> 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.
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.
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-...