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(Salon)   The root of high school problems might be found in calculus   (salon.com) divider line
    More: Obvious, Mathematics, Mathematics education, Arithmetic, rise of data, Steve Levitt, lot of math, difficult math course, Data science  
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1876 clicks; posted to Fandom » on 27 Sep 2020 at 6:05 AM (3 weeks ago)   |   Favorite    |   share:  Share on Twitter share via Email Share on Facebook



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2020-09-27 1:19:42 AM  
How derivative.
 
2020-09-27 2:01:10 AM  
I remember my 'New Math' teacher often quoting "figures don't lie but liars do figure" and wondering: OK which side of that equation are you on?
 
2020-09-27 3:18:51 AM  
Amen.
 
2020-09-27 4:13:18 AM  
To get rid of it for high school, you have to get rid of it for college, since nearly every B.S. is going to unnecessarily require it, either as a prereq for something you also shouldn't need it in for undergrad or simply outright because it seems fancy. Good luck with that.
 
2020-09-27 4:32:40 AM  
There should be a course like applied calculus.

It can be super useful but most of the time courses just focus on deriving equations not using them to do useful things.

/And yes there should be a lot more statistics and other data oriented math taught in schools. Computers can do some amazing problem solving tasks if you know how to set up a problem correctly and right now very few people know how to do this.
 
2020-09-27 4:53:21 AM  
The square root.
 
2020-09-27 6:19:56 AM  

PaulRB: The square root.


i.pinimg.comView Full Size
 
2020-09-27 6:37:31 AM  
We'll never put a non-gendered person on Mars with that attitude.
 
2020-09-27 6:39:57 AM  
I agree with this, and in fact I'd go it all the way down to algebra.  I'm an engineer, and I use algebra and calculus every day at my job, but I use algebra about zilch in my daily life (oddly I do use calculus a bit in day-to-day, though more conceptually than actual formulas).  No really, I have never needed to solve the quadratic equation while I'm out shopping.  All you're doing is wasting a bunch of kids time teaching them something useless when you could be teaching them something actually useful, like statistics, that still also developes general mathematical thinking.  Getting a feel for the difference between a percentile from a fraction will be more helpful to more people than all the solving for x in the world.

Keep algebra and calculus around for the STEM people who will actually use it in their future jobs, or for smarter people are interested in it, but teach actually useful math to everyone else.
 
2020-09-27 6:41:19 AM  
I remember having to take Stats in college. 25 years as an engineer now, and I've used it twice, maybe.

Calculus--far too often.
 
2020-09-27 6:51:29 AM  
Argh! I think that first year calculus can be almost a religious experience, but I can't really come down and exclude what they're calling "data science." I'm willing to grit my teeth and leave linear algebra and complex analysis to college, but people are just confronted with a fire hose of data these days.

I dunno. Maybe patch together enough to teach day-to-day activities such as understanding simple spreadsheets, compound interest, and then crank up algorithms and logarithms and "easy" infinite series, then bop back to spreadsheets to let them play with more complex algorithms and data visualisation, and then you give the kids just the tip of pre-calculus so they get a taste of the good stuff.

// Okay, maybe I can't really judge this objectively. Gonna go fire up Matlab...
 
2020-09-27 7:08:40 AM  
Schools should also probably teach things like how interest rates work on loans, taxes, and things to help a bunch of college and pre college age kids learn how not to be drowning in debt by the time they're old enough to drink.
 
2020-09-27 7:46:38 AM  
Calculus is the only reason I haven't gone back to college at some point in my life.  I don't want to take the 2-3 prerequisites I'd need to get to it just so I can start the first term of my actual degree path.
 
2020-09-27 7:50:42 AM  
The purpose of primary education is to provide a breadth of knowledge. It's not meant to be a collection of things you use in daily life, it's a collection of cognitive models which help you find new ways of thinking about and experiencing the world. "Dur, I never use calculus," sure, and I also almost never quote "Of Mice and Men", but I'm a richer person for having read it in English class.
 
