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Lindsey Kuper

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Like someone who could do math [Nov. 24th, 2008|07:11 pm]
Lindsey Kuper
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Back in undergrad, I used to get excited when I got a grade better than a D on a math test. I did badly on exams right on up through linear algebra. In retrospect, it wasn't that I disliked math, and it wasn't that I wasn't trying. It was more like the whole thing was in a foreign language, one that I didn't even know how to ask "¿Cómo se dice...?" in.

I understood some of what went on in linear, but things didn't really start to come together until I took combinatorics. I kept waiting for the incomprehensible part of the course to start, as had happened in every other math course sooner or later. It kept on being comprehensible -- hard, but comprehensible. Then, one day, I went to my professor's office to ask a question about something or other, and an amazing thing happened that I'll always remember: she treated me like someone who could do math.

After that, I began to make a point of hanging around the department lounge with my combos book, so that the other professors would see that I was still doing math despite their best efforts. The following year, I took CSC 341, which was cross-listed as a math course. One afternoon early in the semester, I went to my professor's office hours to ask a question. I ended up waiting in the hallway for a while because one of my classmates was already there talking with him. As their conversation floated out into the hallway, I suddenly realized that they were talking about the same problem I was having trouble with, and furthermore, I could understand them. I could actually understand a math conversation between native speakers! It was so exciting! I don't remember exactly what happened next, but I think that when the other student left, I bounced in there and blurted something like, "Yeah! I see what you mean about the frobnicating foobar!" Dr. Stone may have been a little taken aback.

When I could finally speak the language, it was a joy every day. And I was surprised how many computer scientists there seemed to be who viewed it as a chore. I feared that I would be mistaken for one of those people. That's one reason why when I came here, failing the theory qual was so troubling. It wasn't so much that I thought I deserved to pass. It was that I was afraid that I had blown a chance to get the people at IU to see that I actually really liked math. I wanted to yell, "No, you don't understand! I didn't fail because I don't like it! I'm just not very good at it! Wait, come back! Do-over! Best of three!"

Ahem. So anyway, right now I'm taking B501, the first graduate theory course at IU. Now, I know it's bad form to talk about grades, so I usually try not to subject anyone to it (except Alex, who just has to suffer). But given my checkered mathematical past, this is really exciting for me, and I can't keep it to myself. We just got the results back from the second midterm, and I got a 94. According to the histogram my professor posted, it was either the highest or the second-highest score in the class.

Admittedly, the strongest theory students tend not to come here. (IU's traditional strengths are in programming languages, cognitive science, and high-performance computing, and the department seems to attract the students and faculty who are already into those things -- a self-propagating imbalance which I can't think how to fix.) Still. Still. This is objective proof that I'm not so bad at this!1 It shows that at Grinnell, they weren't just being nice to me in combos and automata so that I would graduate on time or something. Here, nobody much cares when I graduate. Actually, when I look at it that way, I'm kind of glad I failed the qual, because it shows that nobody here is doing me favors. When I pass (and I will friggin' pass the thing next year!), it will be because I can demonstrate a thorough understanding of the material.

  1. Whenever I say things like this, Alex is like, "Dude, Lindsey, you're good at math. Internalize it already." But he didn't know me in 2002. He doesn't know what it was like all that time in calc II, when I wanted so badly to understand it but just had no clue what in the flying fuck was going on. Actually, part of me wants to go back and try to learn calculus again, but another part of me is scared that I still won't understand it, and then they'll revoke my math license and I'll die hungry and alone and so on.

[User Picture]From: unya
2008-11-25 03:24 am (UTC)
Rock it, Lindsey!
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From: rmfleming
2008-11-25 03:49 am (UTC)
If you ask anyone in countries where everyone is good at math, they'll all say that ones goodness at math is directly related to their effort. Here, we have some messed up "innate math ability" thing going on. There is no innate math ability, any more than there is innate speaking old church slavonic ability.

