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>You know they will never use it in adulthood, outside of certain career choices. If somebody says stuff like this, then they do not understand math, imo. Im

>You know they will never use it in adulthood, outside of certain career choices. If somebody says stuff like this, then they do not understand math, imo. Im a little bit sad whenever somebody argues for math by using "no phone available at the moment" argument. Math is insanely powerful world modeling tool. Starting from calculating right amount of fence for your garden, to estimation of 500km route arrival time while taking traffic statistics into the account, to data science, ML, whatever more complex. Since math modeling is everywhere in "modeling" industries like engineerings, financial-ish jobs and other Then you basically not only get better tools to operate (model) in real world, day2day life, but also it opens you doors to highly paid careers. But the goal is not to have fancy jobs, but being able to do real world modeling.

raincole 3y ago
I don't think you need calculus to calculate right amount of fence for your garden. > Since math modeling is everywhere in "modeling" industries like engineerings, financial-ish jobs and othet In other words, certain career choices, as the OP says.
- l__l 3y ago
  This makes the same mistake being called out in the comment you're replying to. The point isn't about the mechanics of solving a differential equation, it's about gathering the intuition about a way of approaching problems. (Also, while it might not be the tools needed for the average homeowner, there are plenty of optimisation problems similar to "how much fence do I need" which are most easily solved by solving the Euler-Lagrange equations)
  - DrScientist 3y ago
    Interesting I've seen the opposite in highly trained mathematicians - they can really struggle with taking an intuitive leap without the safety net of the working out the numbers. While it's always better to work out the numbers if possible, sometimes it isn't possible and people get trapped trying.
- hardware2win 3y ago
  No, it is side effect while the goal is modeling which can be applied in your whole life, not just job.
keerthiko 3y ago
IME a big part of this misdirection stems from school focusing on the mechanics of math, rather than the intuition of math. In the long run, the mechanics of math (how to do long division, or differentiate an expression, or expand a geometric series) are important only insofar as to help us model and predict and analyze the world, intuitively. However, students who do not intuitively see the power of mathematical intuition as a tool for understanding and modeling the world better, think that they are taught the mechanics of math just for the sake of "no phone/calculator/computer available" circumstances.
- deleted 3y ago
  [deleted]
- butterNaN 3y ago
  I can only speak for myself here, but my journey with Maths did start with concrete, practical relationship between concepts and usage. I still remember fascinated by Geometry and Trigonometry, because how it can be used to create graphics and video games is obvious. The more abstract it gets, the more it warrants an introduction with "here's how it's used in real life". I can recall the point when it started becoming mechanical - it was when I started doing Derivatives and Integrations. I was 'just solving puzzles' until I hit a chapter, tucked away way back in the syllabus, almost at the end of the 2 year arc - a chapter about Applied Differential Calculus. I still remember the feeling of "Oh... I get it now" euphoria, with a tinge of sadness - why wasn't this covered early on? Same thing would have happened in Engineering as well, but at the time my teacher was good. They started by explaining the applications of Fourier Transform before we actually got to learn the mechanics of it.
- roel_v 3y ago
  I've never taught mathematics but I think it's much harder to teach the intuition, and I also think that more people are capable of learning the mechanics than the intuition. So from the point of view of someone designing a methodology and curriculum - you have to design for scale. I have the same thing with learning languages: I despise focusing on the rules of conjugation and word order and rote memorizing rules, exceptions to them and exceptions to exceptions. I much prefer to bootstrap with some vocab and then acquire by immersion, even if that means I get the conjugations wrong in the beginning. But I also find myself in the minority by far, to the extent that pretty much all language teachers I ever had (except my high school French teacher - she was awesome letting me translate MC Solaar lyrics for grades) didn't even really seem to believe that there are other ways of learning other than studying rules.
jokethrowaway 3y ago
I don't get why calculus is always brought as an example. It wasn't particularly hard, the entire class had to learn it in high school. We all had it (in a slightly harder shape) in every university course (no matter how detached from what we actually needed) I forgot all my calculus after high school, had to relearn it in uni and then I promptly forgot again. Exactly as the article says, it was more about proving we had the capacity (proxy iq test?) to learn it. You don't need calculus in real life and I think the focus on calculus is ridiculous when we could explore other more practical areas, like category theory (which only my lucky friends who did advanced math got to play with)
- throwbadubadu 3y ago
  But what is the general application of category theory, outside computer science.. and even there the average programmer who hasn't some type theory experience will stare at you with huge eyes when you mention it.. I love the wikipedia intro: Calculus is the mathematical study of continous change, the same way geometry is the study of shape and algebra... that's it perfectly. And the most basic application is in everyone's life and also one of the basic physics thing: The relationship between location, speed and acceleration. I find this very essential, vs category theory at least..
