I don't *need* my calculator to do these things... but it's either the calculator or stupid mistakes with matrices, or it's either the calculator or a big table of trig function values.
It's mostly a time saver, so that I can do more math and less arithmetic. I can do arithmetic and I can do algebra, but there's no reason why I should have to do a bunch of pointless calculation if I actually have a good understanding of what's going on.
But that said, I don't think we should require these big, fancy graphing calculators in high-school... just teach derivatives earlier instead of teaching them in a mysterious calculus class, after all the only thing these calculators are ever used for in high-school math, besides playing games, is finding the minima and maxima of functions. And matrix math... but the worst we ever did in high-school was 3x3, and you can usually write down a minimal amount of work and do the rest of those in your head. (when doing expansion by minors for example)
Otherwise, I remember a few times in an algebra class where we were tested on whether or not we could solve a system of equations by plugging coefficients into matrices in our calculators... of course, we were never taught *why* the methods worked, only how to do them on a calculator. Because most (probably all) math classes in high-school in the USA are a stupid waste of time.
It wasn't until college that I started to really think math was nifty... and this happened my first semester when my professor (unlike all of my high-school teachers) took the five minutes out of his schedule to explain Euler's identity to me. I added a math major that day.
And this article is the best they can do?