Our Chaotic Times Are New?

 Seb Falk in "The Light Ages" quotes the fourteenth century poet John Gower"

"For now at this time

men see the world on every side

changed in so many ways

that it well-nigh stands reversed."

I'm just through the first two chapters, and I like it very much.  Particularly enjoyed the explanation of math operations using Roman numerals (turns out to be not that hard with the tools and processes which had been invented). 

Do Away With Plane Geometry?

 That's what Kevin Drum proposed.

I remember plane geometry fondly.  I think it was my best subject in high school.  I enjoyed the process of figuring out the logic, the deduction from axioms through a step-by-step process.  Its appeal stayed with me through my job at FSA; I almost always told people to walk me through the process, whatever software or problem we were discussing, step by step.

My teacher was suffering from diabetes. I think he'd come to the Forks district the year before, teaching us algebra I.  He was very good despite his illness, which started to get worse during the next year, the year of geometry, the year when he gradually went blind, though continuing to teach, the year when I weakly agree to provide answers to another student.  He died, I think, that summer.  I still remember that year with pleasure and with shame.

Those Were the Days (of Dashed Math Dreams)

Andrew Gelman posts some memories of fellow competitors in the Math Olympiad program. 

I was never on that level, but I did have contact with Prof. Nura Turner, who seems to have ramrodded the program in its early years.  In 1957-8 school year some of us Chenango Forks students took a math test, I think sponsored by some math society--maybe John Turna our math teacher pushed it. Anyhow, IIRC I got into the top ranks in the region--which may have been upstate NY, don't remember.  Anyhow I must have been one of these because Prof Turner included me in the people she tried to track.  

I write "tried" because I wasn't too cooperative.  IIRC my scores in my senior year were lower, an omen of what happened in college.  I was placed in the calculus course for math majors, not the one for math geniuses.  The teacher had a thick accent, I forget from where, and I never got into it. So after one term any interest in pursuing math was gone--government and American history were much more interesting.

Comparative Advantage in People

The economists have an ancient law which they call "comparative advantage".  Essentially it says a country should do whatever it does best at, even if its best is poor, poorer than other countries.  If countries follow the rule, they'll end up trading goods at the lowest possible price.  For example, American workers are good at assembling stuff, but they're also good at creating Disney films.  Chinese workers are pretty fair at assembling stuff, but they aren't not good at creating Disney films.  So the answer is obvious.

The NYTimes has an op-ed today which (mis)applies, without saying so, the theory to people.  Barbara Oakey notes that academically girls are good at reading and writing, better than boys.  But tests show that girls and boys have roughly equal aptitudes for math.  She argues that girls, finding that they do better than boys at reading/writing will think they're less good at math and so choose to focus on reading/writing and slight their math.  Her answer is to resist this, and to push girls to study math more.

Now Prof. Oakey is more focused on choices before college, not the ultimate choice of occupation. But drawing on the comparative advantage idea, she may be pushing a rock up the hill.  She ignores the psychology on the other side: boys will find themselves outclassed at reading and writing by the girls, so will tend to focus on math. 

[Caveats: all this is very general, phrased in ideal types, not real people.]

Less Equality Everywhere, Including Math

Atlantic has a nice piece on increasing achievement by American teenagers in math.  Why?  "problem solving", outside class programs, STEM parents.  But these things are available to the richer among us.

"National achievement data reflect this access gap in math instruction all too clearly. The ratio of rich math whizzes to poor ones is 3 to 1 in South Korea and 3.7 to 1 in Canada, to take two representative developed countries. In the U.S., it is 8 to 1. And while the proportion of American students scoring at advanced levels in math is rising, those gains are almost entirely limited to the children of the highly educated, and largely exclude the children of the poor."

Once upon a time I was good in math.  Participated in a state-wide test (the Mathematical Olympiad) in my junior year, did well, again my senior year, not so well.  It's been downhill from there.