[tivert]

>> If you need Copilot to code in Python, have you really learned Python?

> Does it really matter though? It sounds awfully like when a school teacher said you're not going to have an calculator in your pocket.

Yes. A younger me had teachers say that to me, and that younger me thought they were wrong.

But it turns out they were right, and younger me was wrong. Calculator dependence created a ceiling built from "educational debt" that many years later severely limited my mathematical ability.

The problem is focusing too much on getting the "answer," and losing sight of building the abilities that allow you to get there with your own mind. Eventually the need to manipulate your automated crutch turns into a bottleneck.

[Aeolun]

It’s also kind of annoying to intuitively get to the correct answer and have everyone claim they can’t distinguish between that and you using a calculator.

I wonder if that would be an issue if nobody had any.

[golergka]

> Calculator dependence created a ceiling built from "educational debt" that many years later severely limited my mathematical ability.

Can you explain how your problems with arithmetic affected your ability to reason and prove things? I struggle to see how the two are connected.

[tivert]

Isn't it obvious? If you can't do arithmetic without a calculator, it makes it hard to do algebraic manipulation. (Un)luckly a calculator that could do that arrived in my lap just in time. Then you get to calculus, and it was the same story. I eked by with a lot of furious typing, but the mental workload of that made it untenable towards the end and I wasn't really gaining much anyway because of that. It would have been far better if I'd just hadn't been allowed to use a calculator from the start.

It didn't affect my ability to reason and prove things, just as long those things don't strongly require the knowledge and skills I should have gotten from the calculator shaped gap in my education. I lack a lot of the background knowledge and/or familiarity and comfort with many skills that I should have.

[golergka]

I think we're using the term “mathematical ability” in different ways. For me, it's an ability to prove a theorem, not to solve a differential equation.