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The Calculus Trap (2005)
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Re: The Calculus Trap (2005)
#12[deleted]
Re: The Calculus Trap (2005)
#13Reminds me of Arthur Benjamin's talk on focussing on statistics instead of calculus.
http://www.ted.com/talks/arthur_benjamin_s_formula_for_chang...
Re: The Calculus Trap (2005)
#14Although I have a PhD. in mathematics, I found the field needlessly, gratuitously competitive--nasty even--and I left. Math education--another related subject which mathematicians often feel competent to pronounce upon--seems to be a mine field [1]. There are only a few thousand mathematicians who are paid to do mathematics--for the rest of us, the opportunity cost is almost infinite. This is, for me, the real disincentive: the light at the end of the tunnel is hardly more than a few photons.
[1] A double entendre. A mine field is a set with the standard field operations, which belongs only to the educator.
Re: The Calculus Trap (2005)
#15I totally agree that calculus is unlike "real math" (reasoning from first principles, proofs, abstractions). Perhaps learning linear algebra would be time better spent[1]. Sill, calculus is the first applied math course and is very useful for many areas of science so I'm not altogether in agreement that learning calculus is bad for you. On the contrary---in combination with a mechanics class it can be very good in terms of learning how to model the real world.
That being said, I think UGRADs spend waaaaaay too much time learning calculus: Calc I, Calc II, multivariable, vector calculus, etc. That's like 4 semesters of calculus! This signals to the student that calculus is somehow a big deal, when in fact it is not: it's just calculation techniques. I think this should be cut-down to 2 semesters: Calc I+II together, then multivariable+vector calc. Just learn it quickly and get it over with[2].
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[1] Gilbert Strang saying we should learn more LA and less Calc. http://www-math.mit.edu/~gs/papers/essay.pdf
[2] My short book on Calculus and Mechanics http://minireference.com/launch40 (disclaimer: self-plug, but on topic)
Re: The Calculus Trap (2005)
#16Steve Yegge had a good essay that touched on this.[1] He argues that the right way to learn math is breadth-first, rather than depth-first - basically, learn the basics of a wide variety of fields within mathematics, and then you will know where to look when you need to understand a given problem.
[1] http://steve-yegge.blogspot.com/2006/03/math-for-programmers...
Re: The Calculus Trap (2005)
#17I feel like Calculus was very eye-opening for me, personally, and I felt like it was a refreshing finisher to the traditional math courses. When you're in the lower level classes, it's often hard to see where the practical applications are going to start coming around... for me at least, Calculus was where it all came together. I started to see just why I'd taken so many years of math: they all built up to this very practical and fundamental set of mathematics. That isn't to say that there's not a place for other math courses - of course! But Calculus in particular is the "money shot" of math, in my opinion. The applications are firm, and build the fundamentals of physics among other subjects. If I hadn't taken Calculus, I don't think I'd have been as positive about math as I ended up being. That's just my two cents, however.
Re: The Calculus Trap (2005)
#18People studying hard sciences, engineering, statistics and mathematics should study calculus, because they need it to understand and solve problems in their domain.
High school students would be much better served in life studying statistics instead. Far more important decisions in life and public policy are informed by statistics than by calculus.
There was a time when I thought more breadth - number and set theory, proofs, and so on - would be better in place of calculus. And while I think it would be an improvement on teaching calculus, it would not be nearly as useful for most students as a better understanding of statistics.
Re: The Calculus Trap (2005)
#19"you’re in ninth grade and you’ve already taken nearly all the math classes your school offers" I thought most high schools taught calculus. Both my and my wife's did. Why is this 15 year old going to a local community college or university for that? http://www.maa.org/the-changing-face-of-calculus-first-semes... agrees, and points out that 3x more people take AP Calculus now than when I was in high school. Which is…
My high school ran out of math classes for me and 10% of my classmates after 11th grade.
Ran out at which level? The author apparently went to a high school without calculus. I'm trying to get a feel for how common that is, especially since it looks like several times more schools offer calculus now than when the author went to school in the late 1980s.
Re: The Calculus Trap (2005)
#20"you’re in ninth grade and you’ve already taken nearly all the math classes your school offers" I thought most high schools taught calculus. Both my and my wife's did. Why is this 15 year old going to a local community college or university for that? http://www.maa.org/the-changing-face-of-calculus-first-semes... agrees, and points out that 3x more people take AP Calculus now than when I was in high school. Which is…
My high school ran out of math classes for me and 10% of my classmates after 11th grade.
This happened to me too (they offered calculus, but I was finished by 11th grade). They also ran out of science classes. But I couldn't graduate because for some unimaginable reason four years of high school "english" and "history" classes are required. So there I was, day almost empty, taking English 12, History 12, a required art class, and the language sequence (fourth-year Latin) that I'd wanted to take the year before, but couldn't because it wasn't offered at all.
In sum: as far as my experience goes, educational standards are set up specifically to frustrate and impede fast learners.