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Why don't we use the math we learn in school?

94 points by enigmatic02 5y ago

paulpauper 5y ago
It is like this for all subjects. Beyond the 5th grade, applicability drops a lot. Knowing how to read simple sentences, perform elementary math is enough to get by with most tasks, but personal finance will be a struggle.
ramesh31 5y ago
I can remember failing math class hard throughout my entire academic career. I never passed a math class past primary school, and ended up dropping out of high school. The concepts simply never made sense to me, and as they were presented were just meaningless rote exercises of memorization. Math was something I had completely written off as ever being able to understand. Then I took calculus and trig classes in college. Since I was also learning graphics programming at the time, I was able to actually make sense of math with a real world connection. Playing with little graph equations on shadertoy.com made me realize graphics was all just math. Everything immediately clicked. I was able to intuitively visualize the trig functions and graph equations and do transformations of them because I could picture what the resulting image would look like. Ultimately the problem for students I think is just creating this connection to reality.
- ajuc 5y ago
  My experience too - I wanted to make games so when we had trigonometry and analytic geometry in class I was like "yes please, I can use this, more". Same with vector and matrix algebra later. Meanwhile I had little use for calculus so I only learnt it enough to get a good grade.
- pthread_t 5y ago
  It would be incredible if trigonometry classes had a lab component where students work on a 2D game, such as tower defense. I ended up taking a fun programming elective in college where my team did exactly that -- we created a 2D game. That experience made me appreciate trigonometry more than my high school teachers and Khan Academy ever did.
- eschneider 5y ago
  Having a real world problem to apply it to makes learning math far easier. I spent a lot of time in 2020-1 tutoring kids in math and the first thing I did was find out what they were into and then worked math into helping them do that thing.
ohiovr 5y ago
My school rarely ever directed mathematics instruction in relation to another skill or problem. Sure math might be used in industrial arts, or in home economics, but the instruction phase of the math is always 100% abstract. If people knew all the interesting things you can do with math they would be more likely to use math more often and remember what they learned. This was certainly the case for me and may have been the only thing that made me even care about math at all. I am referring to only one math class I took in high school which did this, and that was geometry. I loved my geometry teacher. He was the only math teacher I ever found likable. I loved the geometry class because it helped me a lot when thinking of practical considerations to 3D graphic arts I was creating on Amiga computers at the time not to mention the value of the discussion of area and volume. Did you know Pythagoras was a kind of cult leader? Geometry wasn't just abstract, it was practical. How much carpet do I need for a room? How much water will fit in this cylinder? If I have a disc that has to be one square foot, what would the diameter be? I had some enthusiasm for algebra one level math for solving an unknown variable using what is already known. I didn't learn the value in this at school. My dad was an electronic technician (Worked at Argonne Labs) and I was interested in what he did there. He taught me all there is to know about ohms law, finding resistance, conductivity, current voltage, using simple procedures. We did parallel circuits, tank circuits, ac theory. In less than a years time he gave me a complete 2 year associates degree understanding of dc and ac circuits. Most of us found our math teachers some of the most arrogant people in the school. They demanded that we show our work and show it going down the way they personally approached solving problems. If the result was correct but if they didn't like your preferred procedure they would lower your scores. They never could offer a sound reason for their demands. Perhaps they did have a sound reason. They just didn't bother to sell us on it. I suppose it isn't right of me to condemn all math teachers this way as my experience is kind of limited. This is just what I felt about it while being a student in high school and middle school 30 years ago.
- RealityVoid 5y ago
  My math teacher was not like the ones you describe, he really let me go off the reservation if I ever wanted to approach the problem in some wierd zany way. IMO, that's how it should be. On the other hand, mastery of the tools and methods requires repeating it and spending a lot of time with them untill they "make sense" or rather, you get used to them. So that is useful as well. Most people can apply mechanical methods well, but the part where I see a disconnect is applying them to new problems and new contexts. It's like... Most people don't even realize you can do that. Would love to find a scalable way that teaching can approach that as well. It is a crucial mental tool.
jcun4128 5y ago
Heh I used cross product first time in like 9 years for a little robot project.
- kevin_thibedeau 5y ago
  I just did some regressions to model sprinkler head flow rates for variable pressure and spray angle.
- globular-toast 5y ago
  Yeah. One underappreciated thing about education is exposure. It's not that I've been walking around every day for the past decade being capable of matrix multiplication. But having been exposed to it once, it's amazing how quickly the knowledge comes back when you need it. I did advent of code over Christmas and when the 3D transformations came up I thought about it for a bit, then remembered... something about matrices... linear algebra..? And then searched for the resource I needed to refresh myself on it. Just the fact I was exposed once a decade ago means I was able to refresh myself in a few minutes.
  - deleted 5y ago
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imglorp 5y ago
Given the relative innumeracy of the public, some argue we should teach stats and probability instead of calculus, if there's a choice. Those things are more applicable for everyday choices like "should I buy a lottery ticket or invest in the market?" "How likely am I to die from disease X versus side effects of its vaccine?" "Should I buy comp insurance or pay out of pocket if I break my car?" etc.
- zozbot234 5y ago
  We should teach calculus first, because one cannot understand the foundations of stats and probability without calculus.
  - Jtsummers 5y ago
    Using probability and statistics and understanding their foundations are two distinct things. Prob/stat can be taught (to the point of utility) without calculus and often is. More advanced applications are inaccessible or only learned by rote without calculus, but that doesn't mean that you need calculus first. Of course, this is what commonly comes up in topics like this, a confusion over the two notions: Understanding the basis of something and understanding it well enough to utilize. You don't need a graduate level physics course in electromagnetism to be a competent electrician.
rland 5y ago
Math is incredibly useful; probably everyone here knows that. But it's actually fine that most people don't use it. What we really need is for every student to realize why math is useful -- so that if they want to, they can go learn it so that they can make some kind of technological contribution to the world. The fact is, you need to be good at math to make some new fundamental breakthroughs in technology. Those breakthroughs benefit everyone, even those who don't know any math at all. But you won't really get why that's the case until you know enough about sines and cosines to make sense of modern technological development. The real issue is that we just teach the math, hoping that students will understand on their own that it's fundamental. What we should do instead is try to instill that sense of wonder about the world that inspires people to study math. We don't need every person to know calculus, we just need everyone to understand why calculus is useful -- then they can be inspired to go further. Educators say that they're trying to do this, but I'm sorry "how many meters of fence does Farmer Bob need to keep the sheep inside the pen" is not inspiration -- it's drivel, no better than "find the perimeter given a=5, b=6." If every person understood why math is so useful, we would have many more people who are motivated to work on improving the state of things.
- Shared404 5y ago
  > it's drivel, no better than "find the perimeter given a=5, b=6." Not only no better, but actually worse - if you add a word problem around the problem that doesn't fundamentally add anything or make the problem easier to understand [0] all you've added is another layer of text to parse through. [0] Sometimes it can be helpful. Adding a relevant layer of physicality to help reason about the problem can be nice, especially in calculus.
  - netizen-936824 5y ago
    Adding the extra physical descriptions to calculus actually helped me better understand what the equations meant and represented. Definitely beneficial in some scenarios to some people
    - Shared404 5y ago
csdvrx 5y ago
You don't - I do (including some math only seen in uni). It all depends on your job, and since we can hardly know in advance, school tries to cover all bases. Drill and practice or the other proposed solutions won't help with that.
jessenichols 5y ago
Because most school is forced knowledge work on problems that don't fit the person's problem situation. When people are free, they learn the math they need for the problems they are trying to solve. Traditional, compulsory school forces children to solve problems they don't have. See Karl Popper's idea of the bucket theory of mind, or David Deutsch and Taking Children Seriously.
- bjarneh 5y ago
  > most school is forced knowledge work on problems that don't fit the person's problem situation. Have you never been in a situation where you are about to take train going at 80 mph; wondering when you'll meet up with your friends going in the opposite direction at 90 mph?
  - mulmen 5y ago
    I recently saw a great photo [1] by Ben Cooper of a Falcon 9 on ascent crossing the Moon from the photographer’s perspective. I wonder how much math went into finding that vantage point. [1]: http://www.launchphotography.com/Starlink_4-6.html http://www.launchphotography.com/Starlink_4-6.html
    - dekhn 5y ago
      It's not really that hard. I set up several systems to do this for the previous total solar eclipse. The ephemerides for the moon are easy to download and calculate the position in the sky (IE, altitude and azimuth at time t) with a python script. I believe also the launch vehicle has a launch window (the moon moves 15 degrees per hour) and launch trajectory. I'm lazy so I'd compute the extends of the launch vehicle's motion in the sky (from earliest possible launch to latest possible launch), and then intersect that geometry with the moon position geometry without explictly trying to solve the equations simultaneously. That should back-project to shapes on the ground at which point you could reasonably expect to be able to get a good shot, and then you'd do some adjustment in your pointing in real time. A smart college senior could do it directly (IE, not lazily compute a bunch of points and manually intersect them on a screen).
graycat 5y ago
Uh, there is a carpenter with a Web site that uses the "3, 4, 5 rule", of course, the Pythagorean theorem. The first order ordinary differential equation initial value problem d/dt y(t) = k y(t) ( b - y(t) ) can be use to model viral growth. Once it kept two crucial FedEx BoD members from walking out and saved the company. Similarly for the law of cosines for spherical triangles for finding great circle distances. Linear programming (LP) gets used right along for actual, genuine LP problems and also as a means of approximation for problems that are not linear. The problem of minimum cost flows is a special case of linear programming. If want to sort keys, e.g., for some positive integer n, if want to sort n numbers into ascending order by comparing numbers two at a time, then heap sort does that in worst and average case in O(n log(n)) and, thus is the fastest possible -- this is from a cute counting argument, the Gleason bound, A. Gleason. Statistics is important and parts of it are awash in math, not all of it trivial. The design and operation of the Webb telescope is awash in math.
- mlyle 5y ago
  > Uh, there is a carpenter with a Web site that uses the "3, 4, 5 rule", of course, the Pythagorean theorem. Knowing a triplet ain't employing Pythagorean theorem. > [lots of following examples that are moderately deep applied math used in lots of skilled professions] Most people don't do this kind of work or analysis.
