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).