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.
Where I live these are not allowed in the classroom until 7th grade or so, i.e. when the kids have learned the skills and can then employ calculators mindfully.
I will occasionally do long multiplication in my minds eye just to make sure I can lol. Anything more complicated than that, most people will not be doing anyway. University students however, almost universally do need to write sometimes. Similarly if I had decided to do something maths heavy at uni I would be expected to be able to do some pretty complex maths without a calculator first, even if I don't need to do that all the time. It's pretty standard that higher education requires a level of intellectual rigour that is totally unecessary for day to day life. In the case of ChatGPT, it's allowing people to completely bypass that process even in those settings. Meaning you NEVER learn to do it, not just that you don't do it day to day.
>Similarly if I had decided to do something maths heavy at uni I would be expected to be able to do some pretty complex maths without a calculator first, even if I don't need to do that all the time
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.
I order to get in to the engineering degree though you would have had to do maths exams in school that required you to have proficiency in doing maths without a calculator that the average person does not have and will never need. I did not do an engineering degree but I did do a higher level maths class in school. I failed 2/3 of the exams but that still means I have learnt to do calculator free maths to a higher level than the vast majority of the population has ever even considered. And they don't need to. Probably doesn't impact their lives at all. That doesn't mean that there aren't some people who should really should learn to do that stuff. There's a reason I abandoned the idea of Physics or similar disciplines as a university degree choice - because I did not have the maths foundation to build on. Any arts and humanities degree, if not any degree really needs a foundation of writing skills in the same way.
You don't allow students to use calculators for operations they haven't personally mastered. If you don't learn how to add two numbers on your own, the rest of your learning is in serious jeopardy.
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.
Not a super big fan, honestly. I'm a bit horrified when I see high school seniors who are smart, and have been through the entire HS math sequence... dig around in their backpack for a calculator to find 5 times 1.5 or 20% of 11.
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.
From my experience, the more advanced math you learn, the worse you become at arithmetic. I knew a lot of math majors in college, and all of them used calculators all the time.
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.
Calculators are reliable and predictable, so losing skill at that kind of calculation is a safe, compartmentalized offloading. We offload an extremely clearly defined set of tasks, and it gets executed cheaply, immediately, and perfectly.
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.