The statistics which is currently taught in HS is no more respected than an AP CS course. Colleges do not trust them and are reluctant to offer credit, and this is a very big deal. The undergraduate intro course to statistics, such as the ones given to social science majors, is a big grab bag of memorized facts. It is soul killing by cultural reputation.
And whether we're talking about social sciences like econ or math, cs or physics, for anyone seeking continued education, students are well served by getting a boost in Calculus, especially when there's a stratum of HS infrastructure which can deliver results that colleges are willing to trust. This isn't true for stats.
I would argue that the point of math and foundations isn't rigor. Rigor is a tool for professionals to make sure long bouts of work don't go to waste. But we're talking about pedagogy.
IMO the point of mathematical foundations is: (1) it will provide the pedagogical bridge to how mainstream resources talk about a subject, (2) it will connect more smoothly to college programs anywhere (3) you want to develop the mental machinery which generates new facts and thoughts about math, rather than memorize what feels like large and incoherent bags of facts.
Perhaps Linear Algebra should be what is taught. Linear Algebra is one of the most petite subjects at the undergraduate level which packs a disproportionate amount of firepower. And it would be an excellent foundation for studying data.
That was taught in my undergrad stats class in 1991. I still remember one of the examples was about using the true/false positive/negative rates in AIDS testing to estimate that if someone tests positive for AIDS, do they likely have AIDS?
> The statistics which is currently taught in HS is no more respected than an AP CS course.
I fail to understand the relevance of this point. You like HS calc but not HS stats, and colleges like neither?
> The undergraduate intro course to statistics
Except we're talking about HS math pedagogy, not college. HS English classes are also taught rather different than college English classes. Plus, HS classes are mostly taught by teachers trained in pedagogy, while most college ones are not.
I still can't believe how my grad school dropped wet-behind-the-ears grad students like me into TA'ing courses, and making up our own quizzes for students, without any real guidance on how to teach or make tests.
You make broad assertions about soul killing. I point to existing HS classes in statistics. Are you really saying that those courses are soul killing? On what basis do you make your strong assertion?
> especially when there's a stratum of HS infrastructure which can deliver results that colleges are willing to trust
You just said that the calculus courses are no more trusted than the statistics courses. You can't have both ways.
> This isn't true for stats.
Where is your evidence?
Your pedagogical views:
(1) is a matter of cultural change. If people believe statistics education is important - which it is - then there's a new bridge. Just like how Euclid's Elements was once that cultural bridge, replaced by a focus on calculus. Now the emphasis is that focusing on a single bridge is wrong as it dissuades students interested in other bridges.
(2) assumes nearly everyone will go to college. For those who don't go to college, will statistics training be a better education than calculus? Indeed, part of the complaint is that this pedagogical emphasis on calculus overly biases education towards a specific type of college-track student - those with money, or those not afraid of taking on possibly life-crippling debt
Based on my experience some 30 years after college, I think there should have been more statistics training in my education and less calculus.
(3) I pointed you to various resources which, to my mind, demonstrate that the goal is indeed the development of mental machinery. You have only continued to repeat your assertions, not provide evidence.
I took a college course in Linear Algebra. I have not needed to compute an eigenvalue in nearly 30 years, and rarely do I need matrix multiplication for my work. I need to know statistics much more often than that.
How would learning the basics of linear algebra for most people (medical doctor, social worker, plumber, lawyer, fire fighter, or news reporter, mechanic, office manager, etc.) be better than learning the basics of statistics? Surely these are all people who need the mental machinery to understand if evidence is credible and to make predictive models.
"If you mean Statistics as in the introductory undergraduate stats course ..." While I mentioned my being in an undergraduate stats course, the LA Times piece and most of the references I gave refer to secondary education, not tertiary. So, no I don't mean that.
The AP Statistics test in the US doesn't require calculus. "Recommended Prerequisites: A second-year course in algebra" at https://apstudents.collegeboard.org/courses/ap-statistics , suggesting it's "College Course Equivalent [is] A one-semester, introductory, non-calculus-based college course in statistics".
To double check, https://tb2cdn.schoolwebmasters.com/accnt_42975/site_42976/M... shows Statistical Reasoning with Algebra 2 as a prerequisite, and AP Stats require only pre-calculus. https://www.pike.k12.in.us/userfiles/15934/my%20files/2018-2... requires Algebra 2.
Which means statistics is already being taught in high schools, without calculus or linear algebra. Do you really think those courses are 'murdering' the interest of most students any more than any of the other classes they take?
The argument, quite clearly made by the math education advocates in California, is that the traditional math education progression is just that - tradition. The pieces can be put together in different ways and still give a good education, only with a balance which is more appropriate for more people.
I find knowing about Bayes' Theorem to be much more useful than integration by parts, but the former was never taught in my high school. And I haven't used the latter in over 20 years.
No, a high school stats course isn't going to be rigorous Mathematical Statistics. But then again, a high school calculus course also isn't rigorous Analysis.
In high school I used cosine and log functions on my calculator, without knowing how they were computed. I certainly couldn't have done it by hand outside of a few well-known special cases. From what I infer looking at things like https://www.northernhighlands.org/cms/lib/NJ01000179/Centric... , the goal of stats education is to understand how to use and apply a tool like linear fitting, and what concepts like "correlation" and "residual" mean, not the full underlying mathematical treatment.
Entirely appropriate for high school, yes? Otherwise, when and how should students learn that sales prediction, height prediction, etc. are not esoteric concepts but things they can do themselves?