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“When are we going to use this in our everyday life?” (2017)

• drewm1980 4y ago
  This is also starting from the assumption that calculus is not fun. It's where a lot of seemingly disconnected mathematical ideas suddenly come together like a beautiful puzzle.
• Nursie 4y ago
  Calculus helped me understand the relationships between speed, distance and acceleration, among other things. It has also helped me draw some beautiful fractals. It's a shame for people who have had no benefit from it, I have though.
• adhesive_wombat 4y ago
  Kinda, yes. But also, specifically for calculus, thinking of things of the areas or slopes of other things, and how incremental changes affect them, is a very simple and powerful lens for lots of things. Of course, lots of teachers just hammer the fiddly memorisables until the wonder is dead because they're easy to test and/or they don't have an intuitive feel of the underlying meaning themselves. And, for calculus, the fiddlies have never been so needless to know as everything non trivial is a computer job and no one is limiting things carefully to closed forms. Few people need the chain rule specifically, they'd be much better served with knowing that there's a thing called the chain rule and what that means, rather than the exact painful calculations and lists of forms.
• saint_fiasco 4y ago
  Surely there are ways to exercise one's brain that also happen to be useful in everyday life. It's hard to pick something that everyone would find useful and engaging, so I understand why schools just pick an arbitrary subject and stick with it. It would be nice if they were honest about it. If they were, they might say something like "We could train your brains with something fun like chess practice, or something useful like programming classes and statistics. But we already have calculus teachers around because some kids will become engineers or whatever, and we don't want to hire a thousand teachers for a thousand niche subjects so we'll use the teachers we already have".
  • weaksauce 4y ago
    > We could train your brains with something fun like chess practice, or something useful like programming classes and statistics. except probability and stats does require calculus. maybe not at the high school level but if you are doing it in college it's almost certainly going to have some needing of calculus.
    • eastbound 4y ago
      How can one be a citizen if they don’t understand stats, and how to cheat them? The citizenship should only be automatic if you pass that class. Which is what the majority at 18 intends to do.
    • saint_fiasco 4y ago
      Even better. If you teach them basic statistics first, you can teach calculus later and they won't have to wonder why. Just tell them they need calculus to make statistics easier. That's what my physics teacher did. Whenever he had to explain something basic about Newtonian mechanics he would say "this would be much easier to explain if you knew calculus already".
  • deleted 4y ago
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• seba_dos1 4y ago
  I never understood people asking those questions. High school stuff is so basic that it's less about learning a particular subject and rather more about getting to know some common language that can be used to discover the world around. I hated some of the subjects I wasn't interested in back then, like biology or history, but I'm still glad that something has remained in my head because now I can have at least some basic clue in conversations surrounding those subjects and have some reasonable starting point in case I actually decide to pursue some understanding of a given topic. I believe that's the whole point of high school education after all. And not even talking about the fact that if you don't know <SUBJECT_NAME_HERE/>, you're simply not going to notice all the places where applying it could be useful.
  • munificent 4y ago
    > High school stuff is so basic For many kids, that's not true of all subjects. Some find certain courses very difficult.
    • seba_dos1 4y ago
      I said that it's basic, not that it's easy. Learning basic history wasn't easy for me either.
  • ajsnigrutin 4y ago
    The problem with a lot of high school subjects is, that you have to memorize a bunch of dates and years, random names of random plants and animals, that you then immediately forget after you pass the exam. For example, (for me), the "important things" about world war 2 is, who, why and how... what was before, what made people make decisions they did, how did it start, what happened during, and why and how it ended... the exact date when some named general attacked some small city somewhere is pretty irrelevant (atleast not a thing you should keep memorized), but a lot of history classes focus on exactly that... on which date which unit/general took over which town where did they break through, etc... I'd prefer half less memorization data and a googling class for kids to find the dates needed, and more focus on the whys and hows, because history repeats itself, while dates and names don't.
• lordnacho 4y ago
  There's a number of angles to this. Want a fancy job? This is one of the hoops to jump through. Same as leetcode further down the line, you won't do it at work but you will do it to get work. But that's also a pretty tragic take on it. Practice for other things, sure, that is also a way to see it. You won't bench press the other team but you will make yourself stronger. But for what? A sport you'll never play? What are you preparing for? Here's another one. Math, especially pure math, is a thing that is totally separate from observation. It just sort of exists without being anywhere, and yet there's all this depth to it. You can get a puzzle that cannot be solved by any anything other than thoughts, and you can keep building on these puzzles that don't exist. Go nowhere and explore. Lastly I note that it's mostly math class that gets asked this "what's the point" question. But you may as well as this about everything else you do in school, and you will mostly find that you'll have spent years to learn French for 4 weeks of actual use in France, dissected frogs for no reason, and learned how to play the recorder. All things that I'm sure you can find positives for despite the superficial benefits being quite small.
  • allturtles 4y ago
    > Lastly I note that it's mostly math class that gets asked this "what's the point" question. I think it tends to come up as a way of resisting something hard and unpleasant, and math tends to be the subject that most often feels hard and unpleasant to a plurality of young people. Of course most of us, if we had been freed from HS math as teenagers and left to our own devices, would not have gone off to do something really useful. We would have instead spent that time on something far more useless, like browsing HN. :-)
    • eastbound 4y ago
      Also, we would be gullible to whatever new trend is invented by the people who do master those topics. I have interns upset because I don’t want to pay them in bitcoins or give them shares in the company, while we’re quietly churning 1m$ ARR with just two engineers and myself (and others are doing orders of magnitude better). The same interns getting tired after 3 lines of documentation and suggesting that every documentation page should be a video, generated by those american SAAS for a hefty price. They are basically illiterate trying to cover their lack of skills. The divide between those who use and those who get used is getting wider. And I don’t appreciate belonging to the first group, knowing how little my wisdom is.
• wizofaus 4y ago
  It's hard not to wonder then whether it would be beneficial to keep solving differential equations on a weekly basis to keep our brains in shape even long after we've finished our formal education...
  • seba_dos1 4y ago
    It absolutely would and I really wish I had done that. Starting again after many years is incredibly hard, I feel like I would need to start much lower than differential equations to get back in shape :)
  • NotYourLawyer 4y ago
    Nobody solves differential equations by hand anymore. Almost without exception, the interesting ones have no closed-form solution.
    • JackFr 4y ago
      I had the experience of coming upon a differential equation, in the course of some research, which I could not solve explicitly. Mathematica choked on it and my boss and his office neighbor (both math PhD's) were unable to solve it explicitly. When I was about to give up set off to do it numerically my boss's neighbor suggested they call another fellow they both new. Two days later he delivered two neatly written sheets of paper with an explicit solution which featured a really novel (to all of us) substitution which facilitated the solution. Now in the grand scheme of things the differential equation we were looking at might not be 'interesting' in the sense of being representative of a class of problems in a rich branch of math, but it was sure interesting to us, as it modelled the behavior of the system we were studying. We all were pretty sure there wasn't a closed form solution (but certainly weren't going to spend time proving that) and were pleasantly surprised. The solver did not get a co-author credit in the eventual paper, but he did get a shout out in a footnote.
      • NotYourLawyer 4y ago
        That’s awesome, but it’s very much the exception. (And yeah I would absolutely count that kind of equation as “interesting.”)
• munificent 4y ago
  I have had to answer this question to my kids (one of whom abhors math). The explanation I gave is this: For many subjects, most kids will end up never using them. But, we have no way to predict which subjects will be useful for which kids. Without the ability to do that, our priority is maximize each child's opportunity. We never want a kid to be in the situation where they would have been interested in a subject and a career path but never ended up discovering that and using it because we didn't expose it to them. So we teach some of every subject to every kid. That way no matter which path they end up following, they are as prepared for it as we can make them. (Also, yes, I agree that math is good general training for cognitive rigor. Also, numeric literacy is vital for all adults since we live in an ecomonic world and participate in a democracy where statistics are necessary to understand policies.)
  • twelvechairs 4y ago
    What we definitely should teach kids that isnt taught is discounted cash flow analysis as almost everyone has a loan at some point in life and few know how to calculate them
    • jakub_g 4y ago
      Also, understanding basics of statistics.
