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"If you want to learn trig or calculus, it's set at such a pace in schools that it guarantees that only the absolutely best students will learn it." Pardon my

"If you want to learn trig or calculus, it's set at such a pace in schools that it guarantees that only the absolutely best students will learn it." Pardon my elitism, but only the absolutely best students need to learn trigonometry or calculus. I'd much rather high schools offer useful classes like personal finance or civics or creative writing than make average, uninterested students take a trig or calc class that they will have absolutely no use for later in life.

Jach 16y ago
Since when is education about only learning the things that a student, in their current ignorance, project they'll need far into the future? Trig and calculus are trivial, learn them. (I'd argue that a solid understanding in both would make personal finance a lot better a subject too.) In any case, my high school offered all of those classes, with personal finance being required and trig being taught along the way in several required math courses.
- jemfinch 16y ago
  Since when is high school education? High school is preparation for the real world: it has replaced the old apprenticeships and parental involvement that served as life preparation for centuries. High school fails in this purpose when it wastes time teaching trigonometry and calculus to those who have no need for it. The majority of people do not graduate college; of the ones that do graduate college, many will never use trigonometry or calculus in their occupations or personal pursuits. It makes no more sense to teach every high school student trigonometry and calculus than it makes to teach every high school student how to retread tires or operate a band saw.
  - jacobolus 16y ago
    I think it makes a great deal of sense to teach every student how to operate a band saw. And also how to dance, and how to read poetry, and how to draw with perspective, and how to use a potter’s wheel, and how to solve Newtonian mechanics problems, and how to build simple electrical circuits, how some basic cooking chemistry works, and how double-entry bookkeeping works, and some basic music theory, and how to operate a non-linear video editor, and on and on. Not every student necessarily needs to learn every thing, but schools should have the resources to teach many things to every student. If kids are going to spend half of their time for 13 years (!) in school, I sure hope they’re learning all sorts of useful things. Drilling them on geography or historical dates or the content of 19th century “classic” novels, &c., certainly isn’t the only important thing in the world.
    - jemfinch 16y ago
      I'm sorry, but at what point are you disagreeing with me? "Not every student necessarily needs to learn every thing" is essentially the point I'm making.
      - jacobolus 16y ago
        Okay, how about this: every student should learn trigonometry and how to dance and how to cook and how double-entry bookkeeping works and how to speak several foreign languages, most (personally I think all or nearly all) students should learn calculus, and a large (much larger than now) percentage should learn how to operate a band saw. Calculus is just absolutely fundamental to so much of the technology that we use every day that students who do not learn calculus are at a serious disadvantage comprehending our built environment.
        jemfinch 16y ago
        Calculus is not fundamental to the technology that we use every day. I work an extremely technically challenging job and I'm serious, I haven't used calculus or trigonometry since my last physics exam in undergrad. Am I happy I know them? Sure, because I like knowing things. Are they even remotely useful in my everyday life? Not a bit. Please, by all means, demonstrate a place where a person who doesn't know calculus is at a disadvantage interacting with the technology of the world around us. Until then, I'm calling bullshit.
WalterBright 16y ago
Learning trig and calculus are very beneficial in that it teaches thinking skills that are applicable to a wide variety of useful life skills.
- btilly 16y ago
  Those same skills could be taught by teaching a course in discrete math and probability. The latter would give people more useful life skills.
  - duncanj 16y ago
    But at some point in understanding probability, as it is actually used in the real world, you need calculus. The same is true for economics, which you didn't mention but often comes up as something everyone should learn. I think by not covering calculus, students are forced to learn things (economics, physics, statistics) the hard way and without understanding them deeply. Unfortunately, calc generally requires trig. It should be taught while teaching calculus.
    - btilly 16y ago
      But at some point in understanding probability, as it is actually used in the real world, you need calculus. At SOME point, true. But that point is very, very far off, and very few people ever get there. It is possible to understand what the normal distribution is, and how to lookup significance values, without worrying about how to calculate it. This is how virtually every non-statistician does it, and is what statisticians themselves do more of the time. The point where you have to calculate it and prove properties about it does require Calculus. Unfortunately, calc generally requires trig. It should be taught while teaching calculus. I'm sorry, but this is not a good idea. What Calculus requires from trig is a solid understanding of what sin, cos, and tan are (else the derivatives of the same won't make sense), and a solid understanding of trig identities for use in integration. Both uses require several layers of abstraction on top of the idea of trig. My experience is that it is a bad idea to layer abstractions on top of material before making sure that that material is solid. I therefore want people to have a solid understanding of trig before they arrive in a Calculus course. That said, I think that a lot of the use of trig in integration is a now useless skill, given the widespread availability of programs like Mathematica that can solve all of those problems very quickly and much more accurately. It was once important for people to learn those skills, but now it doesn't seem that useful to me. You should be able to verify that the integral differentiates correctly. But integrating complicated expressions isn't in my view that critical of a skill.
Semiapies 16y ago
Creative writing? I'd settle for plain old English composition. This is no "those darn kids" gripe - I get emails from people in their 30s and 40s that are excruciating to read and require a follow-up call just to find out what they were trying to say.

