Practice 1 in my CAPM packet (mostly if not all stolen from Kelly O’Shea) has this problem, which asks students to find the acceleration at 4 seconds, where velocity is zero. All three groups that presented this (in three classes) correctly wrote that the acceleration was 2 m/s/s. However, in two of the classes someone brought up that it would be zero as velocity was zero, and in a third class I prompted that question. Serious debate ensued. Lots of back and forth, lots of awesome arguments, lots of learning.
This was a student trying to make an argument about, I think (it’s been a couple days since then, to be honest), displacement being negative. While the argument doesn’t seem to be correct looking at the picture, I was impressed at the time mostly with how the student generalized the argument by trying to explain it symbolically, rather than resort to specific cases which students usually do. I think he wanted x2 to be less than x1, not greater. Also, there is a partially erased delta next to the x on the bottom.
Today we were working on practice 1 problem b (again stolen from Kelly O’Shea), which asks students to find the acceleration of Object B represented with the v vs. t graph below.
After significant discussion they were fine with the acceleration of A being -1. The student who presented this was re-solving the problem on the front board, and said “so the acceleration is obviously negative,” after which he very carefully and obviously drew a line through the negative to make it a positive. Hilarity ensued.
We discussed this for quite some time before finally coming to a consensus that the acceleration was in fact negative.
I stole a chapter from Kelly, again, and started day 2 of the paradigm lab for CAPM by having a discussion about the different ways we can make a cart move by itself on a ramp using the beauty of “save latest run” on LoggerPro. Then I did something different for each class, because I had a number of different ideas how to run the discussion part after this and I wanted to try them all. Stupid scientist in me, I guess.
The one I settled on was actually going back to a board meeting, where students make a circle and each group presents their data on a whiteboard in front of them. Students make observations and claims, which I record, and they try to come to a consensus about what the graphs tell them. The class that proceeded this way only took 10 minutes to nail down that slope is acceleration (which we defined more precisely as the rate of change of velocity) and that the intercept is the initial velocity, IF the data is time adjusted so that t=0 is when the cart is released from the hand.
We had some time left so we discussed what acceleration means (for now, the amount of velocity added or subtracted each second), and looked at the fact that a cart slowing down can have both positive and negative accelerations (we did the same trial, pushing the cart up from the bottom and stopping it near the top, both with the motion detector at the top of the ramp and at the bottom).
Oh, I almost forgot. In each class we discussed the graphs above in different ways, but in one I did something I really liked; I had each group pick one and sketch it on their desk, then list observations or claims. Then I had groups rotate to evaluate those observations and claims or to add their own. We rotated twice then went back to our original spots and re-evaluated the original work. Here’s some pics of what kids wrote for this.
Finally, I saw the best v vs. t graph ever, sketched by a student today.
Today we started ##CAPM. I took Kelly O’Shea’s idea of starting with a ramp in front of the class for the standard drop of a cart on a ramp, then we discussed the aspects of the situation that we could change to investigate further. Students came up with ramp angle, mass (a later experiment, I said), detector location (at bottom instead of top), push cart down, push cart up. Then I set them loose and they investigated for the rest of the hour, to be discussed and analyzed tomorrow.
I have had a couple students ask me recently, “What exactly is CVPM?” This is what I came up with. Anything you have to add or change?
Today we had our first group problem solving session, and this was typical of at least half the groups. Awesome to see that my emphasis of multiple representations this year seems to be paying off!
My colleague Ben shared this awesome mistake with me today. This is why we Whiteboard; I don’t know that a single person would have guessed a student would make this mistake without the significant formative assessment that is whiteboarding.
Note that the problem was a written description, as shown at the top of the note, and the mistake is everything below that. Consistent!
Today I ran the practicum lab for CVPM. I started class by telling them simply they have around 5 minutes to find the speeds of the two cars in front of them (I made sure they each had one car with normal speed and one with an aluminum foil slug in place of one batter so it is slow). Then they put the cars back on the front table. Then I showed them the corridor, made with two 2.2 meter pasco tracks, between which I had laid a tape measure such that zero was on the edge of the table (so a car can’t start with the front at zero), and a marked crash site. They had to figure out how to get the cars to crash at the crash site, with the only rule being that they start outside the corridor. I told them the positions of the start and end of the corridor as well as the crash site and the endpoints. A few groups realized they could simply let the carts go at different times, probably the easiest (but clever) way to solve the problem.
The cleverest thing I saw however is what is represented above for finding the speed of the cart. One group put tape on the car, trailing along, and then made a mark on the tape every second as it pulled the tape along. Very cool considering I didn’t explore anything like that with them!
Have improvements to my procedures? Let me know!
These are some notes I took while working with a math teacher on how to bring more experiential and inquiry learning into the math classrooms, which I get to help with as part of my job as a technology integration specialist (they are looking at the Explore-Flip-Apply model of flipping the classroom based on my recommendation). We are looking at ways to teach the actual meaning of exponent rules, and I had a great twitter conversation with some folks over the weekend who gave us some great ideas. Fun to be working on math stuff again! (I taught Geometry for 6 years but haven’t since 2011).