Integrals -> Derivatives -> Series -> Limits? That’s not a progression I am familiar with. In trigonometry and precalculus I learned Series then Limits, then in calculus derivative first then integrals. There are definitely new directions to go with Series and Limits after learning integrals, but the concepts are prerequisites to calculus (and arguably trigonometry).
I remember when I took calculus we studied those topics in the order of: Limits -> Derivatives -> Integrals -> Series.
Calculus they won't teach you [video]
71–80 of 124 posts
Re: Calculus they won't teach you [video]
#72Earlier quoted context omitted.
> Would be interesting for someone to attempt to write a non-historical physics textbook. I recall some prominent physicist saying they've never read Einstein's original papers on relativity; and they don't have any real desire to, since we understand it much better now, and have better examples, notations, etc.
Most physicists have never read them, fwiw, as interesting as they may be for their historical role. Most classic papers go unread, and it’s not a bad thing pedagogically. How things get sorted out is usually a huge mess and following the real history can be an enormous distraction (and can confuse and misdirect students).
Re: Calculus they won't teach you [video]
#73Let me know, not if anyone here can do Calculus (that is ordinary; who can't? ), but rather whether you actually personally use Calculus, and please describe generally an example of needing Calculus to figure something out in the last 5 years. I think my point is that the history of mathematics is exponentially more interesting than mathematics. We like mathematics, but we like stories far more than we like whatever…
Do tools that use calculus count? If so, switch-mode power supply design uses quite a bit, mostly differential equations. I let the CAD software do the numeric simulations, but there's always some hand calculation needed to pick initial component values.
Re: Calculus they won't teach you [video]
#74Let me know, not if anyone here can do Calculus (that is ordinary; who can't? ), but rather whether you actually personally use Calculus, and please describe generally an example of needing Calculus to figure something out in the last 5 years. I think my point is that the history of mathematics is exponentially more interesting than mathematics. We like mathematics, but we like stories far more than we like whatever…
> that is ordinary; who can't? In my experience, almost everyone out of college who I've met who claims to know calculus.
Re: Calculus they won't teach you [video]
#75Earlier quoted context omitted.
This is the same progression that I learned, but I am not sure it is the best one. I wonder if there has been any rigorous scientific study on the pedagogical benefits one way or another?
Yeah why don’t we do more a/b testing or controlled testing in education?
If your local educators are not required to participate in this system of continuing education and improving techniques, that's a local government decision and you should seek to fix that.
Fixing it is often hard in the states because there is a not insignificant amount of Americans that see schools as undermining their authority, see education as a useless and undesirable endeavor, often as a "radicalizing" and "socialist" influence and institution, and so they fight back against any improvement of schooling. There are states in the union that allow pretty much anyone, with no qualifications or certifications, to become "educators", and other states in the union that require a masters degree and 12 credits of class work every few years to continue to be an educator. Outcomes often imply a correlation between those requirements and the result, and yet the states with much lower bars of entry do not increase them. Education in the states is a politics issue, for some stupid reason. There are people who believe for whatever reason that middle schoolers are being taught "Critical Race Theory", as if that isn't a college level course that the vast majority of humanities majors don't even experience.
Re: Calculus they won't teach you [video]
#76Earlier quoted context omitted.
Heh, ditto. I don't think I got any new info that I didn't get in high school calculus, but it is a well done review of things I hadn't seen in a couple of decades
I got calculus in college, from mathematicians. :-( We spent about 15 minutes (well, ok, one lecture) on series, then a couple weeks on limits, then limits and differential calculus, then the rest of differential calc. (throwing the limit stuff away), then limits and integral calc., and finally the rest of calculus. Limits are a horrible way to learn calculus if you're trying to understand it at the same time as doin…
The anecdote I always reach for is find someone who has been taught a higher level math subject by both a university professor, and an adjunct or local community college professor who might not have higher level knowledge of math. Many people prefer the "less expert" teacher.
Consider if you have been in software development for a long time, and how hard it is to remember what NOT understanding a variable was like.
Re: Calculus they won't teach you [video]
#77Earlier quoted context omitted.
I don’t see why the history of discovery of something should be a particularly good way to rediscover it. As a concrete example, if someone asks “how do we know the Earth is round” or “how do we know the planets orbit the sun”, one could go through ways to figure this out with math and minimal technology. But one could also point out that we have spaceships and probes and have actual pictures! You can see the Earth f…
Another concrete example of the conflict is classical vs quantum physics which is nearly exclusively taught as the historical story of the quantum revolution or whatever you call it around 1900. It would be trivial to skip the historical story and just "yo here's a FET transistor, a solar cell, and a vacuum tube, and the math just works, so get used to it" but nobody is ever taught that way. Would be interesting for…
And yet nand2tetris is one of the most common suggestions for people who actually want to figure out how computers work. Because you actually are posed with problems that real world engineers used to struggle with, and are allowed to play with the problem before finding out the answer. It builds a much deeper understanding than "it works like this because it is"
Re: Calculus they won't teach you [video]
#78Earlier quoted context omitted.
Yea, it has gotten worse in the US thanks to the common core bullshit. My daughter’s math education has been eroded with shitty ed tech apps like the ones from MHM[0]. I’ve been able to support her but there’s many kids that are not so fortunate. [0] https://www.hmhco.com/
What's wrong with common core?
There are some SERIOUSLY garbage work books available for common core curricula. Some of them are obviously trying to touch on the understand that common core is trying to push, but seemingly written by someone who never understood that concept themselves, so they are basically nonsense word salad.
I remember when I was a kid, our state pushed a different direction in math education about helping students understand how to turn situations and problems into a mathematical equation to solve. Local parents decried the situation as "New Math" (importantly this stuff was distinct from the actual 70s era "New Math"), and that it was terrible and blah blah blah the same thing that happens any time you have poorly educated parents struggling to understand their children's educational material.
Of course, we children did absurdly well in education terms, literally a stand-out class of students in terms of educational outcomes, maturity, flexibility, and standardized test scores. Unfortunately it would be difficult to tell what the heck caused the improvement because there were MANY weird things to happen to my class (we were called the "Guinea pig class", we had second language schooling from first grade, our middle school scheduling was changed up to give us more specialized teachers and more classroom variety, and we always got brand new curricula to test out, along with just plain notable demographic changes happening in the area at the time)
Re: Calculus they won't teach you [video]
#79Let me know, not if anyone here can do Calculus (that is ordinary; who can't? ), but rather whether you actually personally use Calculus, and please describe generally an example of needing Calculus to figure something out in the last 5 years. I think my point is that the history of mathematics is exponentially more interesting than mathematics. We like mathematics, but we like stories far more than we like whatever…
As to your question I've touched on a little for manipulation of some of the classic equations in ecology and population biology, growth curves, population growth, etc. Barely needed to crack an introductory textbook to do it though. Had I learned real calculus and maybe differential equations there is some really interesting modelling I'd be able to do in this space, but instead I'm stuck seeing the diffuse shadow of the idea on the wall of Plato's cave. That's not a wistful lament though because to your point, time spent boning up on linear algebra instead of calculus would provide at least an order of magnitude more utility for my work.
Re: Calculus they won't teach you [video]
#80Earlier quoted context omitted.
Do tools that use calculus count? If so, switch-mode power supply design uses quite a bit, mostly differential equations. I let the CAD software do the numeric simulations, but there's always some hand calculation needed to pick initial component values.
If I asked if you ever use arithmetic, and you asked me if using calculators counts, what do you think my answer would be?