    • habnds 4y ago
      I definitely learned a present value calculation in high school at some point, it's not an actual DCF but does teach that fundamental principal about the time value of money.
    • alfnor 4y ago
      So why can't they use calculators for that?
  • nicolashahn 4y ago
    I agree with this. A less tactful way of explaining it: "When am I ever going to use calculus in my life??" You? Probably never. But we're teaching everyone on the off chance that one of you goes on to do something useful with it. Enabling that one person to find a way to make rockets more efficient or something is well worth the tradeoff of wasting the rest of the class's time, from a societal point of view.
• deleted 4y ago
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• magila 4y ago
  Football players lift weights because it is known to be one of the more effective ways to build muscle strength. Do we have evidence to support the claim that learning calculus is particularly effective at improving general cognitive ability?
  • passion__desire 4y ago
    Good question. Maybe rigorous mathematical expositions should be replaced with visual metaphors or explanations that will get the idea across without children going through tiresome process of manipulating symbols and calculations.
    • rileyphone 4y ago
      "The power to understand and predict the quantities of the world should not be restricted to those with a freakish knack for manipulating abstract symbols." http://worrydream.com/KillMath/ http://worrydream.com/KillMath/
      • mr_toad 4y ago
        Most people can’t do more than the simplest derivations in their head, the symbols are just a notational placeholder, and also used to communicate with others. The abstraction is the what you have to have a knack for, not the symbols themselves.
• thraizz 4y ago
  I believe that another, quite important, part about teaching kids math is to train their abstract thinking and logical approach to a given problem. This goes far beyond math, it is applicable to most important areas of life.
• mkl95 4y ago
  > “It’s the same thing with calculus. You’re not here because you’re going to use calculus in your everyday life. You’re here because calculus is weightlifting for your brain.” There are many non calculus things that are weightlifting for your brain, including many math fields that high schoolers don't even know about. Calculus is taught to teenagers for historical reasons, do not overthink it.
  • nightski 4y ago
    I've only maybe used differentiation/integration a few times in my professional career (use it more on personal projects actually). That said, having a solid intuition about first/second order derivatives, rates of change, is incredibly valuable when thinking about the world. I probably use this intuition quite a bit in day to day life without even realizing it. I do wish more probability & statistics was taught earlier on though.
    • mkl95 4y ago
      I agree on the intuition. But once the intuition and the fundamentals are there, should teenagers spend months crunching calculus heuristics? It's still the way it's taught in Europe and it's incredibly inefficient.
      • sarchertech 4y ago
        “Young man, in mathematics you don't understand things. You just get used to them.” —John von Neumann I’m sure there’s room for improvement, but intuition and understanding are usually the result of repetition.
        • mkl95 4y ago
          Ironically, if von Neumann was alive today he would probably encourage kids to use some number crunching software rather than "getting used to it". In that sense civilization may actually have regressed since the von Neumann / Feynman days. Ditching pen and paper for sophisticated computing tools gave us nuclear power and moon landings within 20 years.
• hjkl0 4y ago
  The question includes this part: > There are literally math concepts taught in high school and middle school that are only used in extremely specialized fields or that are even so outdated they aren’t used anymore! So a more appropriate analogy would be doing the wrong exercises for the type for the type of sport being played. It’s still exercise, so probably increases the chances of winning somewhat?
  • roflyear 4y ago
    Yeah I like this better. If 99% of the people are not going to use 99% of the things taught in that class, certainly there are subjects that are equally beneficial on a problem-solving basis that are also useful.
• nradov 4y ago
  It would be better to change the required mathematics curriculum in high school and college to focus more on statistics and less on calculus. Sure it's useful to understand the basic principles underlying calculus. But even in engineering work, only a small fraction of engineers actually use calculus. Statistics is just as good for strengthening the mind, and is more broadly applicable to many real world fields.
  • yamtaddle 4y ago
    I've long held a notion that doing exactly the opposite of what lots of math PhDs think we should do in primary and secondary school would be the right path—take math education much farther from "real math". Focus almost completely on math as a tool for solving real problems. I have a feeling the people who were going to become math majors would do so anyway, under such a system, and the rest of the kids would learn and retain more math than they in fact do with how we teach it today—"here's 6 weeks on how you solve quadratic equations, without a hint of a reason for doing this, feeling motivated yet?"
  • rramadass 4y ago
    You are going to love Methods of Mathematics Applied to Calculus, Probability, and Statistics by Richard Hamming (one of the greatest applied mathematicians).
• didgetmaster 4y ago
  I learned a lot in calculus and physics classes in high school and college that I have never used over my 35 year career. But learning those principles was tangentially beneficial in many ways. It taught me how to solve problems and think through several steps to come up with an answer. When I hear or read stories about outer space, power generation, or communication signals; I have a framework that I can build upon to understand the issue. I have kids now in high school and when I help them with some math problems some of it comes back to me, but many of the formulas I memorized so many years ago are long gone from my memory. But that is ok.
• posharma 4y ago
  Tumblr is still around?
  • whateveracct 4y ago
    no it's not don't sign up and use it instead of HN pls
• psychlops 4y ago
  Now, about how you use football in everyday life.....
  • AnimalMuppet 4y ago
    I'm 60. I learned things in high school football - about physical conditioning and discipline, and being able to push myself - that have been valuable over the last 40 years.
    • annyeonghada 4y ago
      In high school P.E. I learned how if you're sufficiently athletic teachers will let you bully weaker kids. On the other hand I use calculus everyday and it is fundamental to my understanding of the world.
  • sliken 4y ago
    The value of exercise, communication, leadership, training, taking risks, knowing the competition, and predicting your opponents to name a few.
• davnicwil 4y ago
  A lot of the stuff you learn in school is basically just a peek under the hood of how something works. So in the best case you leave with kind of a shallow sample of quite a few really deep subjects. This shallow knowledge is fairly useless by itself, for sure, beyond the very practical basics, but it gives you a bit of a hook into a variety of core disciplines that you can later - maybe much later - use to connect to other things you do go deep on, even and perhaps especially in completely unrelated fields. I think really this is the value of an education done right, almost making you aware of what you don't know and giving you just enough context on it that it's not a completely unknown unknown, or unapproachable or unknowable 'magic'. So by itself any one thing you learn might be pretty useless, all together as a big picture it starts to get a lot more useful. But to get to that big picture you just have to grind through the hard, small, useless seeming stuff piece by piece!
  • adhesive_wombat 4y ago
    I still remember the lecture when it all lined up, like the Omega molecule in that Star Trek episode. Everything from Newton's laws, the quantum mechanics of a single electron, bulk materials (Ohm's law), semiconductors devices, communications theory (esp. Shannon's limit, Nyquist etc), Norton and Thévenin models, logic gates, ALUs, frequency domain operations, state machines, coding theory, all of it. It was a lecture where we basically figured out the required ADC clock jitter upper limit to get a certain number of bits at a certain sample rate[1]. At some point something fundamental like conservation of energy was invoked and I had a holy-shit moment when it all made sense. However, I do question how much of the grinding away at the maths is necessary and how much is tradition that may have made sense in slide rule and table days. Perhaps a more holistic and intuitive method with an emphasis on "if you need to do this in detail, remember this is where you go". Personally, I can barely remember any domain equations at all, other than Ohm's law![2] [1] It popped out as something like femto or attosecond and the lecturer said something like "and consider this when buying expensive audio files" (this was back when they were hard to get). [2] as the same lecturer as above told us on the first day in campus: "honestly, all you need is Ohm's law, everything else we're going to teach you is just that in a dress, you just need to know how to get back to it".
• tonymet 4y ago
  Expecting immediate or predictable payoff with any activity will set you up for failure or at least mediocrity in life.
  • NotTheDr01ds 4y ago
    Quoted from some source or are you just extremely quotable. Serious question - That is a great viewpoint!
• dnissley 4y ago
  I used to hate math up until about 8th grade when I had the realization that math problems are just puzzles and when looked at in that way can be fun and interesting. Eventually this lead to the realization that so many other things can be viewed in the same way, and that fostering this ability to change how I view things was pretty crucial to leading a happy life. School is terrible at helping foster such an attitude though, perhaps because it is incredibly difficult to do so at scale (even at classroom scale), but also because most teachers don't have this ability within themselves.
