I have a relevant story about the topic of this post. It's actually my life story.

When I was about 12 or 13 I dropped out of school.. I was too bored, too frustrated, and too unhappy to actually stomach it any longer: the unsightly pleasure adults took in dominating children, the teachers who knew less than I did but refused to admit it, the way smart kids often ended up at the bottom of the pecking order... The only thing I enjoyed was writing simple QBasic games for my friends and me to play.

After a protracted fight with my parents (I actually went on strike on the roof of our house) I got what I wanted and they let me drop out of school. This was probably the best single decision of my life, and the credit really goes to them for being brave enough to allow it.

I started out teaching myself C++ templates, and the basics of electronics. I got obsessed with high voltage, and started dumpster diving to find good parts. Once, after I took a (harmless) 40kV shock, my mom started to worry she'd come back from her teaching job to find me dead on the floor. I convinced her I knew the actual parameters of heart stoppage well enough to avoid this!

I built plasma globes and an improvised vacuum pump. I started rewiring our telephone lines. I made an amplifier. I built a coil gun and tuned it using my computer's sound card as a digital storage oscilloscope. I taught myself Python, and dived into the theory of digital signal processing.

I even had the good fortune of acquiring some Perl contract work through a family friend. Using the money to buy my own computer at 14 was probably the most satisfying experience of my life. Old school-friends would come to visit and oggle my enormous 21" CRT. That made me realize that I didn't have to follow the ordinary rules to survive in this world.

All the while I took distance education courses, a measure my parents insisted on (luckily). When I got high grades on A-level physics, I got the opportunity to attend university. Still a year young, I ended up studying pure math at the best math university on my continent (lots of Soviet bloc math emigres who moved to Africa for the sun).

The weirdest contradiction for me was hanging out with many of the other "nerdy kids" in math and physics who had gone the traditional route, and finding out that they really weren't all that interested in what they were doing. They seemed to be more consumed with perpetuating their high marks. Most frustrating of all was that achieving those high marks often boiled down to the most 'mercenary' kind of pillaging of old exam papers -- actual understanding didn't have much bearing on it.

Pure math was different -- you really had to think, be creative, and understand things to achieve good grades, at least in the more advanced courses. And sure enough, that was the one discipline I got very good grades in. But funnily enough, only when it got hard. For the first 2 years I didn't realize I had any interest in math at all.

By and large, my experience of formal education is best summed up by one little anecdote: I once handed in a 3rd-year physics practical in which I had taken an extraordinary large amount of care: I did the experiment several times because to better resolution on the spectrometer, I researched error propagation and did a more principled error analysis, I wrote it up carefully in LaTeX, and so on.

I got a mediocre grade for the practical. In fact, my explanation of how I had used a genetic algorithm to fit Gaussians to the spectrographic peaks had the word 'genetic' crossed out and replaced with 'generic' -- the ignorant tutor thought I had just misspelled it!

In contrast, a classmate put some last-minute work together that had (illegitimately) small error bars, and got 90%. At that point I lost interest in getting good grades in that subject, and stopped trying.

There is a happy ending: industry proved to be very meritocratic indeed. And my current job means I can actually bring all this random knowledge I have to bear, and bootstrap my way into new fields (like, recently, graphical models).

What are my conclusion here? I think the main conclusions are:

* Teaching yourself on your own has the benefit that you get used to doing what you do because you love it, not because people reward you for it. And this is what really matters in the end.

* Metrics to reward behavior will almost always tend to corrupt the behavior they are meant to be promoting (this has been enshrined as http://en.wikipedia.org/wiki/Campbells_law). Grades are the best example of this.