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 natural sciences (at least physics) and certainly in engineering.
Even taking all natural science and engineering majors into account (which is a stretch since many natural science majors are going to end up in medicine or an unrelated career, and electrical engineering is a bit different from mechanical engineering) you’ve still got only 16% of the student body.
I’d say that the physics students (and engineers) are a minority that we ought to consider.
If all students need A and some students need B, then go to A first and the students who need B can still go to B afterwards.
Not really; Bayesian statistics really does build on calculus.
Most colleges are still focused around frequentist statistics in undergrad to the best of my knowledge. That’s a separate debate entirely.
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.
Well, typically colleges are expecting you to take 3 semesters of calculus (although this 3rd course varies somewhat) as a prerequisite for just about everything, so if you can agree it should only be two, that’s another problem solved. But I would go much further.
Yes, sets, series, and sequences are used in advanced stats, but there’s no reason to teach those and trig at the same time. It’s just a century old convention that no one ever corrected. If the 3 calculus courses were condensed down to what is actually used in say, 2 or 3 courses of stats, I’d bet you wouldn’t even be left with a semester worth of material.
Albeit I can see a role for a introductory “statistics-light” class for non-STEM majors that does not require calculus as a prerequisite.
I don’t see this single stats course as sufficient. But if a student wants to go further than this basic course, they generally have to take 3 calculus courses first. And then the other programs expect you to take the basic stats class and then calc I and II because they know it’s not practical to expect every student to have the equivalent of a math minor just so they can take more than 1 course in data analysis.
Well, at least we agree there is leeway for a redesign; that’s one problem solved.
There is no redesign needed. I first studied vectors and trig in high school before I’d ever had calculus. Its been a while, but I believe I studied vectors in 10th grade, trig in 11th and calculus in 12th. Admittedly, colleges seem to treat calculus as a prerequisite for linear algebra (at least mine did) for no apparent (to me) reason.
electrical engineering is a bit different from mechanical engineering
This is true. However, both require calculus, vectors and trig (from a fundamental level, not just a curriculum design level).
Well, typically colleges are expecting you to take 3 semesters of calculus (although this 3rd course varies somewhat) as a prerequisite for just about everything, so if you can agree it should only be two, that’s another problem solved.
If we’re just debating whether 2 or 3 semesters of calc is needed for statistics, then I agree; there is no argument. From what I can remember of my calc courses (its been a few years), I suspect 2 semesters of calc should be fine for most introductory to intermediate stats courses.
I don’t see this single stats course as sufficient. But if a student wants to go further than this basic course, they generally have to take 3 calculus courses first.
If you are advocating requiring a lot of stats courses for non STEM students; I’m not sure I agree with that. As far as I can see, most non-STEM students are not going to want to take, nor will they benefit from, more than an introductory stats-lite course. Of course there are exceptions (e.g. some business/marketing, economics and sociology students for example might want more advanced stats courses). But, any kid with the aptitude and desire for intermediate stats courses is not going to have too much trouble with calc 1 & 2, and will need these to really get a handle on the stats (frequentists stats, like Bayesian stats, deals with concepts (probability density functions and the like) that are based on calc). And, of course more advanced stats classes may require additional calc past 1 & 2.
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.
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.
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.
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,
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.)
Well, at least we agree there is leeway for a redesign; that’s one problem solved.
TINSTAAFL
That physics and engineering majors represent only a minority of the student body.
Even taking all natural science and engineering majors into account (which is a stretch since many natural science majors are going to end up in medicine or an unrelated career, and electrical engineering is a bit different from mechanical engineering) you’ve still got only 16% of the student body.
If all students need A and some students need B, then go to A first and the students who need B can still go to B afterwards.
Most colleges are still focused around frequentist statistics in undergrad to the best of my knowledge. That’s a separate debate entirely.
Well, typically colleges are expecting you to take 3 semesters of calculus (although this 3rd course varies somewhat) as a prerequisite for just about everything, so if you can agree it should only be two, that’s another problem solved. But I would go much further.
Yes, sets, series, and sequences are used in advanced stats, but there’s no reason to teach those and trig at the same time. It’s just a century old convention that no one ever corrected. If the 3 calculus courses were condensed down to what is actually used in say, 2 or 3 courses of stats, I’d bet you wouldn’t even be left with a semester worth of material.
I don’t see this single stats course as sufficient. But if a student wants to go further than this basic course, they generally have to take 3 calculus courses first. And then the other programs expect you to take the basic stats class and then calc I and II because they know it’s not practical to expect every student to have the equivalent of a math minor just so they can take more than 1 course in data analysis.
There is no redesign needed. I first studied vectors and trig in high school before I’d ever had calculus. Its been a while, but I believe I studied vectors in 10th grade, trig in 11th and calculus in 12th. Admittedly, colleges seem to treat calculus as a prerequisite for linear algebra (at least mine did) for no apparent (to me) reason.
This is true. However, both require calculus, vectors and trig (from a fundamental level, not just a curriculum design level).
If we’re just debating whether 2 or 3 semesters of calc is needed for statistics, then I agree; there is no argument. From what I can remember of my calc courses (its been a few years), I suspect 2 semesters of calc should be fine for most introductory to intermediate stats courses.
If you are advocating requiring a lot of stats courses for non STEM students; I’m not sure I agree with that. As far as I can see, most non-STEM students are not going to want to take, nor will they benefit from, more than an introductory stats-lite course. Of course there are exceptions (e.g. some business/marketing, economics and sociology students for example might want more advanced stats courses). But, any kid with the aptitude and desire for intermediate stats courses is not going to have too much trouble with calc 1 & 2, and will need these to really get a handle on the stats (frequentists stats, like Bayesian stats, deals with concepts (probability density functions and the like) that are based on calc). And, of course more advanced stats classes may require additional calc past 1 & 2.
Business, social, and behavioral sciences represent over a third of students. They’re more than double the size of STEM. It’s a pretty big exception.