Oddbean

There are many learning materials like this, from a time before search engines and inexpensive calculators. I sometimes think about how this kind of thing might have expanded in a world without computers as we know them. And I wonder what other kinds of insights might have been unlocked by millions of people trained to think in such ways. 3/

It's tempting to focus on the stunted creativity, the time wasted memorizing without understanding. And I think that's likely the bulk of the effect of such a system. But, I don't think it's the whole story. Just something I'm thinking about in the context of one of the sci fi stories I've been thinking about. 4/4

@134318c2 like, there was just a kinda background assumption until the mid 20th that the world would continue to get more complex, and we'd have to adapt & train human brains increasingly to manage that growing complexity but instead we just tacked silicon onto our extended phenotype

@0b086a8e As much as I am skeptical of my dad's idea of "learning calculus" Which was to keep reading that book over and over until you could answer all the questions correctly. My dad did understand calculus well enough to help me with my homework. Though I liked how my mom would explain it better, she always started with the theory. My dad was all examples. And "Don't forget this fact!" He'd start problems by thinking of the problems they were like he'd done before...

@134318c2 "thinking of the problems they were like he'd done before" Yup. As you said earlier in the thread this can also be one pathway to the deep understanding (possibly even the best pathway for a small subset of folks) but more commonly leads to purely instrumental "understanding". Interestingly that second pathway is (for me, personally) how I best understand many fiction #writing tools & techniques - "bulk familiarity" unlocks the pattern/purpose more easily than explanation, oftentimes

@134318c2 to this day... the vast majority of kids taking calculus aren't expected to question, wonder, understand... either. it was the first math class that bored me. so MANY machines to learn. i did my questioning outside of math class context.

@134318c2 there is a vast genre of mediocre children dinosaur books that are written in that spirit. except unlike the math books this ones tend to be filled with innacuarate, outdated and sometimes outrigh false claims. you dont even get sterile contextless facts

@134318c2 It’s currently in storage, but the have a math primer from c. 1900 that is intensely practical oriented word problems. What caught me were the problems that would now be taught as algebra were then taught as brute force arithmetic.