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https://news.ycombinator.com/item?id=6187014 https://news.ycombinator.com/item?id=6187014 With that being said, I've always loved this essay. As of recently, I

https://news.ycombinator.com/item?id=6187014 https://news.ycombinator.com/item?id=6187014 With that being said, I've always loved this essay. As of recently, I've viewed it as relevant to the recent argument that programming should be a requirement in American public schools, either as a tool in math and science classes or a free-standing course. This kind of mathematical reform might actually be a prerequisite for programming and computer science, given that it would develop mathematical maturity much more effectively than the current system does.

jnbiche 12y ago
Yes, but Lockhart is arguing against any practical applications of math in the early years. I'm almost certain he would oppose any attempt to connect math to programming, for the reasons outlined in his essay (roughly, "math should be about imagination and playing, not applications"). In fact, I disagree with this essay, for reasons outlined in [1]. 1. https://news.ycombinator.com/item?id=8847132 https://news.ycombinator.com/item?id=8847132
- birdsareweird 12y ago
  Who do you think mathematical programming has to be practical?
  - saraid216 12y ago
    You're taking away the wrong thing from the grandparent post. If you teach math as a prerequisite for something else, you're naturally going to be undervaluing it. Math should be taught for the sake of learning math, not because it's the gateway to something else. It is, yes, but that's not the point.
    - birdsareweird 12y ago
      You know the problem with that sentiment? Most people do not find abstract patterns and rote symbolic manipulation to be interesting. They simply don't, and if you teach math class mistakenly assuming they do, 90% tunes out. If you can show them how those abstract patterns reflect things in nature, and how those symbolic manipulations represent ideas and algorithms and systems, and can explain complicated things, that's something else. e.g. You don't need computer graphics to teach linear algebra, but how many people who 'know' matrix algebra know that the columns of a matrix are the basis vectors for the principal axes, and that matrix multiplication is the (affine) transform tool from photoshop? I would also suggest that if you want to get kids interested in trigonometry and you fail to mention that every single thing in a 3D video game is made out of triangles, you are a bad teacher and you should feel bad.
      - Ntrails 12y ago
        Rote symbolic manipulation is not inherent to solving the mathematics described in the paper. That's part of the point. I'd argue that the endless swarms of people playing bejeweled variants suggests pattern analysis is extremely popular. Mathematics is currently taught with the excuse "you'll need this later, it's useful - honest". If you're advocating an additional helping of that, why is THIS future possible application relevant in a way that the others aren't?
      - saraid216 12y ago
        I'm not interested in teaching math to people who don't want to learn math, honestly. It baffles me why so many people think that if someone is uninterested in math, they must be tricked into being good at it anyways. Teaching shouldn't be so dishonest.
        birdsareweird 12y ago
        Why do you think creating interest from real life is going to make them not "want to learn math"? That makes no sense. Teaching is all about benevolent dishonesty. The first thing a teacher does is dumb themselves down to their students' level.
        saraid216 12y ago
        > Why do you think creating interest from real life is going to make them not "want to learn math"? That makes no sense. I don't. I think it's entirely possible to cram knowledge into people's minds unwillingly. But you're making an unnecessary assumption: that you have to teach everyone math. Why is that?
        birdsareweird 12y ago
        Why do we teach everyone history? Because it's valuable to know where we came from, and to realize that whatever's going on today, it's probably happened before. Why do we teach everyone math? Because it creates quantitative literacy, because it helps people deal with systems and complexity, to break down problems logically, and to not let biases get in the way of the truth. Or at least that's what I wish it would be focused on, instead of producing droids who know how to execute symbolic algorithms.
- yawaramin 12y ago
  Something like MIT Scratch can be both 'imagination and playing' and 'applications' (programming).

jnbiche 12y ago

Yes, but Lockhart is arguing against any practical applications of math in the early years. I'm almost certain he would oppose any attempt to connect math to programming, for the reasons outlined in his essay (roughly, "math should be about imagination and playing, not applications"). In fact, I disagree with this essay, for reasons outlined in [1]. 1. https://news.ycombinator.com/item?id=8847132 https://news.ycombinator.com/item?id=8847132

birdsareweird 12y ago
Who do you think mathematical programming has to be practical?
- saraid216 12y ago
  You're taking away the wrong thing from the grandparent post. If you teach math as a prerequisite for something else, you're naturally going to be undervaluing it. Math should be taught for the sake of learning math, not because it's the gateway to something else. It is, yes, but that's not the point.
  - birdsareweird 12y ago
    You know the problem with that sentiment? Most people do not find abstract patterns and rote symbolic manipulation to be interesting. They simply don't, and if you teach math class mistakenly assuming they do, 90% tunes out. If you can show them how those abstract patterns reflect things in nature, and how those symbolic manipulations represent ideas and algorithms and systems, and can explain complicated things, that's something else. e.g. You don't need computer graphics to teach linear algebra, but how many people who 'know' matrix algebra know that the columns of a matrix are the basis vectors for the principal axes, and that matrix multiplication is the (affine) transform tool from photoshop? I would also suggest that if you want to get kids interested in trigonometry and you fail to mention that every single thing in a 3D video game is made out of triangles, you are a bad teacher and you should feel bad.
    - Ntrails 12y ago
      Rote symbolic manipulation is not inherent to solving the mathematics described in the paper. That's part of the point. I'd argue that the endless swarms of people playing bejeweled variants suggests pattern analysis is extremely popular. Mathematics is currently taught with the excuse "you'll need this later, it's useful - honest". If you're advocating an additional helping of that, why is THIS future possible application relevant in a way that the others aren't?
    - saraid216 12y ago
      I'm not interested in teaching math to people who don't want to learn math, honestly. It baffles me why so many people think that if someone is uninterested in math, they must be tricked into being good at it anyways. Teaching shouldn't be so dishonest.
      - birdsareweird 12y ago
        Why do you think creating interest from real life is going to make them not "want to learn math"? That makes no sense. Teaching is all about benevolent dishonesty. The first thing a teacher does is dumb themselves down to their students' level.
        saraid216 12y ago
        > Why do you think creating interest from real life is going to make them not "want to learn math"? That makes no sense. I don't. I think it's entirely possible to cram knowledge into people's minds unwillingly. But you're making an unnecessary assumption: that you have to teach everyone math. Why is that?
        birdsareweird 12y ago
        Why do we teach everyone history? Because it's valuable to know where we came from, and to realize that whatever's going on today, it's probably happened before. Why do we teach everyone math? Because it creates quantitative literacy, because it helps people deal with systems and complexity, to break down problems logically, and to not let biases get in the way of the truth. Or at least that's what I wish it would be focused on, instead of producing droids who know how to execute symbolic algorithms.
yawaramin 12y ago
Something like MIT Scratch can be both 'imagination and playing' and 'applications' (programming).