  - graycat 5y ago
    > Knowing a triplet ain't employing Pythagorean theorem. 3^2 + 4^2 = 5^2 = 25 guarantees that the angle between the side length 3 and the side of length 4 is a right angle which is what the carpenter very much wanted to know. E.g., the sides might be 30 feet, 40 feet and 50 feet, e.g., for the foundation of a house, and presto, bingo the carpenter knows that the 30 foot side and the 40 foot side form a right angle, are square, which can be very important to a carpenter and not so easy to know otherwise.
    - mlyle 5y ago
      Yup, and knowing that having triangle sides multiples of 3,4,5 guarantees that it's a right triangle is not the same as employing pythagorean theorem. You know one triplet, and not why it works, or that e.g. it works for 5, 12, and 13 and 11,60, 61 as well. A whole lot of people know that measuring a bookcase corner to corner is a good way to square it up, too. But they may not be masters of geometry beyond knowing a rule of thumb.
aweofjwef 5y ago
So much of modern math education, especially once you get into high school, is centered around _computation_ instead of _reasoning_, so you get a lot of kids who spend an entire year doing random integration problems or charting a bunch of useless functions/conic sections instead of really understanding fundamental structures, reasoning, problem solving, etc. It's just rote computation, but we have computers for that now.
- owlbite 5y ago
  cynically: computation is easier to mark than reasoning.
  - aweofjwef 5y ago
    Oh, I have no doubt that it's easier to teach in general, because you don't need to actually shape the way the students think.
syntaxing 5y ago
I can understand the average person not using the math we learn in school, but it’s crazy to me that even the average engineer doesn’t beyond basic arithmetic. I don’t mean this in an elitist sense but I feel like I was the same way a couple years ago. Until one of my mentors kinda guided me through the thought process and understanding the math is extremely powerful and useful.
jeffbee 5y ago
In my opinion serving up 2/3 cups of a semi-solid cheese and reserving a quarter of that demonstrates a quite excellent intuition about the problem of 3/4 of 2/3. Probably 3rd-grade children would be congratulated upon discovering this strategy.
mlyle 5y ago
The article mentions "More drill and practice" ... I don't think this is the right way. I believe something happens with math to many/most students which leaves them less than fluent in mathematics. Somewhere along the way, they stumble for a few weeks and fall behind. Maybe their family took a vacation. Maybe the teacher's explanations don't make sense to them. And then there's a deficit. Pretty soon, supporting that student through math becomes a whole lot more about drilling and memorizing strategies and understanding is deprioritized. This becomes insurmountable, especially with the "layer cake" model of how math is taught in US schools. Pretty soon you'll never catch up in understanding. But you probably just attribute it to "not being good at math". I'm working with a student right now, who is in precalc and "bad at math." He is actually really bright. Some missing knowledge and intuition about fractions has made everything since much harder. And the problem's never been fixed because he's constantly been in a survival mode in his math classes. These students never end up doing the kinds of things that kids are ahead in math are taught to do to crack free-form problems: - Make a good guess of the answer - Form a mental picture and use it to select strategy - Work a simpler problem and see how this can be extended - Organize your givens ; use dimensional analysis for a hint as to what operations may be required or what picture should be drawn - Look for symmetry and transformations that result in simpler cases - Does positing an incorrect answer reveal any information about the solution? IMO, teaching these things -- strategies-- should be more the goal than doing lots of kinds of applied math work by rote in a way that deeply depends upon previous work.
- the_only_law 5y ago
  There was another “I’m bad at math” thread a while back I stumbled across and drilling was considered basically the way to get good at math by most people posting. … which is all the more reason I’ll never become good at math. I’d rather drill a hole in my head than subject myself to drilling back to back, contextless, boring problems I don’t care about.
  - mlyle 5y ago
    I think there's a few points where drill makes sense. In each case, after you have a good understanding, and you're seeking to become fluid and avoid dumb mistakes. (Even if you have a good understanding, if you're consciously thinking about each step you'll error a fair bit, and on a 20 step problem you can't afford this error rate and slowness) Arithmetic facts, basic algebraic manipulation, big polynomials, derivatives and integrals. But we do much more drill than that. And, worse, it's often as homework, where you can be guaranteed a decent slice of the class is practicing it wrong.
globular-toast 5y ago
I think I've used almost everything I learnt in maths at school at one point in my adult life. And not just because I'm a programmer. The other day I was using trigonometry to work out how to install a projector into a room. From what I can tell, most people don't do things like install projectors into rooms. They either get someone else to do it, or just figure out some placement that is good enough via intuition or trial and error. If people have jobs that require it, they usually remember the bare minimum for their job and aren't remembering general concepts to help them solve brand new problems. If there is causality here, I'm not sure which way around it is. Either they don't need maths because they don't stuff that needs it, or they don't do stuff that needs it because they can't do maths.
lordnacho 5y ago
This is a good question, why is it that seemingly nobody uses the math they've been taught? When I was in school, my math teacher used to write AMBS on the board before calculus lessons: Algebra Must Be Strong. What happens when you study calculus is you end up rehashing algebra over and over again until it's second nature. Consequently if you find someone who's done well at calculus, you can be sure they can do algebra. Someone mentioned this in relation to RenTech. Why do they hire mathematicians who have studied incredibly complex things with seemingly no relation to trading? One reason might be that people who have done that know the fundamentals very, very well. Similarly accountants don't use vectors or geometry at work either, but they certainly are comfortable with arithmetic and its application in spreadsheets. When I look at my own education, it is also the case that the things I'm least sure of are the deepest, latest courses that build on everything else. Probably if I built on top of those I'd be more comfortable with them. Taking this line it would appear that you can't just teach people the math they'll use, because they won't really get it until they try to do the next thing. A thing that needs addressing is the notion that we should only teach people things that will be useful, which seems to underlie this article. We should teach people how to explore, and math is the premier example of a large space that can be explored with very little access to resources and evidence. You can do it just in your mind, and you don't need any apparatus or conclusions from people who had such apparatus, like you do in science.
ioseph 5y ago
When I started learning woodwork I was really excited to apply geometry which I hadn't used much since highschool (even working with geospatial data vis). However as I've progressed I find myself using math less and less and it's often faster and more accurate not to measure or calculate. To give an example, making a three legged stool I needed 3 equally spaced spaced points around a circle, I could find the center, draw the first point then use a protractor to find the other 3 points at 120 deg. But it was far far quicker to just use a divider, step around the circle a few times adjusting until 3 steps takes you back to the first point. Of course this is still some form of math, but it doesn't involve any calculation. I feel there's a whole world of very useful techniques that work on a different abstraction, though I'm struggling to name or describe to properly.
- deleted 5y ago
  [deleted]
- jimmygrapes 5y ago
  A similar trick is the 3:4:5 rule[1] which I have not used for woodworking but that's where I first heard of it. I have used it for general site planning for tents and ensuring fire breaks and similar, though. [1]: https://www.ezwoodshop.com/345-triangle.html https://www.ezwoodshop.com/345-triangle.html
voldacar 5y ago
> Many students are only taught math as symbol manipulation. Less instruction is focused on identifying situations where it might be useful. We need to give students more training in noticing and converting everyday situations into the math problems they know how to solve. No, please don't do this. When I was learning math as a kid I found word problems incredibly irritating and stupid. It's just a way to waste a few seconds of my time when I just want to solve the problem and get to the next one. Word problems are just disrespectful
- pfranz 5y ago
  I think the reason most word problems suck is that they're manufactured abstractions on the same problems elsewhere on the worksheet--which seems to be your critique. In real life, a lot of those situations are hidden, but there are often multiple correct ways to approach the problem and hopefully some intuition will help you if you're too far off track. 2/3rds of 3/4ths of a cup of cottage cheese shouldn't be more than one cup and shouldn't be a tiny amount, either. (I also don't see a problem with people who scooped it onto the table). Similarly to the woodworker (elsewhere in this thread) trying to evenly measure out where 3 legs on a stool would go.
basscomm 5y ago
To me this is coming at the issue from the wrong angle. Sure, mathematics classes in elementary through high school have the veneer of teaching mathematics, but they also teach logical thinking and problem solving. Identifying a problem (in math class the problems usually come pre-identfied until you tackle the dreaded story problems) and breaking down the problem into logical steps, are useful skills to have even if someone never does another math problem in their life.
jfengel 5y ago
My answer: because most of the math we learn in school is useless. I see a lot of math homework questions on Quora, because students copypaste their homework all the time: What is log (3x +2)- log2 =1? How do you prove that X^2-3 is irrational? What are the roots of the equation x4−4x3+6x2−4x+4=0? When on earth are you ever going to use any of that? The word problems are no better. In a group of 20 adults, 4 out of 7 women and 2 out of 13 men wear glasses. What is the probability that a person chosen at random from the group is a woman or wears glasses? Mr. Tay had 20 female fish and 5 male fish in a pond. Mr. Tay’s father brought some male fish and put them in the pond. Then he found 1/5 of the fish are female. How many male fish did his father put into the pond? In a school interhouse competition, 80% of the students turned up for the athletic competition, 60% turned up at the football match. What percentage of the students attended both functions? These just aren't the kinds of questions anybody ever actually asks. The math required to solve them is pragmatic; are there no pragmatic examples they can come up with? The fact that students are copypasting their homework doesn't thrill me for their ethics or their intelligence. But the fact that the problems themselves are so stultifyingly dull almost makes it seem reasonable.
- eternityforest 5y ago
  Maybe they should get engineers to teach math courses the way they wish they had been taught them, rather than math people who sometimes still seem to think we will be doing this without a calculator?
  - jfengel 5y ago
    Engineers have specialty interests. I'd just as soon have it taught by a home economics department, or at worst an MBA. Things everyone should be able to do: read a bill, allocate a budget, estimate how much food to buy for 2 people versus 10 people, plan for retirement, maybe convert a recipe from metric to imperial units. Perhaps get a shop teacher. Let the future STEM majors learn the rest in their classes. It takes a long time for a lot of that stuff to pay off, and much of it remains irrelevant.
    - 5y ago
kkwteh 5y ago
