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This brings to mind the visual solution to calculating triangle area in James Somers post “I should have loved biology”: > In his “Mathematician’s Lament,” Pau

This brings to mind the visual solution to calculating triangle area in James Somers post “I should have loved biology”: > In his “Mathematician’s Lament,” Paul Lockhart describes how school cheapens mathematics by robbing us of the questions. We’re not just asked, hey, how much of the triangle takes up the box? > That’s a puzzle we might delight in. (If you drop a vertical from the top of the triangle, you end up with two rectangles cut in half; you discover that the area inside the triangle is equal to the area outside.) —https://jsomers.net/i-should-have-loved-biology/ https://jsomers.net/i-should-have-loved-biology/

Waterluvian 4y ago
I vividly remember math class one year boring me to death so bad that I distracted myself with my own puzzles like this. It was when I discovered the Fibonacci sequence inside Pascal’s triangle. I didn’t think this was a new discovery but it was new to me and it felt like lightning. I think that might have been an early glimpse of my later discovery that all my best learning would be done outside school.
- mananaysiempre 3y ago
  > [A]ll my best learning would be done outside school. Choose one: - Experience of discovery and survival of curiosity to adulthood; - Set of job-relevant skills well defined by names of subjects; - Standardized testing and easily comparable grades. (In my admittedly limited teaching experience.) I would guess that the last point will always get chosen, because it’s bureaucracy-friendly, and a bureaucracy makes the choice. But one of my most bizarre experiences is (some) HN readers being quite vocal about their support for it as well, where I haven’t seen it be anything but harmful. The bullshit admission process at US colleges might be to blame—I’m really not sure. References: Lockhart’s “Lament”[1], of course, for describing the feelings that (good) teachers have on this subject; Quinn’s “Revolution in mathematics”[2], as a more clinical analysis of how the bureaucracy won and got to basically redefine what “mathematics” even means for the majority of the population (in a way that’s as hopelessly obsolete as it is intensely harmful to the subject proper). The point shouldn’t be specific to mathematics, but it’s what I have the references for. [1] https://www.maa.org/external_archive/devlin/devlin_03_08.html https://www.maa.org/external_archive/devlin/devlin_03_08.htm... [2] http://www.ams.org/notices/201201/rtx120100031p.pdf http://www.ams.org/notices/201201/rtx120100031p.pdf
Tao3300 3y ago
I hated math for most of my childhood. I tested into an advanced track and had to be sequestered into lower level courses in the next higher grade do to a lack of effort. Then when I hit college and had Discrete and Calculus, I found out I loved it and wound up minoring in math. Though my arithmetic is still slow and my trig has major gaps in it due to school math just sucking in general.

Waterluvian 4y ago

I vividly remember math class one year boring me to death so bad that I distracted myself with my own puzzles like this. It was when I discovered the Fibonacci sequence inside Pascal’s triangle. I didn’t think this was a new discovery but it was new to me and it felt like lightning. I think that might have been an early glimpse of my later discovery that all my best learning would be done outside school.

mananaysiempre 3y ago
> [A]ll my best learning would be done outside school. Choose one: - Experience of discovery and survival of curiosity to adulthood; - Set of job-relevant skills well defined by names of subjects; - Standardized testing and easily comparable grades. (In my admittedly limited teaching experience.) I would guess that the last point will always get chosen, because it’s bureaucracy-friendly, and a bureaucracy makes the choice. But one of my most bizarre experiences is (some) HN readers being quite vocal about their support for it as well, where I haven’t seen it be anything but harmful. The bullshit admission process at US colleges might be to blame—I’m really not sure. References: Lockhart’s “Lament”[1], of course, for describing the feelings that (good) teachers have on this subject; Quinn’s “Revolution in mathematics”[2], as a more clinical analysis of how the bureaucracy won and got to basically redefine what “mathematics” even means for the majority of the population (in a way that’s as hopelessly obsolete as it is intensely harmful to the subject proper). The point shouldn’t be specific to mathematics, but it’s what I have the references for. [1] https://www.maa.org/external_archive/devlin/devlin_03_08.html https://www.maa.org/external_archive/devlin/devlin_03_08.htm... [2] http://www.ams.org/notices/201201/rtx120100031p.pdf http://www.ams.org/notices/201201/rtx120100031p.pdf

Tao3300 3y ago

I hated math for most of my childhood. I tested into an advanced track and had to be sequestered into lower level courses in the next higher grade do to a lack of effort. Then when I hit college and had Discrete and Calculus, I found out I loved it and wound up minoring in math. Though my arithmetic is still slow and my trig has major gaps in it due to school math just sucking in general.