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Catching up on old mail.
On 5/19/2012 4:39 PM, Philip Keller wrote:
No defense necessry! I agree completely. In fact, I almost mentioned in my last post that students DO gush when they see calculus used to derive with ease what we struggle to show without it. I think that's another example of making a deeper connection.
In fact, I take a moment to teach the calculus-based relationships to my
algebra/trigonometry-based high school classes, at least at the honors
level where many of my students are also taking calculus. I make sure
to show them the relationships in both directions--differentiation and
integration, even though I get to these in kinematics before the
calculus class gets to differentiaton or integration. (The calculus
class in my high school starts with limits. They typically start
differentiation in early October and integration some time in December.)
This year, the lesson was enthusiastically received by a handful of
gushing students. Quite a few of the others filed it away in their
minds because they weren't sure what to do with it. Several of those in
the latter category gushed to me a couple of weeks later when the
calculus class started learning differentiation--they were delighted
that not only did they already know one of the tricks, they already
understood the basic idea behind it.
Not long after this, the calculus teacher found me and explicitly
thanked me for it.
--
Jeff Bigler
Lynn English HS; Lynn, MA, USA
"Magic" is what we call Science before we understand it.
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