@@MathTheWorld I totally agree with what you say in your videos and I wanted to let you know that there is a sub-community in the field of mathematics education who are developping a new "paradigm of teaching", as they call it, which intends to tackle some of the issues you named, that are caused by the inflexibility of standard curricula. The theory they subscribe to is the "Anthropological Theory of the Didactic" (or "ATD") and the teaching method they promote is that of "Study and Research Paths" (or "SRPs"). So far, their method has mostly been used at university level though. The goal of the method is to define a "real" real world problem and to let students research which kind of mathematical knowledge can be used in the solution of this problem. Engineering students might be asked to design a machine with certain specifications; economics students might be asked to delevop optimal business plans for some startup. The initial question would be predicted to require certain mathematics, so there remains a loose element of curricular planning. Sometimes the projects are implemented in real life (so there would be a real demand coming from a real startup, etc.). Students will lear the necessary mathematics in parallel with working on the project that requires this knowledge. The learning is mostly project based, but guided by trained university staff. This method is more widespread in French- and Spanish-speaking countries, than in English- or German-speaking ones.
My favorite math teacher answered it like "with this stuff, honestly unless you go into some specific fields you might never use it again, but you're learning a set of tools and practicing implementing them to solve problems, and that skill generalizes to problem solving in life."
I always found this answer very valuable as well! You learn how to reason and problem solve which are very valuable skills even if you don't take all of the math you ever learned with you
i mean i do get the idea but it does feel sorta unsatisfying cus “problem solving skills” are a pretty abstract thing and not being able to personally observe the effects doesnt really make me feel like it had any ofc not gonna deny math has values in that sorta thing, but not being able to observe it directly does make it a bit hard to be satisfied with it
Although, if the goal of the excersice is more general than the specific math problems, then some students will find other ways to achieve the goal without doing the math. If you want them to practice their skills in learning, then let them learn whatever they want however they want and apply what they learn to another area to show them how much better they've become at the general skill of learning. However, if you want them to learn math in particular (which you usually do in a math class) there will be consequences for lying about the goals.
The Karate Kid Theorem. You spend all that time learning how to "Wax On, Wax Off" thinking that it had no practical application to whatever it is you want to learn or do. Only to realize that it was applicable to your goals the whole time but you just didn't know how it fit.
I think this can be explained with a scenario from a book "A concise introduction to logic" by Hurley. It goes like this: "On the first day of any logic class, we ask our students if they regularly go to the gym. The majority say that they do. We then ask them what they do at the gym; many reply that they walk or run on a treadmill and that they lift weights. We ask them “why do you do this?” After all, they are not likely to encounter a treadmill in “real” life or to bench press weights in any other than a gym setting. As the dialogue continues, students eventually reveal that the reason they do these specific activities in the gym is because by doing so they build or maintain the muscles they need for other activities they enjoy do ing, such as, surfing, hiking, biking, skateboarding, or just going for a walk on the beach. We tell them that doing logic is, in many ways, like going to the gym for your brain. While you may never be called upon to do a formal logic proof in the context of your everyday activities, learning how to construct such a proof hones the skills needed for those routine activities." Things you learn in school you may never use. But you learn how to approach concepts from different angles to pass quizzes, you learn how to absorb and retain information to pass quizzes, you learn how to struggle to understand ideas and get through them, you learn how to learn. All to pass quizzes and tests. But at the end of the day when you take a step back, is that all it's for? Or have you become a more all round intelligent person? Here's a quote from Albert Einstein (I paraphrased since I don't remember the exact quote): He was asked what was the speed of sound, to which he could not answer. He said, "One does not go to school for the memorization of facts, rather the ability to think." In other words, life is about thinking. Not trivia. Anyway, good job on the video. I wish you luck on your future videos!
Very insightful comment. I thank you for taking time to write all these ideas,opinions about the meaningfulness (or the lack thereof,) of everyday activities and how a "sense" of meaning can be created through acquisition of skills that can be in some "meaningful" way can be generalized or "mapped" across various domains of human experience which was shown by your understanding that (sometimes) we have narrow minded intentions that motivate us to desire external metrics (in this case) like "passing" "failing" and various forms of reasonings and rationale.
Great insights! The analogy with working out I think resonates a lot with students (at least older ones). So much of what we learn might not be used literally or exactly but it teaches us certain skills and techniques that can be transferred to other lines of work
@@MathTheWorld The more I get into higher level mathematics, the more I realize that math has a bad name. Math should really be called the art of problem solving. There are so many fields for general and specific reasons used to solve problems and gain insight, whether its applicable or just for the sake of it. Take game theory for example. The common connotation with math as just numbers and equations is because those constructs are a very general and useful tool to solve problems! I think it's like you said in the video, people use concepts in math without realizing, "Math is a part of you". Number theory, group theory, set theory, game theory, knot theory, proofs and logic etc... All of these are things we made to solve problems, once I realized I could make my own, I think that's when my perspective on math changed to thinking of it as a way to think and solve problems. Where numbers and equations are no longer the main subject but rather a specific result of the need to solve problems. I apologize for my lengthy comments but I just want to mention one last thing about how I would answer "When Will I Ever Use Math?" to students, rather, demonstrate it. I would give them a real world problem that doesn't seem to have much to do with math. Let them discuss it and come up with their own ways of solving it and explain their thought process. I would then show them how the problem can be described mathematically. Show them how doing this allows them to solve the probably more precisely and gain better insights into the problem. I would then claim that 99% of problems can be expressed and solved this way. Whatever it is, there's probably a field of mathematics that's just the right tool to solve it. If not, make your own! Whether it's finding out how much groceries will cost you or coming up with a theory of Quantum Gravity. (Again, sorry for the lengthy comment Haha😅)
@@MathTheWorld One can also use a backward analogy by looking a "books" used to learn how to read and ask:"how often do you come across a sentence such as 'A cherry is red' ? And yet, you had to go through these to learn how to read".
