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But the problem is that we spend ~9 years on those drills which is more time than a typical engineering student spend on algebra and above. How come we can teac

But the problem is that we spend ~9 years on those drills which is more time than a typical engineering student spend on algebra and above. How come we can teach so much higher math in such a short amount of time? It is not possible from scratch, the reason we can do it is because some bored students played around with the drills instead of just doing them and thus learned a lot of related concepts which are cached in on in later years. The losers are those who just spent years learning how to do the drills, getting good grades but didn't learn anything worthwhile at all. It would be good if we could catch those and correct their behavior before they had wasted 9 years on it, but as is we don't notice that most students fail to learn anything before we test them on more interesting problems in high-school. Note: I am not saying that we shouldn't teach arithmetic, on the contrary I'd argue that arithmetic is one of the most important things to learn in math since everything else is built on top of that intuition. We just have to realize that we practice arithmetic to build intuition and not to become a human calculator.

adrianN 7y ago
An engineering student can learn more advanced math in a shorter time because a) they're older, b) they have mastered the elementary stuff already.
- dagw 7y ago
  Also let's be honest, how many engineers actually learn the more advanced math. Most of them cram it into their brain for the test and then promptly forget it.
abdullahkhalids 7y ago
> How come we can teach so much higher math in such a short amount of time? 1. Because, higher ed students are a subset of school students who are on average better than and more interested in solving math problems. 2. Because, the mental micro-skills needed for higher math are many and diverse and learning one during school doesn't make you better at any other. You have to learn all of them, which is why initial training takes longer. Once you have most of the micro-skills trained, you can use them to cover new material faster. Micro-skills include fast mental arithmetic, application of logical tautologies (If A=>B, then NOT B=> NOT A), visualization skills, the hand-eye coordination to draw and recognize complex symbols. There are also macro-life-skills like being able to sit and listen to a teacher for an hour without getting bored.
bitwize 7y ago
Because it takes about 9 years for a kid with an underdeveloped brain to learn the skills and the self-discipline necessary to stick with a problem and call upon lower level math skills on demand. And no, they don't need to understand the rationale behind things like carrying and borrowing. They just need to do it. Understanding can come later. It is much easier to drill known good practices to mastery than it is to explain why they work and teach them to mastery. These are kids whose parents are still in the "because I said so" stage of parenting. Intuition comes from mastery. I can factor polynomials in my head; I'd be flummoxed at that task if I didn't know my times tables by heart. And I wouldn't know those if I didn't drill. Drilling is paramount to early math education. Nothing else that's been tried works. Let me put it this way: who is more likely to get a programming job, a bricoleur with an incorrigible need to understand HTTP, networking, etc. from first principles before he can use them, or a certified professional who has chosen a framework and practiced building apps using that framework and related best practices, while knowing nothing about how the framework actually works? The world needs surprisingly few bricoleurs and surprisingly many people who can get shit done.

adrianN 7y ago

An engineering student can learn more advanced math in a shorter time because a) they're older, b) they have mastered the elementary stuff already.

dagw 7y ago
Also let's be honest, how many engineers actually learn the more advanced math. Most of them cram it into their brain for the test and then promptly forget it.

abdullahkhalids 7y ago

> How come we can teach so much higher math in such a short amount of time? 1. Because, higher ed students are a subset of school students who are on average better than and more interested in solving math problems. 2. Because, the mental micro-skills needed for higher math are many and diverse and learning one during school doesn't make you better at any other. You have to learn all of them, which is why initial training takes longer. Once you have most of the micro-skills trained, you can use them to cover new material faster. Micro-skills include fast mental arithmetic, application of logical tautologies (If A=>B, then NOT B=> NOT A), visualization skills, the hand-eye coordination to draw and recognize complex symbols. There are also macro-life-skills like being able to sit and listen to a teacher for an hour without getting bored.

bitwize 7y ago

Because it takes about 9 years for a kid with an underdeveloped brain to learn the skills and the self-discipline necessary to stick with a problem and call upon lower level math skills on demand. And no, they don't need to understand the rationale behind things like carrying and borrowing. They just need to do it. Understanding can come later. It is much easier to drill known good practices to mastery than it is to explain why they work and teach them to mastery. These are kids whose parents are still in the "because I said so" stage of parenting. Intuition comes from mastery. I can factor polynomials in my head; I'd be flummoxed at that task if I didn't know my times tables by heart. And I wouldn't know those if I didn't drill. Drilling is paramount to early math education. Nothing else that's been tried works. Let me put it this way: who is more likely to get a programming job, a bricoleur with an incorrigible need to understand HTTP, networking, etc. from first principles before he can use them, or a certified professional who has chosen a framework and practiced building apps using that framework and related best practices, while knowing nothing about how the framework actually works? The world needs surprisingly few bricoleurs and surprisingly many people who can get shit done.