Graduation was on Thursday — as you can see from the picture of me wearing my hood above. My merry band of seniors graduated, and that’s the end of them. Yeah, one of them might stop to write an email here and again, or pop by the school when they’re back in town, but let’s face it. They’re gone. And am I okay with that?

Surprisingly, yes. I honestly don’t know why, but I am. Not that I won’t miss them — they might be the standard by which I judge all future calculus classes — but I honestly think I’m okay with the “they come into your life, they go out of your life” revolving door aspect of teaching.

Picturesque and poignant defined the ceremony. It was held outside, with our 1851 Hogwartian brick building acting as our backdrop, light streaming through leaves as the sun slowly started setting, with a gentle breeze punctuating the warmth and a few butterflies fluttering around. Students sang, surprisingly mature speeches had us laughing, and then like the end of a really good chapter in my life, it was over.

While the seniors graduated, I also thought about all the colleagues who I’ve come to respect and truly like who are leaving; they also are graduating. And from that, my mind moved on… Graduation was the first time I was able to take a moment away from the hustle and bustle of the End Of Year Things To Do, and I finally really realized I too had graduated. I finished my first year teaching, and I loved it.

Congratulations, me!

So previously I touted this as being the best comic ever. (Click link to see.) However xkcd has outdone itself with this one.

Although the funding structures have altered this in recent decades (where anybody knows where once physics was on top after WWII, now biology is on top), I still admit this overarching bias in my thinking. Math reigns supreme, lording over all other sciences, which are mere derivative structures, polluted more and more as you descend down each rung on the ladder of knowledge. Ka-chow!

This year was my first year teaching, period. But it was also my first year teaching seventh grade, which I was not trained to do, nor did I anticipate liking. Junior high was a mess for me. I didn’t do terribly well, and I had almost no friends, and I’ve honestly blocked it out of my memory. I can’t remember my teacher’s names or anything that I did. I took the job in spite of this class — because I liked the school that much. And in fact, I ended up loving teaching my seventh graders. They are so sweet and awesome! But still, not knowing what I was doing with this age level, I had to improvise how I acted with them.

Oh Thursday last week, while I was at my college reunion, I had them write comments for me (flipping things around… in my school, teachers write narrative comments on each of their students twice a year… I thought I’d give them a chance to reverse that). The feedback was very positive overall (huzzah!).

A quick and dirty analysis of things that srtuck me below [things in quotation marks are direct quotations]:

• A common refrain was “your teaching style is great, but different.” A few said that something to the effect that “it took me a while to get used to you and your teaching style [but then I loved it]” I actually am surprised by this, because I didn’t think I taught differently than any other middle school teachers! I wonder what makes me different.
• A couple of the students thought I could “explain subjects a little more” and that one student “didn’t understand what you were explaining in class till the day before the test.” Yikes! But to mitigate, many others said the class was at the right level for them.
• A number commented on how they loved how I ended each class wishing them a “Marvelous Monday, Wonderful Wednesday, Terrific Thursday, or Fabulous Friday” and a few wished me a “Super Summer.” (And one wished me a “Stupendous Summer.”) Interestingly, I didn’t know they really paid attention to this quirk of mine, that I picked up from my dad when I was younger, but it stuck with them!
• Many students (even the ones who got really good grades) found the course pretty challenging and fast paced. And this actually made me happy, because that was explicitly the goal. In seventh grade, I’ve noticed, they can pick things up really quickly! When their minds are this moldable, it’s great to get a lot in there. We did some extraordinarily hard stuff (find the volume of an equilateral tetrahedron knowing only the side length) which messed with their minds. And the best part is: they got the hard stuff. Not barely got it or grasped onto it, but they *got* it.
• In concert with the last point, the students seem pretty conscious that I hold them to a high standard: “I also learned that you had very high expectations of us that were achievable but we were not of expecting them.”
• Almost universally, the students commented on my  “enthusiastic attitude” and energy level. Which I think translates into one student saying that I’ve taught her to “have so much more confidence in my math because you know I could do it and I did.”
• A few said that the other teacher held review sessions, and I should have done that, instead of sending my kids to her sessions, because she taught things slightly differently. I buy that. And a few wanted more personal one-on-one help. The difficulty with that is that I teach in the upper school, so it’s hard to have a solid presence in the middle school. But to deal with that, I always sat in the lunchroom on Wednesdays to answer questions. And I always met with students when they emailed me for help. The students who commented that I didn’t provide personal help never asked for it! They never came to my lunch table on Wednesdays either. Maybe it’s my fault, and that in the middle school, I should be the one asking them if they need help? But maybe not.