As a mechanical engineer I have never found my self asking why I know all this math that I never use. I am always asking why do I not know the math that can help me solve this problem, before having to look up some type of math that I need or think I need to solve a problem. Math an physics is how I see the world, honestly I have a hard time imagining how the world would look without it, and how it would look if I knew even more.
Me too. My puny brain can't fathom the universe without mathematical, physics, chemistry laws. It's a mystery really, how Math,Physics and Chemistry can create order , or at least , give us a "sense " of order.
As a recently graduated engineer, I value my education for showing me what's out there. There are a lot of things I learned and promptly forgot -- but those topics are now "known unknowns" rather than "unknown unknowns".
as a new teacher I am struggling with exactly this, the worst part is I am doing re-takes for students who failed their highschool tests here. In Britain we do highschool tests at 16, but a lot of further education institutions will accept you with maths on the basis that you redo it alongside your course, I am at a technical college teaching trades workers, and I have carpenters asking me "when will I ever use trig though" ...carpenters! IF people don't understand it they use heuristics, guesses, apps, and they never understand WHY those things work. I think I will pay close attention to this series and read your paper, thank you for making it
Here is a brilliant article about carpenters in South Africa who use math in a not so traditional way! Absolutely love it and you should have all of your students read it too haha. www.sciencedirect.com/science/article/pii/104160809190002I. If the link doesn't work you can also google "An ethnographic study of the mathematical ideas of a group of carpenters"
So it's been a couple of years since I taught math. I'm a highschool teacher (MA in physics), and I mostly teach physics and programming. But if there's some spare math hours available I happily teach them. Honestly, I don't believe students ask this question because they genuinely want to get an answer to it. I've had students ask me this question during math class, and in my experience they really weren't asking a question at all. They were either not understanding the material, or weren't feeling like putting in the work. The question was a way to cope with that. What I ended up doing at one point was spending 2 to 5 minutes a week on the 'completely useless math fact of the week'. Sometimes they were related to the class, sometimes they weren't. They were almost always things I thought they would NEVER use in real life. Students knew this. And they almost unanimously praised it as the most fun part of the class. It was light hearted, wasn't going to be on the exam, took the pressure off a bit, and was still math. I think in general we've strayed a bit too far from doing math just cause it's fun and teaches us how to think. By the way, did you know february has exactly 8! minutes (ignoring leap years). Work it out! It's a pretty little completely useless math fact.
As a Spanish teacher, I really related to this. I don't have to think about grammar when I have conversations in Spanish, so the "math as a part of me schema," really applies for foreign language too. Application problems are similar too. Everyone probably remembers strange sentences from a language textbook (or Duolingo), but that's also because those examples are meant to focus on very specific vocabulary words or grammatical structures (while avoiding ones students haven't learned yet). I'm looking forward to part 2! Thank you for this video!
Multiplication use: - quicker counting - knowing how many tiles you need for a floor - convert between units - changing the size of a recipee Pythagorean theorem - finding the diagonal length (there are so many things in which you need that or that would be relevant)
I started making games as a hobby, and it surprises me the amount of math I need to get a cube moving! As a result I got more interested in vectors and matrices. I think being familiar with its applications makes learning math a bit more fruitful
I mostly teach physics and astronomy, but the challenges with explaining why it’s useful to a student if they’re not planning to work in this field are very similar. So those dilemmas you mentioned are painfully relatable. Really looking forward to the second part and more useful insight!
Last semester I was taking a linear algebra course and truly unintentionally became "that person" who asked the question, though it genuinely came from a place of curiosity. The professor, unfortunately, got somewhat defensive, which is understandable with how often it is asked in bad faith, but I was just curious about some jobs or some times in life when it comes up. Especially for something as beautiful (and often described as incredibly important in engineering) as linear algebra. It's not that I'm trying to tear down what you do with that question, I asked so that I can better understand it. If I can't be curious about math then what am I doing here. In any event, this video was a good watch for sure, definitely a good thing to think about.
When I was studying linear algebra I took an elective course in electrical engineering. It became clear very fast how useful linear algebra was in engineering and it motivated me but also gave me useful contexts for understanding the work. Was cool.
I struggled with that too because often the subject is shown in a vacuum often making unclear the properties and qualities of certain thing (ex: determinant determines) and when you don't know that it is impossible to find use. Unfortunately for these things you need to search in the depths of the internet to find clues and then piece togheter the whole picture. You need to use other tools with it or it's useless like network theory or calculus
To be honest, this point is kind of what we get at in part 2... though maybe I would phrase it a little differently haha. If you haven't already go check out part 2! ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-i7qoq3KQiaw.html&themeRefresh=1
Once I had a student ask "Why do we need to learn all this math if calculators can do it all?" I said "Because if you always rely on calculators, what will you do when skynet takes over?" He said that was the best answer to that question any teacher has given him.
I was not into math in school at all. It was okay to me, and certain topics were kinda cool, but it just didn't feel like anything I could see myself doing. Then I discovered math YT like Mathologer or Numberphile, and everything changed. Every video was about answering a mystery in the world using math, and it was so cool. Math became something I loved. And Eddie Woo has proven the exact teaching strategy you describe at the end, and it works really well.