  • gumby 4y ago
    My kid hated maths in school. I told him that unfortunately he was just "learning the alphabet" and it would just take a long time. This didn't console him. Then in grade 11 he did physics and calculus and suddenly it all made sense! He was super excited. Years later he says "I guess this is just more learning the alphabet" but it sounds to me like he's trying to convince himself. :-/
• xyzzy4747 4y ago
  They should just replace some of the math classes with finance classes.
• nedsma 4y ago
  Bravo!
• diet_jerome 4y ago
  Can I get some evidence to show that practicing calculus will make you more intelligent?
• School-Cotton 4y ago
  I’ve never understand why people bitch about having to study math, but are seemingly fine studying history, literature, etc., which are just as useless in everyday life.
  • _yb2s 4y ago
    because those don't take as much effort as math
  • pshc 4y ago
    My take is that studying history and literature aids in understanding human behavior and connecting with different people, valuable in many situations, but not sufficient by itself as having hard skills/opportunity/leverage/etc are just as important.
    • asdff 4y ago
      Reading good writing also helps you write better. It makes you a better communicator no matter where you find yourself in life.
  • almenon 4y ago
    Studying history is extremely important for doing your civic duty as a citizen and voting.
    • School-Cotton 4y ago
      So is quantitative thinking, in fact I think it’s more important.
      • asdff 4y ago
        You can get that without calc
    • shultays 4y ago
      This would make sense if they teached recent history, which was at least not part of our curriculum and not to mention even if it was, it would be even more "regulated" But no, at least in where I lived (Turkey) the history classes are ancient history, then some Turkish civilizations in Anatolia, Ottomans and early Turkey history. Then we have like a 60-70 years of empty space. Is this different for other countries?
• sergiotapia 4y ago
  But even this answer is bullshit. The real answer is these are just hoops you need to jump through to get a good job. My daughter will most likely grow up to become a great artist, she has talent for it and she loves it. I can't see her ever doing algebra and beyond in her career or interests. Why do we continue to torture kids with this one size fits all? It's terrible
  • aaaaaaaaaaab 4y ago
    I was always good at art. Until the age of 14 I wanted to be an artist. I paid no attention to math - I spent most of those classes practicing graffiti lettering in my notebook. It was around this time that we got Internet in our household, and I wanted to create a custom website for my artworks, because I found deviantART lame. So I started looking into how websites are made, and ended up cobbling together a basic PHP page on a free hosting provider. I was fascinated by web programming, so I decided that I would go on to get a software engineering degree, but I still considered graphic design and illustration my main forte. The first class on the first day of university was Introduction to Linear Algebra, which started with matrices, determinants and Gauss-Jordan elimination. I vividly remember it was that first 2-hour lecture that made me realize math was actually awesome! It sounds stupid, but it was at that lecture that I realized for the first time that vectors are just lists of numbers. Like, what the hell? It all made sense, and it was beautiful! As the years went by, each new topic that I’ve learnt seemed like some kind of revelation: the fundamental theorem of calculus, Fourier- and Laplace transforms, Cauchy-Riemann equations, the central limiting theorem, Markov chains, quaternions, Galois theory, and the list goes on. I felt like I was living in Plato’s cave before, being oblivious to this infinitely complex and fascinating world. I still love making all kinds of art, but it is mathematics and software engineering where I feel truly at home. (the pay is also nice) Anyway, my point is that you shouldn’t assume someone with artistic talents wouldn’t find math enjoyable, or that they wouldn’t be talented in it if they gave it an honest try. It can “click” at any point in life, not just high school - but if it “clicks” it’s going to be an awesome journey.
• softwarebeware 4y ago
  I'm sad to see this because we literally do use calculus every day of our lives. We just don't often recognize it. The weather report is made using calculus. The calculation of the minimum payment on your credit card bill is made with calculus. Calculus is used in computer animation and video games. It's part of statistical analyses that affect government and financial institution decisions. It's used in manufacturing. It's impossible to live a day in the modern world without calculus. It's a huge missed opportunity to liken it to working out.
  • nicolashahn 4y ago
    You can use all of these things without you personally knowing calculus. The point of the question is that it's posed by the people who aren't going to go on to create weather reports, credit card payment systems, video games, etc.
    • yamtaddle 4y ago
      Maybe we can try, "you have to learn calculus so you can land a job that lets you pay for things & services that handle calculus for you, so you never have to think about it again". ... except most of those are cheap. So. Hm.
    • alistairSH 4y ago
      Except the kids taking high school calculus likely ARE going to do those things one day. Maybe not all of them, but some. Heck, I don’t use calculus directly in my daily life. But I’m glad I took it because I recognize where it is used, and how, and that helps me understand my world better then without.
    • yummypaint 4y ago
      I would argue that saving money and personal financial planning uses calculus concepts, and that they are enhanced by formally knowing calculus. It makes questions like "how much money will i have after x years given my mortgage, income, and assets?" approachable. It isn't feasible for most people to hire a human financial planner, and i wouldn't want to use automated tools without understanding enough to be able to perform sanity checks.
• deathanatos 4y ago
  IDK if that's the reason I'd given for calculus. I might not literally solve integrals, but the base knowledge of what an integral is, what a derivative is, yes, I absolutely use those. I'm also a SWE/SRE, so … there's that. But how often I see graphs from products whose entire job is metrics that are just labelled wrong, e.g., w/ the base unit instead of the rate, or what actually use the base unit instead of the rate, making for a difficult UX¹. If the devs of those products understood … calculus (let alone stats!) maybe the products would be less garbage? As it is, I still need to know that as a user. But yeah, I've not taking a literal integral in a while. Usually I'm doing some sort of very crude integration. Similar w/ the CS degree and everybody in this field going "it isn't needed" and then going "why isn't the database answering this query quickly, when there is an index on those fields?²" and follow that with a discussion of how B-trees work (or rather, don't)… And should I ever need to solve an integral, I will recognize that problem when I see it, and know what Wikipedia articles I need to page back into my brain. ¹what I mean here is, e.g., like what Azure Metrics does. E.g., there's a graph I use that measures throughput, but the unit is just "Bytes". But each point is "number of bytes transmitted during the window of time represented by that point" so it's really "bytes / 5 minutes" or something. But of course, then, you zoom, and now it is "bytes / 10 mintues" … but the axis doesn't tell you that. This has the effect that as you zoom in or out … the numbers change! Which makes no sense (obviously the effect of zooming a graph does not go back in time and alter the readings) … but only if you were properly measuring bytes/sec. (But as it is, there's a constant / divisor caught up in there.) (And that ignores harder problems with zooming metrics, like aliasing or resolution, or other metrics problems like percentiles on aggregates or efficient computation of calculated values and where to put windows, etc. … but pfft I'm in the stone age over here.) ²and it's almost always a 2D range query or a range + exact value and the exact value is the second column in the index…
• renewiltord 4y ago
  At no point in my life have I ever related to people who can ask this question. The closest I got is thinking if the names and dates I was memorizing about the Wars were worth anything. In the end, it turned out that I either have a tremendous memory through either that training regimen or that I have a memory that gives me an advantage in that test protocol: either one is a winner. And either is worth it.
• eterevsky 4y ago
  The problem with this explanation is that it doesn't answer the question "why calculus in particular". Why not chess or video games or crossword puzzles? All of them improve your mental abilities. It's useful to understand calculus because it is a basis for science and engineering. Understanding calculus will bring you one step closer to understanding how things work.
  • ActorNightly 4y ago
    Yep. By the analogy of working out for the football game, people should be taught the following * computer skills * finance math * formal logic/critical thinking/rational philosophy/bias identification * electrical/plumbing/auto/construction repair skills * cooking * principles of fitness
• wildrhythms 4y ago
  The mitochondria is the powerhouse of the cell. https://knowyourmeme.com/memes/mitochondria-is-the-powerhouse-of-the-cell https://knowyourmeme.com/memes/mitochondria-is-the-powerhous...
