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Topic:  Calculus without calculus 
Related Item:  http://mathforum.org/mathtools/tool/3522/ 
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Subject:  RE: Calculus without calculus 
Author:  proofpad 
Date:  May 10 2011 
after all, for showing students in 6th grade Geometry classes the area formula
of a circle; namely that it helps introduce the idea of variables as well as
irrational numbers that serve a particular purpose (much like the circumference
of a circle). If there is a reason behind the math  or behind using technology
to do the math for you  then it can be a very powerful lesson. If there isn't
a project or goal that leads you from that answer to some other connection,.
then what are the students learning?
Again, this isn't because of the lack of proof before using. Try "proving" why
addition works. Try discussing the derivation of the Quadratic formula in
Algebra 1 (before they learn about completing the square). How about
Pythagorean's Theorems? How many of us go through any of the proofs with our
students to do that piece when we first look at it (and I get kids in Geometry
who know the hypothesis to the theorem, but not the condition). If there is a
reason for the shortcut, though, then it makes perfect sense to show them the
techniques of using technology or the basic rules of calculus to solve certain
shapes.
BTW, if you want a proof of the area of a circle without calculus:
http://curvebank.calstatela.edu/circle/circle.htm has an animation to help
illustrate it.
 
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