I think it gives you a leg up, personally. (I speak as an "innate math ability" wash-out -- after I got to a certain point I thought, "wait, I don't really like doing this..." ) You've got coping skills and interest/passion, and I'd be willing to bet that most of your peers lack one or both of these.

Not to badmouth your peers. Peers, you're awesome, too!
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[User Picture]From: jamey1138
2008-11-25 05:41 am (UTC)
My own guess is that there actually is some innate ability involved, which can make math really, really easily for those that have it. This is, by no means, to say that math is impossible for those who lack that innate bonus, nor even to say that it has to be difficult for them: the foreign experience you cite is prove to contrary of that.

The problem (I suppose, as a professional math educator, myself) is that math curricula in this country (and in all English-speaking countries, really) have been historically developed by those who are predisposed towards math ability (in the same way that some people may be predisposed to linguistic ability, to take your old church slavonic example to heart...) These curriculum-writers have generally not given much thought to what is actually difficult to learn in mathematics, because they didn't find much of any of it to be difficult to learn.

Which is a long-winded way of saying, "Yeah, you're pretty much right, but we have our math teachers as much to blame as anyone else for it."

Hopefully, my own career as a math teacher will eventually lead to some long, hard examinations of what we choose to teach (and how it compares to what other cultures choose to teach) in mathematics, and why-- with a side-track that dispels the "innate math ability" thing, or at least clarifies it ("Yeah, 10% of the world are bastards for whom it's easy. The rest of you will have to work for it. Nut up.")
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From: sherwooddotnu
2008-11-25 04:07 am (UTC)
Oh, man. I miss math so much. I dropped combinatorics about three weeks in when I took a medical delete on all my classes that semester, and I was so sad to say goodbye to that class. Never took math again. Now I'm considered a math genius in my work place for being able to calculate a percent change or do simple algebra. I tell myself, "I used to be able to do derivatives!" But "used to be able to" isn't so great.
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[User Picture]From: pmb
2008-11-25 05:22 am (UTC)
How is it that a professor treats someone who is good at math? I would like to make sure I treat my students this way, but if there are any telling attributes or manners, then please help me out...
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[User Picture]From: jes5199
2008-11-25 06:14 am (UTC)


Surely you realize that by becoming a professor that you will be personally responsible for tossing at least one student into the maw of crippling despair?
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[User Picture]From: pmb
2008-11-25 06:17 am (UTC)

Re: counterweights

Most definitely. Probably one a year. But I can also save some from that. And I would like to maximize my saved/destroyed ratio.
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[User Picture]From: lindseykuper
2008-11-25 08:49 pm (UTC)
You know, I made it sound like my professors' behavior changed drastically when I got to combos, but I think it was my behavior and my attitude that changed.

In calc I and II, when I had questions about the homework, I took them to the Math Lab, where the student tutors for intro math courses were. I don't remember ever going to my professors' offices to talk about a homework problem. In fact, if I came by, it was usually to ask "How much did my grade get hurt?" after a bad exam, which was probably a conversation they didn't like having. Moreover, it's not a conversation about math! If, from their point of view, I only wanted to talk about grades instead of about math, then it's no wonder they viewed me as someone who didn't much like or care about math.

In linear, our professor was months away from retiring, and it didn't seem to me like my dumb little homework questions were worthy of a 70-year-old man's time. (Of course, I realize now that this was the wrong attitude on my part -- as long as he was there, it was his job!) Also, I was the oldest kid in the course (most CS majors had gotten the linear requirement out of the way their first or second year; it was my third), and I was embarrassed to even be there and mostly kept my head down and didn't talk to my professor much at all.

In combos, first of all, I wasn't embarrassed to be there -- half the class was other CS kids in my year. (Man, that was a good feeling, looking around and realizing that I was catching up.) Second, it felt like advanced enough of a course (and my professor seemed sufficiently far from retirement, heh) that I didn't feel unworthy of going and talking to her about the homework. So, when I did go to talk to her, our conversations were about math. Therefore, lo and behold, she treated me like someone who could do math, or at least like someone who cared about math.

