A few shockingly linear graphs

There’s a recent working paper by economists Ruchir Agarwal and Patrick Gaule which I think would be of much interest to this readership: a systematic study of IMO performance versus success as a mathematician later on.

Here is a link to the working paper.

Despite the click-baity title and dreamy introduction about the Millenium Prizes, the rest of the paper is fascinating, and the figures section is a gold mine. Here are two that stood out to me:

There’s also one really nice idea they had, which was to investigate the effect of getting one point less than a gold medal, versus getting exactly a gold medal. This is a pretty clever way to account for the effect of the prestige of the IMO, since “IMO gold” sounds so much better on a CV than “IMO silver” even though in any given year they may not differ so much. To my surprise, the authors found that “being awarded a better medal appears to have no additional impact on becoming a professional mathematician or future knowledge production”. I included the relevant graph below here.

The data used in the paper spans from IMO 1981 to IMO 2000. This is before the rise of Art of Problem Solving and the Internet (and the IMO was smaller back then, anyways), so I imagine these graphs might look different if we did them in 2040 using IMO 2000 – IMO 2020 data, although I’m not even sure whether I expect the effects to be larger or smaller.

(As usual: I do not mean to suggest that non-IMO participants cannot do well in math later. This is so that I do not get flooded with angry messages like last time.)

___ Students Have to Suffer

This will be old news to most of the readership of this blog, but I realize I’ve never written it down, so time to fix that.

Fill in the blank

Let’s begin by playing a game of “fill in the blank”. Suppose that today, the director of secondary education at your high school says:

“___ students just have to suffer.”

This is not a pleasant sentence. Fill in that blank with a gender, and you’d be fired tomorrow morning. Fill in that blank with an ethnic group, and you’d be fired in an hour. Fill in that blank with “special needs”, and you’d be be sued. Heck, forget “___ students”, replace that with “You”. Can you see someone’s career flashing before their eyes? How could you possibly get away with saying that about any group of students?

Those 500 hours

“Smart students just have to suffer.”
Director of Secondary Education at Fremont Unified School District

This happened to me. I haven’t told this story enough, so I will tell it some more.

When I was a senior in high school, I was enrolled in two classes and would thereafter run off to take graduate math at UC Berkeley. (Notes here.) This was fantastic and worked for a few weeks, so I got to learn real analysis and algebraic combinatorics from some nice professors.

Then the school district found out, and called me in for a meeting. The big guy shows up, and gives me this golden quote. I was then required to enroll in five classes a day, the minimum number of classes required for me to count towards the average daily attendance funding for my school district.

And that is why, for three periods a day, five days a week, I was forced to sit in the front office, saying “Hi, how may I help you?”.

(I didn’t even get paid! Could’ve asked for a cut of that ADA funding. It didn’t all go to waste though; I spent the time writing a book.)

Everywhere Else

Since I’ve had fun picking on my school district, I will now pick on the Department of Education.

“While challenging and improving the mathematical problem-solving skills of high-performing students are surely every-day objectives of those who teach such students, it is not a problem, relatively speaking, of major import in American education.”
Department of Education Reviewer

Oh boy.

The point is that the problem of neglecting gifted students isn’t at the level of individual teachers. It’s not a problem at the level of individual schools, or individual cities. This is a problem with national culture. The problem is that as a culture we think it’s okay to say a sentence like that.

Replace “high-performing” with any adjective you want. Any gender, any social class, any ethnic group, whatever, and you will get a backlash. But we’ve decided that it’s okay to mistreat the gifted students, because no one complains at that.

Maybe it’s too much to ask that schools do something special for top students. Can you at least not get in their way? Like not forcing students to be an office assistant for 500 hours to obtain ADA funding? Or more generally, how about just not forcing students to take classes which are clearly a waste of time for them?

Next Actions

So what can you do to change the national culture? As far as I can tell, this is mostly a lost clause. I wouldn’t bother trying.

The reason I wrote this post because I went through most of high school not really being aware of just how badly I was being mistreated. I’m really writing this for myself four years ago to point out that, man, us nerds really got the ugly end of the deal.

What you can do (and should) is make small local changes. You can persuade individual schools to make exceptions for a kid, and frequently individual teachers will do what they can to help a gifted student as well. Each individual student has good chance of finding a way around the big bureaucrats that rule the wastelands.

Ask a lot of people: if one administrator says no, ignore them and ask another one. Be prepared to hear “no” a lot, but keep waiting for the one or two crucial “yes” moments. If push comes to shove, switch schools, apply to college early, etc. Take the effort to get this one right. (See 56:30-60:00 of this for more on that.)

Dear past self, yell a little harder at the big guy when he comes, maybe you can save yourself 500 hours as an office aid.

Addendum: A Happy Story

In the comments, someone wrote the following:

Did your mistreatment as a gifted student hinder you in any significant way? … Where would you be today had the system not failed you?

I think it’s impossible to know. But here’s another story.

  • When I was in 7th grade, my school tried to force me to take pre-algebra. My mom begged the school teachers until they finally relented and let me take Algebra I. At the time, my 12-year-old self couldn’t have cared less: both classes were too easy for me, and I spent most of Algebra I playing Tetris on my TI-89.
  • Two years later this happened again: the school wanted to force me to take Algebra II. This time, my mom begged the teachers to let me take precalculus instead, which they eventually did. My 14-year-old self also couldn’t care less; both classes were too easy anyways, and I spent most of precalculus playing osu on my iPhone.
  • Two years later I was in Calculus BC, again bored to tears and in the last HS math class offered. That’s when my parents were able to persuade the school to let me take classes at UC Berkeley instead, since I had exhausted the HS math curriculum. I did very well in my first undergraduate classes, which then allowed me to take graduate classes for the rest of high school.

These professors were the ones that wrote my reference letters for college applications, which got me into all the top schools in the country (Berkeley, UCLA, MIT, Princeton, Stanford, Harvard). Without these reference letters I would certainly not have had as many options; winning the USAMO and making the IMO didn’t happen for me until the end of senior year.

But it wasn’t until I met the guy quoted above that I found out that I had unwittingly “broken district rules”, and technically shouldn’t have happened. (Belated thanks to those individuals who stuck out their necks for me!)

So here’s a surprisingly clear example of a near miss. Suppose that my mom had been more polite, or my school had been a little more firm, and any of the three events above didn’t occur. Not only would I have lost some college choices (potentially including MIT), I wouldn’t even know that this was the key event I could have changed.

[Bonus question: I estimate about 2% of USA high school students take the AMC. How would my life have changed if I had been in the other 98%?]

By analogy, if you ask me now what ways I’ve been affected, how am I to tell you? Without an Earth simulator I can’t point to which of the other 100 times I was mistreated hurt me the most. All I can do is point out that I (and many others) are being mistreated, which really should not be okay in the first place.

Or maybe a better argument: if you halve the amount of time I have to learn by making me go to high school for six hours a day, and then I get a gold medal at the IMO, I do not think the conclusion should be “it had no effect”, but something more like “I could have gotten two gold medals at the IMO”. Not that gold medals scale linearly with time but you get the point.