> I concluded that no one had actually checked to see if he could understand math. North American students hardly try calculations now; they're given calculators at a very early age.
That was something that caught me off guard a few years ago. In 2008 I was considering becoming a teacher (high school math/technology). For various reasons I chose a different path, but I sat in on some courses at a friend's school to get a 'day in the life of' feel and an opportunity to talk to other teachers. One class caught me by surprise. It was a 7th grade math course, essentially pre-algebra. However, the students did everything with calculators. The lesson that day was on interest, simple and complex, a way to try and tie the concepts down to real world examples. The students did everything with calculators, not one was using pencil and paper to work out the math (though they all recorded the steps they'd done on the calculators). Talking to the teachers, that was how their curriculum was setup, not just a one off case.
That wasn't what turned me away from teaching, but left me confused about how things had changed so much in the 15 years or so since I'd been in those seats.
I think calculators for interest calculations makes a lot of sense. I'd be pretty impressed by students doing P(1 + r/M)^N without a calculator, though I suppose you could do repeated tedious multiplications of P*(long decimal number). We definitely used calculators for that 20 years ago.
Well, that particular exercise was something like: You have $P and the interest rate is I% per month, what would you have after 1 month, 2 months etc. It was easily doable at the level that exercise required by hand. However yes, if the formula had been more complicated then calculators would've made sense. From talking to the teachers though, the sense I got at the time was that calculators were never restricted regardless of the difficulty or ease of the exercise.
EDIT: Did mention complex interest, that part made sense to use the calculator for. My observation was merely attempting to point out the ubiquity of the calculator in the classroom. I'd be interested to see the capability of students after a curriculum like that at doing mental and hand calculations, my understanding is that here in Georgia the various classwide exams they take also permit calculators so the students would have little occasion to demonstrate that skillset.