There are many subskills that you must be proficient in without tools, before you can learn more interesting skills. You need to know how to do multiplication by hand before you rely on a calculator. If you can't do multiplication with a calculator, you're not going to be able to make sense of the concepts in Algebra.

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noosphr 4 days ago | parent | next [-]

Algebra has nothing to do with long hand multiplication, people who say otherwise can't do either.

We know, because we taught computers how to do both. The first long multiplication algorithm was written for the Colossus about 10 minutes after they got it working.

The first computer algebra system that could manage variable substitution had to wait for Lisp to be invented 10 years later.

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twic 4 days ago | parent [-]

Baby rather than Colossus. Colossus wasn't programmable.

	▲	noosphr 4 days ago \| parent [-]
		>Jack Good, a veteran of Colossus practice at Bletchley Park, later claimed that, if appropriately configured, Colossus could almost have carried out a multiplication but that this would not have been possible in practice because of constraints on what could be accomplished in a processing cycle. We have no reason to doubt this, though it would presumably have required special settings of the code wheels and message tape and been, even if possible, a rather inefficient alternative to a desktop calculator. This fact has been offered as proof of the flexibility of Colossus, which in a sense it does attest to: a device designed without any attention to numerical computations could almost have multiplied thanks to the flexibility with which logical conditions could be combined. Yet it also proves the very real differences between Colossus and devices designed for scientific computation. Multiplications were vital to computations, and a device that could not multiply would not, by the standard of the 1940s, be termed a “computer “or “calculator.” https://www.sigcis.org/files/Haigh%20-%20Colossus%20and%20th... The limitation seems to have been physical rather than logical.

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mlloyd 4 days ago | parent | prev | next [-]

There are also many subskills not worth learning to some people. Sometimes traversal is what's needed and not understanding. (Though I'm never going to knock gaining more understanding)

Tools allow traversal of poorly understood, but recognized, subskills in a way that will make one effective in their job. An understanding of the entire stack of knowledge for every skill needed is an academic requirement born out of a lack of real world employment experience. For example, I don't need to know how LLMs work to use them effectively in my job or hobby.

We should stop spending so much time teaching kids crap that will ONLY satisfy tests and teachers but has a much reduced usefulness once they leave school.

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superposeur 4 days ago | parent | prev | next [-]

Yes, totally. Relevant study: https://www.media.mit.edu/publications/your-brain-on-chatgpt...

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petra303 4 days ago | parent | prev | next [-]

I doubt they’re talking about entry level maths.

	▲	bootsmann 4 days ago \| parent [-]
		Why should other subjects be any different?

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sdwr 4 days ago | parent | prev [-]

Are multiplication and long division by hand really necessary skills?

I never need to "fall back" to the principles of multiplication. Multiplying by the 1s column, then the 10s, then the 100s feels more like a mental math trick (like the digits of multiples of 9 adding to 9) than a real foundational concept.