Loved to hear Katherine G. Harris' description of her experience using the TI-82's. I have often heard the argument that students must learn all their number facts before they can even start algebra.
If that were the case in all subjects, we would never have Little League teams. Anyone with kids knows that you learn the rules as you play, not before. If everyone had to know the vocabulary before they picked up a book, we would all be at the 3rd grade reading level. We learn most of our vocabulary through reading after the 3rd grade -- or so I have been told. (Took courses on reading in subject area many years ago in NJ.) So I believe that letting students go on, even though they haven't mastered all the basics, is appropriate.
Technology dependent? I certainly am. I need my word-processor and spell-checker. Why is it okay to use a computer to do word-processing but not okay to use a calculator? We let students use slide-rules, which were calculators of sorts. Was that okay because it was so *#@* hard to do? In real life the important thing is to be able to solve the problem, not that you do it without a calculator. Use whatever tool is required and appropriate. Your students could not find a graphical solution with- out figuring out domain and range, and then understanding just what a "solution" was. If they'll work twice as long and hard with a calculator, then go for it! Eileen Schoaff Buffalo State College