My geometry students always ask me if they can use their calculators. Always. You'd think by now they would know that the answer is going to be no. They think that because I'm a big geek I must want them to break out the TI's and go to town, but this, of course, is geometry. This isn't stats, where some actual number crunching power can be useful. It's not even algebra, where a graphing calculator can be a nice visualization tool or spiffy time saver for solving tedious systems of equations.
Obviously, I'm not entirely anti-calculator. They have their place. I use a calculator when I'm writing out bills. I broke one out tonight in my statistics class to compute some especially painful combinatorics. I got out the world's coolest calculator (aka, Maple 11) for my numerical analysis class since we were building algorithms for estimating Pi and repeating calculations 10 million times (literally) to increase accuracy just wouldn't have been pretty with pencil and paper. But for my geometry students, it's not going to happen without a fight.
We were reviewing area today (just plain old vanilla plane figures) and I briefly considered letting them use calculators to handle a few exercises calculating the areas of circles with decimal radii. I'm not mean after all and figured that squaring numbers like 2.37 wouldn't add much to their understanding of area. However, when first one, and then another student asked why their answer of 4.74 was incorrect, I knew that the calculators weren't coming out for a while.
As with all computing tools, whether it's Google for research, or a calculator for mathematics, it's all too easy to just let the tool do what it does and plop answers in your lap. My students had no problem finding the x-squared button on their calculators; unfortunately, half of them didn't understand the difference between squaring 2.37 and multiplying it by 2.
This may be a fairly old rant. Students rely too much on technology, students lack fundamental skills, blah blah blah. But until the students coming up the pipeline to me know their times tables through 20 cold, I'm going to keep ranting. Our approach to using tech needs to change at the elementary level with serious pedagogical and practical training in mathematics for our primary school teachers. Overall, these folks do a great job, but you don't become a second grade teacher because you just weren't sure what to do with that undergrad degree in applied math.
So yes, kids, you can use your calculators. As soon as you have jobs and bills to pay, and your mortgage company doesn't give partial credit for stupid math mistakes.