I read your essay instead of watching the video. Really, honestly great stuff. I'm absolutely going to adopt a lot of it the next time as student asks me what the value of learning any particular thing is. One point I will contend with comes from the section "Just Look it Up". We certainly know more than what knowledge we have. This is exemplified by the sentence "I wish I had the words to describe how I feel". Sure, you can split hairs about how we know we have some emotion (so we are not in a zero-knowledge state), but what we don't have is a description for it. Following your logic, we cannot describe that emotion because we don't have the language to do so. But how did we learn to describe any emotion in words, then? At some point in our history, we didn't have those words at all, but we certainly had the emotions. Afterall, if we now feel things we can't describe, this was certainly the case in the past. At some point, we had to have no knowledge of language before we had some. Taken to an extreme, we can ask "How is language itself invented if we don't have language to describe it?" Well, it's simple--human beings don't need pre-existing knowledge to have ideas or to generate knowledge. That's the difference between creative sets and productive sets. Not everything that human beings can do intellectually is productive. Much of it is creative, and therefore may require no pre-existing knowledge or even rules on how to imagine it. That said, your point still stands mostly intact. It is much easier for us to imagine when we have more to imagine about. It is always better to know more than to know less, for precisely every reason you mentioned.
Good answer to the question so far! I'm much more interested in math as an adult than I ever was as a student, I think because it took living in the world to see how useful it can be.
I consider myself “ok” at math up to about the college algebra/trig level. When I started developing computer games as a hobby, it quickly demoralized me at the amount of math I needed to understand to be able to build fictional expressions in code. It made me have to go back and study math again just to be able to progress towards making things work on screen. I found myself enjoying this very much because I was looking at the concepts from a practical perspective and was excited to learn new concepts in math that I could see would have a direct application in a game project.
There are very few things you "need" to live your life. You dont really need to know anything about History or Literature. But it obviously helps shape your worldview and gives a somewhat common knowledge base that can be a good jumping off point when learning other things.
When I looked at the SAT I found it really interesting how easy the mathematics level was there. In Romania we are forced to learn a more advanced level of math even if it doesn't help you in all domains of science. But the SAT literally teaches you the most basic math which you will eventually find everywhere. Here's the idea. Mathematics is the tool you need to understand how science works. If you want to have a job related to computer science, economics, physics (basically anything with the word engineering), chemistry etc you need to know a good level of math to comprehend what is happening. If you are still not convinced ask me anything about math and I can give you several reasons for why you need to learn it.
The succinct answer is "so you aren't continually lied to and defrauded, because you cannot understand or cannot check." There is a great line attributed to Mark Twain, but almost certainly predating him: "Figures don't lie, but liars do figure."
Interesting video, with some neat questions being brought up. Looking forward to part 2! That being said, the first part only partially convinced me. I agree, stuff like basic multiplication (maaaybe cross-multiplication and simple probability calculations if I'm feeling generous) are reasonably often used without us keeping the event in mind... but that's about it, I think. Other, more complicated math and geometry lessons are a bit more difficult to sell with this argument, no? I'm pretty sure I haven't done much work with factorials in the recent past...
I actually use factorial not that seldom when I want to calculate some probability I encounter. It doesn't mean I would start multiplying the numbers from 100 down in my head for example, but knowing what factorial does and how it's useful can give you fast and accurate answers when it comes to combinations, variations, arrangement of objects and so on
One giant problem is terminology. Math is not calculating and calculating is not math. But calculating is all students learn in the first 5 years of so, but it is called math and so they see actual math as just a continuation of this, having prejudices and at the same time being surprised that the same old "shut up and follow the scheme" doesn't give em the little gold stars.
In economics class we are told that all concepts may well be rubbish and useless. But passing the tests shows you can persevere and learn, signalling to future employers that you're a smart and hardworking person. This is mentioned in the economics class about signalling and asymmetric information, thereby showing that at least this one concept may be useful.
I'll always remember that online class where my math teacher tied shooting a missile from the ground(a big missile attack was at the news at the time) to parabolas. she explained how you can calculate the missile hitting point using the formula we were just learning. it made the online class and material more understandable
I usually answer the why are we learning this? With a parallel to learning a poem by heart or reading a book for literature. You won’t need that poem or book in real life, the value is in the inspiration and understanding it provides you which you will be using. Math is much the same way, you probably won’t use a specific theorem but understanding how to prove it will give you tools, structure and inspiration for reasoning and solving the problems you will actually encounter.
I use math almost daily, sure I'm not always working things out with pen and paper like I used to in school, calculator apps are just faster for basic computation, it's what they're designed for- But math has a place in everything from just about every aspect of games, be it the player side, in use in actual gameplay, the dev side in formulas and programming, the cheat code side, where you learn how to not just calculate in decimal, but hexadecimal to find related values that correspond to actual in game resources, to even just an enthusiast who knows exactly how their favorite game works, like knowing exactly how much strength is needed to throw various people in Baldur's Gate 3 off cliffs- And that's just all the game related applications I use every day- As a fiction writer the applications are nearly endless, I once wrote an essay to answer someone's question on the theoretical applications and conversions of someone with the super power to manipulate carbon, down to the details of how much CO2 they would draw from the air to create diamonds or coal, only to find out that if such a power existed, they could practically solve global warming by the sheer amount of CO2 emissions they could siphon from the air to create a simple small object made out of diamond. I've heard stories of other people using theoretical science and math to calculate just how much glucose a photosynthesizing human being would produce, and how they would avoid the curse of space diabetes as a result- Art is math in many ways, with intricate geometry, and even in how color combinations can be perceived as pleasant or unpleasant, or simple, or over-complicated- Math and science aren't just "things that you put up with to pass a test", they're the things that are used to logically break down the fundamental nature of existence, and how almost every part of our every day lives function- Be it the statistics and data collected that show us what techniques are most effective in managing our psychology in clinical studies, or how many times your favorite RU-vidr was revived by their fans in a single playthrough of a game- Be it knowing how to pay taxes and be an adult, or how much money you would theoretically need to make, save, and invest in order to comfortably retire for the rest of your life in the next 5-10 years. Math and math adjacent fields aren't just used in the lives of Harvard students- They explain how life works. Math isn't just "math". It's art, language, culture, philosophy, psychology, rocket science, computer science, creativity, music, cooking, baking, economics, and so, so much more... And you never realize it until you get out of school and forget half of what you originally learned.
