When I started Undergrad my school had just started a mandatory laptop program for all freshmen so I had a fancy laptop that I felt should be used for class. I proceeded to sign up for the laptop sections of math where I took multivariable calculus and differential equations using Maple. I aced the course and got quite accomplished with the software but I did not LEARN diff. eq, or even really multivariable calc as I later found out during my 3rd year classical mechanics course. I still only know enough diff to realize how to recognize them most of the time.
I also really don't think that it was the professor's fault. I think that math requires a certain amount of mechanical crunching in order to become a useful tool. I therefore really think that math should be performed naked, in PEN, if you are studying physics or engineering then by all means teach numerical methods and use simple software to automate the calculations if it makes sense. Otherwise keep in mind that math is a philosophical toolset, and you don't get better at philosophy or logic with wikipedia, you get better by arguing.
Programming is a skill that should be taught in school, research is also another useful skill that these days requires internet, (though primary source essays are a better method IMHO), but school is not the place to train white collar workers how to use PWP.