On math curriculum, that advanced classes build off of calculus is a function of current design.
Not really; Bayesian statistics really does build on calculus. This is true of the Bayesian methodology itself - not just curriculum design. Once you get beyond introductory probability problems using Bayes' rule, Bayesian statistics quickly gets into probability density functions, sampling from posterior distributions and so forth; all of this is based on calculus. I'm pretty sure a student trying to work through an introductory work on Bayesian data analysis (Kruschke, for example) without a year of freshman calculus under his/her belt is going to run in to some significant difficulty.
You're going to have a hard time convincing me that trigonometry and vectors are a necessary precursor for regression analysis or Bayes' theorem.
Your statement, in a post about scientific thinking, was that statistics and data science are much more useful than calculus. This is not true; as stated previously, calculus is of critical importance to many scientific fields. Moreover, vectors and trig (which, technically, one can study independently of calculus) are also of great importance in the natural sciences (at least physics) and certainly in engineering. I am surprised that you find this point to be controversial.
The minority of students in physics and engineering that need both calculus and statistics should not dictate how other majors are taught.
I'm not sure what you are saying here. Are you claiming that the minority of physics and engineering students need both calculus and statistics? All physics students and all engineers (at least in the traditional engineering fields) need calculus, so I don't know why you would claim that only the minority need both calculus and statistics. I don't think that you mean to claim that only the minority of these students need statistics, but that would follow logically from your claim.
Or, you might be saying that only the minority of students are in either physics or engineering. That may be true. But, since the OP is about scientific thought and scientific education, I'd say that the physics students (and engineers) are a minority that we ought to consider. And, natural sciences beyond physics also require calculus. Plus, as already stated, getting beyond the introductory level of Bayesian stats itself requires calculus.
Fixing the curriculum isn't an easy problem, but they've had more than a century to solve it and there seems to be little movement in this direction.
I honestly think that you are trying to fix something that is not broken. What's wrong with having kids learn calculus and statistics? Albeit I can see a role for a introductory "statistics-light" class for non-STEM majors that does not require calculus as a prerequisite. But, I think many colleges have this already (e.g. Tulane's Probability and Stats I does not have a calculus prerequisite).
Regardless of the above, I agree with a lot of your OP. In particular,
What's most damning is that our scientific curriculum in schools don't teach a lot of scientific thinking
seems to be true, at least in most of K-12. I was actually fortunate enough to have an outstanding physics teacher in 12th grade, who was able to convey some sense of the scientific method to the students. However, prior to that, much of the K-12 science curriculum seemed to consist of learning facts (or stamp collecting, as Ernest Rutherford would have said.)
Moreover, vectors and trig (which, technically, one can study independently of calculus)
Well, at least we agree there is leeway for a redesign; that's one problem solved.
What's wrong with having kids learn calculus and statistics?
TINSTAAFL
I'm not sure what you are saying here.
That physics and engineering majors represent only a minority of the student body.
...calculus is of critical importance to many scientific fields. Moreover, vectors and trig (which, technically, one can study independently of calculus) are also of great importance in the nat