I appreciate you making an entire channel based on this thought along. To be honest, I get a bit annoyed when teachers try so hard to find how some incredibly advanced mathematical concepts will apply to real life, well some of it wont apply and that's just part of the deal, you won't get to use all of it but the way that you process and apply it in textbook problems can and will be useful for your thinking, analyzing, and problem solving skills. And it's not that I hate math, I take interest in figuring out how it works and get all excited when I do, I just recommend finding the beauty in the 'order' of it all.
This was a pretty interesting video. I studied Applied Mathematics in College and whenever I mentioned the subject I was studying I almost always got asked "So are you going to be a teacher?" or "So what kind of job are you going to do then?" or "So what use does that have?" At the time I never really was able to answer that cause I was studying the subject simply, because I thought it was interesting. I work as a Statistician in the Automotive Industry now. Always wish I could go back and convince others that studying Mathematics has use not only in helping with those everyday problems you mentioned, but helps tremendously in any kind of problem solving or critical thinking. Am curious on seeing you expand on this topic in some follow up parts.
I once replied to the "When will I ever use this in the real world?" with "You might if you become a doctor/engineer/scientist" The kid replied "But I don't want to be any of those things!" So I said "But don't you like being given the option? Would you like to be sorted in 3rd grade after learning multiplication into 'promising' students who would learn all the advanced stuff and the 'lost cases' who would barely learn how to scrape by with the most basic of math or grammar, just because they didn't look promising when they were 9 years old? Don't you like the freedom to choose to become literally anything that you want? Sure, some people aren't going to be a doctor, no matter how much math and biology they learn, but how could we ever make that call? The vast majority of kids has no idea what they actually want to be. A lot of kids has no idea even while graduating secondary school at 19 years old. I've had classmates change majors in their graduation the day they had to choose them, because they suddenly decided that yes, they DID in fact want to be doctors, so they went on to study a subject they were hopeless in for the past 4 years. THAT is the freedom and power general education gives you. Instead of being sorted out when you're a kid, you get to explore what you're interested in and good at, you get to improve at what you're not, you're given the freedom of choosing for yourself. If you find a class boring, at least you know what you don't like. Imagine graduating high school knowing literally nothing about biology or science, because you wanted to be a janitor. You never learnt why trees shed leaves, you never learnt why the sun is shining of why a car starts when you turn the key, let alone how can a metal airplane fly. Might as well be all magic to you, or a government conspiracy. That's not just sad, that's also incredibly dangerous. Sure, we can talk about how subjects are taught, what are the best methods, etc, but there is no question that these things have to be taught, and have to be taught equally to everyone."
In still unconvinced that people need to learn anything beyond multiplication and division unless they’re going into a technical field. If you enjoy doing math, great! But don’t delude yourself into thinking it serves some higher purpose that people would be lost without. To me, math is full of people with superiority complexes over their hobby. I think literature, history, and linguistics are all super interesting and add value to my everyday life, so I study them. I’ve never felt the need to force others to study them too.
I would say that math passed a certain level might be useless in our daily life but does that make math useless ? Learning math make you a better thinker and just take your phone, drive your car or look at a tall building… without math it wouldn’t be the way it is ! And as a math student I think math is fun and can fell magical
I like the story about Euclid's answer when a pupil asked him when he will use this stuff. Euclid sarcastically gave the pupil a coin so that he would profit from learning the math. Why does education have to be about gaining *skills* that you will *use*? What does "use" really mean anyway? Math is intrinsically beautiful. Aren't people curious? Unfortunately, the answer is largely "no."
I personally rarely use the specific things I was doing in upper level math classes, but I use the methods of thinking I learned while doing them every day. Studying math like weight training, not like on-the-job training - it's for expanding your capabilities, not teaching you to do a specific thing for you to do repetitively.
Well done, Dr Doug! I enjoyed this on two levels: 1. as a someone who asked the same question and who never went beyond basic algebra, and 2. your teaching style, explanations, and delivery. I value superb teaching in any topic. -Bro Sher :-)
It won’t apply to all gamer students, but as a person who always wished video games were designed to be more fun, I would’ve greatly appreciated my teachers/textbooks connecting their lessons to programming graphics, physics, and AI. Like, examples of where specific concepts/concept combos would be found. Also, this is unrelated, but in game design, it’s important to teach the game well to prevent it from being too difficult. Tutorials shouldn’t TELL or SHOW, but instead allow the player to discover the answer by themsleves by limiting options obvious, then gradually introducing further contexts. I always thought that textbooks or even interactable courses were missing the tenets of play.
