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Calculus they won't teach you [video]
- adammarples 4y agoliterally what they taught me
- sethammons 4y agoHeh, 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
- User23 4y agoAnother possibility is that mathematics education has gotten worse since you were in high school.
- pryelluw 4y agoYea, 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/ https://www.hmhco.com/
- ultra_nick 4y agoWhat's wrong with common core?
- mywittyname 4y agoMost of the hate seems to stem from the changes in mathematics teaching. Instead of focusing on rote memorization, the curriculum wants students to understand the concepts, thus it teaches more ways to tackle a smaller pool of topics. I believe this idea comes from the way that mathematics is taught in countries whose students outperform Americans. A friend of mine who was schooled in eastern Asia claims his daughter is learning the same methods he did growing up. FWIW, I learned some cool techniques that I didn't know about when my friend showed me his daughter's homework. But I can see how parents of fifth graders who aren't able to help their kids with their homework because they don't understand it / never learned that way would be angry. States all had their own standards, which were largely the same, but just kind of different enough. Prior to Common Core, private companies sprang up to fill the need of mapping all of the different state standards to a common standard.
- zozbot234 4y agoModern "teaching" practices are just pretending to teach concepts; they're mostly based on the expectation that the students will somehow "rediscover" everything on their own. You can't truly understand concepts without doing quite a bit of solid practice. Many teachers will fail to provide the needed guidance, if only because they often never properly learned the subject themselves; and "Common Core" ends up being used as an excuse for substandard teaching.
- comte7092 4y agoIn the past, teachers would just hand out endless worksheets to drill students. I don’t see how that is any less of an excuse for substandard teaching.
- zozbot234 4y agoWell, if we're going to have substandard teaching either way, let's pick the kind that actually works. Drill baby drill.
- yamtaddle 4y agoIt could be worse but one thing that constantly bothers me is the stupid new vocabulary. One of the worst examples: "number sentence". It means what you, an adult, might guess it does (well, it means one of the things you might guess it means) but why use it at all? They introduce it before the kids have a decent idea of what a normal sentence (what, a "word sentence", I suppose?) is. Many of the symbols in them aren't numbers (+, -, =). They don't really act like sentences or serve the same purpose. It's misleading as hell and the kids don't even have the context that might, even hypothetically, make it useful for scaffolding, when they introduce it in kindergarten. They do this for lots of stuff. There's a whole Common Core Math jargon the motivation for which I just can't grasp. Also, much of the approach is effectively what you do with kids who are struggling in math—you shower them with techniques and explanations for the same thing, hoping one will stick. The "show 5 different ways how you could have solved this" worksheets drive gifted kids, at least, batty, and that's most of the work. "I fucking solved it, I've already shown you a hundred times I understand this other technique (which I'll never use because I also know several better ones), why are you still bothering me?" They'll have them do two problems with all that extra stuff, in the time and space the kids could have practiced ten problems. It's making my kids hate math in early elementary. Wonderful. Just wonderful. [EDIT] To illustrate by example why I find "number sentence" in particular so deeply stupid: would anyone think a good approach to introducing sentences to very young children, in language classes, might be to label them "word equations" or "word formulas" or "word algorithms" or anything like that? Would anyone think that would be an improvement? God no, it's plainly a bad idea—but that's exactly what someone, somewhere, decided to do, in reverse.
- lern_too_spel 4y ago"Number sentence" does not appear in the common core standards. https://www.nctm.org/uploadedFiles/Standards_and_Positions/Common_Core_State_Standards/Math_Standards.pdf https://www.nctm.org/uploadedFiles/Standards_and_Positions/C...
- yamtaddle 4y agoThe standard matters not at all. What matters is what students and parents end up seeing.
- mrguyorama 4y agoMost people's complaints stem from assuming their local schools implementation of common core, and who they purchased the teaching materials from === "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)
- comte7092 4y agoCommon core seems fine tbh. I can’t speak to the “shitty Ed tech apps” but that seems like an orthogonal issue in comparison to the standards.
- mcguire 4y agoI 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 doing the algebra. :-)
- mrguyorama 4y agoMy argument has always been that making unmotivated (it's remedial and annoying work for them), math experts, ie people that probably have never struggled with math in their life, teach entry level math to lots of people who don't "intuitively" get things like the teacher did 20 years ago, has been a huge mistake. These professors never seem to understand what it's like to NOT understand calculus. 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.
