I spoke to a Math Professor a while back about this. He said that in Eastern Europe, the kids aren't allowed to use calculators all the way thru. When they get to the US for grad school, and their contemporaries are using calculators - they do too then, the Eastern Europeans KNOW when the calculator has an illogical answer, the American kids don't.

I don't know anyone who does truly complicated math without a calculator - no matter how proficient they are at their facts. But a good understanding of math & high proficiency is necessary if you're going to be able to use a calculator well.

I guess as an educator, you have to decide when your student has reached that point.

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Anna makes a great point. I am helping Raquel with her statistics class. A lot of it is calculator work. I can't imagine calculating standard deviations in your head. But you need to know when an answer is out of range. One skill you need is to know when you have worked a problem incorrectly and the calculator gave you an answer that can't possibly be right. I have been hacking together Perl scripts to verify Raquel's calculator work. When I got a standard deviation of several thousand on data with a range of less than 50, I knew my code had a bug somewhere. And when she got a mean of -60 when she did not have a single data point that small, we knew she keyed something wrong. That was one of the skills I was taught in school--checking the reasonableness of an answer.

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