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Arithmetic teaches systematic manipulation of abstract ideas which is the foundation for programming. It's not that arithmetic is the only thing that could be t

Arithmetic teaches systematic manipulation of abstract ideas which is the foundation for programming. It's not that arithmetic is the only thing that could be taught. I could think of many formal systems we could start with like lambda calculus. However arithmetic has the advantage of being immediately obviously useful, and also helps build intuition for other things. Also, the question is... Would people use post algebra math more if they knew it? I use calculus regularly when I'm building things for my kids. But I've noticed most people have stopped building things by hand anyway and instead rely on mass manufacture

solardev 3y ago
> Arithmetic teaches systematic manipulation of abstract ideas which is the foundation for programming. I know this is the conventional wisdom, that math is the underlying foundation for programming, etc. And I think that's true in the strictest sense: there is certainly a lot of math underlying all our software and hardware. But for learning basic programming? Honestly, I don't think it matters at all. I was first exposed to programming via Logo (as in the turtle mover), and while there's math there, I never really got beyond "bigger numbers move the turtle further / rotate it more". What really taught me logic & programming was the visual Warcraft 3 map editor, basically an early version of Scratch where you would compose logic out of nodes and make things happen in the game. Having that instant visual feedback of seeing units follow your automated commands was much more effective than sitting in a classroom doing math problems. These days there are a bunch more games like that (shameless plug: https://github.com/arcataroger/awesome-engineering-games https://github.com/arcataroger/awesome-engineering-games) > Would people use post algebra math more if they knew it? I use calculus regularly when I'm building things for my kids. But I've noticed most people have stopped building things by hand anyway and instead rely on mass manufacture Maybe people stopped building things because we focus too much on the theoretical in-classroom parts, as opposed to the hands-on stuff? I bet kids would be much happier, and learn a lot more, if they could swap out math hours for time in the woodshop, on the potter's wheel, or making maps for Roblox or Fortnite or whatever -- none of which require a heavy investment in math at first. (Reminds me of this place: https://www.blueoxmill.com/blue-ox-school.htm https://www.blueoxmill.com/blue-ox-school.htm, a continuation school for high schoolers who don't do well in the classroom. Instead, they learn woodworking, smithing, print-setting, etc. alongside the basic curricula). Then you could ease them into the math by showing them how can it help them make different shapes, then show them how real-world CAD and Unity/Unreal work, etc. Work backwards from instant gratification to ancient theory, and only cover the details if they really care. But otherwise just let them know that somebody else did the hard work (much appreciated) so they can move shapes around on a screen. It's not that different from graphics designers making art without ever having to know how a Bezier curve is calculated.
- anon291 3y ago
  Your conception of math is too limited. There are various different kinds of algebras. Elementary and middle education in the United States focuses on one of these (the natural numbers and their extensions). Programming deals with alternate algebras. However, intuition from one algebra typically carry over. For example, the intuition that all fields have an identity element (1 in 'grade school' arithmetic) carries over into computer arithmetic (which is the natural numbers modulo 2^n, n = 32 or 64 or something). In particular, you speak of learning programming via logo (an algebra in and of itself) and a map editor composing logical ops (boolean algebra is another subfield). The systematic manipulation of symbols that both of these require is the skill learned even in grade school math. Realistically, you can probably achieve the same results teaching any algebra systematically. What matters is the intuition, which only naturally develops if you're made to repeatedly do tedious problems. > Maybe people stopped building things because we focus too much on the theoretical in-classroom parts, as opposed to the hands-on stuff? Perhaps but I doubt it. In my experience, when thinking about new projects, we shy away from things where any of the parts seem hard. For myself in particular, I became way more into 3d game creation once I learned linear algebra, whereas before, I wanted to be able to do it, but was incapable, so i never started.
  - solardev 3y ago
    I'm sorry, I don't understand what you're saying anymore (you're being perfectly clear, it's just over my head now, not having studied math beyond the middle-high school level). As for the difficulty of new projects, it's not so much "we should teach kids to build houses before they can count to 100", but that learning by doing & mimicking often helps a lot of people compared to learning in the classroom by theory. If I wanted to make a game today, I'd probably just watch a Unity or Unreal intro on YouTube rather than starting with math... but that's just me.
    - anon291 3y ago
      Here's how I see this conversation. I say it's important to rote practice math. You say no we shouldn't because here are a bunch of things I wanted to do that didn't require numbers. I then point out that these are also math. I agree with you! We should teach these things. It would greatly simplify teaching higher level math. However, there is also an innate utility to the integers and their extensions. An extension is something like 'all quotients of integers'. Recall that the quotient of any two integers may or may not be an integer. The full set is the rationals, which we typically study (incorrectly in my opinion) as decimals and fractions. Nevertheless, there's utility in adopting the colloquial terminology, even if it's not useful for every field. > If I wanted to make a game today, I'd probably just watch a Unity or Unreal intro on YouTube rather than starting with math... but that's just me. I would suggest instead of teaching children to 'make games' we teach them to make the 'game engines'. The latter would involve math, whereas the former is more a creative endeavor.