15 years after learning simultaneous equations in school, I stumbled upon an actual use case for it when I was playing a mobile game where 1. I needed to level characters by feeding them experience, 2. had two different types of experience to use, one being three times as effective as the other, 3. I can only feed up to 20 at once, and 4. there's a small chance of a "great success" where the experience I fed my character became three times as effective (so I cannot just stuff their faces with experience until they level up if I want to be efficient). Once I got the amount of experience needed to reach the level cap, say, a, it's just solving x + y = 20, 3x + y = a / 3 (Still trying to figure out when I would use calculus though LOL)
I loved math in school. Not sure why I started to, but I was doing olympiads, where math knowledge was connected to each other and result of one equation is part of equation from other field of math. This is satisfying to see how it comes up together, and I was thinking that everything in the world has such connections. At some point I started realizing math and natural science isn't really what gives you ultimate understanding of world, but I still think of world as complex interconnected system, which is interesting to explore
I teach a "crash course in math" for social and health science grad students and applications turn out to be very good for them. They get those right away. However the math has to line up with things they get, so I use things like genetics, survey research, vision, and so on. These things tend to help them get past the "will I use this?" question because chances are good there are things they have encountered before or will use, or at least they can imagine how it would be important. But yes, I agree with you, these are very tricky to work out and require a lot of knowledge on the part of the instructor as well as a willingness on the part of the students.
Sometimes math can be useful in just regular things. :) Basic math will always be useful for just life, but other hobbies or jobs or other regular tasks need higher level math too. I’ve used trig in sewing a surprising number of times lol. It comes about when you least expect it.
I'm a computer scientist and I tutor kids in math sometimes. And when they ask the question, I always ask them, "if the traffic light is red, do you cross the street?" They'll give some answer, usually no. Some kids say "only if I can see there are no cars." If doesn't matter what they say. Next, I ask them why they said what they said. They'll say things like "it's dangerous to walk into the road, you might get run over." Then I ask them again, "why is that bad?" They say "because you will get injured or die." And then I reveal to them that they just did math. Yes, logic itself, the basis of reasoning, is math. When you say something like "if A is true, B must also be true" or "event B follows event A", things we do every day thousands of times, that's a form of math called formal logic. That often gets them hooked already. Sometimes, when there's extra time, I like to give them a quick intro to modular arithmetic. That's an area of math that, at first glance, sounds complicated and seems niche and useless to most people. When they express that much to me, I ask them what time it will be in X amount of hours. They tell me the time it will be. Boom, you just did it. You added 5 to 11 and got 4 instead of 16. That's modular arithmetic. And lastly, I show them some stuff I built for fun using my math knowledge. Not things I needed to do but just things that give you a satisfying result that's fun to look at. I have many examples of that. I show them some of the projects I have done that elegantly visualize some math concepts and I try to show them that, even if you never have to use math in real life, maybe when we're done, you might just WANT to do math as a hobby sometimes because, yes indeed, math is a fun activity! One, all or a combination of these usually gets my kids interested in learning what they have to learn. I think that's the crux of the issue. Teachers in high school have a really hard time conveying to students the beauty of their subjects. That, to me, was the key to liking math. I hated it in high school and when I went to college, I thought I'd do the minimum amount necessary and "60% is still a pass." But then I was blessed with a good math professor who managed to show us the beauty of math, the elegant relationships, the fascinating ways in which beauty emerges from simple concepts or relations. And that's what got me into math to the point where I aced every test because I just loved doing math in my free time, even complicated higher math. So I try to give that revelatory feeling to my students when I tutor.
Thanks for the great insight! If you haven't already go check out part 2! ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-i7qoq3KQiaw.html&themeRefresh=1
Usually when this question is asked, it's geometry and algebra 2, which means it's usually trig or quadratics that gets the question. And it's... Kind of a fair question, I guess. You're going to do math every day to some extent, be it basic arithmetic or simple algebra, but Trig is a tool that's useful just enough that you should know it, but not enough that you'll remember it without practice unless you're an engineer. Quadratics even more so, though quadratics are easy enough. Even computer science, unless you're delving into security or AI, you won't need to do anything more complex than calculus with logarithms and euler's number or trig functions
You'll never use math unless you learn it. I use my knowledge of calculus and trig to help me do things so mundane as take better turns while driving. Mathematical intuition is extremely powerful, there's almost no situation where some math intuition isn't useful. Even just reach down to pick things up off the floor is made more efficient with some quick math. But then if you want to make video games or launch rockets, math is the only way you're getting there.
@@MathTheWorld Yeah! But the other side of that is hard to describe to people, that you almost always use what you do know. It strengthens your thought process like a muscle gaining more tissue.
Math is like rope. You might not know how you're going to use it, but it's essential in various new and surprising ways, creating opportunities for solutions which would otherwise be impossible. If you were packing a "survival backpack" and someone saw you packing rope, asking, "What are you ever going to need that for?", it might be hard to give them a convincing scenario--indeed, probably the most honest answer is something like: "Experience suggests that it'll come in handy when I need it--and I almost certainly will." Likewise with math; unless you will never face novel challenges (or plan to always buckle at the first obstacle), mathematics--and mathematical thinking, more broadly--will surely come in handy.
Good exploration of a deceptive question. I realized most students asking that question simply didn’t want to put in the effort. I bet they asked the same thing in every other class to try to get out of reading fiction, studying a historical event, or learning a scientific topic, too. There was no answer I was ever going to come up with that would magically satisfy them, and make them hunker down and learn the material.
