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As a student in my first /real/ real analysis course (called "Advanced Calculus I" by the registrar, predictably), I have a slight quibble with your characteriz

As a student in my first /real/ real analysis course (called "Advanced Calculus I" by the registrar, predictably), I have a slight quibble with your characterization of high school "calculus" as real analysis. What we did in high school, which I now think of as nothing but "calculus" in scare quotes, is to real analysis as arithmetic is to mathematics proper---because that's all it was, glorified arithmetic. Even though I had a great teacher and an understanding principal who allowed me to just go and study math on my own for two years, even then I was misled into the glorified-arithmetic world of studying "calculus" for advanced standardized tests. That's all high school math ever was, and when I scored in the 99th percentile on all the standardized tests, it was because they quite literally just asked arithmetic questions (sometimes disguised as "plug this into the quadratic formula", sometimes as "take the derivative then plug in this value"). TL;DR: high school math, and even much of what's taught in an undergraduate degree now (in math!), is just glorified arithmetic.

jerf 13y ago
"I have a slight quibble with your characterization of high school "calculus" as real analysis" Yeah, I know, but if that's not what high school math is, what is it? As hostile as I am I'm not quite ready to write it off as "entirely not math"... there's some math content in there, after all. I do want to point out that I am in contact with reality and do not expect students to start with number theory, nor do I realistically expect high school to ever cover what you covered in "real" real analysis. (Real numbers are terribly complicated things and I don't think high school should cover all the endless, endless corner cases of those either; time is short and the fields are vast.) What I'm really looking for is dropping a lot of stuff that is both practically and theoretically pretty useless, and replacing it with a lot of stuff that is, well, both more practical and more theoretically useful. Some of the core will survive (integration and differentiation aren't going anywhere, those really are fundamental to any reasonable math education, though we might spend several fewer weeks walking through all the special cases of each), but there's a lot of room for improvement.
rayiner 13y ago
> TL;DR: high school math, and even much of what's taught in an undergraduate degree now (in math!), is just glorified arithmetic. Is this a bad thing? You can design and build airplanes with what doesn't amount to anything more than glorified arithmetic. I don't see the value in teaching kids more than that.

jerf 13y ago

"I have a slight quibble with your characterization of high school "calculus" as real analysis" Yeah, I know, but if that's not what high school math is, what is it? As hostile as I am I'm not quite ready to write it off as "entirely not math"... there's some math content in there, after all. I do want to point out that I am in contact with reality and do not expect students to start with number theory, nor do I realistically expect high school to ever cover what you covered in "real" real analysis. (Real numbers are terribly complicated things and I don't think high school should cover all the endless, endless corner cases of those either; time is short and the fields are vast.) What I'm really looking for is dropping a lot of stuff that is both practically and theoretically pretty useless, and replacing it with a lot of stuff that is, well, both more practical and more theoretically useful. Some of the core will survive (integration and differentiation aren't going anywhere, those really are fundamental to any reasonable math education, though we might spend several fewer weeks walking through all the special cases of each), but there's a lot of room for improvement.

rayiner 13y ago

> TL;DR: high school math, and even much of what's taught in an undergraduate degree now (in math!), is just glorified arithmetic. Is this a bad thing? You can design and build airplanes with what doesn't amount to anything more than glorified arithmetic. I don't see the value in teaching kids more than that.