I think this question stems from a confusion as to what school is actually for. It seems to me that school is at least as much about orderly management of the social hierarchy as it is about teaching useful skills. The reason why math is taught in school is not because math is useful (it is useful in certain situations, but this is only tangentially related). We teach it because it keeps students busy and out of trouble, and lends itself well to unambiguous testing and is therefore an effective tool for sorting students into the various social classes. This all became clear to me when I was in the middle of my math PhD and wondering why all of the math courses I had taken did next to nothing to prepare me for actual mathematical research. Viewed from this perspective, it’s obvious why we don’t use the math we learn in school.
flint 5y ago
bell-cot 5y ago
Why don't we use the [History|English Lit.|Chemistry|etc.] that we learn in school? As a generality, isn't the math taught to most teens in public schools aimed pretty squarely at preparing them to take the standard calculus courses in their first couple years of college? If so, hardly surprising that most ex-students don't notice much use for that stuff in the real world. And since the social function of that is usually to demonstrate that you're determined / focused / upper-class enough to successfully slog your way through it - gee, what would be the point to remembering or using it after getting your "made it through" bragging rights?
- Gigachad 5y ago
  English is critically important to help you understand complex written works and to write in a way that is clear and doesn't make you look dumb. Advanced chemistry might be useless, but basic chemistry/physics is useful. And I feel that people would understand what they are doing a lot more if they understood physics a little better. For example a lot of people think a cone makes amplifies noise rather than understanding that it simply directs them in to a smaller space. Chemistry helps you understand why oils stick to your hands and don't wash off until you use soap. Basic math is very useful but highschools go so far off basic math that they teach massive amounts of seemingly useless stuff.
eternityforest 5y ago
People don't use math because... it's only useful if you actually really know it. "Useful" to me means "Lets you do something you couldn't before with a phone". Aside from imperial inch fractions(Not a fan of those!), most things require fairly little understanding of fundamentals. Because most people aren't in tech jobs where they can use it. I don't have a checkbook or do my own investing. I'm single, and very little math is needed to pick whatever is cheapest, especially when only certain sizes of some things are practical for one person. CAS systems can do basic algebra, FreeCAD does geometry... FreeTaxUSA does taxes, I don't have a car to optimize insurance costs for... It's always pretty cool to see a chance to use math IRL just because it's such an uncommon novelty, but I don't see it very often. To unlock new capabilities you have to learn all those basics, then move on to learn the advanced stuff that computers can't already do. It's a pretty long term investment of time. Maybe worth it, but still a lot of work.
- aardvark179 5y ago
  > FreeCAD does geometry FreeCAD can do geometry, but if you can’t reason your way through the constraints you need to set for it to do that then you’ll be flailing around. FreeCAD definitely saves me from doing arithmetic, but not from doing maths.
  - eternityforest 5y ago
    I usually find the constraints are a pretty direct translation of how I would describe a part in non-tech nical writing. Math definitely is helpful, but unless you are a full time MechE, it's not like you need to be able to pass a high school geometry class to be able to print a replacement part for something.
- mulmen 5y ago
  When you say “imperial system” you almost certainly mean US Customary Units. These are not the same system. The United States has never used the Imperial System. Also, US Customary Units have been defined in terms of SI units since 1893. Personally I don’t find multiplying by two any harder than multiplying by 10. https://en.m.wikipedia.org/wiki/United_States_customary_units https://en.m.wikipedia.org/wiki/United_States_customary_unit... https://en.m.wikipedia.org/wiki/Mendenhall_Order https://en.m.wikipedia.org/wiki/Mendenhall_Order
kelp 5y ago
I feel like there could be an Explanation #4 which is something like: for many people lots of math is used so infrequently, it's hard to retain after you're done with school. Maybe more drills would help that? I did pretty well in high school math and got through the most advanced math classes my small town school district had to offer. Then I opted out of driving to the next town over to do a more advanced math class with something like the 5 other kids who qualified. I think it was pre-calculus or something. So I ended up not doing math for a year, then I really struggled in my first college math classes, and had to retake one of them. Since then I've basically just forgotten everything because it comes up so rarely. How often do I need to do fractions? almost never, and when I do, I can just look up a factions calculator. Never mind trig or calc. Day do day, I think I need basic addition, subtraction, multiplication, and division. And I figure out percentages a lot. But I'm also doing all of that with a calculator. I think financial cautions, like compounding interest are the most advanced things I run into regularly.
neptunesoda 5y ago
I have a different take on this situation (thought it bears some resemblance to "Explanation #2" in the article). My years of experience in maths education has led me to the conclusion that the role of maths, particularly in child education, has, or should have, little-to-nothing to do with maths itself: it is a means unto a different end, and should not be used as the end unto itself. For example, why do we make (US) high-school students study elementary algebra? You would be hard-pressed to find an application of the quadratic formula in everyday life, and yet I maintain that it, and the course at large, has an important pedagogical role. All pre-collegiate levels of maths education (arguably including elementary calculus, but certainly everything before that) presents the student with increasingly complex situations, the tackling of which requires increasingly complex problem-solving strategies. From this perspective, all levels of maths education are effectively drilling structured logical reasoning, problem decomposition, pattern matching, rule application, abstract thinking, abstract/concrete translation, precise/"technical" communication, etc. Maths simply provides a rather nice vehicle for presenting these concepts in an ordered fashion with natural increases in complexity. I even believe that the introduction of integers to pre-schoolers is a valuable vehicle for introducing causality and linearity of time. Along the way, there are certainly valuable real-life skills that are clear applications of maths concepts, and I would agree with the article that most maths programs are woefully deficient in really underscoring the value of these applications. The article opens with a comic about needing "two-thirds of three-quarters", but anyone who has ever scaled a recipe, or worked with so-called "bakers percentages" knows that this is far from being simply a theoretical word problem. As an aside, I spent a number of years teaching elementary arithmetic to adult students (usually in their 50s-60s, and, without a hint of hyperbole, commonly unable to solve "2 + 2" without memorization). My role was to find creative ways of communicating arithmetic concepts to people for whom the traditional approach often failed. This strengthened my belief in the above perspective by providing an interesting corollary: many of these people had come to learn the "maths-adjacent" skills, traditionally taught via maths instruction, in fascinatingly creative ways. If the ordering and equal-spacing of the integers was not something they were able to truly grasp as children, sometimes they would surprise me with their approach to other parts of their lives for which perhaps you and I would have a more "normal" solution to.
pohl 5y ago
It's my understanding that American Football players frequently wonder, during a game, why there are no automobile tires strewn about the field for them to step into.
- wanderer_ 5y ago
  Very... well said my friend.
patja 5y ago
I used quite a bit of high school trigonometry when building new stairs and guardrails for my deck.
temp8964 5y ago
There’s a sickness in today’s American/western culture related to learning / education: against practice. Teachers design all sorts of activities to facilitate student learning, but they are disgusted to do the most important thing for early learners: repetitive practice. When students start to learn algebra, many of them can’t even do two digits addition/subtraction by hand. Not to mention to do calculations in the head. Why learning to do basic calculations/numerical processes fast is important? Basic psychology: reducing cognitive load in thinking through complex processes. Repetitive practice is the building block of learning everything. Of course there’s more in learning psychology, but that’s off topic.
- wanderer_ 5y ago
  Then again, those who are more naturally proficient, like myself, were often left to do 30 problems as homework on a topic that they could have done without even attending class that day.
- Ekaros 5y ago
  Basic math and algebra are the fields where I actually see that repetition is needed and useful. Huge part of being proficient is pattern recognition and repetition is only way to get to this. And I actually often wish that I had bee teached more than 10x10 tables... Maybe up to 20x20.
sumedh 5y ago
In school back in India, I quickly learned that I dont like Math, I just find it too difficult specially concepts like polynomials, trigonometry etc but I had very strict parents and they would not be happy if I failed in Math so I had to come up with a plan. So I used my superpower, turns out I had good memorisation skills, so my plan was to memorise all the questions (and their answers) which were asked in exams for the last couple of years because most of the questions are randomly picked from the same set of questions which were asked in the last couple of years. My plan worked and I got good scores in my Math exam, my parents were happy.
- gjs278 5y ago
legitster 5y ago
The failure is with story problems. Story problems are perhaps the most important part of math education. A story problem requires using math to actually problem-solve. But they are often terribly written and introduced too little too late. In some of my classes, they were nearly ripped out of the curriculum entirely because students struggled so hard with them.
- ohiovr 5y ago
  My mom was a special ed teacher and she would always teach math and arithmetic in whatever every day like problem may encounter for them. She covered making change, doing budgets, using multiplication for finding area, understanding recipes. Her students appreciated that.
tqi 5y ago
I don't use my lessons on different animal species or cloud types in my adult life either, doesn't mean the experience of learning wasn't useful or important or that my teachers failed to teach it properly...
uejfiweun 5y ago
I would really love it if there was some type of Leetcode for math. I grew up in a very liberal artsy environment and was actually warned against taking advanced math for most of my life. It wasn't until college, taking requirements for my CS major, that I realized I actually find it fascinating and have an aptitude for it - but then college ended and I just have barely done any math since. If anyone has any resources on this or general advice I'd love to hear it. It seems to me like all the coolest cutting edge stuff in Tech right now requires a lot of math so I'd love to start grinding at it.
- Jtsummers 5y ago
  > I grew up in a very liberal artsy environment and was actually warned against taking advanced math for most of my life. What possible rationale was there for that?
  - uejfiweun 5y ago
    Don't get me wrong, what I mean by this is like I took AP Calc AB in 11th grade instead of AP Calc BC. I still was in accelerated math classes. It was more so that my parents both tried the top most advanced math in their education, and both did poorly, so it was a pitfall they warned me about.
- btheshoe 5y ago
  Look of art of problem solving's alcumus. It's targeted at children who do competitive math, but leetcode is also easier than high school level usaco problems, so you might find it challenging. In general, aops has some decent textbooks.
rossdavidh 5y ago
