Re: Relationship between Earth Moon

["John S. Denker" <jsd@MONMOUTH.COM>]

At 10:47 AM 9/15/01 -0500, John Clement wrote:
>  Since ... do not understand ratios, they
> probably also do not understand scaling.

Indeed!

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This leads to some questions about pedagogical strategy and tactics.

It is a proverb in pedagogy that
        Learning proceeds from the known to the unknown.

So what is the point in teaching earth/moon ratios to kids who don't
understand ratios AND don't know the most basic facts about the earth and moon?
 -- Are we using earth/moon ideas to teach them about ratios?  Bad idea.
 -- Are we using ratios to teach them earth/moon facts?  Bad idea.

Learning proceeds from the known to the unknown.  It would be better, IMHO,
to start from something that they understand and care about, and proceed
from there to learn new things.

In theory, before asking students to make a drawing "to scale" of an
unfamiliar thing (the solar system), it would be good to let them practice
making a map "to scale" of familiar things (such as the schoolyard).  [As a
motivational stratagem, you could use the map to bury treasure one day and
find it again a week later....]

I said "in theory" because in practice most students wouldn't have a clue
how to begin the task, and I suspect most teachers aren't sufficiently
familiar with the subject to teach it properly.  Unclever mapmaking is
extremely laborious, and likely to lead to highly unsatisfactory maps.

Even if you're not trying to teach scale-drawing skills, but only to test
them, it would still be appropriate to test scale-drawing skills separately
from astronomical-fact knowledge.  This would be just one of a number of
"control experiments" required to untangle the numerous competing hypotheses.

============================

There's more to the story than developmental maturity.

 -- Some 13-year-olds know quite a lot about the earth and moon and stars,
having spent dozens or hundreds of hours looking through telescopes.  But
this isn't exactly typical!

 -- Most adults don't know the first thing about earth/moon geometry...
Try asking them how big the full moon appears, compared to a dime or
quarter at arm's length.  It's just not an important part of their life.

I believe they could learn such things if they wanted to -- but they've
never had a good reason to do so.