Comment by ARandumGuy | Hacker News Reader

Comment by ARandumGuy | Hacker News Reader

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Why do we teach kids how to do basic arithmetic by hand? After all, calculators are basically ubiquitous at this point. Why waste the time teaching a skill that's not necessary as an adult?

The reason is because doing arithmetic by hand teaches kids how math actually works, while using a calculator just teaches them how to find the answer. This base-level understanding is crucial for understanding more advanced math. But it's also important for making mental estimations, or just having a basic grasp on how the world works.

This is why students using ChatGPT is a problem. If you never put in the actual work in the first place, you never gain any actual understanding. A doctor "great at using ChatGPT" won't know how to check the results carefully if they've relied on ChatGPT for their entire education. Having a baseline skill set is crucial for evaluating LLM output, and for handling situations that LLMs can't handle. And there will always be situations LLMs can't handle, regardless of how advanced genAI becomes.

> Why do we teach kids how to do basic arithmetic by hand?

I think kids waste way too much time doing hard arithmetic by hand. As a particularly egregious example, I visited a Montessori primary school where they demonstrated what is essentially a complex single player board game, for calculating square roots by hand. It's a process whereby a 5th grader would take ~10 minutes to calculate the root of a 3 digit number, by moving dozens of pins around. It looked so silly, and while other Montessori equipment offers geometrical intuition, this one seemed to offer none. Squaring with trial and error would have been so much easier.

Other more typical examples are of kids spending hundreds of hours practicing long multiplication and long division of e.g. 4 digits, and then getting punished and stressed out about having made silly mistakes. While in the real world, no one in their right mind would choose to perform these calculations by hand any more, and would instead use a tool incapable of making arithmetic mistakes.

I don't have a clear solution, but would tend towards an educational system that teaches only the very basics of performing each mathematical operation (probably up to the level the average literate adult would do mentally), and then focus the rest of the time on problems where the students are the ones posing the question, using a calculator/computer to solve it, and then check whether the answer makes sense in the original context.

EDIT: For those curious about it, I just found a blog post demonstrating the logic behind this square root peg board. The author of the blog argues that it does help build understanding, but from what I saw, I would politely disagree.

https://borisreitman.medium.com/square-roots-the-montessori-...

Obviously there's a balance to be struck. There are certainly schools and teachers that teach arithmetic poorly, and there's a practical limit to the amount of hours spent doing equations before it becomes tedious busywork.

But I still think it's important that kids are taught how to do arithmetic by hand. And part of that will involve repetition, both to help reinforce and practice skills, and so educators can more accurately gauge a student's ability. You can't just bypass the need to sit down and do the work, even if the exact amount of work necessary is debatable.

This argument can be extended downwards infinitely. You can argue against teaching addition and writing of any form with this mindset.

I also think this argument means that theoretically someone with a 6th grade education and a 12th grade education should have the same economic output, as they both know how to read and add/multiply numbers. In real life the reason someone drops out before/during high school is always extenuating life circumstances, so the outcomes are much worse for them. But in a world where that didn't happen, do you think the outcomes would be essentially identical?

There are too many confounding variables. But yes, I think that in a future world where kids who grow up in a stable family can choose to easily move between schooling and the real world (including work experience, travel, alternative education and just the occasional slacking off), you'll see improved outcomes for those who do these other things.

> what is essentially a complex single player board game

Perhaps this sounds silly, but I think that’s actually deeply interesting. There is a profoundly deep relationship between calculation and games. This applies not just to ordinary arithmetic, but also things like game theoretic proofs to prove the soundness of logical inference rules. Exposing children to that relation, even with a toy case, sounds like it could be fruitful.

This seems like it's replying to a misunderstanding of their comment.

> A doctor "great at using ChatGPT" won't know how to check the results carefully if they've relied on ChatGPT for their entire education.

They didn't rely on ChatGPT for their education; they relied on ChatGPT for finishing homework. If they go over the generated essay and make sure it doesn't have any inaccuracies and they consistently do so correctly, what's the problem?

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