4 ms·

Huge agreement. Calculus is one branch on the tree of mathematics and one of the more useless ones in modern society (that can be taught to HS students).

lotsofpulp 5y ago
How can you understand statistics without understanding basic calculus? e.g. Central Limit Theorem, probability density functions, etc.
- endisneigh 5y ago
  You don't need to take an entire year or semester of calculus to understand statistics.
  - Jensson 5y ago
    You don't need to take an entire year or semester of statistics to understand statistics either if you put the bar that low. Basic statistics is already taught to most kids and there isn't much value in teaching them more complex formulas without also teaching them the needed background to properly understand those formulas.
    - endisneigh 5y ago
      > there isn't much value in teaching them more complex formulas without also teaching them the needed background to properly understand those formulas. We'll just have to agree to disagree. I believe with a strong background in algebra and simply knowing how to take an integral and derivative you can go far in stats. Will you be an expert? Obviously not, but high school level stats knowledge can easily be attained.
      - Jensson 5y ago
        But what is the point? Formulas get forgotten, the class needs to teach them a concept or it wont stick. Calculus at least teaches people how to think about rate of change and slopes, what would a statistics class teach? Probabilities and event chains is already in the base curriculum before calculus, so it isn't that, and I don't see how learning about the normal distribution and the formulas for different statistical tests would help them at all in life. The people who need it already takes statistics, and nobody else needs to learn those formulas, and just learning those formulas doesn't teach you to understand statistics (as we can see how they get heavily abused in every non-quantitative field). Edit: Now from this discussion, I just realized that the fields that abuse statistics a lot are also the fields that doesn't require you to learn calculus. So maybe calculus is needed to understand statistics after all?
- dmos62 5y ago
  In my limited experience, it's natural to learn things by looking at a problem I want to solve, looking at solutions, and then looking at how to adapt solutions. That's pretty much a high-level to low-level progression. Once you reach a low-level understanding (calculus in this example) that opens a lot of doors, but it's hard for me to imagine starting there. That said I've never been good at schools and this experience is from learning on my own. I think there are people who have found ways to make "low to high-level" learning work well for them.
- jasode 5y ago
  >How can you understand statistics without understanding basic calculus? Because "understand" has different levels. Your question can be reworded for Calculus itself: "How can one one understand calculus without understanding Real Analysis?" And yet some college degree requirements (e.g. Business Admin) do let students take Calc I without Real Analysis. Your question has the following bias because you happen to know both <X> and <Y>, so you then believe <Y> can't be taught without <X>. But we do that all the time at all ages. E.g. we teach kids how to find area of circles and spheres -- without teaching them calculus methods to derive those formulas. We can expose people to many statistics topics such as Bayesian reasoning without calculus. There are several college professors of Calculus that also agree that substituting Statistics or Linear Algebra for Calculus at the high school level is not a bad idea.
  - lotsofpulp 5y ago
    > Because "understand" has different levels. Your question can be reworded for Calculus itself: "How can one one understand calculus without understanding Real Analysis?" I agree, but I think with the tools and technology we have today, I think more can be expected of kids. There are countries where every high school graduate is expected to have some experience with calculus. Maybe in 50 years, real analysis will be in the purview of high schoolers, just like 50 years ago, and programming was not. > Your question has the following bias because you happen to know both <X> and <Y>, so you then believe <Y> can't be taught without <X>. But we do that all the time at all ages. E.g. we teach kids how to find area of circles and spheres -- without teaching them calculus methods to derive those formulas. I probably do have that bias, but I think a lot of things taught in school are automated away, yet they are still taught to teach “how to think”. There is software that spits out areas of circles and spheres and regression models and p values, but I would think the goal is still to provide as much background as possible to build as accurate of a model of the world as possible. > There are several college professors of Calculus that also agree that substituting Statistics or Linear Algebra for Calculus at the high school level is not a bad idea. I can see Linear Algebra being useful too, but I would actually hope high schoolers are graduating with introductions to both Calculus and Linear Algebra.
    - 5y ago
helmholtz 5y ago
A bit misinformed. Differential equations form the backbone of much of the following: simulations, animations, fluid dynamics, FEA, financial modeling etc. A lot of computing is numerical methods and needs significant calculus knowledge.
- amcoastal 5y ago
  Sure, but you don't need to spend 32 weeks learning 10 different ways to do integrals which is what our calculuses classes would teach. Learn the concepts of derivatives and integrals and then move on to the actually interesting stuff you just mentioned here.
  - Jensson 5y ago
    You can't skip those steps without overwhelming your students. Advanced classes are already seen as hard even when students have practiced all this math a lot, remove the practice and you'll make the class impossible to pass for almost everyone.
    - amcoastal 5y ago
      I'll just continue to disagree, I guess. I was able to learn algebra just fine even though I didn't know my multiplication tables, while the rest of the class spent a year memorizing them. Our methods of deciding when someone "knows" something so they can "pass" needs to be radically rethought. We spend all our time practicing how to integrate by parts when in reality a computer will do that for you, and youre needed for higher level thinking and abstractions that the math classes don't bother to get to until graduate school. Sad imo.
      - Jensson 5y ago
        There have been countless experiments along your lines of thinking, none of them has actually worked well at scale. If you think that educators love math, then think again, almost every teacher hated math when they were a student just like you do. And even though they hate it we still have it in its current form, that really tells you a lot about its merits.