The reality is, people need to know how to use spreadsheets well and accurately, more than they need to be able to do algebra in their head. Math class should be focused more on how to set up a spreadsheet to solve your problem, something like income tax or household budget or home mortgage that nearly everyone will need to do at some point. There are still programmers who can program in Assembler. Most programmers do not, even if they had to learn how in college. If most people knew how to use a calculator (their phone) and a spreadsheet (their laptop), they could do all of the math they need to do (except for the few of us who need something more, or who just enjoy it). The problem is, we evaluate people on how well they know their school math, but we don't evaluate school math by how well it serves most of the people who had to sweat through it. I like math, most people don't, we should focus our education system more on how they can use the tools today to do what will come up often in their life.
after_care 5y ago
> Only 13% of Americans scored as “proficient,” while over half were “basic” or “below basic.” A score of below basic (being unable to sum two monetary values) should be viewed as a failure of the education system on the same level as illiteracy.
ineedasername 5y ago
It doesn't help that the current (US) curriculum, at least in text books in my area, ask deceptively complex questions without explaining what sort of answer they're looking for. My first grader would have questions like "Sarah has 9 apples and then adds 3 more from another basket. How many apples does Sarah Have? Write the answer in equation format, then Explain why the answer is true" That last part is a strange question or at least phrasing. A proper answer verges on number theory, while the actual answer they're looking for is a tautological "Because 9 + 3 = 12". These sorts of questions confuse my kids because they realize the "explain" the book wants is just repeating the answer again, which doesn't make sense, so they think that can't be what the question is really asking.
ww520 5y ago
I was at the courthouse a while back for a traffic related matter. When I left, I passed by a woman in her 30's at the courthouse's steps. She's clearly in distraught. She said her husband was in jail and she needed to post bail. She's getting a bail bond and asked how much was the 10% of the bail (10% is the upfront fee bail bond companies charged on the bond). I felt sick in the stomach. Here's a person in her 30's who didn't understand a simple math concept and couldn't compute a percentage of something at the moment she most needed. I looked at the paperwork and it's only couple hundred dollars and let her know. Don't tell me math is useless and you won't use it in life.
yason 5y ago
The idea of taking 2/3 cups, spreading it out, and removing 1/4 to get 2/33/4 cups is pretty damn clever and totally street-smart about dividing a hard problem into smaller, more easily manageable problems on the fly. I'm not sure I could've come up with that method just like that. I would've been conditioned to look out if the fractions reveal an easy answer that I can deduce immediately without calculating anything, and then probably just ended up doing 23 and 3*4, revealing the answer. If it had been something more complex -- such that couldn't have been able to intuit abstractly about it I think I might have eventually come up with some variant of a more visual, hand-measurable method.
- huffmsa 5y ago
  Yeah I immediately failed it and started thinking of physical ways to do it. Totally forgot I could just multiply the fractions. Though my mind was also in reading mode and not math mode
parentheses 5y ago
education is not about implementing everything you learn. it’s about teaching you how to learn and giving you a basic shallow understanding of EVERYTHING. i use things i learned in school ALL THE TIME! for math this is particularly true thanks to Richard Hamming
dekhn 5y ago
After doing linear algebra for many years in grad school, I had a weird situation of memory. I was working with inverting a matrix and reading up on gaussian elimination. I realized I had completely forgotten, or at least repressed, a high school class where we learned gaussian elimination. I had completely forgotten (or rather, removed from immediate memory and thus not a candidate for a solving technique) it because it was boring to me at the time! On the other hand, my biggest memories of school math was factoring polynomials (which I have never ever done after) and determining if limits diverged (ditto). The other thing I learned and repressed was constraint solving. We did any number of constraint problems using various techniques and then years later, when I learned about integeger and linear programming, felt a strange feeling of deja vu.
Havoc 5y ago
Went through a similar thing with accounting. Huge amount of mechanical & detailed training...which I promptly forgot 99%. It leaves a lasting imprint/instinct on you though that I've come to appreciate though. Similarly you might train someone in stats, they forget it all but then subsequently are better at detecting fake news because they can see the claimed stats are bullshit. So I don't think "we don't use it" is all that straightforward
duhduhk 5y ago
As a maths graduate, I would like to see discussion around maths moving to computer science. Is it more instructive to teach some maths concepts via programming, perhaps from ages 11-12 (algebra)?
severak_cz 5y ago
I think that sometimes easier to guess result than to use math to actually calculate it.
motohagiography 5y ago
It's recently clicked for me that our economies and civilization may in fact rely on a vast majority of people without basic quantitative reasoning skills. If I were teaching a middle school kids math today, I'd start by teaching them poker and blackjack with card counting to practice doing fast calculations and then learn risk and probabilities. Then maybe create a stock picking group so they can learn to read charts and calculate simple functions with concepts like averages and moving averages, medians, and then some bayesian statistics, time value of money, interest and compounding on debt with logarithms. An example of a person with two maxed credit cards with different interest rates and a fixed income shows equilibria and how predatory those products are. I might also use a eurorack synthesizer rig with an oscilloscope to demonstrate functions and wave forms, integration, modular arithmetic and combinatorics in musical scales, harmonics, musical transposition as an example of conservation laws, ohms laws and electronics, and pulsed information (binary). Catapults vs. trebuchets and siting a rifle scope for simple ballistics and physics. Bicycle or engine repair to show differential gearing. Another unit would be some variation of cryptopals, because that's an intro to new currencies, economics, number theory, proofs as "shapes," information theory, and computer science. The way I learned algebra in high school was like learning to read music without ever hearing it, let alone playing it. Glimpsing the things I don't understand now as an adult, I can't help but think it was by design.
Kim_Bruning 5y ago
Feynman complained about this way back too. Sometimes kids aren't taught understanding. Just Drill and practice and memorization. For some subjects you can almost get away with that (but not really!) , but for mathematics it's really heavily evident.
t8y 5y ago
This stuff reminds me of New Math[0], I like this video on it[1]. People have a bizarre relationship with math. Somehow it's a huge problem if people don't memorise a lookup table of multiplication of unsigned integers from 1-12, Times tables are not even math! It seems like it's mostly just social and any real math has to be taught later in life. Even teaching real basic math like set theory was rejected by the masses because they didn't know it. I wonder what society would be like is New Math continued. If everyone could do it then the average person would be far better at some (IMO the most important) aspects of programming than most programmers today. Would GDP be 2x, 10x, 100x higher? Imagine if a random hairdresser or landscaper had a perfect understanding on how computers work, it'd be crazy. [0]https://en.wikipedia.org/wiki/New_Math https://en.wikipedia.org/wiki/New_Math [1]https://www.youtube.com/watch?v=lvEcFJANVQo https://www.youtube.com/watch?v=lvEcFJANVQo
addicted 5y ago
The answer to a lot of the reasons why people don’t use math in real life (especially the kind of problems posed in the OP) is because people don’t learn mental math. You’re not walking around with a calculator or a pen and paper all the time. You will use math in your day to day life if you can do the math in your head. We need to spend a lot more time in schools teaching children how to do math entirely in their heads. Not only will this apply far more directly to how they would use it in the future, it will also help them understand mathematical concepts a lot better.
TristanBall 5y ago
I'm 43, I got taught fractions in primary.. wait let me do some math, about 32 years ago. 1 I seem to recall fractions being presented as the necessary "old way" before they taught us decimals, but maybe that was just me. I had no idea* about the multiplying fractions thing to solve the example. 2. Maybe I was tought it, I guess I probably was, but it also just about the last time the curriculum touched on fractions at all, at least until I dropped out at year 10 ( 2 years early ). Maybe those last two years are a fraction filled bonanza.. but I suspect not. So unless I'm super interested on my own, its quite possible it's decades before I find a use for it? Just how effective do you think 5 hours a week for two 4 week periods 30 is at instilling knowledge - especially over decade timeframes. The example is actually a good one, because finding a fraction of a fraction of a cup is the kind of thing you might need when reducing the size of a recipe.. but it also demonstrates the problem... Close enough is good enough.. I can tip out part of the measure and eyeball it anyway - and can do so without thinking about it at all! And I'm cooking.. I'm doing rough measures and adjusting as I go anyway.. If math concepts aren't revisited throughout schooling, with concrete uses how does anyone retain this stuff? ( Of course, I'm a drop out with a notoriously bad memory, so maybe I'm a bad example ) There might be some value in local colleges or whatever running little "hey, now that you're an adult, here's how you can use all that math you've mostly forgotten" classes... 1: The uncertainty is I don't remember which year they taught us, not that I can't calculate the answer!! *2: OK, if I think of them as decimal values it makes sense and is semi-obvious. But I'd still just spoon out a bit of the measuring cup.
jeffwass 5y ago
Once in 5th or 6th grade we had a math homework of a few dozen problems multiplying 3 or 4 digit numbers together. Totally tedious. Instead of mindlessly doing it, I spent a few hours making a BASIC program that did the multiplication, but importantly showed all the intermediate steps that we were required to show (eg multiplying by 634 shows the multiplication by 4, 30, and 600 separately). Writing that program took probably 3x as long, but I wound up learning 50x vs the rote multiplication we were assigned.
- apricot 5y ago
  Exactly. And that's why teaching programming to kids is important. Because nothing teaches you the fundamentals of something like having to explain it to a computer.
frankfury 5y ago
It's maybe people don't take Math seriously. They should realize that Math isn't just for professionals but can be utilized in real life.
sylware 5y ago
Doing maths properly with a computer... can become very quickly very tough. See the various and connected numerical analysis topics on wikipedia.
the_only_law 5y ago
> Few people make use of fractions Huh this is probably the main thing outside arithmetic I find myself using all the time.
pfranz 5y ago
I feel like I have a different perspective than this article. I don't see any problem with how the cottage cheese problem was solved. I feel like most learning is part building a mental model, part rote memorization, and part practicing their interaction. I understand how multiplication works, but memorized my times tables to make harder problems much easier. I practiced multiplying 3 or 4 digit numbers to see them interact. The way people solved the cottage cheese problem shows they understand how fractions work. They just don't use them enough to warrant multiplying fractions and reducing the result. If they were dealing with that problem every day, they would use more efficient solutions. People that work in construction are very good at certain types of math. People working on 3d software are usually good with different types of math like trig or linear algebra. Having a general knowledge helps us muddle through rare problems or have a base to learn more specific types of math.
gk1256 5y ago
I knew people will disagree with me. The kids usually who are good with Maths are gifted. They love solving puzzles, but what about the rest kids? To me, the ultimate solution for this problem is teaching philosophy before maths. The ideal route is philosophy -> history of maths -> maths I heard that Govs don't want to add this subject into school because it will create revolutionary thinkers and it sounds more like obfuscation to me.

