Lather and Rinse

Tell and Repeat courses

Aka student regurgitation. To avoid this, one must come up with questions which test for understanding, rather than information chucking in the vertical direction.

Anyway, Rhett mentions a wonderful conceptual question, and one I had not run across before, as an example.

The only bad thing about this question is that they aren’t trivial to create. Oh snap – well, I just gave away an awesome question. Truthfully, this question has been “out in the wild” for a long time. It is still a great question and you could probably use it on a test. The problem with a question being in the wild is that students can just memorize the solution – this means that question no longer tests for understanding.

One solution is to have a large number of questions, so that simple memorization is difficult, but these questions are hard to come by. Another is to have modular questions, so that you could ask about the same concept in different ways, but that’s far easier with algebraic results, where you change what information is given and which variable you want the students to solve for. I’m not sure to what extent it’s possible with a discussion question. Rhett’s example changes a variable, certainly, but not in the same way as an algebraic problem.

Another, I think, is to phrase a situation with a contradiction and have the students find out what the problem is with the phrasing of the question — a “why isn’t this possible?” kind of problem, or “find the fish flaw.” I see this all the time in crackpot discussions; once you remove the rigor of math, it’s easy to state a model which has some unphysical aspect and contradicts itself, which is why thought experiments alone can never disprove some phenomenon, and why perpetual motion machines are easy to describe but never work.

Here’s a classical physics example: you swing a bucket in a big circle which passes over your head. You adjust the speed so that the bucket comes to stop, with the string taut, directly overhead, at which point the bucket and water fall on your head. Is that possible?

A student may think so, because from a conservation of energy standpoint all you need is to have the kinetic energy at the bottom be equal to the potential energy at the top, so that the kinetic energy vanishes, and presto! You’re wet. But this ignores the requirement of the taut string: in order for that to be true, there must circular motion (not uniform, because v will be changing, but still circular) and this requires that there be tangential movement. Even as the tension tends toward zero, there is still gravity, so at the apex you would still have a centripetal acceleration, and thus v cannot go to zero. The bucket cannot come to a stop directly overhead with a taut string. (and yet it was so easy to state that it would happen …)

2 thoughts on “Lather and Rinse

  1. An undistorted, sp3-hybridized, tetrahedral carbon atom bears four rigorously identical, freely rotating substituents, CR_4. Said carbon atom is a chiral center. Illustrate the general case where this is true and give a discrete example.

    A pair of undistorted, sp2-hybridized, planar trigonal carbon atoms are joined to give an olefin, R2C=CR2. The R groups are four rigorously identical, freely rotating substituents. Said two planar carbon atoms are each chiral centers. Illustrate the general case where this is true and give a discrete example.

    An undistorted, sp3-hybridized, pyramidal nitrogen atom bears three rigorously identical, freely rotating substituents. Said nitrogen atom is a chiral center. Nitrogen umbrella Inversion does not change the chirality. Illustrate the general case where this is true and give a discrete example.

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