Do the math: too much calculus? (2012) • Hacker News Board

Re: Do the math: too much calculus? (2012)

#81

Post by jessriedel » Wed, Oct 19, 2016, 9:27 PM UTC

gnarbarian wrote: post #58

jessriedel wrote: post #55

Earlier quoted context omitted.

> Most universities aren't primarily focused on research. Where are you getting "many" (rather than "some")? The page you link to discusses colleges in addition to universities, and it's well known that colleges exist primarily to educate students. > Even if you subtract the research budget out first you will still arrive at a figure less than 50% for most universities. Where is that numbers coming form?

Sorry here is a better source: https://nces.ed.gov/fastfacts/display.asp?id=75

You continue to not back up your claim. That link talks about "all post secondary institutions", not universities. Why don't you just edit your original comment to remove the claim?

Re: Do the math: too much calculus? (2012)

#82

Post by abecedarius » Wed, Oct 19, 2016, 9:28 PM UTC

dredmorbius wrote: post #48

cgag wrote: post #28

Earlier quoted context omitted.

I believe there's decent support for the idea that you could just teach them nothing until they reached the age of understanding, and theyd pick it up pretty much just as quick without the years of rote.

Source?

A U.S. elementary school principal in the 20th C. got his school to try leaving out any math in the first three grades (iirc), and the kids reportedly came out fine. I can't remember his name, and I'd like to be reminded too.

Re: Do the math: too much calculus? (2012)

#83

Post by thesimpsons1022 » Wed, Oct 19, 2016, 9:28 PM UTC

AstralStorm wrote: post #17

Personally, I have always wondered about the prominent position trigonometry and geometry get. As it is typically taught, it is the most useless thing, the time spent there would be much better spent on algebra, calculus. From basic theorem of algebra flows trigonometry and a lot of number theory, while from calculus with some linear algebra flows geometry. The rationale is probably history.

trig has seemed extremely important to me. specifically using sin and cos. helps a lot in physics as well as computer graphics and many other applications.

Re: Do the math: too much calculus? (2012)

#84

Post by rconti » Wed, Oct 19, 2016, 9:29 PM UTC

baldfat wrote: post #6

I think we teach Calculus wrong in a deep fundamental way. We should incorporate more high math concepts earlier into education BUT people are always afraid of anything past 4th grade math! "A minority of students then wend their way through geometry, trigonometry and, finally, calculus, which is considered the pinnacle of high-school-level math. But this progression actually “has nothing to do with how people think,…

IME the #1 problem is the failure to teach anything WELL. I took AP Calculus in high school, and today, as a 35-year-old, I'm still continually surprising myself with the problems I realize must be related to Calculus-- but nobody bothered to tell me. Things like the 'ol speed vs acceleration vs jerk kind of problems.

All calculus ever taught me was to apply these formulas to those problems (for some reason) and that dx/dy meant derivative of x with respect to derivative of y.

It boggles my mind that nobody simply bothered to tell us what a goddamned derivative was; what the word meant, and what real-life examples were. The "with respect to" was the most confusing and least useful concept. If we knew what the things were in the first place, the fact that one was "with respect to" the other would have been obvious. And "with respect to" could have been replaced with "relative to" in our minds, because we'd know what the things were.

Calculus seemed to be entirely repeating nonsensical mantras and applying impenetrable methods to problem sets and receiving an answer out the other end.

I'll also echo calls for more time on algebra. Surely the problem with algebra was that I wasn't a devoted enough student to repeating problem sets ad nauseum, but I just never got the 'knack' for it. I understood what I was supposed to be doing, but I was never satisfied with the answer "you'll start getting a feel for what to simplify to what after you do enough problems" as an explanation. It was frustrating to not feel like there was a concrete process to it all.

This made later Calculus and Statistics hard for me, because many exams would simply be 2 enormous problems ; the calculus I could get through but I couldn't simplify the problems quickly enough to be able to apply calculus or statistics at all.

Re: Do the math: too much calculus? (2012)

#85

Post by thesimpsons1022 » Wed, Oct 19, 2016, 9:30 PM UTC

dataharry wrote: post #69

sotojuan wrote: post #24

Earlier quoted context omitted.

> another guy didn't even take the AP exam, and another guy just put his head down on the desk during the AP exam. I don't know anything about these people but there's two "good" reasons for this: * Some colleges don't take certain AP credits e.g. the college I went to didn't take AP Bio credit, so I didn't take the exam for it when I took the class * Some high schools give GPA boosts for AP classes. For example, an…

How do you cheat at Calculus? Asking for a friend.

from the back row comment i think they are either cheating off each other or have some notes written down.

