Friday, November 5, 2010

In which a mathematician masquerades as a math teacher.

So I was in a colleague's classroom today, and I wrote down what my notes would look like if I had been a student who took good notes in her class that day. Then I wrote down what my notes would look like if I'd been in a class I taught, covering the same material. Here they are (in order -- although first scan was cut off for some reason.).I think the contrast is quite telling.

On the one hand, there's a shitload more insight in the class as I would have taught it. On the other, if you were a student looking back over your notes to try to figure out how to do a problem, the notes you'd taken in my class wouldn't do you a whole lot of good -- or rather, they would, but only if you had the patience to wade through a lot of conceptual shit in order to get there.

This brings up two questions:

1. These two teaching styles are clearly addressed towards different ways of thinking about mathematics, and different types of learning goals. (Roughly, we could describe those ways of thinking as "how mathematicians think about math" vs. "how people who are not mathematicians, but are pretty good at routine mathematical tasks, think about math.") Which of these reflects how we should be teaching our kids?

2. Is there, beyond the intrinsic value of each of these teaching styles, a value either to diversity or to consistency of teaching styles? Are students advantaged by having experience with both of these? Or do students who are used to one way of teaching/thinking freeze up when they're exposed to another way?

Briefly, I think we do want to be teaching our kids to think about math the way mathematicians think about math -- the understanding is a lot deeper and is rewarding on its own merits, but I think these ways of thinking also enable you to learn new mathematical concepts (and relearn forgotten concepts) much more easily -- because if you focus on understanding the underlying structure of mathematics, you can intuit the definitions and processes that would make sense in the context of that structure.

Unfortunately, my experience has been that there is an advantage to consistency -- and that students often react with frustration to the confusion introduced by exposure to new ways of thinking about concepts they already (at least partly) understand. I think I'm doing more harm than good by trying to teach mathematics the way I see it: by upending the expectations that kids have developed during years of math classes, I take what was once safe and predictable and render it frustrating and alienating. And I think, ultimately, that it's more important for students to have positive relationships with mathematics and with academics more broadly than it is for them to see it in particular ways, no matter how visionary or appealing those ways of seeing may be.

So I think teaching mathematics in shitty high schools is exactly the wrong place for me.

Wednesday, May 19, 2010

In which a supposed "anti-incumbent bias" is clearly more important than a Puerto Rican general strike.

I am getting so fucking sick of hearing about "anti-incumbent bias" as an explanation for the losses of Blanche Lincoln, Arlen Spector, and Trey Grayson. Not only are all three of these people world-class schmucks who have nothing going for them except their incumbency, but I'm willing to bet that the vast majority of people sitting in Congress at this time next year are exactly the same people who are there now.

The thing is, these fuckheads are so used to the idea that they can win every election no matter what that when their win rate goes below 90%, they take this as a sign of bias against them, rather than a slight decline in the level of bias for them. And the mainstream media just slurps it up.

In other news, while the mainstream media echo chamber has been caught up whining about how the power brokers they've been ponying up to for all these years might not be there anymore, you know what they haven't been talking about? The student strike in Puerto Rico, which has been going on for nearly a month, and which is backed by a general strike of all Puerto Rico's major unions.

Check it out, seriously: a Google News search turns up not one source from the mainstream, non-occupied US media.

Wednesday, April 28, 2010

In which we don't actually believe all students can learn.

Educators love to talk about reducing the achievement gap and about how all students can learn – in other words, about not giving up on students at or near the bottom of the spectrum. And it’s admirable that we say these things, and I think we really believe them, in the sense that, all other things being equal, we think it’s worthwhile to spend time on low-achieving students. Some of us would even go so far as to say that – again, all other things being equal – we’d spend more time with students who are doing poorly than with students who are doing well.

But all other things aren’t equal. Most educators believe that different students respond differently to instruction, and that spending the same amount of time with some students will produce more improvement than with other students. Usually this is blamed more on behavioral factors which lead to less time being spent actually teaching, but the fact is that almost always, the students we believe will respond best to instruction are exactly the ones who are doing well.

It’s not that we don’t think the other kids can learn. We do believe they can learn. But we believe that we’ll have to spend so much time on eliciting the sort of behaviors necessary for learning that it just won’t be worth the effort. So we end up prioritizing the students who are doing pretty well anyway, because we know then we can spend our time teaching.

Some people argue that this is missing a key piece of the equation: although it’s true that you’ll have a stronger direct effect if you focus on the “good kids,” there are strong enough indirect effects of prioritizing the “bad kids” to make it worthwhile. In particular, the bad kids spend all their time fucking up your class for other kids. If you spend the resources to enlist them, even though this probably won’t end up turning them into lawyers, they’ll probably stop fucking everything up. So even though it takes a lot of extra work, the payoff is huge not only in terms of the effect on their learning, but the effect on other people’s learning.

