> if you have the base knowledge and skills readily available in your mind.
I have the base knowledge and skill readily available to perform basic arithmetic, but I still can't do it in my mind in any practical way because I, for lack of a better description, run out of memory.
I expect most everyone eventually "runs out of memory" if the values are sufficiently large, but I hit the wall when the values are exceptionally small. And not for lack of trying – the "you won't always have a calculator" message was heard.
It wasn't skill and knowledge that was the concern, though. It was very much about execution. We were tested on execution.
> If you're learning about linear algebra but you have to type in every simple multiplication of numbers into a calculator...
I can't imagine anyone is still using a four function calculator. Certainly not in an application like learning linear algebra. Modern calculators are decidedly designed for linear algebra. They need to be given the rise of things like machine learning that are heavily dependent on such.
I have the base knowledge and skill readily available to perform basic arithmetic, but I still can't do it in my mind in any practical way because I, for lack of a better description, run out of memory.
I expect most everyone eventually "runs out of memory" if the values are sufficiently large, but I hit the wall when the values are exceptionally small. And not for lack of trying – the "you won't always have a calculator" message was heard.
It wasn't skill and knowledge that was the concern, though. It was very much about execution. We were tested on execution.
> If you're learning about linear algebra but you have to type in every simple multiplication of numbers into a calculator...
I can't imagine anyone is still using a four function calculator. Certainly not in an application like learning linear algebra. Modern calculators are decidedly designed for linear algebra. They need to be given the rise of things like machine learning that are heavily dependent on such.