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From: gds@spam.istc.sri.com (Greg Skinner)
Newsgroups: comp.edu,sci.math,sci.physics
Subject: Re: Student and Course Integrity  (was Rising cost of textbooks)
Message-ID: <15561@joyce.istc.sri.com>
Date: 21 Dec 88 16:15:15 GMT
References: <1131@osupyr.mast.ohio-state.edu> <1887@sun.soe.clarkson.edu> <1057@l.cc.purdue.edu> <484@ur-cc.UUCP>
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In article <484@ur-cc.UUCP> bjal_ltd@uhura.cc.rochester.edu (Benjamin Alexander) writes:
>Oh, you are sooooo wrong.  Concepts CAN be tested on multiple choice and
>true false tests!

I have known several people who were able to do well on multiple
choice/true false tests without a good understanding of the material.
They were able to "intuit" the answer from the question in some cases,
or eliminate wrong answers in others.  Some were just good guessers.
Give them an exam where they need to show the steps they arrived at
in solving a problem, and they do not do as well.

>Proofs must be
>memorized, because if you misremember the hypothesis and misapply the
>theorem, you will get wrong answers!

*Some* proofs should be memorized, because they are the foundation of
other proofs.  However, a teacher shouldn't encourage the students to
memorize all of the proofs in the book.  Rather, the teacher should
encourage the student to reason, and to use axioms, lemmas,
corollaries, theorems, etc., to support their reasoning.

>It is EXCEEDINGLY important for an average person to learn how to add.
>Recognizing addition in daily life makes living that much easier.  If adding
>is some kind of mystery black box machine (push the buttons for the first
>number; push the holy and sacred Plus sign; push the buttons of the second
>number; push the almighty Equals key) then ordinary people like Johnny will
>be deceived by clever people throughout his entire life.  [...]

Granted, but there is a limit to how much rote manipulations should be
taught.  Case in point:  in the eighth grade (!!) my math teacher put
long division and addition problems on his exams and homeworks.  (I
got in trouble because I didn't do the homeworks, but I thought they
were silly.)  I should think that after the fifth grade useful
mathematical concepts, such as logic, should be taught.  This will
make the transition to higher forms of mathematics easier as the
manner of conceptualizing will have been fostered in students at an
early age.

--gregbo