...a companion blog to "Math-Frolic," specifically for interviews, book reviews, weekly-linkfests, and longer posts or commentary than usually found at the Math-Frolic site.

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." ---Bertrand Russell (1907) Rob Gluck

"I have come to believe, though very reluctantly, that it [mathematics] consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-legged animal is an animal." ---Bertrand Russell (1957)

******************************************************************** Rob Gluck

Wednesday, January 29, 2014

Of Education and Game-playing

 I often try to steer clear of these education debates, but did enjoy Cathy O'Neil's recent quick take on Diane Ravitch and Common Core standards:


A stupendous amount has been written (pro and con) about Common Core in the last year-or-two, so don't mean to single out Cathy's piece above other views, except I like the approach she's taken.

I grew up at a time when several of my peers were graduating high school without basic reading, writing, and math skills… how these particular students were even being passed along from grade-to-grade, let alone graduating high school, was hard to comprehend. It was, frankly, an embarrassing, deplorable (even fraudulent) situation. Universities found, to their surprise, that entering freshman sometimes lacked the necessary skills for college work… significant remedial programs had to be instituted.

So when, understandably, standardized proficiency-testing programs began implementation state-by-state, I eagerly supported it. Since then, I've often participated in the 'grading' of these standardized tests, and what became apparent within a few years was that teachers were 'teaching to the test.' It had all become, almost inevitably, a sort of game for teachers, whose own evaluation was often based in part on how well their own students did on such tests. So they gamed the system, likely skirting some teaching responsibilities, creativity, and effectiveness in the process.

I've written earlier that I believe the use of 'flipped classrooms,' MOOCs, and digital resources in general is one of the most fascinating, even 'paradigm-shifting' changes in education coming along, yet grappling with "standardized testing" remains a hugely difficult nut to solve. Not only must there be some sort of standardized requirements (especially for mathematics) that all students should meet before graduating high school (…and really, LONG before graduating high school), but I believe they should indeed be national, and not variable state-by-state standards. BUT these should be truly bare, minimalist levels of literacy and numeracy for our adult population (or each grade level), not "high-bar" or accomplished standards.
In some ways Common Core seems like one of those near-comical results portrayed when 'designing things by committee': http://tinyurl.com/mcay7uq

I once attended a college that required a "swim test" (long since dropped) for graduation. The idea was not that everyone should be a good or fast or very capable swimmer, but simply that everyone ought have some ability to float and dog paddle and move through the water, in the event of an emergency -- that this was simply a life skill (even if not an academic skill) one ought have as a college graduate.
The whole nature of "literacy" is rapidly changing… in the future, basic societal "literacy" won't so heavily entail reading-and-writing skills, but rather computer, coding, and office-suite sorts of skills -- THESE will be basic needs to successfully 'swim' in society (having read and discussed "Hamlet" in high school, or knowing how to diagram a sentence, will be of virtually no use!) So I still believe some form of standardized proficiency testing is necessary, but I too have reservations about rigid Common Core standards, as configured -- almost inevitably, they will set in motion another round of diversion and educational game-playing, stifling creativity... while raking in big bucks for the private enterprises developing/administering them.

Perhaps we have become such a society of manipulators, shirkers, and system-gamers that
there is simply no good solution to such a double-edged problem (both no-uniform-testing and mandatory standardized testing are problematic), but only least-bad solutions…. but as Cathy concludes, the first, necessary steps really involve, not reforming our educational system, but alleviating poverty and related underlying conditions that undermine learning. And on THAT score, our nation seems to be moving entirely in the wrong direction. (...Long, one of the most lunatic things to me, has been the way our public schools are funded largely through local property taxes -- a system insuring wide disparity in quality between schools... but that's a topic for a whole different discussion.)

Of course, a LOT more thoughts/news on math Common Core available through Google:

Friday, January 10, 2014

Mathematics In 2013... Read All About It

Another edition of "The Best Writing On Mathematics" (for 2013) is now out, from Mircea Pitici (4th in the series since 2010). It is slimmed down from the last issue, which was slimmed down from the prior one etc. -- don't know if Pitici is becoming more selective in what he chooses, or just doesn't have the time to read as many potential entries as in the beginning (or perhaps it's just an economic publishing decision?). In any event, it is another eclectic collection, that, as I often warn about anthologies, will include some chapters to please most any math-lover... and, some that won't; those two categories will simply vary per person by what interests you bring to the table to begin with.

There are some very big names in this compilation: Roger Penrose writes a wonderful Foreward (a quotation from which I used a few days ago on Math-Frolic), and I much enjoyed the overview of Pitici's own Introduction, which includes this ebullient passage:
"Mathematicians are mavericks -- inventors and explorers of sorts; they create new things and discover novel ways of looking at old things; they believe things hard to believe, and question what seems to be obvious. Mathematicians also disrupt patterns of entrenched thinking; their work concerns vast streams of physical and mental phenomena from which they pick the proportions that make up a customized blend of abstractions, glued by tight reasoning and augmented with clues glanced from the natural universe."
Philip Davis follows with one of the longest pieces of the anthology reviewing the place of mathematics across many cultural aspects of the modern world. Ian Stewart covers one of his favorite topics, symmetry, in chapter 2, and after that, the always-interesting Terence Tao overviews the dual tug of complexity and universality in mathematics. In one fine example he tells the "legendary" story from a 1972 gathering, of mathematician Hugh Montgomery meeting physicist Freeman Dyson for the first time and discovering, in that "chance meeting" (where Montgomery feared they'd have nothing in common to talk about), that remarkably, they had both deduced the same formula, but Montgomery working from the arena of number theory and the zeta function, while Dyson, contrarily, had approached it from "the study of energy levels in the mathematics of matrices."

I thought these first three pieces were a strong beginning to the volume, after which followed a real mixed bag of selections of varying interest (and including a few I wouldn't have included). Charles Seife, Donald Knuth, and John Pavlus are some of the other author-names that might be most familiar to readers (about half the writers included were folks I was unfamiliar with).

 The hot topic of education merited only one entry (from Frank Quinn), which seemed a bit unfair -- that subject almost requires a much wider sampling of opinion if you're going to touch upon it at all (but then an entire anthology on math education perspectives could easily be put together separately if one so chose!). On-the-other-hand there are several entries touching on probability, perhaps a bit overweighting that always-interesting topic.

Appropriately, the volume ends with one of the brief but fascinating updates to one of 2013's math highlights: Shinichi Mochizuki's "proof" of the abc conjecture (which other mathematicians are only very, very slowly coming to dissect).
Anyway, I enjoyed the first and last few chapters of the volume most, with less enthusiasm for some of the middle pieces (…but your mileage may vary ;-)
Worth noting that a few entries involve some significant math background, but most are fairly accessible for a lay reader.
If you've enjoyed the Pitici anthologies from prior years you'll certainly want to add this one to your collection, or if unfamiliar, by all means begin with this one.

In closing, I applaud Pitici for taking on the difficult (even unenviable) task each year of distilling from 12-month's worth of math writings a collection that can appeal to the broad spectrum of varied math enthusiasts that are out there.

(I might just note that Pitici's series is published by Princeton University Press, and is NOT part of the "Best Writing In ______ " series that comes out yearly on several other subjects, and which most readers are likely familiar with.)