Advice for you? Well, if you have students who behave like I did in calc -- who only come talk to you when their grade is in dire straits, and who then only want to talk about the grade -- first of all, don't assume that they don't care about the material. It's possible they care about the material a lot. It's just that at the moment, they're more worried about if they'll graduate. Let them know that they should ask lots of questions, and that coming and asking you questions can only help them and is never, ever a waste of your time. And tell them that coming to talk to you about the homework is a sign of a strong student, not a sign of a weak student. You might have to tell them this a few times before it sinks in.
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[User Picture]From: eliciel
2008-11-25 11:06 am (UTC)

Truly, deeply

I share your joy.
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[User Picture]From: mangoflute
2008-11-25 12:46 pm (UTC)
On the Praxis: I, which is what they make all potential teachers take before they're even admitted to a teaching program, I got all of the geometry questions right. I did most poorly in algebra (very bottom of "average score range", whereas I blew that same stat out of the water by nailing all of the geometry questions). I always thought I was bad at geometry and good at algebra. Maybe my R brain developed after 11th grade pre-calc (the last math/science course I ever took) and my L brain just stopped...
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[User Picture]From: stereotype441
2008-11-25 04:43 pm (UTC)
Your post is curiously timely in coinciding with Boingboing picking up this article: The Effort Effect, which talks about the startling discovery that when people attribute their success (or lack thereof) in an endeavor to innate ability, they stop learning, whereas when they attribute it to the amount of effort, they improve. Maybe this has some bearing on your experiences?

I know it has had a huge bearing on mine--in my adult life I have made my biggest strides in skills where I believed I had the inherent ability to do well but needed more practice (e.g. tango dancing and juggling). But in areas in which I believed I was congenitally bad (card games, of all things) I made little progress. I even made little progress in areas in which I believed I was congenitally very good (like composing music--I know I'm good at it, but I feel like I'm no better than I was ten years ago).

What I haven't yet figured out is how to shift my attitude to one that attributes success to effort. But I'm really inspired by your math success story. I find myself wondering, the transformational experience you had with your professor treating you like someone who could do math, did it cause you to treat yourself any differently? Could you feel any difference in how you mentally approached math after that? When you made mistakes after that, did you look at them differently? I think there may be a big clue lurking in there somewhere.
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[User Picture]From: lindseykuper
2008-12-04 07:23 am (UTC)
did it cause you to treat yourself any differently?

Yeah. Mostly, it helped me see that just because one doesn't happen to understand something the first time it's explained (or the second, or the third), it doesn't mean that one is never going to understand it at all. (Conversely, of course: just because one does understand something the first time, it doesn't mean that it's going to keep on being that easy forever.)

We humans love to put ourselves in boxes: I'm good at this, I'm bad at that. You would never say, "There is no way I can get any better at juggling, so I'm going to stop trying now," because that would be ridiculous. But that is essentially what people are saying when they say "I'm good at this" or "I'm bad at that". I've started to notice that you don't hear true professionals say those things very often. You only ever hear them say "I'm working on...".
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[User Picture]From: deepdistraction
2008-11-26 06:07 am (UTC)
One of the qualities Grinnell appeared to have (at least from my outsider's perspective) was a pervasive atmosphere that the students could be trusted. Trusted to learn, trusted to run their own dorms, trusted to dress for the weather. (Really. At one meeting between prospie parents and an administrator, a parent said she was horrified to see a student walking around shoeless in 50 degree F temps; the administrator essentially told her to get a grip). I'm wondering if you were ALWAYS treated as if you could do math, but perhaps didn't notice because you were rather more concerned with stuff like your 'worthiness' to ask a question or your embarrassment at taking a class in which you were 'behind' the other students..I wonder if it's possible that attitudes like that, which are really nothing more than self-consciousness, have a dastardly way of interfering with learning?
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[User Picture]From: lindseykuper
2008-11-26 09:07 pm (UTC)
It's called 'self-governance' and you're absolutely right. Alex has mentioned this, too, in contrast to Georgia Tech, where, according to him, students are actively distrusted.
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