• abraxas 4y ago
  Maybe I'm lucky. I'm on my fifth job (out of six) where calculus knowledge has been incredibly useful. I'm not even into ML or data analysis. Just a run of the mill software engineer/architect.
• abetusk 4y ago
  This is a weak argument and, taken to the extreme, could have bad results. We teach calculus because it's a prerequisite for many scientific and engineering careers. It's not a mental exercise, it has direct, practical use for many types of scientific and engineering disciplines. We can argue whether people actually use calculus in their everyday lives (I would argue so but it's maybe overly broad) but I think the best reason is because it teaches us how the world works and has direct, practical utility for a variety of fields. On the other end, if the best argument really was that it was good 'mental exercise' then why not teach sudoku in class? Or minesweeper? Why not have people do a crossword puzzle for their final exam? We want education that has enriches and enables students, not mental machinations for the sake of it.
  • MrSqueezles 4y ago
    Yeah, the idea sounds like a black-or-white fallacy. The choice isn't, "calculus or nothing". There may be things we could teach that would be equally important that people would be more likely to use.
• pshc 4y ago
  Calculus is a workout for the brain, but closed form symbolic manipulation has few use-cases in normal life. Now take stats and probability? Also a great way to expand one’s mind, and key to decoding truths and understanding the dynamics of the world.
• tibbon 4y ago
  I wish my teachers had given me better answers to this question. As a teen I was definitely motivated by practicalities. No one could answer when I was going to use matrix math in life. The answer, which is glaringly obvious now is in machine learning. I really wish I had done better in math in particular, enabling more advanced programming, machine learning, 3d modeling concepts, DSP programming, etc. But also, things don't have to be practical to be worth learning. I just think some of the subjects I struggled with in retrospect had much better examples of when they'd be used, and a huge opportunity was missed.
• skizm 4y ago
  "You won't, but the smart kids might." -some smbc that I can't find
• _dain_ 4y ago
  I suspect this exchange never happened, but at any rate: When the teacher justifies the subject not on its own merits, but for its alleged nootropic effects, that's how you know it's either a waste of time or the teacher himself doesn't know what it's for. Same for "it builds critical thinking" -- another 100% reliable hallmark for a bunch of BS meant to waste young people's lives on classroom exercises and homework. 21st century version of digging holes in the desert to build character. Calculus is useful for hundreds of things; if the teacher has to resort to this dodge he ought to be ashamed of himself. What a waste of an opportunity to tell them about its applications in civil engineering, in control theory, in statistics, in orbital mechanics, in 3D graphics, etc etc. If I had heard what that teacher said it would have killed my interest stone dead. Just another hoop I have to jump through, for my own good. And this isn't to say that everything must be justified on utilitarian grounds -- Shakespeare is not "useful" for anything but we have it in schools because it's inherently worthwhile, it's part of what makes life worth living.
• robswc 4y ago
  I think the easiest answer to this is "does it hurt to learn it, though?" Many things you learn aren't directly applicable to everyday life... but learning how to think and _learn_ is priceless. I also assume there's more objective reasons... like teaching 100 things, knowing full well most people will only remember 10... but that's still better than 0. Yea, there's a time cost associated with learning but its certainly not the worst price to pay.
• kazinator 4y ago
  Misuse of literally in first paragraph. Math concepts never exist figuratively or metaphorically in a curriculum. They are always there, spelled out in literal letters and everything. The goal of math is to show you how ideas can be precisely put into symbols, and then symbols can be shuffled around to bring about clear reasoning according to rules that we can objectively verify to be true or false. Just because you don't factor quadratic equations or divide polynomials in real life doesn't meant that math doesn't leave an imprint on your ability to reason. The use of variables comes from math. When people use sentences like "customer C ordered from a company P", that is familiar because of the math you took in school. Math warns you of edge cases like that C and P potentially being indistinct. What's next? Drop gym class because 99%+ people don't need to shoot a basketball through a hoop in their job of personal life? Some lunatic parents being opposed to gym is a thing. Math is needed by people who go into engineering, tech, scientific and business fields. Those fields have more math courses. When you end up working in those fields, you will not necessarily use that math either, but the concepts relevant to your job couldn't be transmitted in their most rigorous forms without the mathematics. Math education is like a booster rocket. You can't declare it having been unnecessary just because it's not there any more once you have reached orbit. Nine months into life, you don't need a placenta any more, so what was the use of clinging to that? What are toddler toys good for? The only grownups using a BusyBox are embedded engineers. The "you're not going to end up using it" argument is pseudo-intellectual and hollow, based on the idea that anything used at any stage of development having to be justified by its indefinitely continued presence and utility, rather than a needed temporary benefit or a boost to the next stage, or other scaffolding role.
• blurbleblurble 4y ago
  You could easily use the reasoning from calculus in your everyday life. For example, understanding even just the basic gist of stokes' theorem could be useful just as a basic cognitive tool. But a lot of people are never challenged to think about this. Like imagine not having any intuition for flux. There are people who have none. That's cognitive impairment if you ask me.
• divbzero 4y ago
  My teacher’s answer to the same question was: “You will use it on your test next week.”
• theptip 4y ago
  There is a good analogy to weight training here. A sports team doesn’t use bodybuilding (maximum hypertrophy) techniques, or powerlifting (max strength) they use functional power training like Olympic lifts or power cleans. If you only had powerlifting it would be better than nothing, but it’s not as good as the best. Similarly, perhaps it’s beneficial to view calculus as “brain training”, but that doesn’t mean it’s the best modality. For example I think Statistics could provide the same challenge, while also being more applicable to the real world.
• pipeline_peak 4y ago
  A lot of kids at least need to have the opportunity of being exposed to something before they can decide if it’s for them or not. The amount of kids who purely decide to take Calculus is next to nothing. They need applied interests to see the usefulness of higher math. For a lot of us, that was software or programming.
• Tade0 4y ago
  I think there a better argument to be made here and it's: you need to understand what's possible and what's not in a broad spectrum of fields. Case in point: a lot of bad cooking/cleaning advice comes from the lack of understanding of high-school level chemistry.
  • Smoosh 4y ago
    Just this week I have watched two videos on YouTube where the presenter is trying to address the comments on their previous videos where people are suggesting (something like) "connect an alternator to the wheels on an electric car to generate "free" energy to run the car". These comments show a thinking, inventive mind wishing to be useful and improve things, but such a basic lack of understanding of physics. I can only think that these people weren't paying attention at High School, were (poorly) home schooled, or have some sort of incapacity to understand/believe the established laws of science. Yet they think that they can invent simple solutions which have somehow eluded the experts in the field. Perhaps it is some form of Dunning-Kruger effect.
    • Ekaros 4y ago
      I overheard my cousin and her father discussing about how lower powered electric kettle would be more "efficient"... And this is relatively well educated person in adjacent field... Smartly I and my father didn't say anything. Sometimes these sort of fundamental blind spots make me wonder about effectiveness of the system.
• ozim 4y ago
  I don't like this answer but I kind of see how it fits this specific scenario - answering bunch of high-schoolers and keeping them somewhat motivated. For me real answer is "if you manage to learn yourself calculus - you will learn how to learn anything". Most of the time when I just pushed through at university I noticed ways I retain knowledge - how after first repeating steps time after time without understanding I was starting to grasp things because I did something 10 times and somehow things fall in place, how trying different approaches helps to connect the dots, how building mechanical movements on basics help me speed up understanding of more complex stuff. Just like you have to grind multiplication table to later solve longer equations quickly. Now lets say you don't solve equations - but whole approach applied to filling in taxes, like first you fill in forms as an example 10 times, try to calculate all on your own 10 times - and yes you are wrong because you don't understand all fields and why you have to fill them in and with which value. If you do it 10 times on your own you submit 11th that you know is most likely correct. You also learn how you feel when you are wrong - so you get intuition that "this is stupid" starts to be "I don't understand it yet - have to dig through a bit more". Well high-schoolers by default mark things "this is stupid" if they don't understand something which is also meta answer for such question - but telling them that they don't understand is not proper answer in class setting :).
