>I think that the ability to analyze the behavior of functions is critical. >How can you even use a graphing calculator if you don't have some idea of >what to expect?
Absolutely. Although I am not an engineer, I trained in a discipline that was suffciently related that I had some distribution requirements in electrical engineering and diff eq, including some analog computing. I also took coursework in lingusitics. I was involved (much later, when I'd forgotten it all) in real-time programming. Also, I read magazines like Science News and Scientific American.
Why the boring bio? Since my physics intuition and skills are really quite poor for someone with mathematical training, the one thing I remember and can "use" from all of this is the importance of sinusoidal functions. And I'm sure the reason I kept that much was because I understood what these curves look like, from the homework assignments and classwork on how to graph them. (I also found this intensely beautiful, even in high school). Even when the crew of the Enterprise is talking about being "out of phase" I have mental images that I can rely on of combining sine curves with different phase shifts.
I too believe strongly in the use of computing technology to simplify the kind of learning experiments that kids need to do to grasp material. But, just as I would be aghast if learning the multiplication tables, or good penmanship, were totally dropped, so I believe that if your own hands don't do it, you don't learn it.
Let's not forget that when slide rules were the hot technology, studenst were expected to know (a) enough arithmetic (including logs and exponetials) to validate the answer; (b) error analysis to know how much the answer could be trusted; and (c) how the system they were making computaions about behaved.