The guy's rhetoric is pretty divorced from the sad state of actual math education today. The way that the standard math curriculum today heads up to a point in a pyramid is a problem in itself since a lot of the topics are made dull in themselves ("This is just something you need to learn for calculus" is a terrible answer for "why should I learn this?" but substituting "Statistics" wouldn't change things much). It doesn't really matter what the point of the pyramid is when most people never get there.
Just as much, the latest economic meltdown was engineered and believed in by statistics experts. For every Mandlebrot debunking the events, there were ten Myron Scholes basking in the glory of validating Wall Street's delusions with some mathematical magic. Statistics doesn't protect from wishful thinking outside of controlled, experimental situations.
And statistics in daily life? One might use some basic probability but the only other use it would have would sorting the pseudo-statistical rhetoric used by the media. A simple course in mathematical literacy with an emphasis on fallacies would be best for sorting this stuff. BUT again, no course can protect from wishful thinking, can protect people from the fallacies that let them ignore possible later dangers for immediate apparent gain. Further, a non-calculus-based statistics or mathematically literacy course isn't a basis for further scientific study the way calculus is, and believe-it-or-not some students still become physicists, chemists and engineers where calculus is indeed the foundation.
I could narcisistically say that my favorite, evolutionary game theory, would make a much better "point" for the curriculum pyramid but really, what is needed is to make every math class interesting in and of itself. With TV-dazed kids and math-apathetic teachers, I don't know if any curriculum could change things BUT I would want to have the curriculum of every class interesting and mentally challenging - taught axiomatically, Algebra and Geometry ARE interesting in and of themselves and a student needs no background at all for them. Math should be rigorous, conceptually challenge and optional past the basics. It seems like we'd need a different world for this but small steps are being made.
Firstly, Art is actually a math professor, and dealing with the low standards of incoming students is a major concern. I don't think he is "divorced from the sad state of actual math education today."
But even more, you say:
> ... taught axiomatically, Algebra and Geometry
> ARE interesting in and of themselves
Perhaps to you, but I deal with students for whom this is absolutely not interesting. They're not interested in puzzles, they're not interested in challenges, they're not interested in anything except texting their friends and talking about films, TV, clothes, football, etc. They don't want to be challenged.
I think we all agree that classes in general should be stimulating and interesting, andshould be better tailored to suit the needs of the individuals, but that's the problem. For a given child we don't know what they'll need, and we don't know what they'll like, and every answer will be different.
The problem is "one class fits all" and that's not going to change simply by re-writing the curriculum.
Perhaps to you, but I deal with students for whom this is absolutely not interesting. They're not interested in puzzles, they're not interested in challenges, they're not interested in anything except texting their friends and talking about films, TV, clothes, football, etc. They don't want to be challenged.
Uh, yeah I've dealt with those students. Notice the last part I add - optional. The thing that kills math interest utterly is those "required" classes which teach nothing to the uninterested.
Modern schooling drags the uninterested through a process of making motions towards understanding - we all know its a waste of time. It really would be better to give up until the students are interested. A motivated student can learn more in a day than the bored learn in the semesters of basic math. That might put you out of a job but those jobs just shouldn't exist. Sorry.
Won't put me out of a job - you've jumped to an incorrect conclusion. I'm not a teacher. I run two companies, and I go out to schools to give talks on why math is fun, interesting, useful, and occasionally exciting. Most of the students I deal with are motivated and interested, but even then, some don't like puzzles, and don't like starting from the ground up axiomatically.
This Saturday I'm talking about the Banach-Tarski theorem, and I'm starting from the result, then wroking backwards, deciding what we need to know as we peel it back. I've found that working backwards from a surprising result can create motivation to understand, but sometimes it causes the students to dismiss the whole thing as useless, pointless and irrelevant.
Sorry, I'm rambling. Reply if you're interested, ignore me if not.
I shouldn't be dogmatic about asking for an axiomatic development.
At the same time, it seems like the social attitude towards mathematics has reached the point where it would be useful for schools to ask students to put aside some of their initial attitude towards math.
The best teachers I've had often demanded more than I was initially capable of accomplishing. It's true that such teachers risked losing some of their audience. But if we don't have such teachers we risk even more.
Oh where to begin?
The guy's rhetoric is pretty divorced from the sad state of actual math education today. The way that the standard math curriculum today heads up to a point in a pyramid is a problem in itself since a lot of the topics are made dull in themselves ("This is just something you need to learn for calculus" is a terrible answer for "why should I learn this?" but substituting "Statistics" wouldn't change things much). It doesn't really matter what the point of the pyramid is when most people never get there.
Just as much, the latest economic meltdown was engineered and believed in by statistics experts. For every Mandlebrot debunking the events, there were ten Myron Scholes basking in the glory of validating Wall Street's delusions with some mathematical magic. Statistics doesn't protect from wishful thinking outside of controlled, experimental situations.
And statistics in daily life? One might use some basic probability but the only other use it would have would sorting the pseudo-statistical rhetoric used by the media. A simple course in mathematical literacy with an emphasis on fallacies would be best for sorting this stuff. BUT again, no course can protect from wishful thinking, can protect people from the fallacies that let them ignore possible later dangers for immediate apparent gain. Further, a non-calculus-based statistics or mathematically literacy course isn't a basis for further scientific study the way calculus is, and believe-it-or-not some students still become physicists, chemists and engineers where calculus is indeed the foundation.
I could narcisistically say that my favorite, evolutionary game theory, would make a much better "point" for the curriculum pyramid but really, what is needed is to make every math class interesting in and of itself. With TV-dazed kids and math-apathetic teachers, I don't know if any curriculum could change things BUT I would want to have the curriculum of every class interesting and mentally challenging - taught axiomatically, Algebra and Geometry ARE interesting in and of themselves and a student needs no background at all for them. Math should be rigorous, conceptually challenge and optional past the basics. It seems like we'd need a different world for this but small steps are being made.