I agree that basic probability and statistics is more practically useful than basic calculus, and should be taught at the high-school level or even earlier. Probability is fun and could usefully be introduced to elementary-school children, IMO.
However, more advanced probability and stats stuff often requires calculus. I have a BS in math and many years of experience in software development (IOW, not much math since college). I am in a graduate program in computational biology, which involves more advanced statistical methods than I’d been exposed to before, including practical Bayesian techniques. Calculus is used quite a lot, even in the definition of basic probabilistic concepts such as expectation of a random variable. Anything involving continuous probability distributions is going to be a lot more straightforward if approached from a calculus perspective. I, too, had four semesters of calculus as an undergrad and had forgotten most of it, but I found it necessary to refresh intensely in order to do well.
“Computational biology,” sounds really cool. Or made up. But I’m betting heavily on “really cool.” (Reads Wikipedia entry.) Outstanding!
Anyway, I concede that you are right that calculus has uses in advanced statistics. Calculus does make some problems easier; I’d like calculus to be used as a fuel for statistics rather than almost pure signaling. I actually know people who ended up having real uses for some calculus, and I’ve tried to stay fluent in high school calculus partly for its rare use and partly for the small satisfaction of not losing the skill. And probably partly for reasons my brain has declined to inform me of.
I nonetheless generally stand by my statement that we’re wasting one hell of a lot of time teaching way too much calculus. So we basically agree on all of this; I appreciate your points.
I agree that basic probability and statistics is more practically useful than basic calculus, and should be taught at the high-school level or even earlier. Probability is fun and could usefully be introduced to elementary-school children, IMO.
However, more advanced probability and stats stuff often requires calculus. I have a BS in math and many years of experience in software development (IOW, not much math since college). I am in a graduate program in computational biology, which involves more advanced statistical methods than I’d been exposed to before, including practical Bayesian techniques. Calculus is used quite a lot, even in the definition of basic probabilistic concepts such as expectation of a random variable. Anything involving continuous probability distributions is going to be a lot more straightforward if approached from a calculus perspective. I, too, had four semesters of calculus as an undergrad and had forgotten most of it, but I found it necessary to refresh intensely in order to do well.
“Computational biology,” sounds really cool. Or made up. But I’m betting heavily on “really cool.” (Reads Wikipedia entry.) Outstanding!
Anyway, I concede that you are right that calculus has uses in advanced statistics. Calculus does make some problems easier; I’d like calculus to be used as a fuel for statistics rather than almost pure signaling. I actually know people who ended up having real uses for some calculus, and I’ve tried to stay fluent in high school calculus partly for its rare use and partly for the small satisfaction of not losing the skill. And probably partly for reasons my brain has declined to inform me of.
I nonetheless generally stand by my statement that we’re wasting one hell of a lot of time teaching way too much calculus. So we basically agree on all of this; I appreciate your points.