Although I think calculators are quite possibly one the most useful tools a student can have, we still need to teach students how to do math by hand. Not teaching children multiplication tables or long division would be a huge disservice to our kids. Calculators, especially graphing calculators, can make long tedious problems easier to solve without stripping away the learning and can make visual representations. Graphing calculators in particular are capable of some serious calculations and can be really useful in classrooms. The first example that comes to mind is quadratic formula. Of course you have to teach students how to calculate the quadratic formula, but once they have gone through the calculations a few times and have memorized the formula, it really isn't necessary to have them do these long, tedious calculations just to get a solution, especially if the solution is part of a larger problem. In this case, a graphing calculator with a programmed quadratic equation solver could shave off ten minutes of calculations. Another great use for calculators is to check your work. If you have a calculator handy, you can see if you got the right answer.
Although I am a proponent of calculators and consider them to be one of the greatest inventions for students, you cannot discount the value of memorization. The fact that whether to teach these or not is even in question is baffling to me.
This isn't a debatable skill, it is a necessity.
I would fight tooth and nail to teach my students multiplication tables and long division. Why would you waste your time putting 5 x 6 into a calculator when it should be automatic? The notion that students could go through life without learning this is ridiculous. Not only do you need this for every subsequent math and science class you will ever take, you multiply things in your mind every day. Leaving a tip, grocery shopping, getting gas, paying your bills, etc. Frankly, if I was a teacher at a school that told me I couldn't teach multiplication tables, I would quit. No questions asked. I understand that we live in an age where convenience is coveted and calculator use is commonplace, but there is no greater tool than your own mind.
Throughout college in all of my upper level math classes we used calculators everyday and we always joked that we are "a product of the calculator generation," but I can guarantee you every single person in the math department could do almost every calculation by hand without whipping out the TI-83. If we don't teach students the basics, we are setting them up for failure. You can't be a doctor without knowing your multiplication tables. How will you prescribe medications? Sure, you could carry a calculator, but what if those 5 seconds you take to input 4 x 90 into a calculator costs somebody their life? You can't be an engineer. You can't be a scientist. You can't be a teacher. You can't work in construction. You probably can't get into college and you probably can't get a job. I have even had to take a simple math test before getting a waitress job. Come on people. REALLY!? Calculators are here to enhance learning, not replace it.