I think technology should be fully integrated into education. I don't see the point of doing complex math problems without a calculator. You're better off building your own calculator if you have to do math problems on a regular basis. Do you know how long it took to do math problems before calculators existed ? Statistics took months or years to complete, which can now be done is microseconds. It would seriously hamper progress if computers and calculators did not exist.

How about instead, building upon technology instead of trying to do without it to prove that you can still do it. How much more could you do if technology would be integrated. Instead of doing math with pencil and paper, you could be programming newer and faster ways to solve problems into your computer or calculator. When I was doing math in school I had a programmable calculator, and made full use of it whenever possible. I wrote lots of programs for it (in a form of BASIC) and it saved me lots of time. I also learned a lot more than by doing things the tedious way on paper.

However, you should still understand what is going on. You shouldn't just use a program to solve your math problem with no understanding of what it is doing. If you program it, then you will understand what it is doing and avoid the tediousness.