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Agreed. Personally I think we should swap our high school curriculum: Geometry -> Proofy Linear Algebra Trig -> Computational Linear Algebra I thi

Agreed. Personally I think we should swap our high school curriculum: Geometry -> Proofy Linear Algebra Trig -> Computational Linear Algebra I think the heydey of Trig was in the age of navigation and the heydey of Geometry was in the age of machines. Meanwhile, today, linear algebra has supplanted both of them, runs the world besides, and it seems to only be getting started.

monocasa 5y ago
Rather than geometry or linear algebra, I'd love to see logic and set theory taught that early as more than a passing topic.
- lstodd 5y ago
  Can only up this. Not teaching set theory is just an abomination. And logic. That year of Prolog taught me so much.
lstodd 5y ago
Which would be utterly useless. Math, and specifically Geometry aren't about useful skills, they are about understanding the world.
- jjoonathan 5y ago
  Linear algebra has geometry flat out beat in that arena, too. This isn't to say that Geometry doesn't help you learn about the world, but it is to say that Linear Algebra should be prioritized above Geometry if your goal is to understand the world. I can't remember a physics class where LA didn't pay heavy dividends -- in particular, differential equations are the language of physics, and you'd be hard pressed to find either an analytical or computational diff eq technique that didn't have a core of linear algebra. Meanwhile, the last time Power of a Point gave me dividends was on math contests.
  - lstodd 5y ago
    LA is a very useful tool. But imagine that you never heard of concepts behind it. It'd just become a more-or-less useful artefact. And in no time it would devolve into a useless ... thing so to say, a decoration, as you lose knowledge how to apply it.
    - jjoonathan 5y ago
      Yes, Geometry makes the funnest puzzles :-) Believe me, it pains me to suggest bumping it back. Introductory proofy linear algebra just hits a quadruple home run: it's astonishingly useful, it's getting moreso, it's simple enough to remain age appropriate, and it can serve as an intro to proofs. As much as I enjoy geometry puzzles, I just don't see how they compete with that. For the true fans, of course, the answer today & in this hypothetical future is still to learn both.
BeetleB 5y ago
> I think the heydey of Trig was in the age of navigation and the heydey of Geometry was in the age of machines. Sorry, but this is crazy. If you're in physics, electrical engineering, mechanical engineering, or civil engineering[1], then trigonometry appears in so many problems - including ones that have little to do with triangles and geometry. Calc II is heavy on trigonometry for a good reason. So many integrals that show up in the "real world" are solvable if you know your trig identities. These show up in semiconductor theory, mechanics, electromagnetics, quantum mechanics, etc. Trig is the one thing I'm glad I was taught well in high school. Used it all the time for over a decade. [1] And probably many other disciplines.
- kevin_thibedeau 5y ago
  Trigonometry has little to do with triangles. It's more appropriately titled circleometry.
  - andrewprock 5y ago
    That's a clever insight. Though the measurement of circles is done using triangles, so maybe there is an even cleverer more Germanic name? Circulotrigometry.

monocasa 5y ago

Rather than geometry or linear algebra, I'd love to see logic and set theory taught that early as more than a passing topic.

lstodd 5y ago
Can only up this. Not teaching set theory is just an abomination. And logic. That year of Prolog taught me so much.

lstodd 5y ago

Which would be utterly useless. Math, and specifically Geometry aren't about useful skills, they are about understanding the world.

jjoonathan 5y ago
Linear algebra has geometry flat out beat in that arena, too. This isn't to say that Geometry doesn't help you learn about the world, but it is to say that Linear Algebra should be prioritized above Geometry if your goal is to understand the world. I can't remember a physics class where LA didn't pay heavy dividends -- in particular, differential equations are the language of physics, and you'd be hard pressed to find either an analytical or computational diff eq technique that didn't have a core of linear algebra. Meanwhile, the last time Power of a Point gave me dividends was on math contests.
- lstodd 5y ago
  LA is a very useful tool. But imagine that you never heard of concepts behind it. It'd just become a more-or-less useful artefact. And in no time it would devolve into a useless ... thing so to say, a decoration, as you lose knowledge how to apply it.
  - jjoonathan 5y ago
    Yes, Geometry makes the funnest puzzles :-) Believe me, it pains me to suggest bumping it back. Introductory proofy linear algebra just hits a quadruple home run: it's astonishingly useful, it's getting moreso, it's simple enough to remain age appropriate, and it can serve as an intro to proofs. As much as I enjoy geometry puzzles, I just don't see how they compete with that. For the true fans, of course, the answer today & in this hypothetical future is still to learn both.

BeetleB 5y ago

> I think the heydey of Trig was in the age of navigation and the heydey of Geometry was in the age of machines. Sorry, but this is crazy. If you're in physics, electrical engineering, mechanical engineering, or civil engineering[1], then trigonometry appears in so many problems - including ones that have little to do with triangles and geometry. Calc II is heavy on trigonometry for a good reason. So many integrals that show up in the "real world" are solvable if you know your trig identities. These show up in semiconductor theory, mechanics, electromagnetics, quantum mechanics, etc. Trig is the one thing I'm glad I was taught well in high school. Used it all the time for over a decade. [1] And probably many other disciplines.

kevin_thibedeau 5y ago
Trigonometry has little to do with triangles. It's more appropriately titled circleometry.
- andrewprock 5y ago
  That's a clever insight. Though the measurement of circles is done using triangles, so maybe there is an even cleverer more Germanic name? Circulotrigometry.