This isn't obvious for those of us from a pre-device era.
Particularly the device isn't something you bought, but instead built a "device internally", whether that's a fast-lookup or a turn by turn reckoning.
> When you rely on something to make choices for you, you don't learn.
My entire history with Calculus is basically "Here's a bunch of random formulae to memorize" and I could do that very very efficiently.
The goal was speed of solving a problem when learning Mathematics, but then you get to Physics classes full of problems without actual equations provided and then your memory just gives up throwing possibilities.
But once a crutch works, it works again. Unfortunately, the crutch only takes you to the bottom of the hill, no more.
And then suddenly, you're in a crowd of people who have made mistakes, recognize mistakes made and correct mistakes instead without an instructor. Sort of like swimming out to the ocean with water wings on and suddenly they start to deflate.
That's when this starts to look like a fatal error rather than an easily recoverable one & even if you survive it, you're stuck with a permanent impostor syndrome.
Particularly the device isn't something you bought, but instead built a "device internally", whether that's a fast-lookup or a turn by turn reckoning.
> When you rely on something to make choices for you, you don't learn.
My entire history with Calculus is basically "Here's a bunch of random formulae to memorize" and I could do that very very efficiently.
The goal was speed of solving a problem when learning Mathematics, but then you get to Physics classes full of problems without actual equations provided and then your memory just gives up throwing possibilities.
But once a crutch works, it works again. Unfortunately, the crutch only takes you to the bottom of the hill, no more.
And then suddenly, you're in a crowd of people who have made mistakes, recognize mistakes made and correct mistakes instead without an instructor. Sort of like swimming out to the ocean with water wings on and suddenly they start to deflate.
That's when this starts to look like a fatal error rather than an easily recoverable one & even if you survive it, you're stuck with a permanent impostor syndrome.