"To study for ten years at a cold window..."

The title of this entry is a line from a 900-year-old poem by the Chinese poet Liu Qi, often quoted by Chinese parents to children whose academic performance has been less-than-ideal.  I heard it at a meeting with officials from East China Normal University, who were explaining Chinese attitudes towards learning and education.  The point of the quote is simply that success doesn't come quickly or easily:  only sustained effort, quite possibly unpleasant, produces results.

How different from the U.S. perception of math education!  A Google search on "no good at math" produces over 724,000 results, and while some are actually echoes of the Chinese perspective (such as this thoughtful piece by my high school friend Jean Marie Linhart), the majority (at least on the first pages) seem to be people saying that they themselves are "no good at math."  Well, of course not!  The last thing most people who believe themselves "no good at math" seem to do is more math, which is pretty much the only way I know to get better at it.

I had a student several years ago who is still legendary for how much of our courses he figured out, on his own, before we could teach it to him.  His math contest results were phenomenal.  But what most people who didn't work closely with Alex didn't realize was that he did math for hours every week:  at least 10 or 15 more than required for class and math team, so about 12-17 more hours each week, at least, than most "ordinary" math students at my school.  Over four years, Alex spent at least 2400 more hours thinking and working about math than the typical math student at my school.  Of course he was good at it!  He'd have had to have--quite literally--some kind of learning defect if that much work hadn't paid off.

I'm not saying that there's no such thing as talent or giftedness in mathematics.  But I don't think focusing on talent or giftedness is useful, for two reasons:

1. We're not very good at discerning talent, unless it comes packaged in very recognizable shapes, sizes, and containers.  Quick at arithmetic, good at spotting patterns, doesn't need to show work--these are all recognizable, and so we spot those relatively easily, especially when the person is someone whom, because of our own biases, we are likely to think of as good at math (e.g. white/asian, male, etc.).  But: other mathematical talents, such as the ability to generalize and synthesize different results, to construct arguments containing multiple ideas, to sift through different approaches for the most fruitful one--these don't show up as early and are harder to see.  In fact, by the time a student is old enough to have encountered a mathematical situation for which these talents are valuable, he or she may already have been "tracked out" of the highest-level mathematics.  And again, we're even less likely to spot a student with these talents who's African-American or Hispanic, or not a boy.
   
2. Math is too hard for sheer talent to get most people very far.  Alex worked on his ideas and chased them down until they made sense.  Discovering and writing a good proof can take hours even when the problem is just a college-level exercise--much less a Putnam problem or (gasp!) an actual theorem.  The people who make it to the ends of such journeys aren't the ones who start out the fastest or the furthest ahead; they're the ones who don't give up because of their passion for the subject and their determination to keep going.  That's where the ten years comes in--whether it's in a study in Princeton, or by a cold window in Xiangsu province.

Marzano points out that there are four ways to explain success:  either the task was easy, or I was lucky, or I was talented, or I worked hard.  Only the fourth of these leads to behaviors that increase the chances of future success:  if my past successes were all based on ease, or luck, or talent, then when I encounter a genuine challenge, I've got nothing.  The Nurtureshock authors go even further, citing research that telling kids they're smart actually decreases future success.

Chinese parents don't tell their kids that they're smart; they tell them that they're smart enough to be successful if they work hard.  And that's a message I think all of our kids should hear.

== pjk