But I’ve recently started hearing about a third approach, which tends to be used especially at really shitty schools. At a school like the one where I just got hired, it’s really difficult to target the bad kids – they’re usually not in school, and there are enough of them that you just can’t do the kind of interventions that you’d need to get them back on track. You need really intensive work with a lot of these kids – probably the equivalent of a full-time worker each, between counselors, social workers, and teachers.

So instead, you target the kids who are pretty bad, but not terrible. Here, the priority goes to students who are failing one or two classes – roughly between the fifth and the twentieth percentile. These are kids who still have some hope for academic success, and who might get there with a little extra help at lunch or after school. By doing this, too, you can isolate the kids you can’t help – you ideally go from having four failing students in a 20-person class to having one, who probably will just stop showing up when ze doesn’t have accomplices anymore.

Beyond that, if you successfully target all the borderline cases, incoming frosh classes will start to see their options differently – and so you’ll get fewer students who fall to the level where you give up on them.

I can’t say I’m really comfortable with this. We really shouldn’t see our choice as being between teaching most of the kids and teaching none of them – especially since a lot of times what we’re doing is ignoring the most vulnerable students (even at a school that’s entirely made up of poor students of color, my impression is that the students we expel or allow to fail are more likely to be homeless, abused, or neglected). But at many schools those really are the only two choices.

Our two favorite phrases, as a profession, are currently “closing the achievement gap” and “all students can learn.” And the thing is, I think we really do believe in these principles. But we believe in them in an abstract sense – where, all other things being equal, we don’t think it’s a waste of time to work with vulnerable, low-achieving students.

But all other things aren’t equal. Targeting those kids is a lot more work. And we need to start asking, “Do you believe you should target low-achieving students from disadvantaged populations even if that means less total learning will take place? Does your belief that all students can learn come with a commitment to make sure all students do learn, even if that means other students don’t learn as much?”

I think most teachers would answer no to both of these questions, and they do, through their actions, all the time.

Monday, April 26, 2010

In which Jesus is a fucking radical.

By the way, my posting volume has been down -- and will likely continue to be so -- because I now have a teaching job, so I've been scrambling to salvage the year for my kids, some of whom have now had three math teachers and two long-term subs.

Let's talk about Jesus, okay? The Sermon on the Mount (or the Plain, depending on whether you trust Matthew or Luke). He says:
If someone strikes you on the right cheek, turn to him the other also. And if someone wants to sue you and take your tunic, let him have your cloak as well. If someone forces you to go one mile, go with him two miles. (Matthew 5:39-41)
Now, I'd always been a little uncomfortable with this. Because the thing is, I'm all down with not fighting back -- that part makes sense to me. But can't you at least block? Isn't some kind of nonviolent resistance okay?

Then I heard new interpretations of these verses that blew my fucking mind.

First, turning the other cheek. Here's what Wikipedia says on the subject:
A literal interpretation of the passages, in which the command refers specifically to a manual strike against the side of a person's face, can be supported by reference to historical and other factors.[1] At the time of Jesus, striking someone deemed to be of a lower class with the back of the hand was used to assert authority and dominance.[2] If the persecuted person "turned the other cheek," the discipliner was faced with a dilemma. The left hand was used for unclean purposes, so a back-hand strike on the opposite cheek would not be performed.[3] The other alternative would be a slap with the open hand as a challenge or to punch the person, but this was seen as a statement of equality. Thus, by turning the other cheek the persecuted was in effect demanding equality.
It goes on to talk about the coat/cloak thing, in the context of Deuteronomy 24:
10 When you make a loan of any kind to your neighbor, do not go into his house to get what he is offering as a pledge. 11 Stay outside and let the man to whom you are making the loan bring the pledge out to you. 12 If the man is poor, do not go to sleep with his pledge in your possession. 13 Return his cloak to him by sunset so that he may sleep in it.
See, if someone sues you and tries to take your tunic, they're not allowed to take your cloak. So by giving it to them, you're putting them in violation of Hebrew law. Furthermore, Shine Thomas points out that if you give him your cloak, you're probably naked -- and your nudity brings shame on the viewer, not on the naked person.

And it turns out that Roman soldiers were allowed to make you carry their stuff for a mile, but no further. So if you carried it for two miles, they were again violating the law.

All of these are a foundation not so much for a tradition of civil disobedience as for one of uncivil obedience. All of them involve allowing (even perhaps facilitating) wrongdoing, but changing the context of that wrongdoing so that the perpetrator feels uncomfortable about it. And there's definitely no civility in it: there's a kind of challenging hostility in the turning of the other cheek that I find really compelling.

