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Did you take geometry in a California public school? I did about 20 years ago, and my impression was that it's an extremely fluffy course that would absolutely

Did you take geometry in a California public school? I did about 20 years ago, and my impression was that it's an extremely fluffy course that would absolutely benefit from being condensed, or at least rewritten. California math education (again, at the time I took it) was already extremely oddly paced. The Algebra 2/Trig class I took was extremely aggressive, and then the year of pre-calc that followed it [1] had about 2 weeks of novel content spread over a year's worth of teaching. I was initially a year behind most of my classmates (starting in junior high), then skipped ahead to do Calculus BC alongside everyone who'd been a year ahead of me---and aced it. On the other hand, the people who were really advanced had already gone on to college courses at that point and basically hadn't bothered with anything in the system for many years. In short, it's a mess and has been for decades. If they can clean it up a bit and make the pacing more even and integrated, I think that would be a net win. [1]: "Introduction to Analysis", I think they called it.

fastaguy88 5y ago
I took geometry more than 50 years ago. From my perspective, it was useless then as well. As far as I can tell, its goal was to illustrate the importance of mathematical proofs. Perhaps they are important to mathematicians, and I suppose they would be important if lots of high-school and college mathematics were potentially incorrect, so we needed a proof to reassure ourselves, but for most of us, even those who actively use mathematics, proofs are a waste of time. It would be better for students to become more comfortable with abstractions beyond multiplication.
- naasking 5y ago
  Real geometry is more important these days since computer graphics, photo and video editing and such are so common.
  - chongli 5y ago
    The geometry of computer graphics is differential geometry of curves and surfaces. As a topic it requires a strong background in linear algebra and multi variable calculus. Not something a typical high school student has any preparation for.
    - naasking 5y ago
      Seems like a disingenuous take. There's a very obvious path to understanding the basics of computer graphics by introducing the basic shapes of geometry, particularly triangles for obvious reasons.
      - chongli 5y ago
        My interpretation of "computer graphics" was based on modern 3D graphics: transformation, lighting, texture mapping, animation, etc. High school geometry will get you the basics but that's a long way from the state of the art. See the rendering equation [1] for an example. [1] https://en.wikipedia.org/wiki/Rendering_equation https://en.wikipedia.org/wiki/Rendering_equation
        naasking 5y ago
        Introduction to geometry is 2D. 3D comes much later. There's plenty of introductory material in 2D alone, even 2D computer graphics.
        chongli 5y ago
        Your original comment didn't say anything about introductory material. This whole discussion is about education to prepare students for university and beyond. No one is pursuing a career in computer graphics with only an introductory high school geometry background.
        naasking 5y ago
        No, this whole discussion is about K-12 education, which includes the very first introductions to geometry, and if you look at the existing geometry content from 2013 [1] it's mostly about 2D geometry, shapes, angles, rotations, translations, etc. That fits squarely in with 2D computer graphics. I also did emphasize "basic geometry" and "basic computer graphics" in my first reply to you. Finally, my first reply was disputing the claimed uselessness of geometry. It's very clear that it's far from useless these days, although some material is certainly less useful than it maybe used to be. [1] https://www.cde.ca.gov/ci/ma/cf/documents/mathfwgeometryjl.pdf https://www.cde.ca.gov/ci/ma/cf/documents/mathfwgeometryjl.p...

fastaguy88 5y ago

I took geometry more than 50 years ago. From my perspective, it was useless then as well. As far as I can tell, its goal was to illustrate the importance of mathematical proofs. Perhaps they are important to mathematicians, and I suppose they would be important if lots of high-school and college mathematics were potentially incorrect, so we needed a proof to reassure ourselves, but for most of us, even those who actively use mathematics, proofs are a waste of time. It would be better for students to become more comfortable with abstractions beyond multiplication.

naasking 5y ago
Real geometry is more important these days since computer graphics, photo and video editing and such are so common.
- chongli 5y ago
  The geometry of computer graphics is differential geometry of curves and surfaces. As a topic it requires a strong background in linear algebra and multi variable calculus. Not something a typical high school student has any preparation for.
  - naasking 5y ago
    Seems like a disingenuous take. There's a very obvious path to understanding the basics of computer graphics by introducing the basic shapes of geometry, particularly triangles for obvious reasons.
    - chongli 5y ago
      My interpretation of "computer graphics" was based on modern 3D graphics: transformation, lighting, texture mapping, animation, etc. High school geometry will get you the basics but that's a long way from the state of the art. See the rendering equation [1] for an example. [1] https://en.wikipedia.org/wiki/Rendering_equation https://en.wikipedia.org/wiki/Rendering_equation
      - naasking 5y ago
        Introduction to geometry is 2D. 3D comes much later. There's plenty of introductory material in 2D alone, even 2D computer graphics.
        chongli 5y ago
        Your original comment didn't say anything about introductory material. This whole discussion is about education to prepare students for university and beyond. No one is pursuing a career in computer graphics with only an introductory high school geometry background.
        naasking 5y ago
        No, this whole discussion is about K-12 education, which includes the very first introductions to geometry, and if you look at the existing geometry content from 2013 [1] it's mostly about 2D geometry, shapes, angles, rotations, translations, etc. That fits squarely in with 2D computer graphics. I also did emphasize "basic geometry" and "basic computer graphics" in my first reply to you. Finally, my first reply was disputing the claimed uselessness of geometry. It's very clear that it's far from useless these days, although some material is certainly less useful than it maybe used to be. [1] https://www.cde.ca.gov/ci/ma/cf/documents/mathfwgeometryjl.pdf https://www.cde.ca.gov/ci/ma/cf/documents/mathfwgeometryjl.p...