Joanne Jacobs has a bunch of testimonials from her readers as to just how worthless high-school, and even college diplomas have become. Particularly dismaying was the inability of young people to do computation without a calculator, or to recognize that an answer was absurd.

Many college students hang on to their calculators much as a young child hangs on to a blanket for security. In my first calculus test, when the professor wouldn't let calculators used, five of 25 students walked out and 10 other students never came back to class. We ended up with nine students at the end of the semester. I have seen the same problem in chemistry, physics and other courses. When courses get hard, most students just drop instead of studying harder.

Hmm, it's my recollection that a calculator doesn't really help in calculus. Or with differential equations, etcetera.

Now calculators are exceptionally helpful in calculus, as long as the professor doesn't require the work being shown. The top of the line ones from 5 years ago could perform derivatives and integrals with ease.
http://education.ti.com/us/product/apps/calcmadeeasy.html

Calculators are nice, but if you don't understand the basics, you won't recognize when an answer is absurd. And since kids are starting out with calculators in kindergarden, they don't understand the basics.

I'm just this shy of being disnumeric, but even I learned basic arithmetic, algebra, and geometry. I even used a slide rule in late high school and college, and could extrapolate to 2 digits. That would blow kids' minds today.

Well, there's no reward for taking hard courses, at least in the eyes of those I grew up with.

It's not just a US thing :(

I helped teach 1st year maths (dunno what grade that would be 11-12 year olds) when I was in the 6th form (16-17 year olds). I was stunned at the basic questions they couldn't do even though they *had* calculators on every desk. For example: being unable to work out the clearance for a bus under a bridge - the bus is 375cm high and the bridge is 425cm high, what is the difference?

I was also somewhat shocked to find that they didn't know how many weeks there were in a year. THen again, it appeared that the 24 year old teacher wasn't all that sure either.

It was something of a realisation to me that when I completed my B.Eng honours degree I was actually better at maths than all but one of my school maths teachers.

Remember that character that Dana Carvey used to do on SNL, the Grumpy Old Man.

"Back in my day, we didn't have any of those fancy moving pictures. Back in my day there was only one show in town, and it was called 'Stare at the sun!' We'd stand there and stare until our eyeballs burst into flames and our skulls caught on fire and we liked it. We loved it. We couldn't get enough of it."

Or

"We didn't have video games back then. We made up our own games, like Chewing the Bark off a Tree!"

The Grumy Old Man has a point; doing things 'the new way' is find and good but unless you understand _what_ is going on underneath, when it all breaks down you're left looking vacant and dumb ...

Taking an example from my professional life; Microsoft has pioneered the use of 'Software Wizards' to setup complicated whoozits and whatsits on a computer. But every once in a while the Wizard breaks down and just doesn't work. If you understand the process you can dig down into the system and fix the internal process that is broken.

If you are simply a slack jawed yokel pushing buttons all you can do is retry the wizard and call for (expensive) help. And after that you _STILL_ won't know what's going on. This can be annoying for a desktop user, fatal (for the company) if the yokel is in IT.

i generally don't allow calculators on exams. i make this known to students early on, so they do some of their calculations by hand on homeworks. i've been toying with the idea of handing out a bunch of envelopes at the beginning of the semester and requiring all calculations be done on the envelopes (on the back, of course).

(btw, i'm talking about junior/senior/graduate level aerospace engineering courses)