While it may be good to contact engineers, scientists, economists, etc. about what mathematics students need to enter these professions, we would then be preparing students to enter these professions in 1995, not 2010. Engineers, scientists, etc. have no idea what mathematics their professions may need in the future -- any more that we mathematicians do. And the mathematics examples they give will be in the form of the types of problems they solve.
Many of us do understand the algorithms involved in computer software. Technology empowers students to explore and learn, it does not do the work for them. A computer is like a vacuum cleaner. You can turn it on and it sits there. It doesn't do anything unless you push it.
What makes you think that the old way of teaching mathematics worked? How many people remember how to find the square root using the algorithm where you put bars over two digits, then after taking the square root of the first group, you did this weird division where you put a number in the answer and at the end of the divisor. Of those of you who remember the algorithm, how many can explain why it works? Just because you can proficiently apply a memorized algorithm does not mean you know what you are doing. Actually asking students to guess at a square root, square their guess, then correct their guess and check again, is a much\ better algorithm because students can understand why it works and its relationship to the meaning of square root.
When students construct their own algorithm, they have constructed their own knowledge. They have not just learned X, they learned how to learn. Hopefully, humans will continue to learn all their lives, including learning new math.
If all math done had to be tied to some practical purpose, then all the neat new stuff would never have been discovered. I'd miss fractals, knot theory, and other interesting ideas. Why even think about primes? Are they used in engineering or science? (Probably, but off the cuff I can't think of where.) Math is beautiful, why make it redundant and boring. Eileen Schoaff Buffalo State College I love discrete mathematics! Especially solving recurrence relations. Now how practical is that? I also love geometry software. My math ed students have also discovered that geometry is exciting and beautiful. Have even had students discover new theorems. Beat that will an algorithm. (Should be "Beat that with an algorithm." I have a louse editor.)