I'm not a math teacher, but I kinda want to try it someday. (Once I decide to retire from engineering, I guess) I've always loved math, so I never really questioned having to learn it. But I recognize not everyone feels that way. I've always thought my answer to students asking why they need math would be something along the lines of, "You don't. You don't really NEED much of any knowledge to get through life. But knowing things like math will only ever help you."
My (I the animator) high school AP Calculus teacher was a retired engineer! I loved how much context he was able to bring into everything we learned. It's the class that got me interested in math as a major!
@MathTheWorld That's awesome! That's why I want to do it. I thought it was really cool in college how most (or at least many) of my engineering professors had long careers in the industry before teaching, and could relate so much of the math and physics concepts they were teaching to real experiences they had in their careers. I've always thought it would be cool if highschool students interested in STEM careers could also have that experience. I got the idea from a family friend, who's an infectious diseases doctor saying he wants to become a highschool biology teacher after he retires
As much as discovery math gets criticized and laughed at, I think teaching kids about math effectively does have to involve some discovery. Otherwise they'll never be motivated to use those skills properly, and will just be learning the quadratic formula like it's the mitochondria being the powerhouse of the cell. There's no meaning to that! I think maybe the academic focus on teaching one topic at a time in isolation, requiring the students to completely understand one topic or concept before moving onto the next, is an issue here. It's like trying to train your strength a single muscle at a time - muscles don't work that way, and you have to train whole groups at once. Learning math (or anything, really) is not like building a wall using bricks - sometimes you have to reach a little further out to find the context you needed to solve a problem.
I remember working on a forge project on Halo and I wanted to build a pointed roof over one of my rooms. In order to get the length of each roof segment, I had to multiply half the length of the room with the secant of the incline angle. Kind of a basic application but knowing trig helps so so much, and at times you don’t expect.
There is something important to learn in math classes that isn't tied to the specific topic: analytical thinking and problem solving. This will help people their whole life but you also can't pinpoint it to a specific situation because it changes your view of the world.
Often i teach my students by giving them actually interesting problems regardless of their skill level, and provide the extra tools they need. I even find some of the most interest they show are in things like abstract algebra and foundations of mathematics, where they're hearing about things that are so far removed from reality that they just accept on the face of it that this idea is a novelty to start with, at least until they hear the solution and realize that this very abstract concept is actually something they use every day.
I'm a scientist who's also been a teacher, and as far as I'm concerned, the answer is indeed that most of the math *and other school subjects* will be useless to you, and is taught only because of (1) inability to think of anything else to do with people your age, (2) inertia and tradition, (3) its being a way to sort people by intelligence and willingness to endure, and (4) its being a self-perpetuating racket. I've told my students many times that school is a racket. Most times when people try to justify math higher than arithmetic as useful, they'll couch problems unnecessarily and obscurely as algebra problems that are simply handled by arithmetic. Sometimes they'll even state them in ways that can only mean the answer is already known, just stated uselessly as a puzzle. So the answer is, "Never. This is just a fancy way to waste your time."
Viewing it like this, math is really like a language. Ideas are expressed through math just as through language, and a piece of math can be beautiful on its own just like a passage of language. You can't give satisfying answers to these questions either: When will I use this specific word/affix/piece of grammar/figure of speech/poem in life? It's either too general or too specific, just like when asking about any specific piece of math.
One thing that really makes me appreciate a math or science topic is the history and genius behind them. I like to know who contributed to the inventions/discoveries and what efforts went into it. I also like to know the etymology of the main words, like algebra and calculus, usually the etymology leads you to understand what the topic really is about. I remember when my school teacher explained the meaning behind algebra, like setting broken bones equal to heal, and said it's like a scale, if you keep the two sides balanced you get to know unknown info. The idea of knowing the unknown from investing what you do know was fascinating to me, it feels like a superpower. Another history thing is that I like to keep present in my mind where in history this knowledge I'm studying became available, for 100s of thousands of years we lived relatively simple lives, but over the last 5000 years we came up with most of the science and math we know today, and it is those inventions and discoveries that allowed us to have our modern world today. And most of those discoveries were built on previous ones, it's all a necessary chain of events. So I see every little topic I study as a little piece of a great whole. It's like a jinga tower, you can't just remove pieces of it without risking the whole tower falling, especially the foundational pieces. Multiplication might seem simple and boring, but if we didn't have it, we simply wouldn't have anything modern. And in this sense I consider myself an inheritor of a great legacy made by all of humankind. My lifestyle is only possible because of everything that came before, if anyone thought "meh what's this useful for? When are we gonna use it?" About something like prime numbers, I would literally be living in a small town today lol. My hometown was a tiny thing not even half a century ago, only modern technology allowed it to grow so quickly into a proper city.
Because math teaches you how to think logically and methodically. All (or most) subjects teach you how to think in one valuable way or another. Sadly many adults today are unable to think. Emotions and gossip rule their decisions. This makes them easy prey to be manipulated and exploited.
Okay, I've watched your video, I can relate to your teacher point of view. But still: As someone who's graduated 20 years ago: more than half of the math I've learned I've used not even once after school. In fact I've forgotten the majority already. And I've worked as an IT technician. I don't deny that basic math skills are essential for life, but anything beyond that is worthless, a waste of students' time. You could teach so much more important stuff instead, like social skills for example. Save that complex, overly complicated stuff for people who actually need it in their job. I really don't want to be the guy hating on math, and back in school I had quite good grades in math. But my math teacher also constantly bragged "one day you will thank me for teaching you all this math". No, I still don't. I would have loved to learn useful stuff instead.