solardev 3y ago

> Arithmetic teaches systematic manipulation of abstract ideas which is the foundation for programming. I know this is the conventional wisdom, that math is the underlying foundation for programming, etc. And I think that's true in the strictest sense: there is certainly a lot of math underlying all our software and hardware. But for learning basic programming? Honestly, I don't think it matters at all. I was first exposed to programming via Logo (as in the turtle mover), and while there's math there, I never really got beyond "bigger numbers move the turtle further / rotate it more". What really taught me logic & programming was the visual Warcraft 3 map editor, basically an early version of Scratch where you would compose logic out of nodes and make things happen in the game. Having that instant visual feedback of seeing units follow your automated commands was much more effective than sitting in a classroom doing math problems. These days there are a bunch more games like that (shameless plug: https://github.com/arcataroger/awesome-engineering-games https://github.com/arcataroger/awesome-engineering-games) > Would people use post algebra math more if they knew it? I use calculus regularly when I'm building things for my kids. But I've noticed most people have stopped building things by hand anyway and instead rely on mass manufacture Maybe people stopped building things because we focus too much on the theoretical in-classroom parts, as opposed to the hands-on stuff? I bet kids would be much happier, and learn a lot more, if they could swap out math hours for time in the woodshop, on the potter's wheel, or making maps for Roblox or Fortnite or whatever -- none of which require a heavy investment in math at first. (Reminds me of this place: https://www.blueoxmill.com/blue-ox-school.htm https://www.blueoxmill.com/blue-ox-school.htm, a continuation school for high schoolers who don't do well in the classroom. Instead, they learn woodworking, smithing, print-setting, etc. alongside the basic curricula). Then you could ease them into the math by showing them how can it help them make different shapes, then show them how real-world CAD and Unity/Unreal work, etc. Work backwards from instant gratification to ancient theory, and only cover the details if they really care. But otherwise just let them know that somebody else did the hard work (much appreciated) so they can move shapes around on a screen. It's not that different from graphics designers making art without ever having to know how a Bezier curve is calculated.

anon291 3y ago
Your conception of math is too limited. There are various different kinds of algebras. Elementary and middle education in the United States focuses on one of these (the natural numbers and their extensions). Programming deals with alternate algebras. However, intuition from one algebra typically carry over. For example, the intuition that all fields have an identity element (1 in 'grade school' arithmetic) carries over into computer arithmetic (which is the natural numbers modulo 2^n, n = 32 or 64 or something). In particular, you speak of learning programming via logo (an algebra in and of itself) and a map editor composing logical ops (boolean algebra is another subfield). The systematic manipulation of symbols that both of these require is the skill learned even in grade school math. Realistically, you can probably achieve the same results teaching any algebra systematically. What matters is the intuition, which only naturally develops if you're made to repeatedly do tedious problems. > Maybe people stopped building things because we focus too much on the theoretical in-classroom parts, as opposed to the hands-on stuff? Perhaps but I doubt it. In my experience, when thinking about new projects, we shy away from things where any of the parts seem hard. For myself in particular, I became way more into 3d game creation once I learned linear algebra, whereas before, I wanted to be able to do it, but was incapable, so i never started.
- solardev 3y ago
  I'm sorry, I don't understand what you're saying anymore (you're being perfectly clear, it's just over my head now, not having studied math beyond the middle-high school level). As for the difficulty of new projects, it's not so much "we should teach kids to build houses before they can count to 100", but that learning by doing & mimicking often helps a lot of people compared to learning in the classroom by theory. If I wanted to make a game today, I'd probably just watch a Unity or Unreal intro on YouTube rather than starting with math... but that's just me.
  - anon291 3y ago
    Here's how I see this conversation. I say it's important to rote practice math. You say no we shouldn't because here are a bunch of things I wanted to do that didn't require numbers. I then point out that these are also math. I agree with you! We should teach these things. It would greatly simplify teaching higher level math. However, there is also an innate utility to the integers and their extensions. An extension is something like 'all quotients of integers'. Recall that the quotient of any two integers may or may not be an integer. The full set is the rationals, which we typically study (incorrectly in my opinion) as decimals and fractions. Nevertheless, there's utility in adopting the colloquial terminology, even if it's not useful for every field. > If I wanted to make a game today, I'd probably just watch a Unity or Unreal intro on YouTube rather than starting with math... but that's just me. I would suggest instead of teaching children to 'make games' we teach them to make the 'game engines'. The latter would involve math, whereas the former is more a creative endeavor.