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Comment by AnEro | Hacker News Reader

When I use a calculator, I atleast try to get with in a few digits of what I think the anwser is in my head. Mostly since when I was younger I had a very passionate teacher about how much slower everyone is now because of calculators on simple math. I just apply the same thing with LLMs, just try and think of how and what I would have said and see how close I was. Only thing I change is I don't trust the anwsers and accept some nuance in the given context. It's a double edge sword because then I crash out over it more than if I don't. When it over and under explaining the wrong sections or when it gets to an objectively terrible solution that technically anwsers the question. It feels like a student trying to get brownie points and/or give fluffed anwsers for the sake of not leaving anything blank on a test.

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OT, but if we made kids learning math use log tables and slide rules for all their calculations I expect that they would engage their brains more and actually think about what they were doing, ie: form a strategy to solve a problem before they started calculating. Also I think that they would get a better "feel" for working numbers in general. I have no evidence, but I suspect that by abstracting away a lot of the "gruntwork" of calculating, we've really hampered people's development in math.

Unfortunately this adds quite a bit of overhead and would make everything take a lot more time. It might be worth it though.

I'm working on this! https://magworld.pw

Looks interesting, I'll give this a listen and a read. :)

This is really cool! After entering the software field, I felt uncomfortable not having a sense of relative size while working with digital storage units. Piece of mind was achieved after sitting down and mapping the units (Gb, Mb, etc) to common artifacts(audio file, plain text, database).

I've been planning forever to do something similar with length, duration, power, etc.

That's basically what we're doing! I'd be curious if it helps you. Send me an email if you wind up listening to or reading anything from the site.

> Also I think that they would get a better "feel" for working numbers in general.

This is called "number sense". I'm pretty sure we do have evidence under searches for that term, it was well-enough known as a concept when I was in school decades ago and is the reason we don't use calculators when first learning math.

Having done a bit of teaching/grading for computer science, I don't know how to do it reliably nowadays.

For math we ask the whole reasoning and not just the answer, but here what do you do ?

What I resorted to is a live code review with the student, and it becomes very quickly apparent if they know the code, know what the AI said about the code, or didn't bother to read the code at all.

But it's way more time and effort.

Yeah, I've always tried to train myself to do calculations in my head as much as reasonably possible when learning about mathematical objects, etc. Like when I was learning linear algebra I made myself invert 4x4 matrices in my head. (Pen and paper is also cheating!) Calculators and computers have been better than me at this sort of thing for my entire life, so in some sense this isn't a change?

We had Mental Math sessions in class. The goal was to teach you how to do math without pen/paper, calculators were not even an option. I try to teach some of this to my 6 y o.

> The goal was to teach you how to do math without pen/paper, calculators were not even an option. I try to teach some of this to my 6 y o.

It works quite well. I do the math lessons during bath-time daily with my 6 yo. He's up to the point were he can add multiply pretty much any number by 2, 3 or 4 as long as the product is under 3 digits.

Going from adding single digits to multiplication of random 2-digit numbers by 4 with lessons only during bath-time (no paper or whiteboard) gives a child a great deal of confidence with numbers.

It's great. Personally I am the worst at mental math and resort to a calculator for any stuff beyond 2 digits multiplications, but at least I know how to do it (very slowly) if I have to, and this means I could have an intuition of an erroneous answer a calculator could have given me (for simple stuff but you get my point).

Computer science teaching really needs to be prepared to do the same progression as math, but even harsher because LLMs are not even deterministic.

The calculator comparisons are truly meaningless imo, a calculator does nothing if you don’t know how to use it and what to input, an LLM circumvents all that, but a lot of people seem to think it’s the same.

It’s not a perfect analogy. I’m approaching it from perspective of a more universal experience of people losing aspects of a skill over time by using a tool. When ultimately the skill learned with out it allows them to use the tool much better

Ah yes, I very much agree on that framing.

Socrates thought similar of reading and writing, if that analogy lands any better.

When I (and I assume others) use the calculator analogy, it's mainly about the teaching method.

You learn math without a calculator, then you learn how to do the boring parts with a calculator that you would still be able to do (slower) if needed.

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