Fair point. Perhaps it's not about what you learned but the skills you gained along way of learning those things? If you haven't already go check out part 2! ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-i7qoq3KQiaw.html&themeRefresh=1
To pure mathematics. May it never be of use to anyone. A hundred years ago newspapers had recreational mathematics in the puzzle section, next to the crosswords. That's where the entire field of combinatorics got started. People don't do that anymore. People don't associate mathematics with fun or recreeation because of the way it is taught in school. Strictly following algorithms with no deviation allowed. I have heard teaches say that Latin is more like marhematics than learning a language because the declinations and conjugations are all about following rules like from a formula book. Politicians, when they were informed that thanks to automation the workplace requires more creative thinking and less unquestionjng obedience, put less emphasis on mathematics in the school curriculum. Which any practicing mathematician will see as absurd: Mathematics is the only art form that requires no medium. Tradesmen have also complained that they have to teach their apprentices how to do sums now.
Great video and I'm excited to watch part 2. It's almost as if siloing math (and any subject) is an inherently limiting way to teach it. Weird that doing this makes it feel impossible to connect it to real life and other subjects. Could it be that the factory model of education is antiquated and ineffective for teaching students to be more than cogs and fodder for an endlessly grinding profit-machine?
Arithmetic (which many people think is synonymous with maths) is "just" a background skill. Calculators deskill this but make estimation (to check for stupid entry errors) much more important. Maths as an abstract discipline, sometimes directly applicable but far more often gives a logical mindset that helps to analyse problems and thus solve them. Group theory is the study of which patterns are common to any system obeying a small list of properties. If you can look at diverse real life systems and spot common patterns then that's really valuable in working with those real life situations. Occasionally those similarities will come from group theory but always recognising those patterns can come from having trained the brain by studying group theory.
One day I asked what calculus was good for. Did not find a good answer until I flipped to some of the problems in the back on my university calculus text book. "Estimate the volume of a lake". "Use Newton's method to estimate the area of a kidney shaped pool" Edit: these problems are not directly useful in my life: but they illustrate problems that are almost impossible to solve any other way. The lake problem is the same as the kidney shaped pool: only with two variables to Integrate.
Math, especially fractions and multiplication, is used all the time when cooking and using recipes. Have a recipe that only serves 4, but there's 8 of you? Guess what, you now have to multiply, and often, you have to multiply fractions.
Definitely hits home with the kids haha. If you haven't already go check out part 2! ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-i7qoq3KQiaw.html&themeRefresh=1
Kids should be building stuff, theory only when theory is necessary for building stuff. If the kids in school would have like a three months engineering problem and had to figure out how to solve certain problems in order to finish the project then learning math become second nature.
I've had a lot of academic (school and uni) interactions with math, up to statistical analysis with gaussian distributions, math analysis with matrix operations, etc... And honestly - 99% of everything i've learned was either useful for another academic subject, or not useful at all. Of course, i can interpret math in a scientific paper, but none of that is actually useful. Anything more than simple math i can do in my head is done on a calculator, and almost all of it is just nested multiplications and divisions. Any actual math is done by computers, ERP software, SPSS, etc... Of course, knowing how those programs operate is important i guess, but i'm still on the fence about this. I think it's far more important to teach students how to find information in case they ever need it, without actually bothering people with problems they forget a week after the exam.
The last multiplication I did on my calculator was 365 * 1/3 ; I think it was to work out a third of a year in days. Not sure why, but I got the 1/3 from 8/24 so it might have been something about how much time is wasted on work. But I remembered that a third of a year was a little over 121 days when I a few days later when I saw in the hairdresser's app that it was 128 days since my last haircut 😅
But I actually had to scroll a while back in calculator history on my phone to find multiplication, apparently I mostly use my calculator for division, since they are way more difficult to do mentally. I use my calculator for division all the time. But in my work I probably write a lot more multiplication and plain arithmetic operations, since I'm a programmer as simple calculations are a basic part of all programs
The response I most disagree with is "math is meant to teach problem solving, not the specific problems" But... if you wanted to teach problem solving, then I'd be in a problem solving class... why isn't there a problem solving class? It would've been so useful. And it's not like there's not enough material for a whole semester because there definitely is.
Oh ho ho. You need to attend BYU's math education master's program! (That's what I just graduated in) and we do indeed have a problem solving class :) If you haven't already go check out part 2! ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-i7qoq3KQiaw.html&themeRefresh=1
A couple nights ago i had a craving for pancakes, but the recipies on the box made enough for a bunch of people, so i had to re-work the recipie to make a single serving.
There's always a valid question of how young it's appropriate to start specializing kids, and I could see why a kid who'll never use it might resent having to take the class. But no question, for undergrads who enter a technical field, most math taught in grade school ends up coming back in some form.
I belong to some groups that study popular music and the Billboard charts. I raised the question once, Who wrote the most top-40 singles but never had a hit record of their own? I added, "I reserve the right to reword the question if the answer turns out to be Bernie Taupin." I was saying that if the answer to my question as worded turned out not to be very interesting, I could reword it to get something more interesting. (Elton John wrote most of his hits with Bernie.) That led me to formulate this answer: Any field of endeavor, whether for fun or professional, can be enhanced through the use of mathematical thinking.
How about this analogy... If you have two people. One who never does anything athletic at all, and one that plays, trains, and practices basketball regularly. Then you introduce both of them to hockey, and get them to play. Neither have even put on a pair of ice skates before. Which person will do better at Hockey? Very likely the basketball player, because they have trained their body for strength, agility, reflexes, balance, endurance... and even though the sports are different, those underlying abilities matter. With math... sure you might not be using the Pythagorean theorem, or solving quadratic equations in the "real world", but you are presented with situations where you need to *think*, and solve problems all the time. And a brain that has "exercised" will do better at solving a problem than a brain that hasn't. Even if that problem isn't directly related to textbook math.
