Dealing with Data
This week we finished up unit 1 with my conceptual-level class and worked on data analysis for a lab report with the AP class. I learned some things in both cases.
First, the conceptual-level class.
My first unit for conceptual physics is focused on graphing and interpreting linear data. If I were teaching an honors-level class, we would also deal with non-linear data in this unit and learn to “linearize” the data in order to write an equation that we could use to model something. However, I will deal with that in the lower-math class when it’s needed, which won’t be until we get to unit 3 on accelerated motion.
Anyway, I borrowed a lesson from Dan Meyer and had my students collect data as if they were planning a trip. They had to go to the USAirways web site and look up non-stop flights in late October. They were to collect time-of-flight data, cheapest fare, flight distance in miles, and type of aircraft. There were a few errors (students found flights that had stopovers, wrote down flight numbers instead of aircraft, and looked up distances on Google maps only to find you can’t drive to Paris) but there was also a student who was miffed that I didn’t examine her work closely for a grade. She said she’d worked really hard on it and it should be worth more points and I don’t do things right. I was really glad she had worked so hard on the assignment and felt proud of what she’d accomplished!
I’ll let you look at Dan Meyer’s lesson to see the results. He got pretty much what my students got, though we got a much larger y-intercept on the time vs. distance graph. Why? Philadelphia has one of the worst on-time records on US airports, that’s why!
When I asked a class of students what they prefer, however, me giving them pre-made data or having to go find data on their own, the clear majority was having me give them pre-made data. While I was a little disappointed by this, it makes sense. The less work something takes, the more it is preferred. I would rather plunk a pre-formed detergent pellet into my dishwasher and go read a book than stand around over a pan of steaming soapy water at the kitchen sink for half an hour. Luckily for me, whether I wash by hand or by dishwasher I get about the same results. I don’t know if my kids will LEARN the same amount from my pre-made data sets for practice graphing as they do from collecting their own data and graphing it.
So, will I re-use this lesson next year? I’ll say probably. A more than 50% chance.
Then, the AP class.
There are several challenges when teaching data analysis to AP students. I do this hoping that next year when they take a college science class they don’t go into shock about how they are expected to deal with data. Like significant figures. We don’t use those. We measure according to the sensitivity of our instrument, average the values, and use the standard deviation of our values to determine the number of figures that are useful to keep in the average value. Then we put error bars on the graph that correspond to the standard deviations, and when we find the slope and y-intercept on the graph we report uncertainties with those values as well. To do that, we have to use the LINEST function on Excel*.
So, I was focused on the data analysis for what I think is a simple lab. We used an inclined plane (PASCO track) and low-friction cart, measured the acceleration using the slope of a velocity vs. time graph as captured by an ultrasonic motion sensor, and graphed acceleration vs. the sine of the ramp angle. Ideally, the slope of that graph should be g. It isn’t.
I emphasized that we would determine g from the slope of the graph (last year, my students calculated “g” for each track angle and averaged them, despite the full year of modeling physics they’d had as juniors) but I did not focus on how to determine acceleration, since they’d worked with ultrasonic motion detectors and LoggerPro last year. And as a result I had to show EVERY group how to use LoggerPro to select a portion of the data and determine a slope. The one group I missed exported their data to Excel and calculated Δv/Δt for every trial…NO WONDER it took them so much longer than it took everyone else. Sigh.
Lessons learned: Review data analysis in LoggerPro on the projector with real data. Or, create a screencast. I am definitely doing a screencast for using LINEST, and when I do I will link to it on this blog.
NOTE: I am writing this blog entry BEFORE I begin reading the lab reports that were generated from this AP lab. I may have another blog entry to write once I’ve read and graded those reports.
*We do our work in Excel, though for some things it might be easier to use LoggerPro. I don’t necessarily want this to be easy, but if they eventually discover they can use a tool that is easier, they can use it now that they know the “difficult” way. And LINEST isn’t really all that difficult.