94 points by enigmatic02 5y ago

It is like this for all subjects. Beyond the 5th grade, applicability drops a lot. Knowing how to read simple sentences, perform elementary math is enough to get by with most tasks, but personal finance will be a struggle.

ramesh31 5y ago

I can remember failing math class hard throughout my entire academic career. I never passed a math class past primary school, and ended up dropping out of high school. The concepts simply never made sense to me, and as they were presented were just meaningless rote exercises of memorization. Math was something I had completely written off as ever being able to understand. Then I took calculus and trig classes in college. Since I was also learning graphics programming at the time, I was able to actually make sense of math with a real world connection. Playing with little graph equations on shadertoy.com made me realize graphics was all just math. Everything immediately clicked. I was able to intuitively visualize the trig functions and graph equations and do transformations of them because I could picture what the resulting image would look like. Ultimately the problem for students I think is just creating this connection to reality.

ajuc 5y ago
My experience too - I wanted to make games so when we had trigonometry and analytic geometry in class I was like "yes please, I can use this, more". Same with vector and matrix algebra later. Meanwhile I had little use for calculus so I only learnt it enough to get a good grade.
pthread_t 5y ago
It would be incredible if trigonometry classes had a lab component where students work on a 2D game, such as tower defense. I ended up taking a fun programming elective in college where my team did exactly that -- we created a 2D game. That experience made me appreciate trigonometry more than my high school teachers and Khan Academy ever did.
eschneider 5y ago
Having a real world problem to apply it to makes learning math far easier. I spent a lot of time in 2020-1 tutoring kids in math and the first thing I did was find out what they were into and then worked math into helping them do that thing.

ohiovr 5y ago

My school rarely ever directed mathematics instruction in relation to another skill or problem. Sure math might be used in industrial arts, or in home economics, but the instruction phase of the math is always 100% abstract. If people knew all the interesting things you can do with math they would be more likely to use math more often and remember what they learned. This was certainly the case for me and may have been the only thing that made me even care about math at all. I am referring to only one math class I took in high school which did this, and that was geometry. I loved my geometry teacher. He was the only math teacher I ever found likable. I loved the geometry class because it helped me a lot when thinking of practical considerations to 3D graphic arts I was creating on Amiga computers at the time not to mention the value of the discussion of area and volume. Did you know Pythagoras was a kind of cult leader? Geometry wasn't just abstract, it was practical. How much carpet do I need for a room? How much water will fit in this cylinder? If I have a disc that has to be one square foot, what would the diameter be? I had some enthusiasm for algebra one level math for solving an unknown variable using what is already known. I didn't learn the value in this at school. My dad was an electronic technician (Worked at Argonne Labs) and I was interested in what he did there. He taught me all there is to know about ohms law, finding resistance, conductivity, current voltage, using simple procedures. We did parallel circuits, tank circuits, ac theory. In less than a years time he gave me a complete 2 year associates degree understanding of dc and ac circuits. Most of us found our math teachers some of the most arrogant people in the school. They demanded that we show our work and show it going down the way they personally approached solving problems. If the result was correct but if they didn't like your preferred procedure they would lower your scores. They never could offer a sound reason for their demands. Perhaps they did have a sound reason. They just didn't bother to sell us on it. I suppose it isn't right of me to condemn all math teachers this way as my experience is kind of limited. This is just what I felt about it while being a student in high school and middle school 30 years ago.

RealityVoid 5y ago
My math teacher was not like the ones you describe, he really let me go off the reservation if I ever wanted to approach the problem in some wierd zany way. IMO, that's how it should be. On the other hand, mastery of the tools and methods requires repeating it and spending a lot of time with them untill they "make sense" or rather, you get used to them. So that is useful as well. Most people can apply mechanical methods well, but the part where I see a disconnect is applying them to new problems and new contexts. It's like... Most people don't even realize you can do that. Would love to find a scalable way that teaching can approach that as well. It is a crucial mental tool.

jcun4128 5y ago

Heh I used cross product first time in like 9 years for a little robot project.

kevin_thibedeau 5y ago
I just did some regressions to model sprinkler head flow rates for variable pressure and spray angle.
globular-toast 5y ago
Yeah. One underappreciated thing about education is exposure. It's not that I've been walking around every day for the past decade being capable of matrix multiplication. But having been exposed to it once, it's amazing how quickly the knowledge comes back when you need it. I did advent of code over Christmas and when the 3D transformations came up I thought about it for a bit, then remembered... something about matrices... linear algebra..? And then searched for the resource I needed to refresh myself on it. Just the fact I was exposed once a decade ago means I was able to refresh myself in a few minutes.
- deleted 5y ago
  [deleted]

imglorp 5y ago

Given the relative innumeracy of the public, some argue we should teach stats and probability instead of calculus, if there's a choice. Those things are more applicable for everyday choices like "should I buy a lottery ticket or invest in the market?" "How likely am I to die from disease X versus side effects of its vaccine?" "Should I buy comp insurance or pay out of pocket if I break my car?" etc.

zozbot234 5y ago
We should teach calculus first, because one cannot understand the foundations of stats and probability without calculus.
- Jtsummers 5y ago
  Using probability and statistics and understanding their foundations are two distinct things. Prob/stat can be taught (to the point of utility) without calculus and often is. More advanced applications are inaccessible or only learned by rote without calculus, but that doesn't mean that you need calculus first. Of course, this is what commonly comes up in topics like this, a confusion over the two notions: Understanding the basis of something and understanding it well enough to utilize. You don't need a graduate level physics course in electromagnetism to be a competent electrician.

rland 5y ago

Math is incredibly useful; probably everyone here knows that. But it's actually fine that most people don't use it. What we really need is for every student to realize why math is useful -- so that if they want to, they can go learn it so that they can make some kind of technological contribution to the world. The fact is, you need to be good at math to make some new fundamental breakthroughs in technology. Those breakthroughs benefit everyone, even those who don't know any math at all. But you won't really get why that's the case until you know enough about sines and cosines to make sense of modern technological development. The real issue is that we just teach the math, hoping that students will understand on their own that it's fundamental. What we should do instead is try to instill that sense of wonder about the world that inspires people to study math. We don't need every person to know calculus, we just need everyone to understand why calculus is useful -- then they can be inspired to go further. Educators say that they're trying to do this, but I'm sorry "how many meters of fence does Farmer Bob need to keep the sheep inside the pen" is not inspiration -- it's drivel, no better than "find the perimeter given a=5, b=6." If every person understood why math is so useful, we would have many more people who are motivated to work on improving the state of things.

Shared404 5y ago
> it's drivel, no better than "find the perimeter given a=5, b=6." Not only no better, but actually worse - if you add a word problem around the problem that doesn't fundamentally add anything or make the problem easier to understand [0] all you've added is another layer of text to parse through. [0] Sometimes it can be helpful. Adding a relevant layer of physicality to help reason about the problem can be nice, especially in calculus.
- netizen-936824 5y ago
  Adding the extra physical descriptions to calculus actually helped me better understand what the equations meant and represented. Definitely beneficial in some scenarios to some people
  - Shared404 5y ago

csdvrx 5y ago

You don't - I do (including some math only seen in uni). It all depends on your job, and since we can hardly know in advance, school tries to cover all bases. Drill and practice or the other proposed solutions won't help with that.

jessenichols 5y ago

Because most school is forced knowledge work on problems that don't fit the person's problem situation. When people are free, they learn the math they need for the problems they are trying to solve. Traditional, compulsory school forces children to solve problems they don't have. See Karl Popper's idea of the bucket theory of mind, or David Deutsch and Taking Children Seriously.

bjarneh 5y ago
> most school is forced knowledge work on problems that don't fit the person's problem situation. Have you never been in a situation where you are about to take train going at 80 mph; wondering when you'll meet up with your friends going in the opposite direction at 90 mph?
- mulmen 5y ago
  I recently saw a great photo [1] by Ben Cooper of a Falcon 9 on ascent crossing the Moon from the photographer’s perspective. I wonder how much math went into finding that vantage point. [1]: http://www.launchphotography.com/Starlink_4-6.html http://www.launchphotography.com/Starlink_4-6.html
  - dekhn 5y ago
    It's not really that hard. I set up several systems to do this for the previous total solar eclipse. The ephemerides for the moon are easy to download and calculate the position in the sky (IE, altitude and azimuth at time t) with a python script. I believe also the launch vehicle has a launch window (the moon moves 15 degrees per hour) and launch trajectory. I'm lazy so I'd compute the extends of the launch vehicle's motion in the sky (from earliest possible launch to latest possible launch), and then intersect that geometry with the moon position geometry without explictly trying to solve the equations simultaneously. That should back-project to shapes on the ground at which point you could reasonably expect to be able to get a good shot, and then you'd do some adjustment in your pointing in real time. A smart college senior could do it directly (IE, not lazily compute a bunch of points and manually intersect them on a screen).

graycat 5y ago

Uh, there is a carpenter with a Web site that uses the "3, 4, 5 rule", of course, the Pythagorean theorem. The first order ordinary differential equation initial value problem d/dt y(t) = k y(t) ( b - y(t) ) can be use to model viral growth. Once it kept two crucial FedEx BoD members from walking out and saved the company. Similarly for the law of cosines for spherical triangles for finding great circle distances. Linear programming (LP) gets used right along for actual, genuine LP problems and also as a means of approximation for problems that are not linear. The problem of minimum cost flows is a special case of linear programming. If want to sort keys, e.g., for some positive integer n, if want to sort n numbers into ascending order by comparing numbers two at a time, then heap sort does that in worst and average case in O(n log(n)) and, thus is the fastest possible -- this is from a cute counting argument, the Gleason bound, A. Gleason. Statistics is important and parts of it are awash in math, not all of it trivial. The design and operation of the Webb telescope is awash in math.

