Deduction and analogy seem like largely different reasoning processes. I suspect that what you're describing is that by learning the notation and doing enough deductive arguments, the tasks begin to become intuitive, that is, they begin to become analogical and not deductive.
Deductive thinking is conscious, deliberative, and "slow." Analogical and intuitive thinking is unconscious, nondeliberative, and "fast." So you're probably right that by learning to relegate many mathematical tasks to analogical thinking, one increases their ef... (read more)
Deduction and analogy seem like largely different reasoning processes. I suspect that what you're describing is that by learning the notation and doing enough deductive arguments, the tasks begin to become intuitive, that is, they begin to become analogical and not deductive.
Deductive thinking is conscious, deliberative, and "slow." Analogical and intuitive thinking is unconscious, nondeliberative, and "fast." So you're probably right that by learning to relegate many mathematical tasks to analogical thinking, one increases their ef... (read more)