There is an article at the Guardian about Stephen Wolfram, the person behind Wolfram|Alpha. Here.
Below is what he says about people losing the ability to perform (tedious) mathematics by hand because now computers do it for them:
"There was a time when we had to cut feathers to make our own pens. Gradually more levels of civilisation and automation happen, and this is another such layer," he says. "What should happen is that you can build on to what is now automated and do the next level of stuff, where you need to add the human touch." It also cuts both ways since, if calculus is mechanised, this opens up new worlds for students for whom solving problems by hand was too difficult.
And I agree. For the last few days I have been going through the new maths text for class 12 here in Bhutan. The chapter was on something called determinants of matrices. There are 12 rules to learn, and then puzzle how to apply them. It is rather like a game of chess, where you have to see several moves ahead. The problems are made harder by using variables instead of numbers. Why? I waded through twenty worked examples trying to see some pattern in the methods. Trying to see some way to explain to the students how they could work out what to do. Their method is to learn them all by heart.
I shared my thoughts with Don, my Canadian friend. He is a real mathematician. This is what he said:
"If you are serious about needing the value of a determinant it will be numbers and you do it on a computer. What you are learning is a lost art and it should be! It is a little silly to require people to learn all those rules.
I hope someone from the curriculum division is taking notes!