What people understand

I wrote the comment below in reaction to

http://habitatchronicles.com/2004/04/you-cant-tell-people-anything/comment-page-1/?unapproved=122880&moderation-hash=5c0d5b5fb23b1a617305d09e3638c0c0#comment-122880


Comment:

Often there is a large disconnect between what we write and what people understand.  Almost everything I've published has been in mathematics where there is less of a problem because we write proofs.  Usually, if all the details are spelled out, the reader (another mathematician) will be able to read what you wrote and understand 95% of what you are trying to convey.  Other fields, generally speaking, are not like that.

On the other hand, when I explain math to students, I sometimes see giant misunderstandings.  Homework problems help a lot to remove misunderstandings.  I recall that it was difficult for students to learn the basics of the orbit of the moon and planets around the sun.  I am thinking that if students needed to calculate 1) when the phases of the Moon and Venus occur, or 2) when sunrise and sunset would occur, then they would actually learn the basics of orbital mechanics, but then again, they might just learn how to do specific orbital problems without being able to solve random questions about orbits and phases.

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