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You're talking about engineers. Of course you need to understand some formulas if you're going to be an engineer. But for most of the people who aren't going to

by xnzakg 9y ago

You're talking about engineers. Of course you need to understand some formulas if you're going to be an engineer. But for most of the people who aren't going to do that, they're useless.

zanny 9y ago
Except the quadratic formula, just as an example, has a lot of positive qualities when taught to children: * The longform is fairly complex, so it is non-trivial to remember or recount. You can't just guess it (at least without knowledge well beyond it). So it looks like "magic". * It is a great introduction to what formulas are. They are non-trivial proofs of concepts that took research and logic to conclude. Learning logic and learning patterns, especially the non-obvious ones like the qf, are what promote analytical thinking. We need more of that, not less. Maybe the problem is more that kids are shown a magic formula and made to mechanically repeat it on a couple dozen data sets than to actually learn how to reach conclusions like the qf. Making kids proof it would probably be more valuable than making them repeatedly use it beyond a few times to assure them it is valid magic math.
- smichel17 9y ago
  One of my teachers back in high school made a comment to the effect of: "This class isn't about learning math. It's about practicing critical thinking skills."
- leshow 9y ago
  At the same time, I think some amount of repetition is important. You don't get a true understanding of something by just studying it, you need to apply it "on a couple dozen data sets" to get a feel for it, at least in my opinion. "Understanding" can initially be a bit transient.
WalterBright 9y ago
Teaching formula plugging is about as useless as teaching history as dates and names. Teaching how to derive the formula, why it works, etc., is very useful (even if one never needs to use it in post school life). Googling for answers is not learning. It's like lifting weights with a forklift is not exercising.
- petra 9y ago
  Not sure. Most people won't remember how to derive equations any,nor they need it, if they need to derive equations they could probably use some piece of software(symbolic solver?), and that's just takes time they could use to understand statistics, for example, which seems more useful.
  - WalterBright 9y ago
    > if they need to derive equations they could probably use some piece of software(symbolic solver?) The point is to understand. Having some software do it for you does not help with that.
gaius 9y ago
But for most of the people who aren't going to do that, they're useless. A system that cuts out a whole range of career paths simply because as a kid someone didn't like maths, is a bad one. Kids don't know what they need in life. That's why our culture takes decisions away from them until they are 18.
- ben_jones 9y ago
  At the same time you can't prep every kid to be a neurosurgeon. Or a prison guard. Or a helicopter machine gunner (which many would probably sign up to be if presented with the option at a young enough age!).
  - leshow 9y ago
    That's exactly why you need to teach a broad range of subjects, including basic math like simple calculus and arithmetic, so kids can actually make a choice about what they want to do. If they never get taught any of that, then they don't have the option available. And just to be clear, quadratic equation is basic math, and not anywhere close to 'prepping a kid to be a neurosurgeon'.

by xnzakg 9y ago

You're talking about engineers. Of course you need to understand some formulas if you're going to be an engineer. But for most of the people who aren't going to do that, they're useless.

zanny 9y ago

Except the quadratic formula, just as an example, has a lot of positive qualities when taught to children: * The longform is fairly complex, so it is non-trivial to remember or recount. You can't just guess it (at least without knowledge well beyond it). So it looks like "magic". * It is a great introduction to what formulas are. They are non-trivial proofs of concepts that took research and logic to conclude. Learning logic and learning patterns, especially the non-obvious ones like the qf, are what promote analytical thinking. We need more of that, not less. Maybe the problem is more that kids are shown a magic formula and made to mechanically repeat it on a couple dozen data sets than to actually learn how to reach conclusions like the qf. Making kids proof it would probably be more valuable than making them repeatedly use it beyond a few times to assure them it is valid magic math.

smichel17 9y ago
One of my teachers back in high school made a comment to the effect of: "This class isn't about learning math. It's about practicing critical thinking skills."
leshow 9y ago
At the same time, I think some amount of repetition is important. You don't get a true understanding of something by just studying it, you need to apply it "on a couple dozen data sets" to get a feel for it, at least in my opinion. "Understanding" can initially be a bit transient.

WalterBright 9y ago

Teaching formula plugging is about as useless as teaching history as dates and names. Teaching how to derive the formula, why it works, etc., is very useful (even if one never needs to use it in post school life). Googling for answers is not learning. It's like lifting weights with a forklift is not exercising.

petra 9y ago
Not sure. Most people won't remember how to derive equations any,nor they need it, if they need to derive equations they could probably use some piece of software(symbolic solver?), and that's just takes time they could use to understand statistics, for example, which seems more useful.
- WalterBright 9y ago
  > if they need to derive equations they could probably use some piece of software(symbolic solver?) The point is to understand. Having some software do it for you does not help with that.

gaius 9y ago

But for most of the people who aren't going to do that, they're useless. A system that cuts out a whole range of career paths simply because as a kid someone didn't like maths, is a bad one. Kids don't know what they need in life. That's why our culture takes decisions away from them until they are 18.

ben_jones 9y ago
At the same time you can't prep every kid to be a neurosurgeon. Or a prison guard. Or a helicopter machine gunner (which many would probably sign up to be if presented with the option at a young enough age!).
- leshow 9y ago
  That's exactly why you need to teach a broad range of subjects, including basic math like simple calculus and arithmetic, so kids can actually make a choice about what they want to do. If they never get taught any of that, then they don't have the option available. And just to be clear, quadratic equation is basic math, and not anywhere close to 'prepping a kid to be a neurosurgeon'.