2020-09-27 7:56:01 AM  
I had to use algebra on Friday at work. I don't normally have to use calculus, but it happens. I don't have to derive anything usually, just interpret what someone else did. It helps to know what's what, though.

I had 4 calculus courses at university and never used anything after the first course.
 
2020-09-27 7:58:55 AM  

t3knomanser: The purpose of primary education is to provide a breadth of knowledge. It's not meant to be a collection of things you use in daily life, it's a collection of cognitive models which help you find new ways of thinking about and experiencing the world. "Dur, I never use calculus," sure, and I also almost never quote "Of Mice and Men", but I'm a richer person for having read it in English class.


It used to be both. Home Ec, Drivers Ed, Shop, all used to be classes everyone had to take. They went the wayside because of budgetary reasons.

I think analytics and data science of some nature should absolutely be taught in school. The reason it isn't and the reason most people stop understanding math is the the curriculum is completely fubar. Instead of the BS Algebra then Trig then Geometry then PreCalc then Calc, we need to teach math more organically. Instead of this stupid subject based path, all of it should be taught and derived and explained holistically. PreCalc in particular is absolutely useless trash. It's mildly historically interesting, but company conceptually and computationally useless as it is supplanted by calculus. Removing that step entirely should absolutely happen.

I do think personal finance, the basic of economics, investment, data science has room. But we should not stop there.

\A vote for me for president is a vote for a math and science literate future
 
2020-09-27 8:04:25 AM  
Calculus has mainly been a stand-in for teaching logic and also as a weed-out course for certain majors. Something more useful and applicable should be used for non-math or non-engineering folk.
 
2020-09-27 8:04:33 AM  

Quantumbunny: I think analytics and data science of some nature should absolutely be taught in school.


I mean, statistics definitely was taught in my school. As was economics. I recognize, this was a long time ago. And I would go a step farther, not only should mathematics be taught holistically, but it should be holistically integrated into other subjects. You could use, for example, the interrelationships between medieval kingdoms as an introduction to graph theory, without ever explicitly using the term graph theory; just, "Look, this situation was complicated, so let's try a tool here to help us better understand what's going on."

(We did home ec and shop in middle school, and you could take more of those in high school)
 
2020-09-27 8:21:34 AM  
As a data scientist I'm getting a kick out of these replies

/calc is useful
//linear algebra is more useful
 
2020-09-27 8:27:40 AM  
One thing most people forget is at heart of most Machine learning and  DS is cal us.

Sure you many not need to write derivatives to train that neural network using a popular library, but if you want to use something that is not canned? You better believe there is calculus.
 
2020-09-27 8:28:06 AM  

t3knomanser: The purpose of primary education is to provide a breadth of knowledge. It's not meant to be a collection of things you use in daily life, it's a collection of cognitive models which help you find new ways of thinking about and experiencing the world. "Dur, I never use calculus," sure, and I also almost never quote "Of Mice and Men", but I'm a richer person for having read it in English class.


It doesn't seem school has managed to give you a cognitive model that you can draw upon to realize that  "school is not meant to be a collection of things you use in daily life" doesn't imply that "nothing you learn school should ever be useful in real life".
 
2020-09-27 8:31:02 AM  

aerojockey: It doesn't seem school has managed to give you a cognitive model that you can draw upon to realize that "school is not meant to be a collection of things you use in daily life" doesn't imply that "nothing you learn school should ever be useful in real life".


And apparently you never mastered reading, if that's what you took from my statement.
 
2020-09-27 8:35:02 AM  

windozer: One thing most people forget is at heart of most Machine learning and  DS is cal us.

Sure you many not need to write derivatives to train that neural network using a popular library, but if you want to use something that is not canned? You better believe there is calculus.


I'm not sure that people "forget" that, so much as they never once even thought about it, since it's totally irrelevant to everyone except for a few people who work in AI
 
2020-09-27 8:35:11 AM  
Go figure.
 
2020-09-27 8:39:53 AM  

t3knomanser: aerojockey: It doesn't seem school has managed to give you a cognitive model that you can draw upon to realize that "school is not meant to be a collection of things you use in daily life" doesn't imply that "nothing you learn school should ever be useful in real life".