  - l__l 3y ago
    This is my field :) Category theory is about connecting the dots between different areas of maths. The "general application" is to allow you to reason over the structure of a problem you're interested in, while throwing away all the superfluous details. It arose when geometers and topologists realised they were working on the same problems, dressed up in different ways. I think the utility for technical people, from this perspective, is pretty clear. As for the general working person? I think it's just an exercise in learning to do abstractions correctly, which is valuable in any line of work. There are actually people who advocate that we should base maths education on category theory much earlier (much as New Math was interested in teaching set theory early on, as a foundational topic). CT is an unreasonably effective tool in a large section of pure maths, so this doesn't sound unreasonable to me; it wouldn't be nearly so scary if it were introduced gently much earlier on (in the same way we start to learn about things like induction in the UK in secondary school, long before formalities like ordinals are introduced at uni). Currently only a very specific, highly-specialised section of the population learn CT, but if something like this were to happen, I'm sure we'd see lots of benefits which are hard to identify at the moment.
Etherlord87 3y ago
I'm using math(s) a lot, trigonometry, matrices, algebra… But most of my friend, family, I couldn't convince to learn math just based on the argumentation they can use it in practice. Yes, calculating the right amount of fence is useful, but not only (as someone pointed out) you don't need a lot of math for that, people just take take a ruler on the plan, or count steps in field, going across the entire length, then estimate, and it works. > estimation of 500km route arrival time while taking traffic statistics into the account Who does this? How would you convince a friend to learn math in order to do this? What people do is they remember how long a 200 km route took and so they estimate the 2.5× longer path will take 2.5× more time. We need examples of real world math applications, because such examples are scarce across the Internet.
- hardware2win 3y ago
  >Who does this? How would you convince a friend to learn math in order to do this? What people do is they remember how long a 200 km route took and so they estimate the 2.5× longer path will take 2.5× more time. Who does it? Navigation app in your phone. They modeled this problem using math. While you could probably model it somehow without math, but why would you want to do it other way, when you have reliable, mature and flexible tool I didnt write that you shouldnt leverage tech. Do it, yet be aware how it works and why. You can leverage math in other custom scenarios
  - toyg 3y ago
    So what I'm hearing is that math is only good when there is no GPS / no phone. Let's be honest: advanced math is useful in programming contexts. Everywhere else, in 2023 you're using computer programs that will do the hard math for you.
    - hardware2win 3y ago
      You didnt understand my message. Math is not about calculators or computers. It is about modeling (e.g real world) It is useful whenever non-standard, already modeled in your calculator problem apprears.
lucideer 3y ago
You've given one day-to-day example (garden fence) which requires only extremely elementary math, and then listed a bunch of stuff related to specialised career paths... which was the OP's original qualifier: > outside of certain career choices. As someone who did a lot of calculus in university, and definitely hit a eureka moment while integrating over vector fields that helped me conceptualise some general day-to-day stuff better in my head, would most people generally benefit from that same conceptual "grokking": of course. Would it be worth the time & effort investment for them if they're not using it in their career: no.
- hardware2win 3y ago
  There is no license required for using math. Yea, if you dont want, then you will not use math. But, if you dont have some mental block, then you may find ways to apply math to your problems. Abstract thinking is really useful during arguments, even about politics, religion, etc.
  - lucideer 3y ago
    > If you dont have some mental block The "mental block" you're referring to here is a combination of individual aptitude, capacity, access to educational resources & time-/effort-budgeting over a lifetime. This isn't some free casual object people are refusing to collect on their travels, it requires investment.
    - RugnirViking 3y ago
      It does indeed require investment of mental effort. But that's it. I'd argue maths is one of the cheapest monetarily skills it is possible to pick up - there have been several great contributions from people with little or no formal schooling. It's not like it's available only to a select few, I think pretty much everyone that gets deep enough in to be able to apply it continues to do so throughout their life. It can be used to fill in for all sorts of problems. I've been a tutor and ive long been a strong advocate for yes you can do it. I've met so many diverse people with excellent spacial reasoning that for whatever reason decided they weren't smart enough or couldn't understand it, yet when given a zealous advocate to encourage them picked it up just as quickly as any stereotypical maths genius
maccard 3y ago
They're not everyday things for a lot of people though. I was in a shop this weekend where the price per 250g of coffee was displayed, but the woman in front of me only had a 175g container. Neither her, the person serving her, or the other person working in the café knew how much to charge her. It's 175/250 * £PRICE_PER_250. In supermarkets, prices of items are displayed beside each other - a sharing bar of chocolate is £x/100g, but the multipack is £y/item, and each item is z grams. Which is better value? Cooking - I have a recipe in a book that serves 2 people, but I'm cooking for 3. How much X do I need?

