Here's a work-energy theorem problem that I assigned for homework in general physics:

A 6-gram bullet fired through a door enters at 800 m/s and leaves at 600 m/s. If the door material is known to exert an average resistive force of 5600 N on bullets of this type at usual speeds, find the thickness of the door.

While most students did it right, too many were careless in their arithmetic. The answer as I calculate it is 0.15 m, that is, 15 cm. I am not concerned if someone gets 20 cm, or 5 cm, or something that reasonably could be the thickness of a door. Big whoop, they divided wrong on their calculators. I'm not teaching a class in calculator use, so these students (assuming they approached the problem correctly) get full or nearly full credit.

However, some folks said the door's thickness was 0.001 m, 0.0002 m, and 20 m. In these students' minds, all they did was make a calculator mistake. I disagree. They made a serious physics error.

Part of teaching physics is developing an instinct and undersatnding for the meaning behind numbers. 0.001 m is a millimeter, 0.0002 m is two-tenths of a millimeter -- I've never seen a door this thick. Or thin. 20 m is the distance across our entire science hallway, so is not door-sized.

How do I insist that students conceptualize the meaning of their numerical answers? Firstly, ridiculous answers that can be excluded on reasonability grounds lose enormous amounts of credit. Where I might take off only 1 of 10 points for a minor mistake in a calculation, I will take 3 or 4 points off for a ridiculous answer.

Secondly, I follow up with quizzes wherever possible. Consider the quiz that's coming tomorrow:

1. A bullet fired through a door enters at 800 m/s and leaves at 600 m/s. Which of the following is possibly the thickness of the door?

(A) 0.2 m

(B) 0.002 m

(C) 0.0002 m

(D) 2 m

(E) 20 m

I don't say that one quiz will stop the flow of 2 cm tall people and cars moving 10,000 m/s. I merely suggest that the cumulative effect of insisting on reasonable answers

*every day*might have the desired effect.
In your example question, there is hardly a reasonable answer. If the answer is supposed to be A, then 20cm is a pretty ridiculously fat door. I've never in my life seen a door 20cm thick. That's almost 8 inches thick, or two thirds of a foot! If the answer is supposed to be B, that is a super thin door at only 2mm. That's thinner than a piece of cardboard and about as thick as a textbook cover! I understand that you're trying to get them to get an instinct for the meaning of numbers, but you gotta be more reasonable than this man. Maybe you should brush up on your number meanings a little bit.

ReplyDeleteThe point is to pick the only one that is in any way reasonable, not to be picky about the precise width of most doors we go through each day. I *have*, though rarely, seen 20 cm thick doors -- think a walk-in freezer, or even the door to our outdoor shed. I have never, and will never, see a 2 mm thin door, nor a 2 m or 20 m door. And that's the point... 20 cm is far, far more reasonable than the other answers. That's number sense.

ReplyDeleteIf you're uncomfortable, cut all the answers in half. The problem would work just as well.

GCJ