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Subject:   RE: Graph Sketcher
Author: Alan Cooper
Date: May 10 2004
On May 10, 2004, Bethany Hudnutt wrote:

... I fixed the discussion.  Thanks for noticing.

Thanks Bethany,
It's good to see that the site is maintained by someone who is paying attention.
(I have seen much worse response times - once a site sponsored by a major math
software developer took over a year after being notified to remove pages on
which reciprocal trig definitions were given for the inverse trig

One last comment. We often act towards students as if the definitions of
mathematics are natural or obvious, when often in fact they are not. In fact, in
common language the phrase "curving up" does naturally correspond (for a person
acculturated to left-to-right reading) to what we in mathematics call
"concave up", but linguistically, "concave up" might better be called "concave
as seen from above". The concavity opens upwards, but the curve dips
(relatively) down in the middle. So I can see how someone might quite logically
infer the opposite of our usual convention, and  in the end the definition is
not something to "see" but rather just to "accept". Maybe this thread isn't the
place for it, but I'd like to see somewhere a discussion of some of these issues
around language and mathematics and what it is reasonable to expect students to
"see" as obvious.

`You never understand mathematics, you just get used to it.' --- J. von

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