mlyle 5y ago
> Uh, there is a carpenter with a Web site that uses the "3, 4, 5 rule", of course, the Pythagorean theorem. Knowing a triplet ain't employing Pythagorean theorem. > [lots of following examples that are moderately deep applied math used in lots of skilled professions] Most people don't do this kind of work or analysis.
- graycat 5y ago
  > Knowing a triplet ain't employing Pythagorean theorem. 3^2 + 4^2 = 5^2 = 25 guarantees that the angle between the side length 3 and the side of length 4 is a right angle which is what the carpenter very much wanted to know. E.g., the sides might be 30 feet, 40 feet and 50 feet, e.g., for the foundation of a house, and presto, bingo the carpenter knows that the 30 foot side and the 40 foot side form a right angle, are square, which can be very important to a carpenter and not so easy to know otherwise.
  - mlyle 5y ago
    Yup, and knowing that having triangle sides multiples of 3,4,5 guarantees that it's a right triangle is not the same as employing pythagorean theorem. You know one triplet, and not why it works, or that e.g. it works for 5, 12, and 13 and 11,60, 61 as well. A whole lot of people know that measuring a bookcase corner to corner is a good way to square it up, too. But they may not be masters of geometry beyond knowing a rule of thumb.

aweofjwef 5y ago

So much of modern math education, especially once you get into high school, is centered around _computation_ instead of _reasoning_, so you get a lot of kids who spend an entire year doing random integration problems or charting a bunch of useless functions/conic sections instead of really understanding fundamental structures, reasoning, problem solving, etc. It's just rote computation, but we have computers for that now.

owlbite 5y ago
cynically: computation is easier to mark than reasoning.
- aweofjwef 5y ago
  Oh, I have no doubt that it's easier to teach in general, because you don't need to actually shape the way the students think.

syntaxing 5y ago

I can understand the average person not using the math we learn in school, but it’s crazy to me that even the average engineer doesn’t beyond basic arithmetic. I don’t mean this in an elitist sense but I feel like I was the same way a couple years ago. Until one of my mentors kinda guided me through the thought process and understanding the math is extremely powerful and useful.

jeffbee 5y ago

In my opinion serving up 2/3 cups of a semi-solid cheese and reserving a quarter of that demonstrates a quite excellent intuition about the problem of 3/4 of 2/3. Probably 3rd-grade children would be congratulated upon discovering this strategy.

mlyle 5y ago

The article mentions "More drill and practice" ... I don't think this is the right way. I believe something happens with math to many/most students which leaves them less than fluent in mathematics. Somewhere along the way, they stumble for a few weeks and fall behind. Maybe their family took a vacation. Maybe the teacher's explanations don't make sense to them. And then there's a deficit. Pretty soon, supporting that student through math becomes a whole lot more about drilling and memorizing strategies and understanding is deprioritized. This becomes insurmountable, especially with the "layer cake" model of how math is taught in US schools. Pretty soon you'll never catch up in understanding. But you probably just attribute it to "not being good at math". I'm working with a student right now, who is in precalc and "bad at math." He is actually really bright. Some missing knowledge and intuition about fractions has made everything since much harder. And the problem's never been fixed because he's constantly been in a survival mode in his math classes. These students never end up doing the kinds of things that kids are ahead in math are taught to do to crack free-form problems: - Make a good guess of the answer - Form a mental picture and use it to select strategy - Work a simpler problem and see how this can be extended - Organize your givens ; use dimensional analysis for a hint as to what operations may be required or what picture should be drawn - Look for symmetry and transformations that result in simpler cases - Does positing an incorrect answer reveal any information about the solution? IMO, teaching these things -- strategies-- should be more the goal than doing lots of kinds of applied math work by rote in a way that deeply depends upon previous work.

the_only_law 5y ago
There was another “I’m bad at math” thread a while back I stumbled across and drilling was considered basically the way to get good at math by most people posting. … which is all the more reason I’ll never become good at math. I’d rather drill a hole in my head than subject myself to drilling back to back, contextless, boring problems I don’t care about.
- mlyle 5y ago
  I think there's a few points where drill makes sense. In each case, after you have a good understanding, and you're seeking to become fluid and avoid dumb mistakes. (Even if you have a good understanding, if you're consciously thinking about each step you'll error a fair bit, and on a 20 step problem you can't afford this error rate and slowness) Arithmetic facts, basic algebraic manipulation, big polynomials, derivatives and integrals. But we do much more drill than that. And, worse, it's often as homework, where you can be guaranteed a decent slice of the class is practicing it wrong.

globular-toast 5y ago

I think I've used almost everything I learnt in maths at school at one point in my adult life. And not just because I'm a programmer. The other day I was using trigonometry to work out how to install a projector into a room. From what I can tell, most people don't do things like install projectors into rooms. They either get someone else to do it, or just figure out some placement that is good enough via intuition or trial and error. If people have jobs that require it, they usually remember the bare minimum for their job and aren't remembering general concepts to help them solve brand new problems. If there is causality here, I'm not sure which way around it is. Either they don't need maths because they don't stuff that needs it, or they don't do stuff that needs it because they can't do maths.

lordnacho 5y ago

This is a good question, why is it that seemingly nobody uses the math they've been taught? When I was in school, my math teacher used to write AMBS on the board before calculus lessons: Algebra Must Be Strong. What happens when you study calculus is you end up rehashing algebra over and over again until it's second nature. Consequently if you find someone who's done well at calculus, you can be sure they can do algebra. Someone mentioned this in relation to RenTech. Why do they hire mathematicians who have studied incredibly complex things with seemingly no relation to trading? One reason might be that people who have done that know the fundamentals very, very well. Similarly accountants don't use vectors or geometry at work either, but they certainly are comfortable with arithmetic and its application in spreadsheets. When I look at my own education, it is also the case that the things I'm least sure of are the deepest, latest courses that build on everything else. Probably if I built on top of those I'd be more comfortable with them. Taking this line it would appear that you can't just teach people the math they'll use, because they won't really get it until they try to do the next thing. A thing that needs addressing is the notion that we should only teach people things that will be useful, which seems to underlie this article. We should teach people how to explore, and math is the premier example of a large space that can be explored with very little access to resources and evidence. You can do it just in your mind, and you don't need any apparatus or conclusions from people who had such apparatus, like you do in science.

ioseph 5y ago

When I started learning woodwork I was really excited to apply geometry which I hadn't used much since highschool (even working with geospatial data vis). However as I've progressed I find myself using math less and less and it's often faster and more accurate not to measure or calculate. To give an example, making a three legged stool I needed 3 equally spaced spaced points around a circle, I could find the center, draw the first point then use a protractor to find the other 3 points at 120 deg. But it was far far quicker to just use a divider, step around the circle a few times adjusting until 3 steps takes you back to the first point. Of course this is still some form of math, but it doesn't involve any calculation. I feel there's a whole world of very useful techniques that work on a different abstraction, though I'm struggling to name or describe to properly.

deleted 5y ago
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jimmygrapes 5y ago
A similar trick is the 3:4:5 rule[1] which I have not used for woodworking but that's where I first heard of it. I have used it for general site planning for tents and ensuring fire breaks and similar, though. [1]: https://www.ezwoodshop.com/345-triangle.html https://www.ezwoodshop.com/345-triangle.html

voldacar 5y ago

> Many students are only taught math as symbol manipulation. Less instruction is focused on identifying situations where it might be useful. We need to give students more training in noticing and converting everyday situations into the math problems they know how to solve. No, please don't do this. When I was learning math as a kid I found word problems incredibly irritating and stupid. It's just a way to waste a few seconds of my time when I just want to solve the problem and get to the next one. Word problems are just disrespectful

pfranz 5y ago
I think the reason most word problems suck is that they're manufactured abstractions on the same problems elsewhere on the worksheet--which seems to be your critique. In real life, a lot of those situations are hidden, but there are often multiple correct ways to approach the problem and hopefully some intuition will help you if you're too far off track. 2/3rds of 3/4ths of a cup of cottage cheese shouldn't be more than one cup and shouldn't be a tiny amount, either. (I also don't see a problem with people who scooped it onto the table). Similarly to the woodworker (elsewhere in this thread) trying to evenly measure out where 3 legs on a stool would go.

basscomm 5y ago

To me this is coming at the issue from the wrong angle. Sure, mathematics classes in elementary through high school have the veneer of teaching mathematics, but they also teach logical thinking and problem solving. Identifying a problem (in math class the problems usually come pre-identfied until you tackle the dreaded story problems) and breaking down the problem into logical steps, are useful skills to have even if someone never does another math problem in their life.

jfengel 5y ago

My answer: because most of the math we learn in school is useless. I see a lot of math homework questions on Quora, because students copypaste their homework all the time: What is log (3x +2)- log2 =1? How do you prove that X^2-3 is irrational? What are the roots of the equation x4−4x3+6x2−4x+4=0? When on earth are you ever going to use any of that? The word problems are no better. In a group of 20 adults, 4 out of 7 women and 2 out of 13 men wear glasses. What is the probability that a person chosen at random from the group is a woman or wears glasses? Mr. Tay had 20 female fish and 5 male fish in a pond. Mr. Tay’s father brought some male fish and put them in the pond. Then he found 1/5 of the fish are female. How many male fish did his father put into the pond? In a school interhouse competition, 80% of the students turned up for the athletic competition, 60% turned up at the football match. What percentage of the students attended both functions? These just aren't the kinds of questions anybody ever actually asks. The math required to solve them is pragmatic; are there no pragmatic examples they can come up with? The fact that students are copypasting their homework doesn't thrill me for their ethics or their intelligence. But the fact that the problems themselves are so stultifyingly dull almost makes it seem reasonable.

eternityforest 5y ago
Maybe they should get engineers to teach math courses the way they wish they had been taught them, rather than math people who sometimes still seem to think we will be doing this without a calculator?
- jfengel 5y ago
  Engineers have specialty interests. I'd just as soon have it taught by a home economics department, or at worst an MBA. Things everyone should be able to do: read a bill, allocate a budget, estimate how much food to buy for 2 people versus 10 people, plan for retirement, maybe convert a recipe from metric to imperial units. Perhaps get a shop teacher. Let the future STEM majors learn the rest in their classes. It takes a long time for a lot of that stuff to pay off, and much of it remains irrelevant.
  - 5y ago

kkwteh 5y ago

I think this question stems from a confusion as to what school is actually for. It seems to me that school is at least as much about orderly management of the social hierarchy as it is about teaching useful skills. The reason why math is taught in school is not because math is useful (it is useful in certain situations, but this is only tangentially related). We teach it because it keeps students busy and out of trouble, and lends itself well to unambiguous testing and is therefore an effective tool for sorting students into the various social classes. This all became clear to me when I was in the middle of my math PhD and wondering why all of the math courses I had taken did next to nothing to prepare me for actual mathematical research. Viewed from this perspective, it’s obvious why we don’t use the math we learn in school.

flint 5y ago

bell-cot 5y ago

Why don't we use the [History|English Lit.|Chemistry|etc.] that we learn in school? As a generality, isn't the math taught to most teens in public schools aimed pretty squarely at preparing them to take the standard calculus courses in their first couple years of college? If so, hardly surprising that most ex-students don't notice much use for that stuff in the real world. And since the social function of that is usually to demonstrate that you're determined / focused / upper-class enough to successfully slog your way through it - gee, what would be the point to remembering or using it after getting your "made it through" bragging rights?