lotsofpulp 5y ago

How can you understand statistics without understanding basic calculus? e.g. Central Limit Theorem, probability density functions, etc.

endisneigh 5y ago
You don't need to take an entire year or semester of calculus to understand statistics.
- Jensson 5y ago
  You don't need to take an entire year or semester of statistics to understand statistics either if you put the bar that low. Basic statistics is already taught to most kids and there isn't much value in teaching them more complex formulas without also teaching them the needed background to properly understand those formulas.
  - endisneigh 5y ago
    > there isn't much value in teaching them more complex formulas without also teaching them the needed background to properly understand those formulas. We'll just have to agree to disagree. I believe with a strong background in algebra and simply knowing how to take an integral and derivative you can go far in stats. Will you be an expert? Obviously not, but high school level stats knowledge can easily be attained.
    - Jensson 5y ago
      But what is the point? Formulas get forgotten, the class needs to teach them a concept or it wont stick. Calculus at least teaches people how to think about rate of change and slopes, what would a statistics class teach? Probabilities and event chains is already in the base curriculum before calculus, so it isn't that, and I don't see how learning about the normal distribution and the formulas for different statistical tests would help them at all in life. The people who need it already takes statistics, and nobody else needs to learn those formulas, and just learning those formulas doesn't teach you to understand statistics (as we can see how they get heavily abused in every non-quantitative field). Edit: Now from this discussion, I just realized that the fields that abuse statistics a lot are also the fields that doesn't require you to learn calculus. So maybe calculus is needed to understand statistics after all?
dmos62 5y ago
In my limited experience, it's natural to learn things by looking at a problem I want to solve, looking at solutions, and then looking at how to adapt solutions. That's pretty much a high-level to low-level progression. Once you reach a low-level understanding (calculus in this example) that opens a lot of doors, but it's hard for me to imagine starting there. That said I've never been good at schools and this experience is from learning on my own. I think there are people who have found ways to make "low to high-level" learning work well for them.
jasode 5y ago
>How can you understand statistics without understanding basic calculus? Because "understand" has different levels. Your question can be reworded for Calculus itself: "How can one one understand calculus without understanding Real Analysis?" And yet some college degree requirements (e.g. Business Admin) do let students take Calc I without Real Analysis. Your question has the following bias because you happen to know both <X> and <Y>, so you then believe <Y> can't be taught without <X>. But we do that all the time at all ages. E.g. we teach kids how to find area of circles and spheres -- without teaching them calculus methods to derive those formulas. We can expose people to many statistics topics such as Bayesian reasoning without calculus. There are several college professors of Calculus that also agree that substituting Statistics or Linear Algebra for Calculus at the high school level is not a bad idea.
- lotsofpulp 5y ago
  > Because "understand" has different levels. Your question can be reworded for Calculus itself: "How can one one understand calculus without understanding Real Analysis?" I agree, but I think with the tools and technology we have today, I think more can be expected of kids. There are countries where every high school graduate is expected to have some experience with calculus. Maybe in 50 years, real analysis will be in the purview of high schoolers, just like 50 years ago, and programming was not. > Your question has the following bias because you happen to know both <X> and <Y>, so you then believe <Y> can't be taught without <X>. But we do that all the time at all ages. E.g. we teach kids how to find area of circles and spheres -- without teaching them calculus methods to derive those formulas. I probably do have that bias, but I think a lot of things taught in school are automated away, yet they are still taught to teach “how to think”. There is software that spits out areas of circles and spheres and regression models and p values, but I would think the goal is still to provide as much background as possible to build as accurate of a model of the world as possible. > There are several college professors of Calculus that also agree that substituting Statistics or Linear Algebra for Calculus at the high school level is not a bad idea. I can see Linear Algebra being useful too, but I would actually hope high schoolers are graduating with introductions to both Calculus and Linear Algebra.
  - 5y ago

helmholtz 5y ago

A bit misinformed. Differential equations form the backbone of much of the following: simulations, animations, fluid dynamics, FEA, financial modeling etc. A lot of computing is numerical methods and needs significant calculus knowledge.

amcoastal 5y ago
Sure, but you don't need to spend 32 weeks learning 10 different ways to do integrals which is what our calculuses classes would teach. Learn the concepts of derivatives and integrals and then move on to the actually interesting stuff you just mentioned here.
- Jensson 5y ago
  You can't skip those steps without overwhelming your students. Advanced classes are already seen as hard even when students have practiced all this math a lot, remove the practice and you'll make the class impossible to pass for almost everyone.
  - amcoastal 5y ago
    I'll just continue to disagree, I guess. I was able to learn algebra just fine even though I didn't know my multiplication tables, while the rest of the class spent a year memorizing them. Our methods of deciding when someone "knows" something so they can "pass" needs to be radically rethought. We spend all our time practicing how to integrate by parts when in reality a computer will do that for you, and youre needed for higher level thinking and abstractions that the math classes don't bother to get to until graduate school. Sad imo.
    - Jensson 5y ago
      There have been countless experiments along your lines of thinking, none of them has actually worked well at scale. If you think that educators love math, then think again, almost every teacher hated math when they were a student just like you do. And even though they hate it we still have it in its current form, that really tells you a lot about its merits.