Math or arithmetic ? Math isn’t arithmetic any more than juggling is theoretical physics.
Mastery of arithmetic involves memorizing lots of heuristic rules that aren’t particularly insightful about, or are outright conflicting with, the structure of math, and learning the structure of math first slows your ability to do arithmetic.
I don’t think any school hands first graders calculators and asks them to never learn arithmetic. But I see no need once you’re doing algebra to be focusing your time on long division or multiplication. These are irrelevant distractions from algebra, time spent and points lost on arithmetic details is a waste of cognition and doesn’t help. This becomes increasingly true through calculus, linear algebra, until you get to real math courses where a calculator is pointless because arithmetic doesn’t even show up.
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Math or arithmetic ? Math isn’t arithmetic any more than juggling is theoretical physics.
Mastery of arithmetic involves memorizing lots of heuristic rules that aren’t particularly insightful about, or are outright conflicting with, the structure of math, and learning the structure of math first slows your ability to do arithmetic.
I don’t think any school hands first graders calculators and asks them to never learn arithmetic. But I see no need once you’re doing algebra to be focusing your time on long division or multiplication. These are irrelevant distractions from algebra, time spent and points lost on arithmetic details is a waste of cognition and doesn’t help. This becomes increasingly true through calculus, linear algebra, until you get to real math courses where a calculator is pointless because arithmetic doesn’t even show up.