A couple of weeks ago, somebody I know took a basic civil-service type math test as part of a local government job application. Maybe fifty candidates were seated at desks in an auditorium. Before the test began, the instruction page explained how to answer a sample question, which happened to involve multiplying two negative numbers. One jobseeker looked at the sample question with surprise, and whispered to the guy sitting next to him: "Multiply a negative and a negative? Can you even do that?"

I'm all for optimizing the educational experience of the most talented students. But "high-school math education" implies math education for the bottom half of the bell curve as well. I'd agree with the original post, as long as its understood that, for most students, we're talking about very, very basic probability and statistics. The difference between the Bayesian and frequentist approach isn't even on the table.

There is a more fundamental flaw in maths eduction than calculus vs, statistics. Very few people come out of school knowing what a maths problem is. If you ask most people to identify a maths problem, they will point to the exercises in a book or a work sheet. Very, very few will point to the world or their experiences. There is no place in the current curriculum that shows people how to frame a question about the world in a way that maths can be applied. Neither calculus or statistics is useful if you don't know how to frame the problem in the first place.

Can we have high school students learn number theory instead? There are things like this which are absolutely awesome.

neither. the time would be better spent on logic, both formal and informal.

So far, all of the following have been suggested as really important, either more important than the others or at least as important. In alphabetical order:

• algebra
• calculus
• logic
• probability and statistics
• programming
• trigonometry

And number theory got an honorable mention for being awesome.

How are people judging what is more important than what? I hope not by looking at how often they use these things themselves.

Not a month goes without my having occasion to use all of these, and 3D geometry, and other mathematical stuff as well. But as an applied mathematician and programmer, I would, and they all seem to me like just a step beyond basic arithmetic. It would be easy, too easy, for me to say that everyone should know this stuff, so I won't.

Instead, FYI and FWIW, here's the current high school curriculum in the UK for A-level maths.

Most people never use their math education higher than arithmetic. I don't see the point of teaching people math skills that they almost certainly will never use.

I'm not quite sure I agree that high school math is focused towards preparing people for calculus as opposed to statistics. All either one of them requires is a basic understanding of algebra. However, I would agree that mathematically competent people should be encouraged more to take statistics (particularly Baysian statistics).

Also: http://www.maa.org/devlin/LockhartsLament.pdf

I wouldn't say statistics as much as data analysis. Statistics too often means conventional hypothesis testing, which I doubt the Bayesian Conspiracy is too hot on.

I remember one very clever fellow who designed speaker systems shared an anecdote about the company he worked in. Apparently, they had a computer program that would generate the frequency and spatial response of speaker systems. With enough use, people would develop an intuition about system design that went far beyond the usual state of design. They had a feel for the right answers that went beyond knowing how to set up the calculations.

What people largely lack is any feel for data distributions. So much of statistics are analytic methods for dealing with data that can be completed more straightforwardly with non parametric methods. Let the computers do the data crunching, and teach people to make decent estimates based on data. That's so much more useful for life, and would provide the added benefit of teaching students that the real world has better and worse answers, not right answers.

I think discrete math is another tragically under-represented math topic that would be of more benefit to most people than calculus. Within that broad topic, I'd single out the essentials of logic, set theory, combinatorics, and basic discrete probability: those are the sorts of things that most people, regardless of what they do for a living, could profitably use to do their jobs better from time to time and to solve the problems that day-to-day life throws at them.

The biggest barrier for me personally in my mathematics education was that it was supposed to be boring, it was supposed to be hard and thirdly you were forced to do an inordinate number of repititions of the same problem untill it nearly killed your brain. Nevermind that spaced repitition would be far more effective.

Before you even debate what to teach you'd better decide how to teach or you're just wasting your time.

Though I suppose my experience may not have been representative, so lesswrong was your mathematics education effective at teaching you what it was trying to teach you?

I am surprised that people think that currently taught statistics is fun. Bayesian statistics is really fun and satisfying, but I found classical statistics rather uninspired. I do agree that on average statistics is far more useful.

Definitely. Statistics and probability theory are more important, more widely useful, and more fun to learn than calculus.

But that's not the only problem with math education. Salman Khan has some good suggestions.

I have had the same thought, except that statistics is also taught in a lousy way to prepare people who will do publishable research, which is almost nobody. I also have the separate concern that since we teach kids new math skills every year, we never have high expectations about their ability to apply them, leading to weak problem-solving skills.

Just have everybody take a class called "Math for Being Smart" in their senior year of high school. First half is solid word problems; second half is probability and statistics, only you learn how to think about it instead of how to do a t-test by rote. Require it for graduation, and pass people on the basis of a skills checkoff instead of test average.

Calculus has shown me more mind-blowing examples of mathematical elegance than my (frequentist) Statistics class.

Though, statistics is probably more useful.

Here's a practical application of all this debating:

I haven't taken calculus yet. I don't know what the best way to learn it is. BUT I do know that it isn't through my current school. How do you think MY math education should be?

I have taken both subjects, and statistics is far more fun. I expect to use both in real life, but I much prefer taking stats and would prefer that the general public know stats. Your mileage may easily vary, though: I prefer statistics because it involves fewer long paper-and-pencil computations, and thus fewer opportunities to make trivial mistakes.

Absolutely -- I saw that quite a bit ago and agree. He summarizes why. Plus, why wouldn't you believe a real live mathemagician?