What's your opinion on calculators?
Update: I meant to compare calculators to something like a slide ruler for logarithms. I'm not from US and I tend to forget that some people use calculators to take 20% of 500.
Update: I meant to compare calculators to something like a slide ruler for logarithms. I'm not from US and I tend to forget that some people use calculators to take 20% of 500.
I got an engineering degree and don't remember ever being required to do math without a calculator. Of course, some things are easier if you don't need to bust out a calculator for everything.
This is the author's lament. These students are skipping over personal mastery.
With a calculator, the end result is still the same: a (typically numerical) answer of some kind. Writing one's own essay vs. getting an LLM to regurgitate it results in vastly different outcomes.
I'm glad that we have calculators and computing devices, but I'm not glad that they have made teens with basic numeracy into an endangered species. Many tools we use expand our understanding, but the calculator causes our arithmetic skills to atrophy.
The point is, one is hard pressed to find anyone who can do much arithmetic-- even trivial things.
But, if symbolic manipulation is done by hand and then numbers just plopped in to get final result and estimation if answer is realistic enough. Well I think that is fair enough.
And spreadsheets are also useful when you need to add up bunch of things or multiply them.
LLMs are different.
A closer analogy would be something like computer algebra systems, especially integration. We can offload differentiation cheaply, immediately, and perfectly, but integration will frequently have a "unable to evaluate" result. I genuinely wonder whether integral-requiring-workers are better or worse at it as a result of growing up with CAS tools. People on the periphery (a biologist, for example) are undoubtably better off since they get answers they couldn't get before, but people on the interior (maybe a physicist) might be worse at some things they wish they could do better, relative to those who came up without those tools.