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> Knowing how to use a relational databases correctly requires no formal set theory. Very true, I guess. But the other way around, someone who has used relatio

by gizi 11y ago

> Knowing how to use a relational databases correctly requires no formal set theory. Very true, I guess. But the other way around, someone who has used relational databases, will immediately understand formal set theory and find it absolutely trivial. Another example would be regular expressions. Anybody who has ever used them will immediately recognize what Kleene's closure is about and effortlessly deal with it. I think that this is generally the case. If you first solve problems with tools that embody a particular theorem, and if later on you read up on that theorem, you will find that theorem trivially simple. In other words, math and computer science are only hard, when you have never used them. Since formal education does things systematically in the wrong order, students tend to consider math and computer science to be hard.

innguest 11y ago
Let me virtually shake your hand. I've always been successful teaching first from the concrete and then slowly abstracting - literally "pulling away" in Latin - as that's how I understand abstraction - it is the common ground between concrete things and therefore it was discovered from those things. To then try and teach students first from the most "pulled away" concept possible to only in the very end try and meet them in the real world - I just never understood that approach. Like you said, the government curricula prescribe an approach that is backwards to what makes sense. In Plato's Meno dialog, Socrates teaches a kid the abstraction called "irrational numbers" by having the kid draw triangles on the sand and then try and find the square root of 2. By playing with a concrete example (sqrt(2)) the kid learned the abstraction (that there are numbers that can't be shown as a fraction). This backwards way of thinking we're stuck with today is so pervasive that one approach I was developing to teach monads - by first writing each instance separately and then later "pulling away" to try and see the bigger picture - was recently excoriated in the Haskell IRC channel for not teaching the actual abstraction. The path is not the destination. You can't pull away (abstract) from nothing.
ccortes 11y ago
>someone who has used relational databases, will immediately understand formal set theory and find it absolutely trivial. This is simply not true, you may understand the very basics of it, but by no means you will understand set theory and much less find it trval by just using relational databases.

by gizi 11y ago

innguest 11y ago

Let me virtually shake your hand. I've always been successful teaching first from the concrete and then slowly abstracting - literally "pulling away" in Latin - as that's how I understand abstraction - it is the common ground between concrete things and therefore it was discovered from those things. To then try and teach students first from the most "pulled away" concept possible to only in the very end try and meet them in the real world - I just never understood that approach. Like you said, the government curricula prescribe an approach that is backwards to what makes sense. In Plato's Meno dialog, Socrates teaches a kid the abstraction called "irrational numbers" by having the kid draw triangles on the sand and then try and find the square root of 2. By playing with a concrete example (sqrt(2)) the kid learned the abstraction (that there are numbers that can't be shown as a fraction). This backwards way of thinking we're stuck with today is so pervasive that one approach I was developing to teach monads - by first writing each instance separately and then later "pulling away" to try and see the bigger picture - was recently excoriated in the Haskell IRC channel for not teaching the actual abstraction. The path is not the destination. You can't pull away (abstract) from nothing.

ccortes 11y ago

>someone who has used relational databases, will immediately understand formal set theory and find it absolutely trivial. This is simply not true, you may understand the very basics of it, but by no means you will understand set theory and much less find it trval by just using relational databases.