It's funny because I actually think learning math the old fashioned way is super important. I used to struggle with math a lot as I'd always had calculators. I went back as an adult and got some old 1980s math textbooks based on Soviet pedagogy (widely considered the best for math at the time) and the impact has been huge. I've been building from the ground up math skills that got entirely skipped in school, and feel much better about it now. Calculators are useful but when LEARNING math they should not be used imo. Except maybe to check an answer after you already get it. Doing difficult things is good.

Tech evangelists rely heavily on logical fallacies. False equivalence is one of the main ones. "A thing happened before therefore this tech is nothing to worry about". They're redirecting the argument to bait people to try to prove why calculators are bad. But of course the past already happened and nobody is going prove otherwise.

Yep, especially in mathematics a calculator is not much of a help in calculus. The moment you put numbers in whatever thing you wanna solve is the point where the hard part is already done.

but it’s not comparable at all unless the math you’re doing is simple arithmetic.

That's what they were studying on the math side

For the first experiment with 354 participants, one group was tasked with solving 15 basic fraction problems

Also

If you’re doing calculus, the skill you’re working on isn’t arithmetic, so the calculator isn’t much of a factor.

Calculators would be a big factor in solving calculus problems. Haven't done calculus in a while but if I recall correctly you are breaking down or rearranging the problem into smaller steps that are more basic arithmetic. One part of a calculus problem could be finding out what the square root of 7 is , if you have a calculator to do that you're more likely to solve the problem more accurately and to not give up on the problem, which were the two metrics this study was looking at.

Over time yes, but this says skills were lost during a single session or short term. It was a random group of people, so unknown on what skills they did have before. I think what they observed wasn't a permanent loss, but a placebo effect of having extra help and it was taken away, so for the rest of the test they felt lacking.

My example of calculators was implying one that could do the test work. All calculators have trig functions, and some have calculus abilities. Would a student forget how to find cosine if the calculator was taken away, or do a derivative of a function? Not in one test. But if they were using it first half and then had to do it themselves for the rest, I imagine there's some psychological stuff going on that makes you feel like you've lost that skill.

A neat result from pedagogical studies is that being given the worked solutions to new problems to study from is much more effective for learning the material than simply practicing.

Finally, something to justify my still-existent hatred of my middle school geometry teacher for literally telling us 'the theorems are on the board' any time we asked her for help trying to solve a problem or for her to show us an example problem. Why the fuck were you even teaching.

There are different ways to learn, some work better for certain people than others.

I would think that the best way to learn is neither of these options, but to be taught how to do the work by someone who understands (like a teacher) and then made to do it after it has been thoroughly explained to you and practiced with you.

That’s what works best for me anyhow, that or literally reading the textbook, lol, but that’s less efficient time-wise.

That was one of my gripes with my experience in college vs hs. In my hs at least, we were taught the most difficult combination of a problem and then everything that we practiced would be able to be worked out from there. In college, we were often taught the simplest example and somehow expected to derive the most difficult version of it on the problem sets. That's how you get students who study really hard for an exam and half of them fail. They never taught the proper way to solve the problem!

I was out of college by the time LLMs came out but I still believe they could be helpful in this scenario if fine tuned and limited as a tutor not an answer-giver. Obviously if you have access to a good human tutor (who doesn't call you dumb like my friend had at the time), but I didn't have access to one.

Immediate practice on something you haven't been walked through yet? I guess the way I phrased it made it sound like jumping in yourself with no guide is better. You definitely need to be taught first, or at least as you go, and not figure it out on your own. The point was that simply watching someone do something isn't enough, you have to develop the process of getting to that point yourself. But only after seeing that route, otherwise you will take lots of wrong paths.

Yes, I'm aware of what they tested and what fractions are...

I was just expanding the point to other things that are comparable. And an LLM for a reading comprehension test is exactly what a large language model would be best suited for, so in essence a language "calculator".

Doesn't change the rest of the discussion, which was about the brain's ability to jump back into things when the crutch is taken away.