Re: out-of-the-box thinking

[Kossom <MKossover@NEWMANSCHOOL.ORG>]

Howdy-

From: John S. Denker
Sent: 6/4/03 4:39 PM

> In your classes, do you set up situations where
> out-of-the-box thinking is appropriate? Necessary?
> Is it part of the routine procedure? Does it
> get rewarded? Can you share some examples?


I am fond of including essay questions on my tests.

One of the questions I often ask during the acceleration section is

      Below is a series of lines made by a machine that marks
      the stripes on the street. If the machine always sprays the paint
      for the same length of time, is the machine speeding up, slowing down,

      maintaining a constant velocity or that can't be determined. Defend
your answer.

       ---  ---  ---   ---    ---     ---     ---      ---        ---

Most students say that the machine is speeding up, giving the usual reasons.
This is a really easy question since we use tape timers in the lab.

Over the years, though, a few students have noticed two problems with the
question. Do you see them?

Should I change the question, or isit  good to let some students find them
on their own? I give bonus points to students who find significant
alternative answers or flaws. I hope that this encourages students to think
outside the box on tests, but it can also cause students to go down blind
alleys on other tests.


* * *

For a bonus on the final I usually have this optics question.

    In front of you is a soap dispenser. Ignore the orange soap at the
bottom; it is
    not part of this  question. Instead look at the two layers of liquid at
the top. The
    top one is clear and the bottom one is blue. Which has a higher index of
refraction?

Since you can't see it.,  I'll tell you that the soap dispenser is a
cylinder.  The students get to actually play with it.

Most of the students say that the blue liquid is one with the higher
refractive index because it is denser. Unfortunately, the clear liquid is
the one with the higher index.

I expect them to discover this by noticing that the when looking down
through the clear to the blue, there is significant total internal
reflection, but none the other direction.  The vast majority who get the
question right do this.

However, several use the dispenser as a cylindrical lens and notice that the
clear part magnifies more than the blue part.

I'm fine with either answer, obviously.


Marc "Zeke" Kossover