Koishikawa-san Is a Carnivore - Vol. 1 Ch. 6 - I am happy now.
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I want Koishigawa-san to devour me.
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No you shut up stupid teacher! 😂
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I use trigonometry rather a lot, in graphic application; but I still find it rather dull. And not only is the more specific study of trigonometry identities deathly dull, but it has very narrow application, and in that application one can simply consult a reference work.
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At first I thought this would become a joke about summer heat and sweating and that the gayru alone stays cool. But. Ah. Author got me there.
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@Oeconomist usage is narrow.
But very necessary
But very necessary
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@Anish_Agarwal—
Extensively teaching trigonometric identities to high school students and to the vast majority of college and university students in STEM fields is essentially a combination of avoidance behavior with the use of educational institutions not to teach but to filter. That is to say that it is a way for supposed educators to fill-up time, and to determine which students will persevere in difficult tasks. Most of these students should be taught other things; and, if we want schools to act as filters, then they should find difficult material that these students will be able to use through-out their careers or otherwise in their lives.
It's extremely valuable to a large group of people that some people to know and understand this material, but the marginal value of a wide group understanding this material is not merely zero; it is negative, because that knowledge is gained at cost.
Extensively teaching trigonometric identities to high school students and to the vast majority of college and university students in STEM fields is essentially a combination of avoidance behavior with the use of educational institutions not to teach but to filter. That is to say that it is a way for supposed educators to fill-up time, and to determine which students will persevere in difficult tasks. Most of these students should be taught other things; and, if we want schools to act as filters, then they should find difficult material that these students will be able to use through-out their careers or otherwise in their lives.
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@Oeconomist The only reason they spend so much time on it is historical, its a relic of the days when they used Euclid's Elements as a math textbook and taught kids to construct shapes with a compass and straightedge. High time we started teaching basic 2D linear algebra instead
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@stray_dog_—
Constructive geometry (the stuff with compass, straight-edge, and stylus) doesn't use trigonometry at all, let alone mess with trigonometric identities. Trigonometry was introduced in the context of Cartesian coördinates. And, while trigonometry is normally taught as a part of geometry as such, extensive drilling on trigonometric identities is associate with the calculus, the underlying geometry of which does not generally arise to the surface in the use of these identities.
That said, I would at least agree that a cultural inertia plays a rôle in the continuation of that drilling.
I doubt that there is a good case for replacing the teaching of these identities with that of linear algebra. I did quite well in the linear algebra courses that I took, but the only time that I've used linear algebra outside of school is in critiquing a book and a paper that used it, and each of those works was pretty worthless. (The paper was a bit more worthy than the book, but was itself a critique of the book, and missed the important issues as the author of the paper flounced-around with linear algebra.)
That's not to say that linear algebra itself is worthless. For example, as you perhaps know, it is used to design airplanes that don't just shake apart in flight. But it is another field such that a society profits mightily from a few people knowing it, but such that the marginal value of teaching it to as many people as it has been taught is negative.
Constructive geometry (the stuff with compass, straight-edge, and stylus) doesn't use trigonometry at all, let alone mess with trigonometric identities. Trigonometry was introduced in the context of Cartesian coördinates. And, while trigonometry is normally taught as a part of geometry as such, extensive drilling on trigonometric identities is associate with the calculus, the underlying geometry of which does not generally arise to the surface in the use of these identities.
That said, I would at least agree that a cultural inertia plays a rôle in the continuation of that drilling.
I doubt that there is a good case for replacing the teaching of these identities with that of linear algebra. I did quite well in the linear algebra courses that I took, but the only time that I've used linear algebra outside of school is in critiquing a book and a paper that used it, and each of those works was pretty worthless. (The paper was a bit more worthy than the book, but was itself a critique of the book, and missed the important issues as the author of the paper flounced-around with linear algebra.)
That's not to say that linear algebra itself is worthless. For example, as you perhaps know, it is used to design airplanes that don't just shake apart in flight. But it is another field such that a society profits mightily from a few people knowing it, but such that the marginal value of teaching it to as many people as it has been taught is negative.
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@Oeconomist i suggested it because basic linear algebra lets you solve most of the geometric problems you can handle with trigonometry without memorizing a ton of trig identities. Also because i use it constantly. i imagine most engineers, most people in the natural sciences, and some people in the social sciences use it frequently as well
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