13 ms·

Knowing what I know of math now, having the high level high school math class be statistics or data science instead of calculus would have changed my life.

guerrilla 5y ago
In what way?
amcoastal 5y ago
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.
pjc50 5y ago
How far can you get in statistics without any calculus? Or do you just take the normal distribution as given?
- hellbannedguy 5y ago
  The statistics I took in college just had Intermediate algebra, and trig. as a prerequisite.
- qsort 5y ago
  Depends on how much handwaving you're willing to tolerate. There's definitely some useful statistics you can do without showing the integral sign. One could similarly say "How far can you get in statistics without measure theory? Or do you just take the definition of random variable as given?". It's still hand-waving, just at a different level.
bllguo 5y ago
"data science" is not a field of math. lord knows the term does not need to be watered down further. is "statistics" not adequate (in a high school context)? (I'm not singling you out - they have a "Data Science" section in the proposed California mathematics education framework) while I do agree that statistics education should be much more heavily emphasized, I still believe it and calculus should both be taught. Understanding the basic ideas of calculus opens a lot of doors in other fields of study. Hell, "data science" math would necessarily involve understanding calculus and optimization
- zippy5 5y ago
  I think you can decompose a calculus course into three key components; principle/concepts, proofs, and procedurally solvable math problems. All three have value but clearly the math problem aspect of it has depreciated in value due to calculators, wolfram alpha, etc yet it tends to remain the focus of many math curriculums. Calculus by its nature is more computationally intensive, meaning that it has experienced the greatest decline. If you really think about it, that curriculum was designed for an era when we called human "computers". There is probably opportunity to make calculus a more broadly valuable class by deemphasizing the mechanics and focusing on the principles and proofs.
  - Jensson 5y ago
    What calculus class did you take? I don't think that there are many calculus classes where computation is a significant part. Rather you learn how to work with and translate equations, but there is little about methods for manually calculating integrals or derivatives by hand with different approximation methods etc. Basically nobody learns that properly today. And the tiny part of the course is the part where you learn and get intuition for the "Area under curve" concept, which is extremely important for basically everything.
Jensson 5y ago
> statistics instead of calculus would have changed my life. This sounds really extreme, what makes you think a statistics class would have changed your life?
slooonz 5y ago
Please explain me how you can have maximum likelihood estimator or cumulative distribution function without calculus.
jimmyvalmer 5y ago
Hindsight is 20/20. As an undergrad in the 90s I distinctly remember the stats major had fewer than fifty students, and I went to a big university.
threatofrain 5y ago
Competitive high schools already offer statistics and data science. The question is not whether schools ought to offer statistics, but whether the state ought to require that children cannot jump forward into statistics or Calculus (or any class whatsoever) regardless of their readiness.

guerrilla 5y ago

In what way?

amcoastal 5y ago

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.

pjc50 5y ago

How far can you get in statistics without any calculus? Or do you just take the normal distribution as given?

hellbannedguy 5y ago
The statistics I took in college just had Intermediate algebra, and trig. as a prerequisite.
qsort 5y ago
Depends on how much handwaving you're willing to tolerate. There's definitely some useful statistics you can do without showing the integral sign. One could similarly say "How far can you get in statistics without measure theory? Or do you just take the definition of random variable as given?". It's still hand-waving, just at a different level.

bllguo 5y ago

"data science" is not a field of math. lord knows the term does not need to be watered down further. is "statistics" not adequate (in a high school context)? (I'm not singling you out - they have a "Data Science" section in the proposed California mathematics education framework) while I do agree that statistics education should be much more heavily emphasized, I still believe it and calculus should both be taught. Understanding the basic ideas of calculus opens a lot of doors in other fields of study. Hell, "data science" math would necessarily involve understanding calculus and optimization

zippy5 5y ago
I think you can decompose a calculus course into three key components; principle/concepts, proofs, and procedurally solvable math problems. All three have value but clearly the math problem aspect of it has depreciated in value due to calculators, wolfram alpha, etc yet it tends to remain the focus of many math curriculums. Calculus by its nature is more computationally intensive, meaning that it has experienced the greatest decline. If you really think about it, that curriculum was designed for an era when we called human "computers". There is probably opportunity to make calculus a more broadly valuable class by deemphasizing the mechanics and focusing on the principles and proofs.
- Jensson 5y ago
  What calculus class did you take? I don't think that there are many calculus classes where computation is a significant part. Rather you learn how to work with and translate equations, but there is little about methods for manually calculating integrals or derivatives by hand with different approximation methods etc. Basically nobody learns that properly today. And the tiny part of the course is the part where you learn and get intuition for the "Area under curve" concept, which is extremely important for basically everything.

Jensson 5y ago

> statistics instead of calculus would have changed my life. This sounds really extreme, what makes you think a statistics class would have changed your life?

slooonz 5y ago

Please explain me how you can have maximum likelihood estimator or cumulative distribution function without calculus.

jimmyvalmer 5y ago

Hindsight is 20/20. As an undergrad in the 90s I distinctly remember the stats major had fewer than fifty students, and I went to a big university.

threatofrain 5y ago

Competitive high schools already offer statistics and data science. The question is not whether schools ought to offer statistics, but whether the state ought to require that children cannot jump forward into statistics or Calculus (or any class whatsoever) regardless of their readiness.