Discussion:  All in Calculus 
Topic:  two different tools 
Related Item:  http://mathforum.org/mathtools/tool/1127/ 
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Subject:  weirdness everywhere  important to understand it 
Author:  George 
Date:  Feb 5 2004 
ones I think you have Craig, would get burdened with calculations and never
attend to the larger picture. Or maybe your students ARE that way :)
If we have tools that at certain points behave differently, the ability to
recognize and analyze "WHY" would be a great indicator of understanding. Would
your trig students be able to answer that question about superposition? I would
actually prefer that to the ability to, say, plot a wave or even "explain the
phase shift", which is the kind of thing my students did when I taught trig a
decade ago.
The Excel spreahsheet that Craig is referring to was put together by Kathleen
Smith as a revision of work by Lindsay Husted. It's available at
www.mste.uiuc.edu/reese/misc/sineCosineLindsayHusted.xls
and the sheet that goes with it is at
www.mste.uiuc.edu/reese/misc/excelhandout.doc
On Feb 05, 2004, Craig Russell wrote:
It's obvious to me what is happening in the Canadian appletthe same sort of
thing that happens in the activity you and Kathleen demonstrated using a
spreadsheet. You can get almost the same effect using a graphing calculator
just make the wavelength (1/omega, essentially) slightly larger or smaller than
a few pixelwidths. Fairly sophisticated math students might be asked to try
to explain WHY the granularity of the display affects the appearance of the
curve. Why does it look like the superposition of two sinusoids of slightly
different frequencies [such as sin(5x)+sin(6x)]?
 
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