I'll need to engage in conjecture over elementary school lessons from 35 years ago, but one thing that comes to mind is we were calculating circle circumferences and areas quite quickly following the formulas. We still learnt arithmetic techniques by hand (though never logarithms, for whatever reason - I guess calculators replaced the log tables!), but when we moved on to broader things like geometry and statistics, calculator use let us focus on the actual topics and formulas and not repeating the grunt work like generations past.

For anything beyond that, I'd need to take it up with whoever wrote our curriculum! But I know it was mildly contentious at the time, much as the use of even more elaborate technologies are now.