Gigachad 5y ago
English is critically important to help you understand complex written works and to write in a way that is clear and doesn't make you look dumb. Advanced chemistry might be useless, but basic chemistry/physics is useful. And I feel that people would understand what they are doing a lot more if they understood physics a little better. For example a lot of people think a cone makes amplifies noise rather than understanding that it simply directs them in to a smaller space. Chemistry helps you understand why oils stick to your hands and don't wash off until you use soap. Basic math is very useful but highschools go so far off basic math that they teach massive amounts of seemingly useless stuff.

eternityforest 5y ago

People don't use math because... it's only useful if you actually really know it. "Useful" to me means "Lets you do something you couldn't before with a phone". Aside from imperial inch fractions(Not a fan of those!), most things require fairly little understanding of fundamentals. Because most people aren't in tech jobs where they can use it. I don't have a checkbook or do my own investing. I'm single, and very little math is needed to pick whatever is cheapest, especially when only certain sizes of some things are practical for one person. CAS systems can do basic algebra, FreeCAD does geometry... FreeTaxUSA does taxes, I don't have a car to optimize insurance costs for... It's always pretty cool to see a chance to use math IRL just because it's such an uncommon novelty, but I don't see it very often. To unlock new capabilities you have to learn all those basics, then move on to learn the advanced stuff that computers can't already do. It's a pretty long term investment of time. Maybe worth it, but still a lot of work.

aardvark179 5y ago
> FreeCAD does geometry FreeCAD can do geometry, but if you can’t reason your way through the constraints you need to set for it to do that then you’ll be flailing around. FreeCAD definitely saves me from doing arithmetic, but not from doing maths.
- eternityforest 5y ago
  I usually find the constraints are a pretty direct translation of how I would describe a part in non-tech nical writing. Math definitely is helpful, but unless you are a full time MechE, it's not like you need to be able to pass a high school geometry class to be able to print a replacement part for something.
mulmen 5y ago
When you say “imperial system” you almost certainly mean US Customary Units. These are not the same system. The United States has never used the Imperial System. Also, US Customary Units have been defined in terms of SI units since 1893. Personally I don’t find multiplying by two any harder than multiplying by 10. https://en.m.wikipedia.org/wiki/United_States_customary_units https://en.m.wikipedia.org/wiki/United_States_customary_unit... https://en.m.wikipedia.org/wiki/Mendenhall_Order https://en.m.wikipedia.org/wiki/Mendenhall_Order

kelp 5y ago

I feel like there could be an Explanation #4 which is something like: for many people lots of math is used so infrequently, it's hard to retain after you're done with school. Maybe more drills would help that? I did pretty well in high school math and got through the most advanced math classes my small town school district had to offer. Then I opted out of driving to the next town over to do a more advanced math class with something like the 5 other kids who qualified. I think it was pre-calculus or something. So I ended up not doing math for a year, then I really struggled in my first college math classes, and had to retake one of them. Since then I've basically just forgotten everything because it comes up so rarely. How often do I need to do fractions? almost never, and when I do, I can just look up a factions calculator. Never mind trig or calc. Day do day, I think I need basic addition, subtraction, multiplication, and division. And I figure out percentages a lot. But I'm also doing all of that with a calculator. I think financial cautions, like compounding interest are the most advanced things I run into regularly.

neptunesoda 5y ago

I have a different take on this situation (thought it bears some resemblance to "Explanation #2" in the article). My years of experience in maths education has led me to the conclusion that the role of maths, particularly in child education, has, or should have, little-to-nothing to do with maths itself: it is a means unto a different end, and should not be used as the end unto itself. For example, why do we make (US) high-school students study elementary algebra? You would be hard-pressed to find an application of the quadratic formula in everyday life, and yet I maintain that it, and the course at large, has an important pedagogical role. All pre-collegiate levels of maths education (arguably including elementary calculus, but certainly everything before that) presents the student with increasingly complex situations, the tackling of which requires increasingly complex problem-solving strategies. From this perspective, all levels of maths education are effectively drilling structured logical reasoning, problem decomposition, pattern matching, rule application, abstract thinking, abstract/concrete translation, precise/"technical" communication, etc. Maths simply provides a rather nice vehicle for presenting these concepts in an ordered fashion with natural increases in complexity. I even believe that the introduction of integers to pre-schoolers is a valuable vehicle for introducing causality and linearity of time. Along the way, there are certainly valuable real-life skills that are clear applications of maths concepts, and I would agree with the article that most maths programs are woefully deficient in really underscoring the value of these applications. The article opens with a comic about needing "two-thirds of three-quarters", but anyone who has ever scaled a recipe, or worked with so-called "bakers percentages" knows that this is far from being simply a theoretical word problem. As an aside, I spent a number of years teaching elementary arithmetic to adult students (usually in their 50s-60s, and, without a hint of hyperbole, commonly unable to solve "2 + 2" without memorization). My role was to find creative ways of communicating arithmetic concepts to people for whom the traditional approach often failed. This strengthened my belief in the above perspective by providing an interesting corollary: many of these people had come to learn the "maths-adjacent" skills, traditionally taught via maths instruction, in fascinatingly creative ways. If the ordering and equal-spacing of the integers was not something they were able to truly grasp as children, sometimes they would surprise me with their approach to other parts of their lives for which perhaps you and I would have a more "normal" solution to.

pohl 5y ago

It's my understanding that American Football players frequently wonder, during a game, why there are no automobile tires strewn about the field for them to step into.

wanderer_ 5y ago
Very... well said my friend.

patja 5y ago

I used quite a bit of high school trigonometry when building new stairs and guardrails for my deck.

temp8964 5y ago

There’s a sickness in today’s American/western culture related to learning / education: against practice. Teachers design all sorts of activities to facilitate student learning, but they are disgusted to do the most important thing for early learners: repetitive practice. When students start to learn algebra, many of them can’t even do two digits addition/subtraction by hand. Not to mention to do calculations in the head. Why learning to do basic calculations/numerical processes fast is important? Basic psychology: reducing cognitive load in thinking through complex processes. Repetitive practice is the building block of learning everything. Of course there’s more in learning psychology, but that’s off topic.

wanderer_ 5y ago
Then again, those who are more naturally proficient, like myself, were often left to do 30 problems as homework on a topic that they could have done without even attending class that day.
Ekaros 5y ago
Basic math and algebra are the fields where I actually see that repetition is needed and useful. Huge part of being proficient is pattern recognition and repetition is only way to get to this. And I actually often wish that I had bee teached more than 10x10 tables... Maybe up to 20x20.

sumedh 5y ago

In school back in India, I quickly learned that I dont like Math, I just find it too difficult specially concepts like polynomials, trigonometry etc but I had very strict parents and they would not be happy if I failed in Math so I had to come up with a plan. So I used my superpower, turns out I had good memorisation skills, so my plan was to memorise all the questions (and their answers) which were asked in exams for the last couple of years because most of the questions are randomly picked from the same set of questions which were asked in the last couple of years. My plan worked and I got good scores in my Math exam, my parents were happy.

gjs278 5y ago

legitster 5y ago

The failure is with story problems. Story problems are perhaps the most important part of math education. A story problem requires using math to actually problem-solve. But they are often terribly written and introduced too little too late. In some of my classes, they were nearly ripped out of the curriculum entirely because students struggled so hard with them.

ohiovr 5y ago
My mom was a special ed teacher and she would always teach math and arithmetic in whatever every day like problem may encounter for them. She covered making change, doing budgets, using multiplication for finding area, understanding recipes. Her students appreciated that.

tqi 5y ago

I don't use my lessons on different animal species or cloud types in my adult life either, doesn't mean the experience of learning wasn't useful or important or that my teachers failed to teach it properly...

uejfiweun 5y ago

I would really love it if there was some type of Leetcode for math. I grew up in a very liberal artsy environment and was actually warned against taking advanced math for most of my life. It wasn't until college, taking requirements for my CS major, that I realized I actually find it fascinating and have an aptitude for it - but then college ended and I just have barely done any math since. If anyone has any resources on this or general advice I'd love to hear it. It seems to me like all the coolest cutting edge stuff in Tech right now requires a lot of math so I'd love to start grinding at it.

