Re: Misconceptions FAQ

[William Beaty <billb@ESKIMO.COM>]

On Mon, 9 Aug 1999, John Denker wrote:

> 1) Here's a metaphor.  Imagine that valid concepts are like points in a
> space. <big snip>

A very good point!

Instead of looking at the space of possible concepts, suppose we could
superimpose the "concept-vectors" of all living students and educators in
a single scatterplot in "concept-space."  I think the overall picture
would be much as you say.  However, there also would be some interesting
features: dense clumps of incorrect beliefs.  Each clump would appear as a
single concept surrounded by a cloud of partially-correct concepts, but in
fact would be an INCORRECT concept surrounded by imperfect versions of
that concept!

These clumps are the "popular" misconceptions.  They have a number of
origins: a specific "disease" which widely infects numerous textbooks, a
"disease" which exists in popular culture but not in textbooks, a mistake
in just a single very popular textbook... or simply a very common mistake
made by large numbers of students.

If we color-coded the individual points in our concept-space plot, we
would notice that the misconception-clumps attract brains to themselves
and pull brains away from the clumps surrounding correct concepts.  In
other words there is competition between correct concepts and popular
misconceptions, and individual brains do not tend to split their attention
between a misconception and a correct concept.

As you point out, in general it is not possible to attack the overall
"dust cloud" ( the immense variety of possible misconceptions.)  However,
if we can prune out the limited number of dense clumps, we probably can do
quite a bit of good.  If we can cause a single popular misconception to
become repulsive, then a significant number of brains will be attracted
elsewhere, and probably end up orbiting around the correct concepts.

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

A counterexample is alcoholism.  Eliminate alcoholism, and a single dense
cluster of unhappiness is dispersed.


<snip>
> 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.

Yes.  The FAQ should be aimed at textbook authors, educators, and at any
students who wish to seek it out.  (Imagine a little black book for
textbook authors entitled "Erroneous Explanations in Physics.")  If
students had already aquired the correct version of a concept, it might be
very unwise to point out the misconception to them.  Some misconceptions
are quite seductive.

On the other hand, if a large section of the population seems to always
suffer from a single misconception, then it still might be beneficial to
treat that specific "disease", even though some people are not currently
"infected."


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