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Programming needs to be taught alongside Algebra I. Especially in a language like Haskell or Scheme where algebraic refactoring of type signatures looks like no

by crb002 9y ago

Programming needs to be taught alongside Algebra I. Especially in a language like Haskell or Scheme where algebraic refactoring of type signatures looks like normal algebra notation.

sanderjd 9y ago
Learning multiple different highly abstract concepts at the same time does not seem like a solution to the difficulty of learning a single highly abstract concept.
- Jtsummers 9y ago
  My experience with this comes from college, but I disagree. I added a math major late into my education (I was one course from a minor, then 4 more from a major so why not?). I ended up in several math courses at once that were often taken separately, but specifically abstract algebra and a higher level (4xxx) linear algebra course. I pretty much aced both, though I probably would have gotten an A in them taken separately. The reason I did better, though, was that they were both algebra. They were both expressing the same concepts, but on different types of objects. The moment that that clicked in my head, my Monday lesson in linear became the clarified by my Tuesday lesson in abstract, which was further clarified by my Wednesday linear. If you structure it correctly (particularly, with programming, by selecting appropriate problem domains for programming exercises), I'm quite confident you could create a better math and programming education experience by properly pairing the two.
  - sanderjd 9y ago
    Maybe! I just don't think programming (even in Haskell!) is similar enough to algebra for this to be effective, no matter how much we all want it to be. Programming still requires a mental model of how machines compute, which is a good thing to learn about but not (in my opinion!) a strong complement to learning math. Don't get me wrong though, I learned programming and calculus at the same time, I'm not saying you can't learn both at once, I just don't think one helps much in learning the other, for a novice in both.
bitwize 9y ago
Scheme doesn't really look like normal algebra notation. Though, arguably, it resulted from McCarthy's attempt to invent an algebraic notation for general expression evaluation (the original Lisp).

by crb002 9y ago

Programming needs to be taught alongside Algebra I. Especially in a language like Haskell or Scheme where algebraic refactoring of type signatures looks like normal algebra notation.

sanderjd 9y ago

Learning multiple different highly abstract concepts at the same time does not seem like a solution to the difficulty of learning a single highly abstract concept.

Jtsummers 9y ago
My experience with this comes from college, but I disagree. I added a math major late into my education (I was one course from a minor, then 4 more from a major so why not?). I ended up in several math courses at once that were often taken separately, but specifically abstract algebra and a higher level (4xxx) linear algebra course. I pretty much aced both, though I probably would have gotten an A in them taken separately. The reason I did better, though, was that they were both algebra. They were both expressing the same concepts, but on different types of objects. The moment that that clicked in my head, my Monday lesson in linear became the clarified by my Tuesday lesson in abstract, which was further clarified by my Wednesday linear. If you structure it correctly (particularly, with programming, by selecting appropriate problem domains for programming exercises), I'm quite confident you could create a better math and programming education experience by properly pairing the two.
- sanderjd 9y ago
  Maybe! I just don't think programming (even in Haskell!) is similar enough to algebra for this to be effective, no matter how much we all want it to be. Programming still requires a mental model of how machines compute, which is a good thing to learn about but not (in my opinion!) a strong complement to learning math. Don't get me wrong though, I learned programming and calculus at the same time, I'm not saying you can't learn both at once, I just don't think one helps much in learning the other, for a novice in both.

bitwize 9y ago

Scheme doesn't really look like normal algebra notation. Though, arguably, it resulted from McCarthy's attempt to invent an algebraic notation for general expression evaluation (the original Lisp).