Which is which? A person who works in either role will do so more quickly by virtue of not needing to constantly consult a machine over trivial problems.
Focusing on algebra, calculus, and so forth would produce more engineers/scientists/mathematicians etc . These are things rote teaching the times table can not do. His not saying let computers do all maths, just the repetitive bits.
Symbolic Manipulation is still necessary.
I learned vectors(Mostly for games), eigenvectors far more intuitively by programming them on computer as a kid, then calculating them by hand.
I knew what adding two vectors actually represented, or what the crossproducts was, rather than just calculating it(Which the computer always did).
I get top marks in calculus, linear mathematics and most college level maths classes, but my little secret is that i'm not actually very good knowing my times tables by 'art. If someone asked me to calculate a basic times table question, it would take a few seconds to work it out manually. Yet the general public thinks that's weird, but I actually found it's quite common at this level.
