How our 1,000-year-old math curriculum cheats America's kids
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Re: How our 1,000-year-old math curriculum cheats America's kids
#2It sounds like a return to the "new math" of the 1960s. Compare this article:
> If we are to give students the right tools to navigate an increasingly math-driven world, we must teach them early on that mathematics is not just about numbers and how to solve equations but about concepts and ideas.
> It's about things like ... clock arithmetic — in which adding four hours to 10 a.m. does not get you to 14 but to 2 p.m. — which forms the basis of modern cryptography, protects our privacy in the digital world and, as we've learned, can be easily abused by the powers that be.
to the Wikipedia entry at http://en.wikipedia.org/wiki/New_Math :
> Other topics introduced in the New Math include modular arithmetic, algebraic inequalities, matrices, symbolic logic, Boolean algebra, and abstract algebra.
Re: How our 1,000-year-old math curriculum cheats America's kids
#3This reminds me of Lockhart's Lament, which I highly recommend reading http://www.maa.org/sites/default/files/pdf/devlin/LockhartsL...
Re: How our 1,000-year-old math curriculum cheats America's kids
#4I don't think that you can appreciate this stuff until you actually have the mechanical background in math.
Unlike most subjects in K-12, you can't BS math. You're right or wrong. There's no subjectivity in evaluation, and no opportunity for lazy students like me to BS a tired teacher with flowery prose that doesn't say much.
Why not make math accessible in easier or more practical ways? My trigonometry teacher walked us out into the schoolyard and gave teams of students assignments to measure the heights of various objects. It was a simple thing, but it made the not-so-interesting mechanics of looking up sine/cosine/tangent in some table real.
Re: How our 1,000-year-old math curriculum cheats America's kids
#5Focusing on the age is probably the wrong approach. Math true then is still true now. The problem is that the curriculum is now held sacred (and I mean that fully as nastily as possible), and it is being held there by people who are now the blind-leading-the-blind unto the sixth or seventh generation. I've gotten around in the math world a lot since primary school, and what I was taught vs. any actual modern mathematical practice, across the entire spectrum from utterly practical to the utterly theoretical, bears surprisingly little resemblance to what I wasted my time with in school. The current curriculum is bizarrely overfocused on real analysis to the near exclusion of all else (a few other disciplines will be introduced, generally poorly motivated either practically or theoretically, fiddled with for a couple of weeks, then dismissed; matrix math, for instance... in primary school nobody ever gave me a clue why we cared about this, and once you're done solving polynomial sets of equations (itself an unmotivated activity), you're pretty much done), and even if we grant that real analysis really is worth crowding out everything else, it still comes with a very 19th century flavor to the whole thing, too, wasting time on some dead-ends and missing some things that would be both mathematically and practically useful, too. (For instance, numerical approximations methods are usually covered as "Newton' Method For Finding Roots", and that's it. There's several things I'd trade away in favor of more of this, and it's easy to motivate why this is useful stuff.)
I'm pretty pessimistic in the short term about any efforts to reformulate math curricula, though, due to the aforementioned blind-leading-the-blind unto the seventh generation problem; math educators aren't even aware how bad the problems are, let alone in any position to fix them themselves, or aware enough to ask for help.
Re: How our 1,000-year-old math curriculum cheats America's kids
#6Frenkel laid out his perspective in a mathematical memoir, much admired:
http://www.amazon.com/Love-Math-Heart-Hidden-Reality/dp/0465050743Re: How our 1,000-year-old math curriculum cheats America's kids
#7And then there's Common Core, which seems to teach children insanity.
Re: How our 1,000-year-old math curriculum cheats America's kids
#8I don't think that you can appreciate this stuff until you actually have the mechanical background in math. Unlike most subjects in K-12, you can't BS math. You're right or wrong. There's no subjectivity in evaluation, and no opportunity for lazy students like me to BS a tired teacher with flowery prose that doesn't say much. Why not make math accessible in easier or more practical ways? My trigonometry teacher walke…
I do maths every day and I do nothing but approximations and fudges to roughly model real situations. It's like recreating a waterfall in lego.
Re: How our 1,000-year-old math curriculum cheats America's kids
#9im so smart I can learn math just by thinking about it
Re: How our 1,000-year-old math curriculum cheats America's kids
#10The biggest problem in education isn't the curriculum or method of teaching or the teachers, it's how motivated the student is (which is usually a product of their home environment). Trying to solve this social issue with "technical" fixes is not going to succeed.