  • yamtaddle 4y ago
    > I don't like this answer but I kind of see how it fits this specific scenario - answering bunch of high-schoolers and keeping them somewhat motivated. The great thing about kids is that they'll often accept shitty arguments as long as they seem legit at first glance. I mean, so will plenty of adults, but kids especially. Which is handy since, as an adult, shitty arguments are most of what I've got.
• agentultra 4y ago
  You need to learn how to think. How to solve problems. How to express your ideas clearly. Maths is excellent training. And it can be enjoyable for its own sake without being practical!
• jawadch93 4y ago
  [dead]
• ergocoder 4y ago
  > It’s the same thing with calculus. You’re not here because you’re going to use calculus in your everyday life. You’re here because calculus is weightlifting for your brain. I doubt that there is no other ways (e.g. lower cost, more effective) to weightlift for your brain than learning calculus. Also, the professor has a conflict of interest here (e.g. making calculus sound important because he teaches calculus). It's like me holding a shit coin and pumping it up, but yeah let's ignore that conflict of interest.
• kylehotchkiss 4y ago
  And I still will never forget that my school never taught me how to write a check, how to file taxes, how to find jobs, how to find community in life. All that stuff about photosynthesis sure helped though!!
• WheelsAtLarge 4y ago
  “Bingo!!” said the teacher. “It’s the same thing with calculus. You’re not here because you’re going to use calculus in your everyday life. You’re here because calculus is weightlifting for your brain.” Total BS... There are better ways to exercise your brain that will be many more times better than Calculus. This is HW so one that comes to mind is programming. But there are so many more. Here are a few, understanding and fixing a car, understanding music and playing music, art appreciation, literature and understanding the human condition and on and on. Recent research has shown that doing daily exercise is a great way to keep a healthy body and brain, rather than sitting on your butt learning a useless subject. Yes, there are professions where Calculus is needed and there are people that truly enjoy math. Cool, take all the math you need and want to learn. You should take it. Anyone that tells you that Calculus is a good way to exercise your brain is just trying to justify their job. Don't for a minute believe that it's the best way to use a limited resource like your time. Source: Me, it took me 3 semesters of Calculus to figure out that it was useless to me and 90+% of the people that take any of it. P.S. note: Many people disagree. Good, you should not take it as absolute truth. I guess my real point is that you should question whether you really need to take Calculus. Don't just take it blindly because you are told you should. You have other options.
  • otabdeveloper4 4y ago
    Seems like the grapes were very sour.
  • behringer 4y ago
    Programmer here. I wish I knew more calculus. It's really tough to learn outside of school and much older.
    • tayo42 4y ago
      Why? There's so many resources now. I actually tried to relearn calculus recently. I ran into the same problem I had the first time in college, it felt like learning for learning sake and didn't have a strong enough motivation for it
    • danielvaughn 4y ago
• DrewADesign 4y ago
  I have a learning disability related to some incredibly common cognitive issues that impact symbol recognition. I can abstractly reason about the concepts vastly more easily than most and can do fairly complex problems in my head quite easily– speaking to a math PhD candidate a year or two ago, he said "you know, you think about math exactly like a mathmetician does. I can't believe you're not interested in pursuing math in school." My cognitive profile, however, makes doing calculations on paper painstakingly difficult– high school geometry (passed in summer school with a D) was about my limit before failure was guaranteed. This shut the door to every college opportunity I was aware of. I ended up graduating in a night school program while working full time. Only after two decades when SATs and high school grades were no longer relevant did I start a BFA program, and soon after I realized how abjectly the system had failed me. I always assumed I was a fuckup with no discipline (which is what I was told) and played the part accordingly. Cognitively, I tore my program to shreds. A solid 4.0 GPA while having the time of my life takes more than the responsibility gained during adulthood. I could have easily competed in a serious ivy league degree program given the opportunity. Sure, learning traditional math calculation can benefit many people– but not everybody is cut out for it, and that's fine. Student should certainly be encouraged to pursue it, but using it or any other individual skill as gatekeepers for an enormous number of educational paths that may perfectly suit slightly different cognitive profiles is fucking stupid.
• didibus 4y ago
  I think it begs the question, but is Calculus the best and only way to exercise your brain? What if you did programming instead? Or learned anything else? More practical math maybe even like Linear Algebra? It reminds me of how my teachers justified why we were learning Latin, it'll make you better at languages, it'll be easier for you to learn other languages after... But all this is true if you learn Spanish instead, and you also happen to have learned a practical skill while you're at it!
• harrisonjackson 4y ago
  The way I explain it to my kids is all about opportunities. I am not going to force them into a career path that uses calculus but I am going to make sure they have as many opportunities as possible to make their own choices later in life and that means right now they will do the math homework.
• sbf501 4y ago
  I was trying to fix a curtain the other day and cursed myself for not paying attention in 6th-grade Home Economics class. And not a month goes by when I don't hear my 10th grade American History teacher's voice in my head. Or my 8th grade teacher's grammar class when I can remember how to reword passive voice in a document, or whether I used a dangling participle in it. :) I'm pretty sure the idea that "90% of what you learn is school is a waste" is just some bullshit spun by adults who got poor grades, various BS artists hawking something (or even their own persona), or people that want to restructure schooling in the US (which might not be a bad thing... in some cases).
  • aidenn0 4y ago
    ... or teenagers who both want to get out of learning things and think being cynical is the same as being mature.
• geuis 4y ago
  I highly doubt it was worth the 20 seconds of my time it took to load that page, dismiss the egregious popup, read the article, then fight whatever javascript was overriding the back button just to get back here to leave this comment.
• Archelaos 4y ago
  The main problem with teaching calculus at school is, that only a few pupils really come to understand it. For most pupils, the educational outcome is the opposite of a meaningful "weightlifting for the brain". In order to pass their tests, they try to memorise some recipes that they have made up from sample solutions. Instead of learning to think systematically, they are taught to somehow muddle through and feign understanding where they know nothing at all.
• imgabe 4y ago
  When are you ever going to have to explain a sonnet or tell someone the the date of the battle of Gettysburg or dissect a frog or know what a precipitate is or… basically any specific thing you learn in school? It’s not that you have to do each thing every day, it’s that they give you a broad understanding of the context of what humans know about the world and how it works so you can understand it. Calculus is part of that too. What would school look like if we only taught things that are used every day? I guess kids would learn how to drive a car and put on pants and sit in a chair and read emails and that’s about it. You know how TV shows with long-running story arcs will have "Previously on..." before an episode to catch people up with what's happening? School should be a 12 year long "Previously on..." the whole of human history so people can go into the world knowing what's happening and how we got to where we are.
• m463 4y ago
  I remember reading "Surely You're Joking, Mr. Feynman!" and remembered the section where he was evaluating math textbooks. He was annoyed that kids would have to learn number bases that were not 10: "Translating from one base to another is an utterly useless thing." But honestly that is something from math class that I use EVERY day (ok, ok, maybe not weekends)
• Waterluvian 4y ago
  I used to be irritated about all the crap I suffered through. School was very difficult for me. University was a complete breeze, which shocked me. But as an adult I look back and am glad that I was exposed to all those subjects and concepts. I forgot most of them but I remember the broad concepts enough that I am at least literate when smart people are talking. This applies to the arts more than the sciences for me. I’m still angry that the website kidnaps me and ruins my back arrow.
• javajosh 4y ago
  Calc is a mental tool, like a library, that you can use to explain things. DEs are a particularly useful abstraction for understanding flows: of things, money, people, etc. But you have to be looking to apply it because hardly anyone else is (although YouTube has surfaced some really great thinkers who do know calc and who do apply it, and I don't think would get audience otherwise). As an application programmer, I think I've gotten the most value out of the concept of coordinate transformations, which is a physics thing. It's hard NOT to see all the different languages (and their framework dialects) as different coordinate systems in which we describe our tiny, fast, valuable machines.
• ifdefdebug 4y ago
  What? I use my high school calculus every day since 30 years intuitively, knowing how things relate to each other through differentiation and integration helps me so much to model the world around me correctly. Having a good mental model about how distance, speed and acceleration relate to each other is just one example, and it's not obvious if you don't know the foundations of calculus.