Jach 16y ago

Since when is education about only learning the things that a student, in their current ignorance, project they'll need far into the future? Trig and calculus are trivial, learn them. (I'd argue that a solid understanding in both would make personal finance a lot better a subject too.) In any case, my high school offered all of those classes, with personal finance being required and trig being taught along the way in several required math courses.

jemfinch 16y ago
Since when is high school education? High school is preparation for the real world: it has replaced the old apprenticeships and parental involvement that served as life preparation for centuries. High school fails in this purpose when it wastes time teaching trigonometry and calculus to those who have no need for it. The majority of people do not graduate college; of the ones that do graduate college, many will never use trigonometry or calculus in their occupations or personal pursuits. It makes no more sense to teach every high school student trigonometry and calculus than it makes to teach every high school student how to retread tires or operate a band saw.
- jacobolus 16y ago
  I think it makes a great deal of sense to teach every student how to operate a band saw. And also how to dance, and how to read poetry, and how to draw with perspective, and how to use a potter’s wheel, and how to solve Newtonian mechanics problems, and how to build simple electrical circuits, how some basic cooking chemistry works, and how double-entry bookkeeping works, and some basic music theory, and how to operate a non-linear video editor, and on and on. Not every student necessarily needs to learn every thing, but schools should have the resources to teach many things to every student. If kids are going to spend half of their time for 13 years (!) in school, I sure hope they’re learning all sorts of useful things. Drilling them on geography or historical dates or the content of 19th century “classic” novels, &c., certainly isn’t the only important thing in the world.
  - jemfinch 16y ago
    I'm sorry, but at what point are you disagreeing with me? "Not every student necessarily needs to learn every thing" is essentially the point I'm making.
    - jacobolus 16y ago
      Okay, how about this: every student should learn trigonometry and how to dance and how to cook and how double-entry bookkeeping works and how to speak several foreign languages, most (personally I think all or nearly all) students should learn calculus, and a large (much larger than now) percentage should learn how to operate a band saw. Calculus is just absolutely fundamental to so much of the technology that we use every day that students who do not learn calculus are at a serious disadvantage comprehending our built environment.
      - jemfinch 16y ago
        Calculus is not fundamental to the technology that we use every day. I work an extremely technically challenging job and I'm serious, I haven't used calculus or trigonometry since my last physics exam in undergrad. Am I happy I know them? Sure, because I like knowing things. Are they even remotely useful in my everyday life? Not a bit. Please, by all means, demonstrate a place where a person who doesn't know calculus is at a disadvantage interacting with the technology of the world around us. Until then, I'm calling bullshit.

WalterBright 16y ago

Learning trig and calculus are very beneficial in that it teaches thinking skills that are applicable to a wide variety of useful life skills.

btilly 16y ago
Those same skills could be taught by teaching a course in discrete math and probability. The latter would give people more useful life skills.
- duncanj 16y ago
  But at some point in understanding probability, as it is actually used in the real world, you need calculus. The same is true for economics, which you didn't mention but often comes up as something everyone should learn. I think by not covering calculus, students are forced to learn things (economics, physics, statistics) the hard way and without understanding them deeply. Unfortunately, calc generally requires trig. It should be taught while teaching calculus.
  - btilly 16y ago
    But at some point in understanding probability, as it is actually used in the real world, you need calculus. At SOME point, true. But that point is very, very far off, and very few people ever get there. It is possible to understand what the normal distribution is, and how to lookup significance values, without worrying about how to calculate it. This is how virtually every non-statistician does it, and is what statisticians themselves do more of the time. The point where you have to calculate it and prove properties about it does require Calculus. Unfortunately, calc generally requires trig. It should be taught while teaching calculus. I'm sorry, but this is not a good idea. What Calculus requires from trig is a solid understanding of what sin, cos, and tan are (else the derivatives of the same won't make sense), and a solid understanding of trig identities for use in integration. Both uses require several layers of abstraction on top of the idea of trig. My experience is that it is a bad idea to layer abstractions on top of material before making sure that that material is solid. I therefore want people to have a solid understanding of trig before they arrive in a Calculus course. That said, I think that a lot of the use of trig in integration is a now useless skill, given the widespread availability of programs like Mathematica that can solve all of those problems very quickly and much more accurately. It was once important for people to learn those skills, but now it doesn't seem that useful to me. You should be able to verify that the integral differentiates correctly. But integrating complicated expressions isn't in my view that critical of a skill.

Semiapies 16y ago

Creative writing? I'd settle for plain old English composition. This is no "those darn kids" gripe - I get emails from people in their 30s and 40s that are excruciating to read and require a follow-up call just to find out what they were trying to say.