And apparently you never mastered reading, if that's what you took from my statement.


Do you deny that you think that?  Ok then.
 
2020-09-27 8:41:57 AM  

aerojockey: Do you deny that you think that? Ok then


I at no point expressed that idea. To the contrary, I expressed that a breadth of experience was important. "Do you deny this thing you never said, and in fact, implied the exact opposite of?" Uh... yes?
 
2020-09-27 8:56:49 AM  
Could also do to re-examine the requirements of college and grad school. Doctors don't need to know how to launch rockets. The highest math doctors outside of a research setting need is algebra. Why do they need calculus 2?  For that matter why do they need to know about atomic valence structures?
 
2020-09-27 9:05:54 AM  
All you need to know about Economics:  STONKS
 
2020-09-27 9:06:44 AM  
I've always thought a required high school class should be half statistics, and half how to lie with statistics.

Never happen cuz the politicians love lying with statistics so much.
 
TWX [TotalFark]
2020-09-27 9:08:06 AM  
Due to a quirk in how I went through my mathematics and science classes, I took Physics and Calculus at the same time.

Physics was taught with a bunch of "givens".  Calculus taught us the underlying mathematics that actually gave us the derivatives for things like distance, velocity, and acceleration.

I enjoyed Calculus, I did not enjoy Physics.  Some of that had to do with the teachers, but a lot of it had to do with how we were required to use those "givens" to make the the Physics teacher's job easier, even if we could do the math with Calculus and get better answers.
 
2020-09-27 9:22:57 AM  

TWX: I enjoyed Calculus, I did not enjoy Physics.


I don't see how you can do physics without calculus.  Other than algebraic stuff like special relativity, most of my 66 hours of undergrad physics was based on calculus.
 
2020-09-27 9:34:35 AM  

t3knomanser: The purpose of primary education is to provide a breadth of knowledge. It's not meant to be a collection of things you use in daily life, it's a collection of cognitive models which help you find new ways of thinking about and experiencing the world. "Dur, I never use calculus," sure, and I also almost never quote "Of Mice and Men", but I'm a richer person for having read it in English class.


This person gets it. That's the POINT of a liberal arts education is to give every citizen a chance to develop broad skills before whittling down to specialized roles before you've explored
 
TWX [TotalFark]
2020-09-27 9:45:01 AM  

syrynxx: TWX: I enjoyed Calculus, I did not enjoy Physics.

I don't see how you can do physics without calculus.  Other than algebraic stuff like special relativity, most of my 66 hours of undergrad physics was based on calculus.


Exactly!  That's what made me so upset trying to take high school Physics.  I literally learned nothing that I couldn't get through just the math in Calculus.

In my humble opinion the two should be taught as a block, with curricula intertwined such that they reinforce each other.  There are probably some aspects of each that can be taught without needing the other, but since the study of Physics seems to be taking a mathematical approach to studying the natural world, it would follow that all of the mathematics learned up to and including Physics would be necessary in order to actually understand those concepts.
 
2020-09-27 9:45:40 AM  

cefm: Could also do to re-examine the requirements of college and grad school. Doctors don't need to know how to launch rockets. The highest math doctors outside of a research setting need is algebra. Why do they need calculus 2?  For that matter why do they need to know about atomic valence structures?


Weed-out courses. That's all. A lot of what doctors learn is just straight-up memorization. Many people can do that without having the slightest idea of how to apply it. Calc 2 keeps down the med school application numbers.
 
2020-09-27 9:45:53 AM  

t3knomanser: The purpose of primary education is to provide a breadth of knowledge. It's not meant to be a collection of things you use in daily life, it's a collection of cognitive models which help you find new ways of thinking about and experiencing the world. "Dur, I never use calculus," sure, and I also almost never quote "Of Mice and Men", but I'm a richer person for having read it in English class.


Incidentally I quoted from Of Mice and Men last week.
 