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- drooopy 4y agoGreat video but there was no need for that clickbaity title.
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- tommiegannert 4y agoI.e. mathematical history. I think one power of calculus (and everything else) is that you don't need the history. The same way I don't need the history of the hammer to use a nail. What drives my interest is the examples. At the end, the book author talks about students not paying attention until the teacher starts talking about examples. To me, that suggests you should first contextualize and create a need for the tool, then describe the tool. Not to start introducing names of dead people, no matter how great they were. (At least where I grew up, this will always devolve into the curriculum requiring you to know those names and dates, draining focus from what actually matters.)
- agomez314 4y agoThe comparison between a hammer and math doesn't make sense, math is much more than a tool. Personally, I'm able to learn best when I understand the context and the "why" questions that people had which led them to the answer. I know other people learn differently so to each its own. Also, I agree with you in that the traditionally-taught history is awful because it lacks relevance. It's now about "how is this useful for me" or even "why should I care" but rather "why did they decide to act that way?"
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- chongli 4y agoI think the dual role of means (tool) and end in itself is part of the reason mathematics is so difficult to motivate. There is this constant tension within the pedagogy between the desires to teach the beauty and the practicality of mathematics. From what I’ve seen, the beauty side tends to come from mathematics teachers and professors who have developed a passion for the subject and genuinely want to share that passion with their students. The practicality side, on the other hand, seems to be driven by industry, administrators, lawmakers, parents, and others involved in the curriculum-setting process. Ultimately, both sides struggle mightily for students’ attention and a typical result is a collective sigh from the class. If were to make any progress I think we need to recognize that student motivation comes from within. Some students are genuinely attracted to the beauty of mathematics while others are interested in different subjects (science and engineering) for which mathematics is only a prerequisite. Perhaps one approach for dealing with this disparity might be to offer students a choice of projects with differing mathematical styles (proof vs calculation).
- thoiwerowier 4y ago[flagged]
- connectsnk 4y agoI am gonna bookmark this and rewatch this video again 8 years from now when my son reaches that age.
- buildsjets 4y agoI am gonna recommend that you youtube-dl it. You really should not expect it to be accessible 8 years from now.
- SllX 4y agoI second this. While it’s still amazing which videos I can still find from 2005 or 2006, there’s not a week that goes by where I’m not kicking myself for not being quicker to the trigger to download something.
- johntortugo 4y agoThis!
- m3affan 4y agoIf the web still exists. That's how you become a data hoarder.
- dionidium 4y agoMy del.icio.us bookmarks go back to 2003. The web of course hasn't gone anywhere, but a significant percentage of those links are either gone or no longer reachable at their original address.
- dotancohen 4y agoThis is exactly the calculus that I was taught in school - right down to the pizza slices analogy.
- michael_j_ward 4y agoIf you don't mind sharing, what grade-level, decade, location were you taught this? The key part about the pizza example is the demonstration of mathematical thinking completely disparate from what I experienced at a Catholic high-school in Chicago during the 2000s.
- dotancohen 4y agoIn Israel it's been taught this way for decades.
- jwsteigerwalt 4y agoIntegrals -> 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).
- blagie 4y agoThat's the historical progression, not the teaching progression. That's the point. Integrals were conceived over 2000 years ago. Derivatives came Newton-ish. Formalism with limits came last.
- pjlegato 4y agoThere was another step: Leibniz' pre-limits formulation of calculus used hyperreal numbers: infinite and infinitesimals (small-delta) numbers. This version is conceptually simpler and for many people more intuitive than the limits-based explanation. It was the standard approach for many years. Infinitesimal calculus was discarded in late 19th century pedagogy in favor of limits as no rigorous proofs yet existed of its general correctness, whereas such proofs had been formulated for the limits version. It was suspected that while infinitesimals were a nice intuition, they lacked rigor which might lead to unknown errors. It was eventually rigorously proven in the 1960s that the infinitesimals approach is indeed as complete and correct as the limits version, but by then standard pedagogy had become entrenched in limits. More on this at https://en.wikipedia.org/wiki/Elementary_Calculus:_An_Infinitesimal_Approach https://en.wikipedia.org/wiki/Elementary_Calculus:_An_Infini... , the modern textbook that re-introduced infinitesimals.