• rolph 4y ago
  if you imagine yourself doing what you are doing now, forever, then you will never use this. if you intend to go beyond what you are now and become catechismically independent; in others words greatly reducing the chance someone is going to pull one off on you, then you will find this very useful and you will know it when that time comes
• raydiatian 4y ago
  I don’t know about the author’s take. It’s good at first blush but the aftertaste feels like a bad over-simplification. It implies to the audience (ahem dumbass high schoolers) that Calculus is just brain teasers. So then, if they just do brain teasers like crossword puzzles or something (remember, high schoolers), they’re getting a substitutable “workout”. Which they’re clearly not. The other thing is the ironic self-fulfilling prophecy wrapped up in all of this: the question is “when will we use calculus?” the “answer” is “never”; the jobs that don’t require calculus are the ones filled by people who never mastered calculus. They’re also statistically speaking, the lower paying jobs. I work in a field that I’m not particularly fond of that has nothing to do with calculus, yet, given that it’s the 21st century, and given that AI is on the rise as an applied technology, rest assured that EVERYTHING uses Calculus.
• mihaic 4y ago
  This nice story has unfortunately two flaws: it ignores the cost of opportunity for doing all that highschool match (the alternative is not nothing, it's learning something else), and it uses a terrible example -- calculus actually is used by a lot of people at least some times in their life.
• Barrin92 4y ago
  Love the comment and I really dislike the "usefulness" attitude. Learning useful everyday things is the task of parents, or a youth group, or a mentor, or what have you. Here in Germany, regarding school, Wilhelm von Humboldt's Bildungsideal has alwas played an important role in framing the function of schooling, and I always found it astonishing how his attitude has if anything become more relevant, given that he wrote this over 200 years ago. "There are undeniably certain kinds of knowledge that must be of a general nature and, more importantly, a certain cultivation of the mind and character that nobody can afford to be without. People obviously cannot be good craftworkers, merchants, soldiers or businessmen unless, regardless of their occupation, they are good, upstanding and – according to their condition – well-informed human beings and citizens. If this basis is laid through schooling, vocational skills are easily acquired later on, and a person is always free to move from one occupation to another, as so often happens in life." Schooling lays the foundation for people to become fully developed adults, citizens and to cultivate the ability to learn. It's why we do sports, read classical literature, take religious classes, even if we don't 'use' them. They're important parts of our culture, and it's hard to imagine how someone could navigate or begin to understand our culture not being equipped with a well rounded basic education.
• tunesmith 4y ago
  I took Calculus in college and stopped there. And while some of it was cool, it mostly felt pointless. Decades later, I'm playing around with some concept at work. I was asked to estimate something, but it was annoying because it depended on multiple things. If one was low and one was high, then the result was low. It was only when neither were low that the result was higher. I could even program a function for it. In a sudden burst of what felt like inspiration, I graphed it out, thinking I could eyeball something, and it was a nice even curve that went up and then back down. I was honestly stuck there for a while. I was eyeballing it and wondering how I could actually figure out where it was at its highest, like exactly. "Huh," said my atrophied brain from college. "You know what's funny, is that the highest point of the curve is also when the line is flat." I stared stupidly at it for a while longer until it finally, finally hit me that I could take the derivative. I still remembered the derivative rule, that part was pretty easy. But coming to the point where I realized I could use it... that took a while. I guess the point is that you get out what you put into math class. You can be drilled on problems but you won't necessarily recognize the situations where you can apply it. (They should probably try and teach that more.) Once that switch clicked on in my brain, I learned to recognize more things like that. Using pre-existing "set" intersection/union functions rather than just slinging arrays. Recognizing when I had a collection of similar linear equations and realizing I could put them in a matrix. And yeah, the occasional derivative. It's "technically correct" that we might not ever NEED these tools in real life, but we're faced with situations where they might be helpful more than we actually realize.
• smeagull 4y ago
  I do think the education system has hurt education by mandating a set of things that every student needs to know, and is under-serving everything else. I'd compare this to the outdated 'literary canon'. Calculus is fun, but I know many people who don't think so. Some that found out it was necessary and had to make it up later. You're never going to convince the kids that it is necessary now to study it as effectively as they might. Ironically I've not needed it anywhere near as much as I though now that autodiff tools exist. Why not allow them to study something else, then come back to it when it has proven necessary for them? There are other exercises for the mind.
• jonnycomputer 4y ago
  All the things that I thought I didn't have to learn ... and then I became a home owner. Calculus is a tool. Wouldn't you rather have more tools than fewer? Because the right tool for the job can turn a real chore into something as easy as pie. If you want to go through life with an empty toolbelt, well, then you'll have to borrow other people's tools (or other people), to do what you could have done for yourself. And that usually isn't cheap.
• analog31 4y ago
  I was a math / physics major in college. Two useless subjects. ;-) But I still love both of them, and use them in my job. Any work site with enough people will hand all of the math related work to the "math person," and that person will be forgiven of other kinds of drudgery. It's a fair trade. Still, that's survivor bias, and I'd be the first person to support reforming math education. I would divide K-12 math into 4 quadrants: 1. Arithmetic, which is the manipulation of symbols, up through algebra and calculus. 2. Computation, which is the use of computers to solve problems. 3. Dealing with data. 4. Theory, which includes things like sets, proofs, and so forth. If any 1 of those 4 things makes math come alive for a larger number of students, it's preferable to focusing exclusively on arithmetic. (Theory is gone, my kids did virtually no proofs in school, and never learned about sets). Note that I didn't mention statistics. Memorizing statistical formulas made sense when computation was expensive, but I think learning about data by playing with random numbers would make a lot more sense, would reinforce computation, and lead to students being able to try things on their own. To this day, despite taking a year of statistics and doing a PhD in physics, I still don't trust myself with statistical formulas unless I check if they make sense by throwing random data sets through them.
  • WheelsAtLarge 4y ago
    "Memorizing statistical formulas made sense when computation was expensive" Statistics is way more than formulas. It's easy enough to learn and, if you understand it, so applicable to one's life that it should be one of the principle courses in school. Here are some basic ideas where it will help. - helps you understand why the most dangerous part of any flight is the time you spend in a car not the plane. - why it's useless to try to break even at a gambling establishment - why the best way to win at the lottery is to never buy a ticket - why birth control is good at its function but it's not absolutely secure I can go on for hours. Statistics needs to be part of any educational reform. It's so useful
    • analog31 4y ago
      I'm in agreement about those examples, and maybe we agree overall to the extent that for me, "way more than formulas" includes working directly with data. I think the ability to interrogate data directly adds to the ability to think quantitatively. It was just not practical to do when I was in school. And the blizzard of formulas is an obstacle to learning for most students.
• throwbabyboom 4y ago
  People who ask this question never understands. By their logic. Educated people vs non educated people will have similar opportunities in life. But I guess if you have to ask these kinds of question, then you are as ignorant as someone uneducated.
• e12e 4y ago
  I think this has more to do with our inability and unwillingness to teach calculus from a practical perspective - somehow stubbornly shying away from measuring the acceleration imposed by gravity, building trebuchets, looking at planetary orbits or doing tests with growth of bacteria in school. I'm reminded of a short aside by Wilde: > “He looks just like an angel,” said the Charity Children as they came out of the cathedral in their bright scarlet cloaks and their clean white pinafores. > “How do you know?” said the Mathematical Master, “you have never seen one.” > “Ah! but we have, in our dreams,” answered the children; and the Mathematical Master frowned and looked very severe, for he did not approve of children dreaming. - Oscar Wilde, "The Happy Prince" https://www.wilde-online.info/the-happy-prince.html https://www.wilde-online.info/the-happy-prince.html
• infinitifall 4y ago
  I have always found questions like "when are we going to use this" repulsive. It is the mark of an individual who sees themselves as little more than a slave, forced to learn things to stay useful. The logical conclusion of this would be a world where everyone only knows exactly what is required of them and nothing more. Answering this question would miss the whole point. What ever happened to general knowledge? Don't you want to understand a fundamental part of how the universe in which you exist works? If you don't know calculus I consider you illiterate and unable to understand much of world you live in, just like you are illiterate if you don't know that the earth is round (and why would you need to know that, I wonder?).
