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.
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
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.
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.
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.
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.
Sure, we can say that as an ideal but we still have to convert the "as much background as possible" into an actionable concrete curriculum.
The issue is a finite amount of time to teach a list of topics and the bias in 99% of recommendations is to always say "kids should be taught X" but we never frame it in the opposite way to reveal the inherent tradeoffs : "kids should be denied being taught Y so that time is used to teach X":
In other words, any recommendation that kids "must learn topic X" means we're silently omitting Y. It's an inherent optimization problem of what to do with limited time window in classrooms. That's why some college Calculus professors recommend switching out Calc I for a Statistics/LinearAlgebra. They're not saying calculus is unimportant. Instead, they're treating it as optimizing the best bang-for-the-buck math topics for 17-year olds.
We can do a lot of radical thinking regarding optimization of high school curriculums. E.g. I've always thought that a semester of dissecting advertisements in newspapers and tv commercials and how they manipulate you would be an excellent class for teenagers. But devoting time to that comes at the expense of something else. Therefore, I'd recommend substituting Shakespeare's plays Romeo & Juliet and Julius Caesar with "Media Manipulation Studies" but of course, some people would complain "how can you possibly understand Western Civilization and humanities without studying Shakespeare?!?". Maybe true but making kids study Shakespeare also means we're denying them <Other_Really_Important_Topics> because there's always a constraint of finite time.
But if it is being done because a subject is too hard and making the population look bad (since other countries seem to manage just find with the same topic), then I would have a problem with that. Which is what it seems like in the California proposal.
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.
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?
This sounds really extreme, what makes you think a statistics class would have changed your life?