2020-09-27 9:55:16 AM  
As a data scientist and BI developer, I think that this should absolutely be taught in high school.  Now if they could figure out a way to teach common sense...
 
2020-09-27 10:15:05 AM  
The dumbing down of America.
The poorly educated vote Republican.
 
2020-09-27 10:31:30 AM  

aerojockey: I agree with this, and in fact I'd go it all the way down to algebra.  I'm an engineer, and I use algebra and calculus every day at my job, but I use algebra about zilch in my daily life (oddly I do use calculus a bit in day-to-day, though more conceptually than actual formulas).  No really, I have never needed to solve the quadratic equation while I'm out shopping.  All you're doing is wasting a bunch of kids time teaching them something useless when you could be teaching them something actually useful, like statistics, that still also developes general mathematical thinking.  Getting a feel for the difference between a percentile from a fraction will be more helpful to more people than all the solving for x in the world.

Keep algebra and calculus around for the STEM people who will actually use it in their future jobs, or for smarter people are interested in it, but teach actually useful math to everyone else.


The UK does something like this.

Up to age 16 you study a broad range of around 9-10 subjects including arts and sciences with mandatory English Language and Literature, science and math. The math component is mostly geometry, statistics/probability, algebra and trig.

At 16 you drop all but 3 or 4, and then continue those at AP/college level and these are the basis of your university admissions application. If you're going into STEM you pick mathematics as one the three, and this is where you really get into calculus.
 
2020-09-27 10:40:55 AM  

koder: To get rid of it for high school, you have to get rid of it for college, since nearly every B.S. is going to unnecessarily require it, either as a prereq for something you also shouldn't need it in for undergrad or simply outright because it seems fancy. Good luck with that.


Get rid of it?  I think you missed the point of the article.
 
2020-09-27 10:42:07 AM  
I can't think of a subject like calculus that made me tensor.
 
2020-09-27 10:42:48 AM  
Calc really wasn't useful for me at all.  Stats and linear algebra on the other hand...
 
2020-09-27 10:53:55 AM  

koder: To get rid of it for high school, you have to get rid of it for college, since nearly every B.S. is going to unnecessarily require it, either as a prereq for something you also shouldn't need it in for undergrad or simply outright because it seems fancy. Good luck with that.


For business degrees, too.  Well, they should.

Had more than one PM go on rants about how "the numbers are bad", and "we need to get the numbers up", but start grinding gears on *what* numbers and how they came about.

/For any managers out there on tech projects, LEARN THE farkING PRODUCT
 
2020-09-27 11:22:27 AM  
Data science is based on stats, which is based on calculus (and similar reasoning in discrete systems). Funneling people toward data science instead of calculus risks the "physics without calculus" problem described earlier in this thread.

The real challenge is how to fit geometry in -- right now it's such a speed bump that they have to teach algebra twice, but you can't just drop it since geometry is a critical link between math and the real world.
 
2020-09-27 11:25:50 AM  
The software world is 99% simple arithmetic, maybe first year algebra occasionally. Thank god.  Anything more complicated, and there's a library for that.  Hvac guys do way more math.

Funny how Joe Sixpack seems to think programmers are math whizzes. We aren't. (Except for the alarming number of math PhD's you run into. Software must derive them nuts).

//started enjoying things in calc III
 
2020-09-27 11:29:15 AM  

scumm: Funny how Joe Sixpack seems to think programmers are math whizzes. We aren't.


When I was a kid, I said, "I want to be a programmer," and my parents were like, "You'd need to work on your math, because you don't do well in math."

I am a programmer. I never did well in math. Weirdly, I actually do end up using a lot of math stuff, because I make art software.

//Just spent the past few months hacking an assembly library together to control walls of LEDs
 
2020-09-27 11:37:00 AM  

cefm: Could also do to re-examine the requirements of college and grad school. Doctors don't need to know how to launch rockets. The highest math doctors outside of a research setting need is algebra. Why do they need calculus 2?  For that matter why do they need to know about atomic valence structures?


greatgodyoshi: Weed-out courses. That's all. A lot of what doctors learn is just straight-up memorization. Many people can do that without having the slightest idea of how to apply it. Calc 2 keeps down the med school application numbers.


