Day 4: Finding the Smallest Trustworthy Digits (Lab Uncertainties this year)
Yesterday, in my pilot section of revised algebra-based physics, we talked about uncertainty for a bit and then students did the buggy lab. Lab went well. Only change was groups who finished early had to revise/apply their model to make a prediction and test it out (e.g., buggy starting somewhere new, going in opposite direction, where will it be/ or how long will it take to ___ ).
Here is a picture of the buggy highway we set up in the hallway:
Lab Uncertainties: Last Year vs This Year
For uncertainties, we used to have students estimate measured uncertainties, calculate percentage uncertainties, and then have students identify the largest (average) percentage uncertainty of all their measurement types before using that to propagate uncertainty to any calculated results (e.g., slope).
Now, we have students take multiple or repeated measurements to help inform judgments about which digits seem “trustworthy”. We defined trustworthy digits as those that don’t change much upon repeated measurements. This leaves some room for ambiguity which is fine– for example, we had clicker question to identify where the smallest trustworthy digit was with repeated measurements of 12.69 ft and 12.91ft. Either the ones place or the tenths place could be justified. For propagating uncertainty, we have students use the rules for significant figures, because that’s what is taught in Knight’s College Physics. Overall, I’m pretty happy with this approach. In the first lab, we actually had interesting conversations about uncertainty instead of mind-numbing conversations about how to apply the rules.
For example, one group had measured time repeatedly in their “Quick and Easy” speed calculation (before a more careful investigation), and found that their time measurements really only had 1 sig fig (something like 5.87s, 7.07s, 6.32s). They were unhappy with rounding 24 cm/s down to 20 cm/s. They felt like this was losing accuracy. When they later found the speed using graphical methods, they got 19 cm/s. They were really surprised that their 1 significant figure rounding was closer than their 2 significant figure rounding. One student said that hadn’t realized that such a thing was possible.