[acbart]

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.

[noosphr]

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.

[twic]

Baby rather than Colossus. Colossus wasn't programmable.

[mlloyd]

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.

[superposeur]

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

[petra303]

I doubt they’re talking about entry level maths.

[bootsmann]

Why should other subjects be any different?

[sdwr]

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.