- makr17 4y agoFor the formal underpinnings of the infinitesimal approach, the phrase to look for is "Nonstandard Analysis": https://en.wikipedia.org/wiki/Nonstandard_analysis https://en.wikipedia.org/wiki/Nonstandard_analysis Fun stuff.
- _fullpint 4y agoIs this Three Blue One Brown?
- jonsen 4y ago"This video was part of #SoME2, a math video making contest created by @3blue1brown in the summer of 2022."
- Maursault 4y agoLet 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 mathematics is. Mythology > Mathematics
- cycomanic 4y agoI do calculations on Maxwells equations all the time, that's s calculus. Doing CAD, or any finite element calculations - > calculus. Modern engineering would not be possible without calculus. Just because software engineers mostly use linear algebra, doesn't mean that most other technical disciplines are the same.
- Maursault 4y ago> Modern engineering would not be possible without calculus. Was not my question. Nearly everyone uses computers. Computers would not be possible without electronics. How many computer users work with Maxwell's Equations or have even heard of Kirchhoff's circuit laws? A very tiny percentage, undoubtedly. The reason I asked was the Penn State professor's epiphany that no engineer among the many he asked actually used calculus.
- noobermin 4y agoHow many programmers use linked lists? I just use the list type in python, it's just "list" not a "linked list". I don't have to deal with individual nodes or pointers. I don't have learn sorting algorithms, I just use list.sort or sorted.
- SAI_Peregrinus 4y agoDo 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.
- fedeb95 4y agoThe diameter of the universe isn't even close to the highest number one could use for a real thing. Try the number of atoms in the universe... but I doubt such a threshold exists
- noobermin 4y agoDifferent strokes for different folks and all that but the concept of infinity doesn't really bother me that much because it doesn't really exist to me as a number more than it is a fact of the unbounded-ness of some set with a total ordering. It is more a statement of potential rather than actual existence, that given an infinite set, you can always find a "larger" element, which to me is just a result of the way it is defined. Infinitesimals to me are a bit more difficult because physics (the real world) doesn't actually need real continuity, otherwise physical models won't work because many continuous quantities in physics (fluid densities, temperatures, etc) aren't really continuous on small scales compared to the problem size, but that isn't needed to model such systems well. It seems like there are only a few pathological examples mathematicians come up with which is interesting and fascinating that require actual continuity, but most physical systems do not need real, actual continuity. On the same token, I guess (countable) infinite sets aren't really needed either.
- ravi-delia 4y agoI think that's why it's so handy to start with epsilon delta limits, or even better sequence limits. Once you can screen off "infinitely" to "arbitrarily" and see when and where the substitution works, you're golden. Of course there are other things in math which might rightfully be called "infinity" but they don't come up in high school calculus
- hilbert42 4y agoFirst, my mind doesn't work at the speed of that presentation, so I downloaded it in NewPipe and played it back at about 0.7 its original speed in VLC. After that it was fine. I can't say I was always good at math as my marks varied all over the place but I never really had problems with calculus. Sure, some of its mechanics were a pain—awkward integrals for instance—but the concepts usually made sense to me. As I've mentioned on HN previously, I'm a strong believer in teaching a simplified calculus to kids at a young age (in primary school). Early familiarization and appreciation of concepts such as limits and rates of change before they enter high school I reckon would greatly ease their burden of learning the subject. This needn't be complicated, introducing calculus to kids with, say, versions of Zeno's dichotomy paradox can be easy and lots of fun for them—especially so when they're asked to solve the seemingly intractable problem of the frog in the center of a pool who never makes it to the bank as each successive jump he makes is only half the distance of the previous one. Kids can clearly see the poor frog never makes it to the bank given those rules but their eyes light up when you tell them there's a 'nice' branch of math that can save him called calculus which says his feet are too big for him to drown. Thus we've introduced calculus as a friendly helpful subject at a young age and not scary frightening subject it's so often portrayed to be. In this example we've introduced them to the concept of infinite series (and infinity), limits and how calculus can solve problems that cannot be solved by simple arithmetic alone.