Harvard apparently has this notoriously difficult math course that the really advanced frosh students take. Like, the ones who have already taken advanced classes (and I’m not talking about the more fundamental multivariable calc, differential equations, and linear algebra). It has a whole “mystique” surrounding it. It’s called “Math 55.” Apparently you’re supposed to “oohhhh” and swoon when you hear that, or at least go “Oh my god! Isn’t that insane?” And then make some comment about it being the hardest freshman course in the country. At least, that’s what the Harvard math department touts it as on their webpage.

I’m surprised I had never heard of it. I only first heard about it by reading this article recently, excerpt below:

Later that first night, the first problem set is released online: 13 questions, each consisting of multiple sections to make a total of 47 parts. While nearly everyone is alarmed by the amount of work, Litt says he’s not too concerned. The class can’t stay this hard for this long, right?

“I figure he’s just trying to get people to drop the class,” Litt says.

He figured wrong. As class attendance steadily thins, the workload does not. The first few problem sets each take about 40 hours to complete. The work burden is reason enough for many extraordinarily gifted students to drop.

Case in point: Ameya A. Velingker ’10 took Advanced Placement calculus his freshman year and ranked in the top 12 for the USA Math Olympiad the year after that. “It was a tough decision to drop,” Velingker says. “You’re around all these people who are beasts at math. But I realized it was not going to work out.”

I don’t doubt that it’s insane.

I can’t help but be struck by the cult that’s grown up around it. The article analogizes it to be like a fraternity. (Of math geeks.) There’s also a lot of working together, burning the midnight oil.

It harks back my own “tough freshman math class.” I certainly was not Math 55 caliber. But freshman year I took 18.100B, the theoretical version of real analysis. We used a slim, blue, and terse book. Yup. The slim, blue, and terse book. And from my perspective, that book had been forged in the depths of hell. And given a $150+ price tag. [see update below]

I didn’t struggle in high school math. But let me tell you, putting myself in a class freshman year where I wasn’t yet mathematically sophisticated was not wise. Everything in class made sense. Well, everything in the first five minutes. Then came a bunch of notes and symbols, discussion about compactness and limit points, and then I left dazed, bumping into random people and pillars on my way to the library to curl up with the book, struggle, and be frustrated at my brain for not being able to “see” “it”.

We had weekly quizzes. I think I usually got a 0, 1, 2, or 3 points on them. Out of 10. My mind didn’t work that way. But I endeavored. I don’t know why. Pride? The belief that I could do it? Not wanting to admit that I couldn’t? And at my school, I thought it was rare that anyone went to talk with the Great Professors and ask for help. I was a freshman. I didn’t know anything.

And so I continued studying like no one’s business. And when the final came around (worth 40% or 100% of my course grade, whichever is more beneficial) I literally lived and breathed that blue book for days before. The final was hard — I think only 4 or 5 questions — and I left depressed. But I nailed it.

I don’t know what the point of this post was, except to recall one of two math courses which kicked my butt. Many of my students go through that struggle and frustration in high school. They study a long time and they still don’t get the grades they want. But I can identify with their frustration. It just came later for me. [1]

For those who want more information, besides the article above:

1. A forum talking about the course.

2. The Harvard math department website discussing Math 55. (Scroll down to Math 55.)

3. A few Math 55 course webpages throughout the ages: Fall 2005, Fall 2002.

[1] I know two main differences though. My students think that somehow their grade should be based on effort, and not merit. That didn’t cross my mind in college. I thought you should get grades based on whether you could work the problems or not. The second difference is that many of my students believe that there is a magic bullet that will help them, like meeting with me on the day before a test. I also knew at that point that there is no royal road to mathematics, no panacea that will force understanding.

Update: A funny comic about that dang book here.