raincole 3y ago

I don't think you need calculus to calculate right amount of fence for your garden. > Since math modeling is everywhere in "modeling" industries like engineerings, financial-ish jobs and othet In other words, certain career choices, as the OP says.

l__l 3y ago
This makes the same mistake being called out in the comment you're replying to. The point isn't about the mechanics of solving a differential equation, it's about gathering the intuition about a way of approaching problems. (Also, while it might not be the tools needed for the average homeowner, there are plenty of optimisation problems similar to "how much fence do I need" which are most easily solved by solving the Euler-Lagrange equations)
- DrScientist 3y ago
  Interesting I've seen the opposite in highly trained mathematicians - they can really struggle with taking an intuitive leap without the safety net of the working out the numbers. While it's always better to work out the numbers if possible, sometimes it isn't possible and people get trapped trying.
hardware2win 3y ago
No, it is side effect while the goal is modeling which can be applied in your whole life, not just job.

keerthiko 3y ago

IME a big part of this misdirection stems from school focusing on the mechanics of math, rather than the intuition of math. In the long run, the mechanics of math (how to do long division, or differentiate an expression, or expand a geometric series) are important only insofar as to help us model and predict and analyze the world, intuitively. However, students who do not intuitively see the power of mathematical intuition as a tool for understanding and modeling the world better, think that they are taught the mechanics of math just for the sake of "no phone/calculator/computer available" circumstances.

deleted 3y ago
[deleted]
butterNaN 3y ago
I can only speak for myself here, but my journey with Maths did start with concrete, practical relationship between concepts and usage. I still remember fascinated by Geometry and Trigonometry, because how it can be used to create graphics and video games is obvious. The more abstract it gets, the more it warrants an introduction with "here's how it's used in real life". I can recall the point when it started becoming mechanical - it was when I started doing Derivatives and Integrations. I was 'just solving puzzles' until I hit a chapter, tucked away way back in the syllabus, almost at the end of the 2 year arc - a chapter about Applied Differential Calculus. I still remember the feeling of "Oh... I get it now" euphoria, with a tinge of sadness - why wasn't this covered early on? Same thing would have happened in Engineering as well, but at the time my teacher was good. They started by explaining the applications of Fourier Transform before we actually got to learn the mechanics of it.
roel_v 3y ago
I've never taught mathematics but I think it's much harder to teach the intuition, and I also think that more people are capable of learning the mechanics than the intuition. So from the point of view of someone designing a methodology and curriculum - you have to design for scale. I have the same thing with learning languages: I despise focusing on the rules of conjugation and word order and rote memorizing rules, exceptions to them and exceptions to exceptions. I much prefer to bootstrap with some vocab and then acquire by immersion, even if that means I get the conjugations wrong in the beginning. But I also find myself in the minority by far, to the extent that pretty much all language teachers I ever had (except my high school French teacher - she was awesome letting me translate MC Solaar lyrics for grades) didn't even really seem to believe that there are other ways of learning other than studying rules.

jokethrowaway 3y ago

I don't get why calculus is always brought as an example. It wasn't particularly hard, the entire class had to learn it in high school. We all had it (in a slightly harder shape) in every university course (no matter how detached from what we actually needed) I forgot all my calculus after high school, had to relearn it in uni and then I promptly forgot again. Exactly as the article says, it was more about proving we had the capacity (proxy iq test?) to learn it. You don't need calculus in real life and I think the focus on calculus is ridiculous when we could explore other more practical areas, like category theory (which only my lucky friends who did advanced math got to play with)

