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Re: Misconceptions FAQ



Hi Folks --

Regarding the proposed Misconceptions FAQ: Go ahead and do if if you want,
but here are some reasons why you might find it to be more difficult and
less valuable than one might have initially thought.


1) Here's a metaphor. Imagine that valid concepts are like points in a
space. They are linked by logical threads to other valid concepts. The
valid concepts are very dilute; that is, each one is surrounded by and
greatly outnumbered by misconceptions. Further imagine that concept space
is very high-dimensional, so that even if we consider only the *near
neighbors* of valid concepts, the misconceptions still outnumber the valid
concepts by an astronomical ratio.

"All happy families are happy in the same way, but each unhappy family is
unhappy in its own way." -- Tolstoy


2) Many misconceptions stem from thinking about the problem in a wrong way,
perhaps using bad notation or bad terminology. In order to set up a
discussion of the misconception, you need to teach people the wrong
approach. That is at best a waste of time, and at worst the wrong approach
is hard to un-learn, and competes with the correct approach during all
future thought processes.

(BTW, I put into this category many of the "relativity paradoxes" that one
finds in a certain genre of textbooks. They drive my bad-pedagogy detector
offscale.)

IMHO, people should not learn (or be taught) misconceptions at any early
stage. It is important that the *first* ideas taught be the right ideas.

I can see the value of circulating a list of misconceptions to new
instructors, to warn them what they might be up against, but otherwise the
value seems questionable, especially in comparison to the usual format:
frequently-asked questions with correct answers.

Cheers --- jsd