  • ablyveiled 4y ago
    >Don't you want to understand a fundamental part of how the universe in which you exist works? Only for a reasonable price. The price differs between individuals for many meaty and mindful reasons.
  • bick_nyers 4y ago
    I think the illiterate part is a bit harsh but I generally agree with the rest of your sentiment. I was just recently giving your exact argument, that if in high school you learned only exactly what was needed to perform your job as an adult, you would essentially be a cog in a machine that requires the world to stay completely static for your entire life in order for you to not get screwed when your skills inevitably become obsolete. The point of calculus (which imo is just the common path of achieving mathematical maturity) is not that you will use math in your day to day, but that you will be a more well-rounded and dynamic person mentally. That being said, uninspired high school mathematics focused on memorization is not helpful for anyone.
• Loocid 4y ago
  Why is it always math that people pick on when this argument comes up. I've never needed to use the periodic table, or calculate the potential energy of something, or know the model of an atom, or analyse a poem, or [...]. I imagine most people don't need any of that yet for some reason it's always math that is the boogieman of "useless" topics we learn in school.
  • raegis 4y ago
    This is exactly the problem. And we're all suffering for it.
• marsven_422 4y ago
• labster 4y ago
  I was planning to be a meteorologist, so I took all of my calculus at community college before transferring. I can remember thinking about how Taylor series were so boring — when would I ever need to estimate a function rather than solve it? Two years later: literally everything is numerical methods. Taylor and I became besties, and model some weather together. Sometimes what you think you need to know is just wrong.
• langsoul-com 4y ago
  There is no such thing as general intelligence exercises (to my current knowledge). You know those brain mobile games, that claimed you'd be smarter by doing some pattern matching games? They got sued for lying about how effective their games are. It doesn't work, only makes you better at said game. There was a post on HN recently lamenting about the calculus cartel and you don't get taught WHEN you need to use calculus. Which is the only time you actually need calculus.
  • THENATHE 4y ago
    To be frank, I disagree. A large amount of thinking at a level higher than day to day mundanities revolves around understanding how to think abstractly and critically. Something like calculus, while completely worthless to many people, teaches concepts like: things that seem overtly complicated are not necessarily, things that appear simple and small could be wildly complicated, and the process of telling the difference through practice, skill, and experience; how to think in ways that are beyond sensory; how to build knowledge on subjects that can provide context (if you know how to perform limit functions you can more accurately estimate what a limit function would look like and then apply that concept or estimate) to the real world in abstract but useful ways. General intelligence exercises is just a term to mean “teaching people how to think in a more abstract way”
• kwertyoowiyop 4y ago
  It’s sad that Tumblr hijacks the Back button. Who on earth is happy to experience this?
• langsoul-com 4y ago
  Every time there's a post about school or uni topics, it's always yeah X is useless, teach Y instead. Or X is actually super useful, it must be kept. If you could rewrite the entire R - Year 12 curriculum, what would it look like? Hell, do we even need to be in school till 18? Why not finish at 16? 12? Etc.
  • raydiatian 4y ago
    As a non-educator, as I am aware that I am unaware of the degree to which teachers as a resource drives and equally limits the opportunity for changes across the strata of education… 1. Delinearization of progression. You don’t “advance grades” until you demonstrate mastery, and it’s not a competition. 2. Allowing aptitude and interest to tailor schedules. I will never need my ability to rattle off the capital of each state, and that was definitely a wasted week or two. Somebody got PAID for that, and it still blows my mind. 3. Better mental health budgeting.
  • asdff 4y ago
    I think programming has to be taught just like writing is taught. Its so generally useful. Everyone has something going on in their lives that they can write a script to do, if they only knew they could even do such a thing. Too many people don't realize what these computers can really do for them beyond the four walls of the gui and software made by someone else, and its kinda sad.
• semireg 4y ago
  My big calculus (I, II, III) takeaways were rate of change, acceleration, inflection points (e.g. accelerating at a decelerating rate), and funky word problems involving filling bathtubs with a flow of water and calculating how fast the water line moved up the tub, or piling grain (cone) and measuring how fast the top of the cone was progressing upward. Mental weightlifting, heh.
• justbored123 4y ago
• pfoof 4y ago
  And I will never forget what one assistant who had classes with us said at the university I was attending: In Poland public universities are "free" (paid from the taxes), and those are known to be of a higher level than their paid counterparts. But it's also common for polish students to skip lectures, very common. So the dialogue went like that: - Do you know how to do this double integral? - silence - Have you been on the lecture? - laughter - saddened You know, I was also a student not so long ago, but you must know that in the US people take loans for life and pay a lot of money for such lectures. I do remember those stories from the US.
  • rawgabbit 4y ago
    I believe your comment his the nail on the head. For non-US residents, they may not realize that a university education for an American is basically indentured servitude. The American student, as of today, must decide upfront what his career path will be. Because he will be taking on a gigantic loan to train for that career. If that career does not provide financially, the American student is burdened with debt that he cannot discharge even in bankruptcy. Yes, Americans want to prepare for their career. That is why they look at calculus and other required subjects as an unnecessary tax on their time in college and monies. For what it's worth, I have had extensive classes in calculus and statistics at the graduate level. For most people, those classes would be useless. They would be better off mastering Algebra and Finance 101 (how loans work and net present value of money). For non-engineering types, I would argue they are better off mastering Statistics as they will be reading and reviewing scientific experiments their entire career. I find the argument you need to master calculus to master statistics disingenuous. Statistics instructors are perfectly capable of teaching all the concepts needed to understand statistics within the class including any that may have derived from calculus. If extra instruction is needed, they can offer a pre-statistics class. This argument, as it seems to me, is that calculus instructors are threatened by statistics instructors.
• chucklenorris 4y ago
  So much of our antropic world is built on top of calculus, that without it it's like being a 17th century man in 21st century. Sure, you don't need to understand the world you live in, that's why we have these nice user interfaces for everything, but when cracks appear in these ui's or if you want to come up with something new, you're stuck making wrong assumptions and are doomed to fail. Even worse, you're vulnerable to all sorts of snake oil peddlers. This is the reason to learn calculus not some sort of fancy crossword puzzle.
• j7ake 4y ago
  People learn math so that they can learn more math. If you don’t want to use math in your day to day life then don’t learn math, there are ways around it. There are probably non-calculus ways to explain and do things such that in a “real job” you won’t need to use calculus. Eg MRI machines use Fourier transform, but a technician doesn’t need to know that. However, if the goal is to learn more math, connect broad concepts, and extend math concepts, then basic fundamentals like calculus is essential. So in terms of being a pure “technician”, you can get away from no calculus. If you want to know why things work and how to extend abstract concepts beyond their use case, then calculus is a fundamental tool.
• animal531 4y ago
  As far as I'm concerned N% of classes should just be replaced with reading (and actively helping kids who struggle to read and/or comprehend). Being able to read/comprehend fast is just as much exercise for your brain. It also teaches you more about how people think/feel (through the author/characters). When it comes to exam time kids who are capable readers have it much easier since they have extra time over other students who struggle with understanding the questions.
  • worldsayshi 4y ago
    I agree with the sentiment but I also think that we might sometimes rely too much on prose to describe the world. The big problems that the world is currently facing is not very well represented that way. I think our efficiency in dealing with hard problems could be greatly improved if there was an easy way to debate using mathematical models instead.
• meigwilym 4y ago
  Wow, I thought of this exact same analogy but with rugby instead of American football. I think the same is true for all subjects. My son has the same issues with English literature, but I explain to him that learning to analyse things is a huge part of the brain gym, Of Mice and Men only being one of them. Being able to look at a problem you don't understand, and at least have a basic set of tools to try and gain some insight is hugely valuable.
• k__ 4y ago
  I think, a better answer (for now) would be, calculus is hard, some people get it, some don't, we don't know which. So, we have to try all of you in the hopes humanity will get enough people out of that practice that understand it and can further fields that rely heavily on calculus.
• quickthrower2 4y ago
  I didn't really touch calculus at any age where I was forced by law to be in school. It was only after the age where I chose to be in school that I "had" to learn it. I enjoyed it too much to worry about if it was useful! Although "something something well paid job, maybe actuary..." sprung to mind.
