That's a good question. We need to keep in mind that computers are never going to go backwards in innovation. Once a computer is capable of some calculation, students will never need to have to do it by themselves again. However, they will still need to know how to interact with that calculation and understand the variables/relationships in order to set up the calculation.
Where do you draw the line?
Instead of just one line, you have to draw two lines. One would be on the more elementary end of the spectrum. Students have to learn the rudimentary basic calculations (or memorization) in order to function well in everyday life and higher levels of education. Simple addition, subtract, division, multiplication, estimation, understanding of relationships would be necessary. As much as I adore algebra, it could be left to the computer. Therefore the first line would be drawn at a point where the material does not show up in everyday scenarios.
The next line would be drawn at the opposite end of the spectrum where humans need to come in and do the higher orders of thinking. Given the right software, students would be able to visualize and understand the basics of the calculations and their relationships without actually calculating them. They would therefore be able to use computers in more applied problems - ones that they would be confronted in their careers later on in life. A few experiments could be conducted to find exactly where this line would be drawn. It would be at the point where humans do the smallest amount of calculation work while still having a solid understanding. Computers may be able to work past this line, but they would end up assisting the students to the point where the students lose the understanding of the concepts.
If the US and other countries truly put the time, money, and effort into this reform, I'm sure they could be quite successful.
However, another tricky thing to think about would be transitioning into this new and reformed type of education...
Once a computer is capable of some calculation, students will never need to have to do it by themselves again
However it is important that they know enough to check if the answer they get is at least reasonable and probably correct. So even if they can't solve the problem exactly they really should know how to show that the answer must be between 1/sqrt(2) and 1, for example, so that they know they made a mistake when the computer tells them the answer is 0.3475.
Yes, that goes along with understanding the basic relationships and estimation techniques. The exact calculations can be left to the computer, and the humans can check the solutions and determine what went wrong if the answers don't seem to be what they had expected.
