Category Archives: Recursion

These are posts relating specifically to recursion and recursive processes.

The SAT’s recursive meaning

If it weren’t for the god awful Analysis comp I’ll be taking on Saturday (and should be studying for now), I would certainly be going to EDcampNYC, the local unconference for teachers and the like. Anna and Justin will be going without me and leading a session or two about mathematical art stuff. If you go, you should definitely check out their session(s). Especially if you’re into making beautiful stuff. (Speaking of mathematical art, I have about 2400 words written about MArTH Madness, the huge math art event we hosted at Saint Ann’s. Must add pics. Coming soon.)

Anyhow, let me tell you about Mai Li. She’s an amazing young mathematician in our mathematical art seminar. She’s also opted out of Trig/Analysis for her junior year in favor of Intro Topology and Modern Algebra electives with Anna and a semester course called Fractals and Chaos. She helped lead the doodling sessions at MArTH Madness, and she just rocks in general. Well, as much as she would love to come help them share MArTH with the people at EDcampNYC, she can’t. She has to take the SAT’s.

No big deal. Whatever. She has to take them. It’s fine, but too bad. All of this is just the setup for some clever little thing that Justin said in our office the other day.

* * *

Q: You know what SAT stands for right?

A: The SAT Aptitude Test.

HA! Love it. It used to stand for “Scholastic Aptitude Test,” but I think they’ve abandoned that. (I wonder why?) I looked over some videos and stuff on the college board site, but I couldn’t find my answer. I did find this, however:

“the combination of high school grades and SAT scores is the best predictor of your academic success in college.”

hmm. Do you buy that?

The problem that I have with the SAT, in particular the math section, is that it cannot test for the applicants ability to do math. If you disagree, it’s simply that we have different notions of what it means to “do math.” I’m not gonna get too deep into this, because I’m mostly writing just to share Justin’s little meme, which might otherwise be lost forever.

“SAT Aptitude Test” is a fitting acronym, because the SAT is only really testing your ability to succeed on the SAT itself. Infer what you will. When students need to prepare, they don’t get a math tutor. They get an SAT math tutor. Could the inauthenticity be any more obvious? The biggest criticism of my department (accurate or not) is that we don’t adequately prepare students for this test. Perhaps that’s only further evidence of my point, since our primary objective is doing real mathematics with students as often as we possibly can. [disclaimer: I am not a spokesman for the school.]

What do the SAT’s demand for success? Technical training, perhaps, which is only one aspect of a mathematical education. Maybe most of all, SAT success requires SAT experience.

Want to prove that you’re SAT apt? Why not practice with the SAT aptitude test? Get it?

* * *

OK that’s it. This is just something I’ve been thinking over and really enjoying. Thank you, Justin for your unending nerdly wit.

Oh by the way, we can keep expanding SAT and get the following, all of which are the same thing:


The SAT Aptitude Test

The (SAT Aptitude Test) Aptitude Test

The [(SAT Aptitude Test) Aptitude Test] Aptitude Test…

and on and on.

* * *

Good luck students, and try to remember it’s a collection of paper and ink. Don’t let it shake you too hard.


The “Lost in Recursion” Recursion


[Recursion]: Video Feedback

I’ve been playing with video feedback since I was kid hooking our shoulder VHS video camera up to a little black and white TV in my grandma’s basement. I have a document camera that plays through the computer in my classroom, so I can achieve the effect anytime, these days. All I have to do is point the camera at the screen and play. My students LOVE it, of course, as does just about everyone who experiences this in person. There is something deeply fascinating to us about this mechanical system observing itself. Infinity? What’s going on in the middle of that screen?

Homage: Drawing Hands

It’s the same effect you get when mirrors face each other, but the camera enhances this in several ways. You can twist and move it, creating incredible and surprising results. The camera/display combo makes small alterations each time the “image” is sent through the loop. As a result, the image deforms, one generation at a time. The color, the shapes, the detail, just about everything is slightly transformed through this recursion, similar to the evolutionary process that shapes all life.

In fact, I see feedback systems as a ubiquitous mechanism in the world. “Memes,” increasingly well-known, are the mental structures, analog to genes, whose interactions affect our ideas, or perhaps even constitute human thought. (Hofstadter’s I am a Strange Loop is all about this.) I’ve never fully explained my choice of “Lost In Recursion,” but perhaps it’s starting to come through. It refers to my own thinking, as well as to our schools – a troubled yet robust, self-perpetuating system, surviving minor alterations, awaiting revolutionary demand for change.

Homage: The Creation of Adam
(out of recursion, life and soul emerge)

By writing this blog, reading others, engaging in conversation on Twitter, and simply sharing my thoughts, I believe I’m taking part in the dynamic collision of ideas that is already shaping education reform and change in our country.

I hope my students will take active roles in this as well, but it won’t happen just by mastering material, meeting standards, passing tests, following directions, or going to the right colleges. It happens when you start sharing ideas, communicating, taking control, pushing back, and effecting change within these systems – most importantly the one inside your own brain.

Thanks to Justin Lanier for helping me take these photos. You can see more pics on the Lost In Recursion flickr page.