• oneby137 4y ago
  If there is a buffet of food, chances are you won't eat most of it. But usually you can sample a wide range of different foods at a buffet. School should be the same way. It should present you with a variety of pursuits so you can find out what you like and what you are suited too. There is no way to tell if "maths" isn't for you until you've had a serious go at it.
• konschubert 4y ago
  An intuition for calculus is essential for being an informed citizen. You can't be an informed citizen in todays' complex world if you do not understand the difference between linear and exponential growth and if you have no intuition how changes in the rate of change affect the total. That being said I think maths is taught quite badly in the US. There is no point learning the rules if you don't have an intuition or can at least prove WHY they are like this. Yet the US focuses way too much on the "rules", and way to little on the intuition.
• the-mitr 4y ago
  > What the members of the mathematical community—especially those in the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM)—have known for a long time is that the pump that is pushing more students into more advanced mathematics ever earlier is not just ineffective: It is counter-productive. Too many students are moving too fast through preliminary courses so that they can get calculus onto their high school transcripts. The result is that even if they are able to pass high school calculus, they have established an inadequate foundation on which to build the mathematical knowledge required for a STEM career. https://www.nctm.org/uploadedFiles/Standards_and_Positions/Position_Statements/MAA_NCTM_background.pdf https://www.nctm.org/uploadedFiles/Standards_and_Positions/P...
  • Aromasin 4y ago
    God can I relate with this. My college/high-school experience of Calculus was miserable. It was built on already shaky Math foundations, so I simply did not understand it at the time. I did enough past papers to memorize the sequence needed to solve the questions in the format they gave it in, and squeaked by with a B or a C iirc. It was never explained to me why I would ever need Calculus, other than to pass my Math exams so I could go to University and get a good job. All this study; 0 context. Lo and behold, I went to university to study electrical engineering. I needed it for everything, from differentiator circuits, to digital signal processing, to current flows. Limits, derivatives, and integrals are the backbone of EE. My foundational knowledge of Calculus was non-existent. We glossed over it on my course because the assumption is that most everyone knew it because it's part of the College curriculum. I had to go through hell and back at university, doing my coursework while simultaneously catching up on all of the mathematics I had failed to grasp in my college days. I would have been much better served by solidifying my Algebra, Geometry, and Trigonometry. Better yet, do a pre-Calc (not really a thing in the UK afaik) course containing 101 real life examples of where this might be useful.
• specproc 4y ago
  I just did a log-log polynomial fit for the first time outside of the classroom. It's funny when things come up.
• galdosdi 4y ago
  Here's the actual story of why calculus is required. It is required because it really was very useful in the jobs of many high school graduates at the time the curriculum was formed[1]. Unfortunately times change but school curriculums have incredible inertia. The concepts of calculus are incredibly useful. If you really think derivatives and integrals are so obvious (let alone, N'th derivatives and N'th integrals), sorry, you are wrong, you just have known these concepts so long you forgot how to think of them as nonobvious. This is a common effect. If you doubt this, talk to someone who definitely has never been exposed to these concepts. BTW the valuable concepts of calculus go further than that. For example, the derivative of an exponential curve is always another exponential. This fact was at the top of my mind at the start of the covid pandemic as it was very relevant, as it means that if either of the "cases per day" or "total cases so far" graphs is an exponential, the other will be too. Similarly, the fact that the exponential is a solution to the differential equation y` = ky is very meaningful IRL. It means anytime the rate of growth of something is proportional to how much something there is -- such as reproducing life forms where their respective reproduction doesn't interfere with each other in some way -- you'll get an exponential. I could go on and on. So, we obviously should not stop teaching calculus. We just need to stop teaching the 80% of the curriculum that focuses on being able to do manual calculations that very few people will ever need to do. This actually allows more time to focus on more important concepts and should leave the rare student who does end up needing symbolic calculus very well prepared to quickly learn it on the fly. Best of all, it allows time to add math that was not so relevant in 1910, but is very relevant today -- discrete math, the math of computers. Counting and basic combinatorics, basic boolean logic, basic graph theory, etc. All very applicable things. Literally every time I go to the grocery store and form a single line but all the other dullards form individual lines, because they don't know or care that a single line is proven to be more effecient, it becomes relevant. Also, more emphasis on probability and statistics. [1] Nobody used to go to high school, essentially. In the early 20th century there was a movement to build a lot more high schools and get more people going to high school. High school graduates were more necessary because of the exploding industrial sector. And who designs the machines and factories and processes? Engineers. And the more you can apply fancy math, the better, more cost effective designs you can produce. And what kind of engineering is this? Mechanical and electrical, occasional chemistry. All uses calculus. And all calculus had to be computed by hand with paper and slide rule. So you had a need for a vastly increased population of people who could be comfortable sitting at a desk all day doing integrals, perhaps referring to a big fat tome with tables and tables of integrating tricks from time to time. It actually made sense at the time. Everything since then is just justification.
• uup 4y ago
  I thought a lot about this over night. As a parent, it's a question I constantly grapple with. "What will I tell my child when they want real-world applications of an abstract, yet extremely important, topic?" The conclusion I've come to is that asking for practical, real-world applications in one's life misses the point. The reason to learn calculus also has nothing to with mental exercise. The reason to learn calculus is that it provides the theoretical foundation upon which modern society is built. Differential equations provide solutions to engineering formulas that allow us to build skyscrapers. We can calculate the trajectory of celestial bodies and use that information to explore our solar system and to peer into the stars. We can train machine learning models that realize our imagination. The list of things calculus enables is near-infinite. Now, do you need to know calculus to survive? No, of course not. You can live your entire life without even needing calculus. But, calculus is one of the wonders of the world. Its beauty is similar to something like the Grand Canyon or Mt. Rainer. Yes, it takes a little work to "see" calculus, similar to how you might need hike quite a distance to reach a beautiful peak, but the view from the top is worth it. There is no need for natural beauty, too. You can easily live your life without experiencing the wonderful things nature has to offer. But to live a life without experiencing nature is dull compared to what is possible. And it's the same with calculus.
• solarmist 4y ago
  Copied from a comment elsewhere. Statements like this are very saddening to me. They completely miss the point of calculus and other high school mathematics. Honestly, I think the idea of non-linear change should be taught starting in elementary school. The ideas underlying calculus are VERY intuitive (adding up small bits of change over time) but completely absent until you reach calculus. The mechanisms of calculus probably don't matter, but calculus is the study of change. In particular, how things change over time in non-linear ways. What things in real life change in non-linear ways? Almost everything! _Linear_ change is nearly fiction in daily life! Calculus is the abstraction of multiplication in the same way that multiplication is the abstraction of addition. THIS is the real reason why calculus is important. Knowing how to study, describe, and understand changes that are not constant. If that isn't important in real life, then neither is counting or multiplication. Unfortunately, calculus is so deeply embedded in the vocabulary and forms of mathematics that even people with a "full education in calculus" often can't describe that. So they resort to stupid metaphors. They only unconsciously understand its value and fail to describe it.
• foxyv 4y ago
  Calculus is where I learned how to solve a hard problem. The kind of problem that takes more than a few moments to solve. It taught me how to sit down and actually focus on finding a solution without getting frustrated and giving up. If you can't do calculus, then solving the even harder problems in physics and engineering is going to be nearly impossible. However, should Calculus be the hurdle that nearly everyone has to jump over to get a degree even if they don't really need it? I honestly don't know. There are probably better ones now with computer algebra systems entering the fray. Then again, having calculators hasn't removed the need to learn times tables. We should certainly change the way we teach Calculus though. The current setup is horrible.
• Py-o7 4y ago
  I was at a talk featuring Richard Thaler a few years ago, and someone in the audience asked a question in a vein that runs through the comments here -- 'is it better to teach high school students stats or calc'? Thaler's response: I don't think it matters as people will forget either. For example, by show of hands, who here remembers anything of substance from their highschool chemistry class? I was mortified that only I and ~5 others raised their hands out of a very large group. (I picked up the ideal gas law and dimensional analysis from said chemistry class and have found the latter to be quite useful.)