Really depends on the type of doctor. If you're a general family doctor you'll spend most of your time on your ipad using apps that tell you stuff via flowchart or likely disorders by symptoms. If you're a specialist who does any kind of research, either you do the math or you apply for grant funding to hire statisticians/mathematicians to do it for you. If you're smart, you do both.
Shortly after I finished my PhD, one of my dissertation committee members (who is an M.D. with a long history of VA funding for renal research) called me back into her office because I had been doing some stuff in my research that she saw an application for in hers. Granted, modern research suites do most of the work for you, but without an understanding of how the math worked, the tool is useless. She wanted about 90 minutes of me showing her my data sets, my results, how I got one from the other, and a few practice runs with her data.
And then I got out of research and haven't used any of it.... but my point remains...
 
2020-09-27 11:53:26 AM  
I have a very worn out Leithold "The Calculus" and I would like to get a newer version that has the fancy stuff like using colors for sub functions so you can trace it through the equations. The author died 15 years ago so I don't think there will be any newer editions.
 
2020-09-27 12:08:02 PM  
I can barely add. Don't ask me to subtract. Yet, I would oppose removing calculus from the high school curriculum based on the idea that it is only useful to a handful or professions. Calculus should be maintained for the same reason that some private high schools grind teens through a mandatory year long course on organic chemistry. That reason being that high school is a time to open doors; to increase opportunities and options for students as far as possible. It is not to the time to close doors to different career paths if that can be prevented.
 
2020-09-27 12:17:31 PM  
I also agree that vo-tech should be returned to the high schools. Budget cuts took those classes out, but I suspect those cuts are sustained at least in part by the lobbying by the for-profit schools that have stepped in to take the place of high school vo-tech.

I'd like to see vo-tech returned and modernized. Let's crank out licensed LPN's, EMT's, radiologists, dental assistants, paralegals, and X-ray techs in addition to hair dressers, plumbers, and young mechanics licensed in traditional, electric, and hybrid car repair.

High school graduates could enter the job market with real skills or hit college with some practical knowledge that might boost future academic performance or their actual career. Imagine pre-med students who licensed LPN's; pre-law students who are certified paralegals; an architect major who is a certified electrician or plumber; or a mechanical engineering major who is a certified mechanic.
 
2020-09-27 12:39:55 PM  
Of course, when you try to design the perfect high school curriculum, it's easy to end up with a 26-hour day. Knowledge and experiential learning are incredibly beneficial. Consider what might be included:

Accounting
Algebra
Agriculture
Anatomy (It was so popular at the high school my kids went to they were on the waiting list until their senior year.)
Arts and practical crafts like woodworking
Auto Repair
Barber/Hair Dressing
Biology
Botany
Introduction  to Biochemistry
Carpentry
Calculus
Chemistry
Organic Chemistry
Computer Science
Dance
Data Analysis
Earth Science
Electrical Work
English
Environmental Science
History
Geography
Geometry
Government
Languages (Why aren't the five most prevalent languages in a given state, other than English, taught in each high school in each state? Why aren't all students enrolled in a second language class?)
Medical Technical Subjects
Music
Nursing
Paralegal Studies
Physics
Physical Education, Sports, and Recreation
Plumbing
Psychology
Sociology
Statistics
Robotics
Theater
Welding
World History
Zoology

And maybe this many subjects again that I have forgotten.

How do you decide what to include? What do you exclude? When you exclude something, how do you know it was not the very thing that would have transformed a student's life for the better?

How many areas do you make mandatory? How much input and free choice should adolescents have? Do you require everyone to take both higher math classes and vo-tech classes? Do you try to incorporate instruction in higher mathematics via the vo-tech classes? Is it possible, for instance, to teach or reinforce the lessons of calculus via a high school Toy Design 101 class that straddles the arts and vo-tech departments?

Is there a perfect high school waiting to be designed?
 
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