College Math Teaching

April 30, 2013

Slate Post on Math Teaching

Filed under: mathematics education — Tags: , — oldgote @ 1:41 am

Ben Orlin in Slate:

As a math teacher, it’s easy to get frustrated with struggling students. They miss class. They procrastinate. When you take away their calculators, they moan like children who’ve lost their teddy bears. (Admittedly, a trauma.)
Even worse is what they don’t do. Ask questions. Take notes. Correct failing quizzes, even when promised that corrections will raise their scores. Don’t they care that they’re failing? Are they trying not to pass?
There are plenty of ways to diagnose such behavior. Chalk it up to sloth, disinterest, out-of-school distractions—surely those all play a role. But if you ask me, there’s a more powerful and underlying cause.

Math makes people feel stupid. It hurts to feel stupid.

Aw. So he goes on to relate his experience as an undergraduate at Yale, in a topology class:

So I did what most students do. I leaned on a friend who understood things better than I did. I bullied my poor girlfriend (also in the class) into explaining the homework problems to me. I never replicated her work outright, but I didn’t really learn it myself, either. I merely absorbed her explanations enough to write them up in my own words, a misty sort of comprehension that soon evaporated in the sun. (It was the Yale equivalent of my high school students’ worst vice, copying homework. If you’re reading this, guys: Don’t do it!)
I blamed others for my ordeal. Why had my girlfriend tricked me into taking this nightmare class? (She hadn’t.) Why did the professor just lurk in the back of the classroom, cackling at our incompetence, instead of teaching us? (He wasn’t cackling. Lurking, maybe, but not cackling.) Why did it need to be stupid topology, instead of something fun? (Topology is beautiful, the mathematics of lava lamps and pottery wheels.) And, when other excuses failed, that final line of defense: I hate this class! I hate topology!

You can read the rest.
Here is his conclusion:

Teachers have such power. He could have crushed me if he wanted.
He didn’t, of course. Once he recognized my infantile state, he spoon-fed me just enough ideas so that I could survive the lecture. I begged him not to ask me any tough questions during the presentation—in effect, asking him not to do his job—and with a sigh he agreed.
I made it through the lecture, graduated the next month, and buried the memory as quickly as I could.
Looking back, it’s amazing what a perfect specimen I was. I manifested every symptom that I now see in my own students:
Muddled half-comprehension.
Fear of asking questions.
Shyness about getting the teacher’s help.
Badgering a friend instead.
Copying homework.
Excuses; blaming others.
Anxiety about public failure.
Terror of the teacher’s judgment.
Feeling incurably stupid.
Not wanting to admit any of it.
It’s surprisingly hard to write about this, even now. Mathematical failure—much like romantic failure—leaves us raw and vulnerable. It demands excuses.
I tell my story to illustrate that failure isn’t about a lack of “natural intelligence,” whatever that is. Instead, failure is born from a messy combination of bad circumstances: high anxiety, low motivation, gaps in background knowledge. Most of all, we fail because, when the moment comes to confront our shortcomings and open ourselves up to teachers and peers, we panic and deploy our defenses instead. For the same reason that I pushed away topology, struggling students push me away now.
Not understanding topology doesn’t make me stupid. It makes me bad at topology.


First of all: it IS in part, about natural intelligence. The really smart math people, in general, don’t have trouble with undergraduate math classes, even those at Yale. I mean, of course, REALLY smart people (no, I am not one of those. 🙂 ).

Now he has an interesting observation about student “employing defenses”; at least some of them do.

But there are a host of other reasons too: some just don’t like the material, some ARE lazy (e. g., they won’t do what isn’t fun) and yes, some aren’t up to the task intellectually. Seriously: there are some subjects that many will never be able to master, even at an undergraduate level.

But one issue: someone on Facebook made the following comment:

Oh boohoo. If you’re bad at something you either make an attempt to improve at it or direct your attention to things you’re better at. Everyone is not good at everything and feeling stupid is not something people should be protected from. If you don’t get told you make mistakes or aren’t made to realize that some things take effort then you’re not improving. Learning disabilities aside, especially in higher math, the kids that are failing aren’t showing up to anything, aren’t doing the work, aren’t asking questions, aren’t studying and they don’t repeat to try and do better the next time. Children need to know what failure feels like (and math teachers were children and they do all likely know what failure feels like) so that they learn to try.

Emphasis mine.

My Opinion:
1. There are things that are too difficult for most of us to learn (e. g. quantum field theory).
2. It is useful to have a grasp of one’s intellectual limitations. All too often I see average people dismissing expert findings because those findings “don’t make sense to them.” People need MORE intellectual humility, not less of it.
3. If you haven’t failed at something, then you haven’t tried enough difficult things.

That said: this article is useful because it does give at least one angle of approach that might work with some students.

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