Jtsummers 5y ago
> I grew up in a very liberal artsy environment and was actually warned against taking advanced math for most of my life. What possible rationale was there for that?
- uejfiweun 5y ago
  Don't get me wrong, what I mean by this is like I took AP Calc AB in 11th grade instead of AP Calc BC. I still was in accelerated math classes. It was more so that my parents both tried the top most advanced math in their education, and both did poorly, so it was a pitfall they warned me about.
btheshoe 5y ago
Look of art of problem solving's alcumus. It's targeted at children who do competitive math, but leetcode is also easier than high school level usaco problems, so you might find it challenging. In general, aops has some decent textbooks.

rossdavidh 5y ago

The reality is, people need to know how to use spreadsheets well and accurately, more than they need to be able to do algebra in their head. Math class should be focused more on how to set up a spreadsheet to solve your problem, something like income tax or household budget or home mortgage that nearly everyone will need to do at some point. There are still programmers who can program in Assembler. Most programmers do not, even if they had to learn how in college. If most people knew how to use a calculator (their phone) and a spreadsheet (their laptop), they could do all of the math they need to do (except for the few of us who need something more, or who just enjoy it). The problem is, we evaluate people on how well they know their school math, but we don't evaluate school math by how well it serves most of the people who had to sweat through it. I like math, most people don't, we should focus our education system more on how they can use the tools today to do what will come up often in their life.

after_care 5y ago

> Only 13% of Americans scored as “proficient,” while over half were “basic” or “below basic.” A score of below basic (being unable to sum two monetary values) should be viewed as a failure of the education system on the same level as illiteracy.

ineedasername 5y ago

It doesn't help that the current (US) curriculum, at least in text books in my area, ask deceptively complex questions without explaining what sort of answer they're looking for. My first grader would have questions like "Sarah has 9 apples and then adds 3 more from another basket. How many apples does Sarah Have? Write the answer in equation format, then Explain why the answer is true" That last part is a strange question or at least phrasing. A proper answer verges on number theory, while the actual answer they're looking for is a tautological "Because 9 + 3 = 12". These sorts of questions confuse my kids because they realize the "explain" the book wants is just repeating the answer again, which doesn't make sense, so they think that can't be what the question is really asking.

ww520 5y ago

I was at the courthouse a while back for a traffic related matter. When I left, I passed by a woman in her 30's at the courthouse's steps. She's clearly in distraught. She said her husband was in jail and she needed to post bail. She's getting a bail bond and asked how much was the 10% of the bail (10% is the upfront fee bail bond companies charged on the bond). I felt sick in the stomach. Here's a person in her 30's who didn't understand a simple math concept and couldn't compute a percentage of something at the moment she most needed. I looked at the paperwork and it's only couple hundred dollars and let her know. Don't tell me math is useless and you won't use it in life.

yason 5y ago

The idea of taking 2/3 cups, spreading it out, and removing 1/4 to get 2/33/4 cups is pretty damn clever and totally street-smart about dividing a hard problem into smaller, more easily manageable problems on the fly. I'm not sure I could've come up with that method just like that. I would've been conditioned to look out if the fractions reveal an easy answer that I can deduce immediately without calculating anything, and then probably just ended up doing 23 and 3*4, revealing the answer. If it had been something more complex -- such that couldn't have been able to intuit abstractly about it I think I might have eventually come up with some variant of a more visual, hand-measurable method.

huffmsa 5y ago
Yeah I immediately failed it and started thinking of physical ways to do it. Totally forgot I could just multiply the fractions. Though my mind was also in reading mode and not math mode

parentheses 5y ago

education is not about implementing everything you learn. it’s about teaching you how to learn and giving you a basic shallow understanding of EVERYTHING. i use things i learned in school ALL THE TIME! for math this is particularly true thanks to Richard Hamming

dekhn 5y ago

After doing linear algebra for many years in grad school, I had a weird situation of memory. I was working with inverting a matrix and reading up on gaussian elimination. I realized I had completely forgotten, or at least repressed, a high school class where we learned gaussian elimination. I had completely forgotten (or rather, removed from immediate memory and thus not a candidate for a solving technique) it because it was boring to me at the time! On the other hand, my biggest memories of school math was factoring polynomials (which I have never ever done after) and determining if limits diverged (ditto). The other thing I learned and repressed was constraint solving. We did any number of constraint problems using various techniques and then years later, when I learned about integeger and linear programming, felt a strange feeling of deja vu.

Havoc 5y ago

Went through a similar thing with accounting. Huge amount of mechanical & detailed training...which I promptly forgot 99%. It leaves a lasting imprint/instinct on you though that I've come to appreciate though. Similarly you might train someone in stats, they forget it all but then subsequently are better at detecting fake news because they can see the claimed stats are bullshit. So I don't think "we don't use it" is all that straightforward

duhduhk 5y ago

As a maths graduate, I would like to see discussion around maths moving to computer science. Is it more instructive to teach some maths concepts via programming, perhaps from ages 11-12 (algebra)?

severak_cz 5y ago

I think that sometimes easier to guess result than to use math to actually calculate it.

motohagiography 5y ago

It's recently clicked for me that our economies and civilization may in fact rely on a vast majority of people without basic quantitative reasoning skills. If I were teaching a middle school kids math today, I'd start by teaching them poker and blackjack with card counting to practice doing fast calculations and then learn risk and probabilities. Then maybe create a stock picking group so they can learn to read charts and calculate simple functions with concepts like averages and moving averages, medians, and then some bayesian statistics, time value of money, interest and compounding on debt with logarithms. An example of a person with two maxed credit cards with different interest rates and a fixed income shows equilibria and how predatory those products are. I might also use a eurorack synthesizer rig with an oscilloscope to demonstrate functions and wave forms, integration, modular arithmetic and combinatorics in musical scales, harmonics, musical transposition as an example of conservation laws, ohms laws and electronics, and pulsed information (binary). Catapults vs. trebuchets and siting a rifle scope for simple ballistics and physics. Bicycle or engine repair to show differential gearing. Another unit would be some variation of cryptopals, because that's an intro to new currencies, economics, number theory, proofs as "shapes," information theory, and computer science. The way I learned algebra in high school was like learning to read music without ever hearing it, let alone playing it. Glimpsing the things I don't understand now as an adult, I can't help but think it was by design.

Kim_Bruning 5y ago

Feynman complained about this way back too. Sometimes kids aren't taught understanding. Just Drill and practice and memorization. For some subjects you can almost get away with that (but not really!) , but for mathematics it's really heavily evident.

t8y 5y ago

This stuff reminds me of New Math[0], I like this video on it[1]. People have a bizarre relationship with math. Somehow it's a huge problem if people don't memorise a lookup table of multiplication of unsigned integers from 1-12, Times tables are not even math! It seems like it's mostly just social and any real math has to be taught later in life. Even teaching real basic math like set theory was rejected by the masses because they didn't know it. I wonder what society would be like is New Math continued. If everyone could do it then the average person would be far better at some (IMO the most important) aspects of programming than most programmers today. Would GDP be 2x, 10x, 100x higher? Imagine if a random hairdresser or landscaper had a perfect understanding on how computers work, it'd be crazy. [0]https://en.wikipedia.org/wiki/New_Math https://en.wikipedia.org/wiki/New_Math [1]https://www.youtube.com/watch?v=lvEcFJANVQo https://www.youtube.com/watch?v=lvEcFJANVQo

addicted 5y ago

The answer to a lot of the reasons why people don’t use math in real life (especially the kind of problems posed in the OP) is because people don’t learn mental math. You’re not walking around with a calculator or a pen and paper all the time. You will use math in your day to day life if you can do the math in your head. We need to spend a lot more time in schools teaching children how to do math entirely in their heads. Not only will this apply far more directly to how they would use it in the future, it will also help them understand mathematical concepts a lot better.

TristanBall 5y ago

I'm 43, I got taught fractions in primary.. wait let me do some math, about 32 years ago. 1 I seem to recall fractions being presented as the necessary "old way" before they taught us decimals, but maybe that was just me. I had no idea* about the multiplying fractions thing to solve the example. 2. Maybe I was tought it, I guess I probably was, but it also just about the last time the curriculum touched on fractions at all, at least until I dropped out at year 10 ( 2 years early ). Maybe those last two years are a fraction filled bonanza.. but I suspect not. So unless I'm super interested on my own, its quite possible it's decades before I find a use for it? Just how effective do you think 5 hours a week for two 4 week periods 30 is at instilling knowledge - especially over decade timeframes. The example is actually a good one, because finding a fraction of a fraction of a cup is the kind of thing you might need when reducing the size of a recipe.. but it also demonstrates the problem... Close enough is good enough.. I can tip out part of the measure and eyeball it anyway - and can do so without thinking about it at all! And I'm cooking.. I'm doing rough measures and adjusting as I go anyway.. If math concepts aren't revisited throughout schooling, with concrete uses how does anyone retain this stuff? ( Of course, I'm a drop out with a notoriously bad memory, so maybe I'm a bad example ) There might be some value in local colleges or whatever running little "hey, now that you're an adult, here's how you can use all that math you've mostly forgotten" classes... 1: The uncertainty is I don't remember which year they taught us, not that I can't calculate the answer!! *2: OK, if I think of them as decimal values it makes sense and is semi-obvious. But I'd still just spoon out a bit of the measuring cup.

jeffwass 5y ago

Once in 5th or 6th grade we had a math homework of a few dozen problems multiplying 3 or 4 digit numbers together. Totally tedious. Instead of mindlessly doing it, I spent a few hours making a BASIC program that did the multiplication, but importantly showed all the intermediate steps that we were required to show (eg multiplying by 634 shows the multiplication by 4, 30, and 600 separately). Writing that program took probably 3x as long, but I wound up learning 50x vs the rote multiplication we were assigned.

apricot 5y ago
Exactly. And that's why teaching programming to kids is important. Because nothing teaches you the fundamentals of something like having to explain it to a computer.

frankfury 5y ago

It's maybe people don't take Math seriously. They should realize that Math isn't just for professionals but can be utilized in real life.

sylware 5y ago

Doing maths properly with a computer... can become very quickly very tough. See the various and connected numerical analysis topics on wikipedia.

the_only_law 5y ago

> Few people make use of fractions Huh this is probably the main thing outside arithmetic I find myself using all the time.

pfranz 5y ago

I feel like I have a different perspective than this article. I don't see any problem with how the cottage cheese problem was solved. I feel like most learning is part building a mental model, part rote memorization, and part practicing their interaction. I understand how multiplication works, but memorized my times tables to make harder problems much easier. I practiced multiplying 3 or 4 digit numbers to see them interact. The way people solved the cottage cheese problem shows they understand how fractions work. They just don't use them enough to warrant multiplying fractions and reducing the result. If they were dealing with that problem every day, they would use more efficient solutions. People that work in construction are very good at certain types of math. People working on 3d software are usually good with different types of math like trig or linear algebra. Having a general knowledge helps us muddle through rare problems or have a base to learn more specific types of math.

gk1256 5y ago

I knew people will disagree with me. The kids usually who are good with Maths are gifted. They love solving puzzles, but what about the rest kids? To me, the ultimate solution for this problem is teaching philosophy before maths. The ideal route is philosophy -> history of maths -> maths I heard that Govs don't want to add this subject into school because it will create revolutionary thinkers and it sounds more like obfuscation to me.