throwbadubadu 3y ago
But what is the general application of category theory, outside computer science.. and even there the average programmer who hasn't some type theory experience will stare at you with huge eyes when you mention it.. I love the wikipedia intro: Calculus is the mathematical study of continous change, the same way geometry is the study of shape and algebra... that's it perfectly. And the most basic application is in everyone's life and also one of the basic physics thing: The relationship between location, speed and acceleration. I find this very essential, vs category theory at least..
- l__l 3y ago
  This is my field :) Category theory is about connecting the dots between different areas of maths. The "general application" is to allow you to reason over the structure of a problem you're interested in, while throwing away all the superfluous details. It arose when geometers and topologists realised they were working on the same problems, dressed up in different ways. I think the utility for technical people, from this perspective, is pretty clear. As for the general working person? I think it's just an exercise in learning to do abstractions correctly, which is valuable in any line of work. There are actually people who advocate that we should base maths education on category theory much earlier (much as New Math was interested in teaching set theory early on, as a foundational topic). CT is an unreasonably effective tool in a large section of pure maths, so this doesn't sound unreasonable to me; it wouldn't be nearly so scary if it were introduced gently much earlier on (in the same way we start to learn about things like induction in the UK in secondary school, long before formalities like ordinals are introduced at uni). Currently only a very specific, highly-specialised section of the population learn CT, but if something like this were to happen, I'm sure we'd see lots of benefits which are hard to identify at the moment.

Etherlord87 3y ago

I'm using math(s) a lot, trigonometry, matrices, algebra… But most of my friend, family, I couldn't convince to learn math just based on the argumentation they can use it in practice. Yes, calculating the right amount of fence is useful, but not only (as someone pointed out) you don't need a lot of math for that, people just take take a ruler on the plan, or count steps in field, going across the entire length, then estimate, and it works. > estimation of 500km route arrival time while taking traffic statistics into the account Who does this? How would you convince a friend to learn math in order to do this? What people do is they remember how long a 200 km route took and so they estimate the 2.5× longer path will take 2.5× more time. We need examples of real world math applications, because such examples are scarce across the Internet.

hardware2win 3y ago
>Who does this? How would you convince a friend to learn math in order to do this? What people do is they remember how long a 200 km route took and so they estimate the 2.5× longer path will take 2.5× more time. Who does it? Navigation app in your phone. They modeled this problem using math. While you could probably model it somehow without math, but why would you want to do it other way, when you have reliable, mature and flexible tool I didnt write that you shouldnt leverage tech. Do it, yet be aware how it works and why. You can leverage math in other custom scenarios
- toyg 3y ago
  So what I'm hearing is that math is only good when there is no GPS / no phone. Let's be honest: advanced math is useful in programming contexts. Everywhere else, in 2023 you're using computer programs that will do the hard math for you.
  - hardware2win 3y ago
    You didnt understand my message. Math is not about calculators or computers. It is about modeling (e.g real world) It is useful whenever non-standard, already modeled in your calculator problem apprears.

lucideer 3y ago

You've given one day-to-day example (garden fence) which requires only extremely elementary math, and then listed a bunch of stuff related to specialised career paths... which was the OP's original qualifier: > outside of certain career choices. As someone who did a lot of calculus in university, and definitely hit a eureka moment while integrating over vector fields that helped me conceptualise some general day-to-day stuff better in my head, would most people generally benefit from that same conceptual "grokking": of course. Would it be worth the time & effort investment for them if they're not using it in their career: no.

hardware2win 3y ago
There is no license required for using math. Yea, if you dont want, then you will not use math. But, if you dont have some mental block, then you may find ways to apply math to your problems. Abstract thinking is really useful during arguments, even about politics, religion, etc.
- lucideer 3y ago
  > If you dont have some mental block The "mental block" you're referring to here is a combination of individual aptitude, capacity, access to educational resources & time-/effort-budgeting over a lifetime. This isn't some free casual object people are refusing to collect on their travels, it requires investment.
  - RugnirViking 3y ago
    It does indeed require investment of mental effort. But that's it. I'd argue maths is one of the cheapest monetarily skills it is possible to pick up - there have been several great contributions from people with little or no formal schooling. It's not like it's available only to a select few, I think pretty much everyone that gets deep enough in to be able to apply it continues to do so throughout their life. It can be used to fill in for all sorts of problems. I've been a tutor and ive long been a strong advocate for yes you can do it. I've met so many diverse people with excellent spacial reasoning that for whatever reason decided they weren't smart enough or couldn't understand it, yet when given a zealous advocate to encourage them picked it up just as quickly as any stereotypical maths genius

maccard 3y ago

They're not everyday things for a lot of people though. I was in a shop this weekend where the price per 250g of coffee was displayed, but the woman in front of me only had a 175g container. Neither her, the person serving her, or the other person working in the café knew how much to charge her. It's 175/250 * £PRICE_PER_250. In supermarkets, prices of items are displayed beside each other - a sharing bar of chocolate is £x/100g, but the multipack is £y/item, and each item is z grams. Which is better value? Cooking - I have a recipe in a book that serves 2 people, but I'm cooking for 3. How much X do I need?