I’m Calling the Sig-Fig Police
Posted February 19, 2011on:
This is year 5 teaching physics. The first year I completely ignored significant figures (aka sig-figs), there was too much other stuff to do. I think that was the right call back then. Now, as the course becomes more defined and I focus on what the students really need to learn and understand, I’m becoming less tolerant of sig-fig abuses.
In our recent lab, the kids had to measure the height of the toy popper. The poppers I have are 3/4″ and 1.5″ in diameter. When students measure these using a mm scale, I routinely get heights of 0.01 meters and 0.02 meters. The next step they calculate the acceleration and give me results to four significant figures. I need to get a few stamps made up for grading. One will say SIG FIGs, another will say SHOW UR WORK, and a third will say FORMULAS? since the kids seem to think I know what formula they are planning on misusing and abusing. Maybe I can boil all of my grading down to a series of stamps.
The problem here is that I tell them repeatedly to measure to at least two sig-figs. You can comfortably measure the popper to 10.0 +/- .5 mm on the scale. I have to take most of the blame here, since I don’t do enough in the beginning of the year teaching them to measure. I need to put together a lab that teaches them how to measure, weigh, and calculate. Then I need to hold them to those standards for the entire year. I don’t understand how students get to the 11th and 12th grade and can’t successfully use a ruler.
I often wish I could go back in time and see if I was as oblivious in 12th grade. Was I this lost? Every time we use the meter stick I instruct them that we only use the metric system in our class, and still a few will measure in inches. (I’ve been saying for 5 years that I will spray paint over the inch scale soon.) We did the Egg Crash Lab yesterday (big success), and more than a few of them couldn’t find “half a meter” on the meter stick. If this was the first time they’ve used a meter stick, I would understand, but we use them pretty much every other week and we are six months into the course. Maybe I’m just expecting too much.
What is interesting is as I’m becoming more aware of the problems with sig-fig abuses, I’m finding errors in other places. The software that maintains our student records keeps the grades to 2 decimal places. (This is essentially 4 sig-figs, although you can technically have a 100.00 grade.) The system rounds the grade to a whole number for the report card, but it also rounds them before calculating a semester and final grade. It should be averaging the entire grade, then rounding. In addition, the system stores the grade point average to 4 decimal places which is essentially 6 sig-figs. I noticed the problem when I recently calculated semester grades and many were off by a point from the system calculated grades. To the student that is struggling to learn physics, that one point can mean a B instead of an A, or an F instead of a D.
To quote Zack from The Big Bang Theory, “that’s the beauty of science, there’s no one right answer.” Bazinga!