Sitting in my lecture next to a good friend and she asked me "So when will I ever use complex numbers in real life?" I looked at her, laughed, then she started laughing and we both continued on listening. We both study maths (It's great btw and I can recommend, tho with a secondary subject like CS, Physics etc. because everytime you have math problems there, they seem trivial in comparison to the math problems from pure math problems. Also I legit use more advanced math stuff when programming for example where you could just use less cool approaches)
The other issue is we never (in the US) really teach students in high school and below math subjects that are interesting just on their own (even though they're also iften incredibly useful). There's no love for abstract algebra, number theory, graph theory, logical foundations/reverse mathematics, etc. Ironically (considering the topic of the video) almost everything taught is motivated by real world applications. Even Linear Algebra when available, is focused on the immediate real world applications and not the😮 significantly more interesting and useful structure.
well, if we were teaching the subject to those particular kids because we had already determined that it would be useful for them individually, instead of just filling a quota like its some kind of factory, then we would have really good, applicable examples already on hand, and this wouldnt be nearly as hard. Food for thought.
Fair points! We need contexts that actually hit home and are useful for students. If you haven't already go check out part 2! ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-i7qoq3KQiaw.html&themeRefresh=1
I think a decent answer would be to say "math is about as useful as english in common life - you will use it every day, and it will not look impressive"
I did have that question. I was home schooled. My mother said that it's to give me opportunities to gain employment and to increase the ease at which I navigate through life. That was enough for me. I didn't really ask her for examples. I had the internet for that.
I often give the example of commercial pilots. Why do they ask quite a high level of maths skills to be able to go in this profession ? To be able to analyze rationally and fast in front of a fuck load of moving parameters, especially if there is an issue or to calculate if they can reach a runway if the motors are not working anymore. And if the guy is not applying rigor thinking like doing a proper check list before taking off etc., would you go on that plane as a passenger ? Then, I also like to point out that all the so good things we have nowadays through physicists and engineers, all had to face hard maths to solve their problems and innovate.
I used to tell my students: You happened to have ended up in a school where you learn what brought humanity to the level of development we see today and math is one of the most important factors. Probably more important than Michelangelo, Shakespeare and Beethoven (even though I like their contributions). Without math there would be no science, therefore no enlightenment and therefore no freedom, democracy, human rights and no equal rights for women (we still have a long way to go).
Mathematics has two forms, and two purposes. Most teached math is used for numerical analysis, like statistics, and taxes. The other form of mathematics, and the way I think others like the most, is minimising work. Either with efficient algorithms or using proofs. It is obvious how efficient algorithms minimise work, and proofs are the assumptions you don't have to check.
The point about applications being too specific and possibly uninteresting is really important. My prob and stats professor in undergrad was both passionate and a good teacher. He wrote a book full of good lectures and excercises specifcally for the class (and didn't publush it elsewhere, so it only cost $20 to get the University's book store to print it on demand), but the entire book was motivated with examples from sports (and to be fair, sports stats was an award-winning recreational activity for the prof). All of those examples were completely uninteresting to me both academically and personally. If I didn't know better from the start that I'd be using prob and stats, the whole class would have seemed useless to me.
Our feeling of learning does not match actual learning. People think they didn’t learn how to do things… but more often than not, they did and just don’t realize it. And making it clear to them about what they are learning doesn’t help either.
I'm an electrical engineer and most of my math classes wasted too much time on lecturing about abstract concepts rather than actually DOING math and explaining how and why. I had to do some partial differential equations in 3 dimensions in one of my physics classes but I had to learn even more than that for my math courses. Despite all of the hours spent in math classes, I didn't learn a lot of the important math for my actual engineering degree. I'd have much rather had an engineering-focused series of math courses than a general set of courses for everyone that was 50% aimed at people becoming mathematicians.
I read a short story like this, with the student asking why learn math, when he's gonna forget how to do it in 10 years or so. The teacher asks him to meet in front of a nearby lake. Once there, he's handed an old dusty pot with a hole at the bottom, and asked to bring back water. No matter how hard he tries, the water leaks out quickly. After failing, he returns to his teacher, who explains that filling it was never the objective. As a matter of fact, the pot was now so clean that it appeared brand new. The moral of the story is that math isn't about always knowing the formula to every problem. It's about learning different approaches to problem solving in general.
here's a good way to show someone how learning math is useful: say you have to count out 100 peas out of a basketful of them, remove them from the basket snd put them on a table. AND, you have to convince someone else that you have indeed placed precisely 100 peas on the table, without them having to count them one by one. they need to see virtually instantaneously that you indeed have exactly 100. you should be able to solve this quickly. its not the math so much as it is how to solve problems that is important. studying math develops problem solving skills. (solution : do NOT put them in a 10x10 sq. array---time is required to count to ten. put them in four 5x5 square arrays.)
my problem with math is that it is tought as the goal of itself, not a tool to describe the world. Too describe, you need time to form opinion, ideas and orient yourself within the idea but with school, tnis just isnt possible
Literally nobody who has ever asked that question has asked it in good faith. How do you answer? You kick them out of the class. The conversation is over the moment they ask it, you will never satisfy them because the only "satisfying" answer they want is: "You're right, you don't have to learn this any more"
It is sad that it is often asked in bad faith, though one other viewer actually commented that they did ask in good faith and curiosity but their teacher took it the wrong way (understandably)
