’ll finish our whiteboard discussion tomorrow.  One final think I’ll add is that I’ve done a very similar lab at a 2 day physics workshop in Jacksonville.  However, the leader (another modeling guy with the exact same buggies) did it differently.  Each group was first given a blue buggy (all same, constant speed) and determine the relationship (found slope of d vs t graph).  When then had to turn that buggy in, and we were given a red buggy (again all red buggies were the same speed, all different speed than the blue buggies).  We again had to determine their speed.  At that point we had to turn in the red buggy as well.  The leader then asked us, using the mathematical models we had developed, to predict at what position the buggies would collide if a red stated at one end of the meter stick and the blue started at the other.  I’m not sure if we’ll do that tomorrow, but I guess I’ll found out then.


One other thing to point out, several of us asked if we should address plotting d vs t or t vs d with our students.  For the most part Jon and Chris were saying to make sure the students could justify why they were plotting it one or the other, and wait until later to broach that subject.  I’m not sure that we be as we progress through our whiteboard meeting or later in this cycle (or a future unit).

 

FIU Modeling Workshop – Day 1

As I mentioned in an earlier post, I’m blogging about my experience at the FIU Modeling Workshop.  Much of this is for me, so that I can remember my experience.  However, maybe this will help someone else to come over to the Modeling Method.  I’m not sure if I’ve mentioned it before, so I might as well state it here, I currently teach Standard, Honors, and AP-B Physics.  I’ve been using the CPO Program, which is a hands-on program.  To me, it’s biggest downfall is that the labs, although well constructed, are cookbook labs.  The students can get caught up in the procedure, and miss the concept.  After joining twitter, I’ve come across several teachers that use the Modeling Method, and have become more and more interested.  Which brings me back to the point of this post, my experience on the first day.  However, before I get into that, I would make the following claim, if this interests you, please go to the workshop, don’t just rely on me.  Even after only one day I can tell that my recount will mean nothing for you without you attending.


Day 1:
We started the day with our leaders introducing themselves (Jon Anderson and Chris Doscher).  They quickly led us through a great introductory activity, that I might very well use with my students.  We each had to come up with 2 truths and 1 lie about our self, and the other people in our small group had to try to determine which is the lie.  After that, each person in the group had to introduce another member from the group to the entire cohort.  To me, it was a fun way to break the ice.


After taking the Force Concept Inventory test, we then got our first taste of whiteboarding.  We were asked to answer the following 3 questions as a group:
1. What are your greatest content-related teaching challenges?
2. What are your greatest instructional teaching challenges?
3. What are your goals for this workshop?

Here are the whiteboards:




After breaking for lunch, we began our first experiment, a Pendulum Experiment.  

In walking us through the experience of the lab, we were given a few questions and comments after we completed the task.  (For the sake of brevity, I’ll omit our responses to the questions). 

Jon set up a simple pendulum and then wrote the following questions in succession:


What do you observe?
(side note, Brian W. Frank  recommended asking “what do you notice,” rather than “what do you observe.” Here’s why)
  • Jon mentioned to try to not give any comments/facial gestures, just write.
  • Ask if you need to rephrase for fewer words
What can you measure?
  • Don’t comment until at the end.   
  • Do you need to pare down the list, do to lack of equipment?
  • Are any measurements redundant, if so discuss with the class.
What can you manipulate to change the time?
  • Edit down after complete based on equipment present
State purpose of lab for students:
To determine the mathematical and graphical relationships that exist between time, length, mass, and angle of release of a simple pendulum.
 (Jon told us that the bold part represents the beginning phrase for basically all the lab objectives)

Before assigning the different types of relationships to different groups, Jon told us two important “rules” for labs:
  1. Fair Test: manipulate only one variable at a time
  2. 8×10 rule: collect at least 8 data points separated by at least a factor of 10
After collecting the data, they then introduced the group to LoggerPro, to analyze the data. We used LoggerPro to analyze our results and then put them on whiteboards to share with the other groups.

During this time, my small group discussed some of the strength and weaknesses with excel vs LoggerPro.  Namely, to us LoggerPro can analyze the data faster, but excel integrates with word docs a little easier.  (We could easily be wrong on this.)

Well, that’s basically it.  A good first day, and I’m excited for the second day.

FIU Modeling Workshop – Day 0

So I was driving down to Miami for the workshop, and to make myself feel even more nerdly, I was listening to Richard Feynman’s famous lectures.  I’m not gonna lie, it was tough to pay attention to his descriptions and drive (at times in somewhat heavy rain) at the same time, especially when he was pointing to slides that I obviously couldn’t see. However, it did help set the mood for the coming 3 weeks.  One part that did jump out at me, was his introduction to the Law of Conservation of Energy.  He developed an analogy of a mother tracking her child’s wooden blocks.  The boy started out with 27 blocks (I might be wrong on that number, but you get the idea).  Then one day, she notices a few missing.  However, she looks under the rug, and there they are.  The next day, she again finds some missing, but notices that the window is open, and there they are.  The next day, she notices a few more, but then determines that a few are were brought by her guest (don’t remember the name/relationship, so I’ll call him Uncle Buck). 

All’s well so far, however, the story starts to get some interesting twists.  The next day, she notices a few missing, but can’t seem to find them, they aren’t under the rug, and they aren’t out the window.  She eventually thinks to look in the chest in the corner of the room.  However, it’s locked, but this is a sneak mom.  She waits till the next the next day that all the blocks are present, and measures the mass of the chest and the mass of the blocks.  The following day, again some blocks are missing.  She again measures the mass of the chest and finds that it has gone up.  She divides that difference in mass by the mass of the blocks, and behold, it matches the number of blocks missing.  Thus, she’s figured out where the blocks went.

I’ll save you/me the rest of the story, he goes on to develop a second “hiding” place in the filled-filthy bath tub (why this over-analytical mom didn’t clean it isn’t discussed), based on the volume of the blocks. 

The reason I bring this up is that I think the story can be tweaked to be a great lead-in.  Can it be changed such that it makes the students want to figure out where the blocks went instead of telling them?  Could it be some salt to get the students wanting to know where they went?  Thus, when you now bring in energy, specifically an energy loss, they begin to think to look for it in other places?  Maybe even leaving it to them to determine how to calculate that lost energy?