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Ask Marilyn "geometry test"



From today's Marily von Savant:

Q: "On a geometry test, Mary devises a set of steps to solve a
problem. Her solution is shorter and more elegant than the method
that she was taught in class. If you were her teacher, how would you
score Mary's answer?"

Marilyn's A: "I'd ask her to solve the problem by the method that she
was taught. If she could, I would give her full credit plus extra
credit for the extra solution. If she could not, I would give her no
credit at all: She doesn't understand what was taught in class.
Methods of teaching are not necessarily the shortest and most
elegant. Instead, they may simply be a good way for students to learn
the principles of the subject."

My comments: I found this interesting and have talked about this with
my classes before, encouraging them to think out of the box and
emphasizing with actual examples that there is often more than one
way to solve a problem. So I don't fully agree with Marilyn. I think
alternate solutions are as good if not better than "my way." However,
I would keep the following in mind:

(a) Marilyn doesn't say what level class it is. I might agree more
with her if it is middle school but not if it is an undergraduate
class or higher.

(b) I would look to see if the alternate method really has some
generality to it, or is just a fluke, a memory trick, or right for
the wrong reasons.

(c) It would probably also depend on how the question was worded. If
I said, "Use Kepler's laws to ..." I might still accept an alternate
solution, but only if it were tied to Kepler's three laws.

Anyhow, I throw this out to see what interesting comments you might have. Carl
--
Carl E. Mungan, Asst. Prof. of Physics 410-293-6680 (O) -3729 (F)
U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mungan@usna.edu http://physics.usna.edu/physics/faculty/mungan/