Re: Do the math: too much calculus? (2012)

#86

Post by CN7R » Wed, Oct 19, 2016, 9:32 PM UTC

Schools should adopt more dynamic curriculum, instead of a one size fits all, for individual students. Not everyone will grow up to be an engineer, but that doesn't mean those who have an interest in advanced mathematics should be held back. Encourage students to pursue their academic passions, and don't limit certain subjects depending on grade level.

A personal anecdote: I didn't start liking math until Calc AB, as subjects beforehand were presented as dry and were relatively easily so I didn't individually pursue mathematics outside of school. But by that time, I was already a junior and as a result, I often wonder what better math teachers and a non static curriculum would've done for my education.

Re: Do the math: too much calculus? (2012)

#87

Post by rconti » Wed, Oct 19, 2016, 9:33 PM UTC

spike021 wrote: post #52

YZF wrote: post #51

Earlier quoted context omitted.

Exactly. Physics becomes so much simpler with calculus. Once you realize e.g. the relationship between position, velocity and acceleration you don't need to memorize 20 different equations for all the different flavours of problems that are basically down to integrating or differentiating ...

But "you need to learn the hard way everybody else did it before X formula/equation was developed!" I agree it's nice to know the logic and background that is the foundation of how we got _here_, but sometimes the older details aren't really as important and take away time from students learning the modern, more useful techniques and concepts. One of the big things about kids and math these days is that you have less…

I couldn't disagree more. It gets too hard when you're asking students to memorize arbitrary equations that make no sense to them. It gets too hard when you give them 30 problems that look identical and they do 3 or 4 and figure that's good enough because they know how to run numbers through the meat grinder of a formula.

I don't see how students can truly learn if they don't understand the formulas they're applying and their relevance to the real world.

Re: Do the math: too much calculus? (2012)

#88

Post by yequalsx » Wed, Oct 19, 2016, 9:34 PM UTC

abakker wrote: post #75

Sample size of one: I think I understand calculus, the needs of calculus, and how it is profoundly meaning to understanding things around me. Can I do calculus? no. I couldn't do calculus because I really couldn't do algebra. I think that if I had been taught the concept and relevance of calculus earlier, and only had to worry about the execution of calculus later, I would have been much better off. understanding wha…

I'm skeptical that a person can really understand why x^(2/3) is not differentiable at x=0 but has an absolute minimum at x=0 without understanding the algebra. I think one can get an idea of the concepts without knowing algebra but I doubt one can understand calculus without knowing algebra.

We always teach the meaning of a given mathematical concept before doing using them or doing calculations. It's just that true understanding comes from the doing the calculation part.

Re: Do the math: too much calculus? (2012)

#89

Post by rconti » Wed, Oct 19, 2016, 9:35 PM UTC

castratikron wrote: post #10

AP Calculus was the most useful course I took in high school. It was rigorous, and I scored high enough on the exam to get two free college classes and start freshman year at the sophomore level, which left room at the end of my college career for more specialized courses. There should be some vetting process for the students who want to take AP classes. A lot of the students in my AP Calculus class had no business b…

Most of my high school classes in the later years were AP, and there was no pressure to take AP tests we didn't see the value in. shrug

Re: Do the math: too much calculus? (2012)

#90

Post by rconti » Wed, Oct 19, 2016, 9:36 PM UTC

yequalsx wrote: post #88

abakker wrote: post #75

Sample size of one: I think I understand calculus, the needs of calculus, and how it is profoundly meaning to understanding things around me. Can I do calculus? no. I couldn't do calculus because I really couldn't do algebra. I think that if I had been taught the concept and relevance of calculus earlier, and only had to worry about the execution of calculus later, I would have been much better off. understanding wha…

I'm skeptical that a person can really understand why x^(2/3) is not differentiable at x=0 but has an absolute minimum at x=0 without understanding the algebra. I think one can get an idea of the concepts without knowing algebra but I doubt one can understand calculus without knowing algebra. We always teach the meaning of a given mathematical concept before doing using them or doing calculations. It's just that true…

Not the parent, but I had the same problem. I understood that kind of algebra but could never figure out how to simplify things well, which hamstrung me in Calculus. Also, they never bothered to explain the purpose of any of the equations in calculus.