At 01:50 PM 9/30/2002 -0400, Melissa Burchfield wrote:

"Do you still ask essay questions or did that 'go out of style' since I was
in college?  (I remember answering essay questions in every class but
math.)  If you do use essay questions, what kinds of questions do you ask?"

Betsy Darken wrote a response with which I have no quarrel. She clearly
discusses one important type of essay question that may occur on a
mathematics test. However, there is another type of essay question that
appears on most mathematics tests. If you ever solved an equation and had
to write out all the steps, then you wrote a little mathematical essay.
After all, the equation "x=2" is a sentence complete with a subject, verb,
and predicate. When students fail to use correct structure and abuse
notation, they often lose some points because they are making grammatical
or spelling mistakes. Now it is true that these essays are quite formal and
are expected to follow a traditional pattern but this can also be said of
sonnets and haikus. In fact, until the formalization of mathematical
notation beginning in the 1500's, solutions to mathematics problems were
written out in the appropriate language of the day. Curiously, Marilyn vos
Savant, in her column in the Sunday supplement magazine Parade, seems to go
out of her way to solve traditional algebra problems without using algebra.
Some of her problems are clever, but an algebraic solution can always
suggest connections and extensions that are hidden by the verbiage of the
fourteenth century approach.

As an aside, my dictionary defines an essay as "a written composition less
elaborate than a treatise" and defines a treatise as "a formal essay." This
gives us a nifty little problem in set theory. Write an essay. It's due
tomorrow.

Ed Rozema
Mathematics Department/Dept 6956

Office:    (423) 425-4584
Fax:       (423) 425-4586
Math Dept: (423) 425-4545