On Oct 15, 2013, at 2:50 PM, Dave L. Renfro <renfr1dl@cmich.edu> wrote:

http://www.mathdemos.org/mathdemos/sinusoidapp/sinusoidapp.html

This is an ominous statement...

"Many textbooks include exercises in which students are asked to determine the coefficients a, b, and c of a sinusoid of the form y = a*sin(b*x) + c or y = a*cos(b*x) + c. Such exercises are static, requiring the use of algebra, and often hold little appeal for students."

But the author does state the following as well...

"The objective is to actively involve students via the software simulations so that the determination of the sinusoidal model has a geometric flavor that complements the algebraic tools stressed in texts."

It is hard to make a final judgement on this author's intent. The examples are well done, and the author obviously knows both the visual and analytical (algebraic) aspects of the material, but I am not sure that the author's intent here is for the student to be as successful at the material as the author is. Most of the time the paper seems to try to present an alternative to analysis rather than a compliment to it.

There are other examples on that site that strike a balance between visual and analytical senses, like this (simple) one...

and then there are poor examples that don't seem to accomplish anything, pedagogically speaking, like this one...

The author also mentions "modeling"...

"This approach also introduces a modeling aspect because in some situations we are approximating real world phenomena with mathematical functions."

The whole point of modeling data with functions is so that you can apply algebra. I am pretty this author knows that deep down but for some reason (because his/her students don't like algebra) he/she feels obligated to ignore that critical detail.

Bob Hansen