Here are the two modern parallels to this kind of behavior that jump into my mind. Neither of them were things I would ever have dreamed of pointing to as Christian examples before this Sunday morning.

One of them is this account of the death of Che Guevara -- particularly the refusal to kneel to be shot, and his comment, "Know this now, you are killing a man." The other is the "Please, Lou, Please" scene from Fight Club -- and, come to think of it, the scene where Edward Norton beats the shit out of himself to blackmail his boss.

What we see here is a very confrontational Jesus -- rather than being a pitiable figure who was willing to suffer because of his unwillingness to use force, we see a figure who urged his followers to use their own suffering as a weapon. The Passion of the Christ image of a Jesus who passively suffered at the hands of his tormentors masks the fact that there are few things more unsettling than someone who, when you hit them, says, "Yeah, hit me again, but this time hit me like you mean it."

I'm also reminded of the reports that people gave of how they were affected by participation in the Milgram experiment and the Stanford Prison Experiment. People consistently talked about how they'd changed for the better when they saw the kind of cruelty they were capable of. They were forced to confront a side of themselves that they hadn't been ready to deal with, and they realized that there was a good chance other people wouldn't stop them from doing terrible things. These realizations forced them to accept greater responsibility for their destructive impulses, and made them less likely to allow those urges to take over in the future.

Notice, also, that all of these were ways of confronting forms of violence that were socially sanctioned: backhanding a slave, wife, or child; taking someone's most urgent necessities in lieu of debt repayment; and conscripting civilian labor for military purposes. All of them were about confronting oppressors with the reality of their injustices, which could otherwise be masked behind the formal sanction for them.

Now I'm just picturing someone losing their house to foreclosure, walking into the bank that now owns their house, and stripping down and handing over their clothes. Fucking brilliant.

Friday, April 16, 2010

In which false economies screw poor kids.

I want to talk a little bit about class sets.

First, a little background: Lots of teachers make absurd amounts of copies. Completely preposterous amounts of paper get distributed to students, who end up throwing it all away or losing it in the sea of mostly-useless papers that their backpacks become. In addition to being counterproductive, this is environmentally unsound and costs schools a shitload of money. So many schools, as a way to counter this, put limits on the number of copies teachers can make, either by giving them accounts on copiers with limited numbers of copies, or by giving them a paper quota and making teachers keep track of their own paper. And some teachers, even when they're not so restricted, feel bad about the paper they're using, and try to cut down themselves on the number of copies they make.

One of the forms this takes is the class set. Since many teachers teach three or four or five sections of the same class, they'll make one set of thirty copies of whatever they would've handed out, and expect kids to use them in class, but then return them at the end of class in a state that allows the next class to use them.

Sometimes, this is done for things like readings -- in which case it makes sense, if we assume that no one is going to re-read these texts after the class ends, and they're simply going to get thrown away anyway, which is often the case. But more often than not, this gets done with things like worksheets, along with the instruction to work on a separate sheet of paper (the same principle is at play when math teachers assign problems out of the book, although on a somewhat longer-term basis).

What gets lost in this is that paper provided by students is also paper. In fact, we end up using more paper this way: we've gone from 150 sheets (one for each student) to 180 (one for each student to write on, plus a class set of the questions). It's actually even worse than this: many teachers know that students benefit, when reviewing, from having the answers and the questions in the same place, so instruct them to copy the questions onto their own sheet, so we now have to have enough paper for two sets of questions (one of them presumably copied in somewhat larger print).

We're also then using class time for the copying of words that are already printed, as well as the extra time the teacher needs to spend making sure to get all the sheets back (as a substitute, this is a huge issue -- teachers are sometimes generous enough to leave a couple of extra copies, but even so, if I lose an average of one in each period, I won't have enough for the last class, and since I don't have copier privileges, it's tough to remedy this) -- this ends up occupying three or four minutes of class time, which sounds trivial until you remember that it's almost ten percent of the class.

So in doing this, we use significantly more resources, all in order to transfer costs from schools to students. And the funny thing is, this always fucking happens in the schools where the students are poorest -- schools with rich students almost universally can afford a few extra copies. We are, on a large scale, transferring the costs of education to poor kids and their parents, and we're calling it "greening."

Thursday, April 15, 2010

In which I write a letter.

Brendan Coughlin
Chair, Nominating Committee
Wesleyan University Board of Trustees

Dear Brendan,

I am writing to tell you that I will not be voting in this year's Alumnae/i Trustee election. None of the candidates can be fairly described to represent me, or any of the thousands of Wesleyan graduates like me.

Of the six Alumni/ae Trustee candidates, five are from the business world. Of the six current trustees who will be returning, three are from business backgrounds -- so, regardless of the outcome of the election, business is guaranteed a majority of alumni trustees.

Outside of business, alumni trustees and candidates represent two professions: medical school professors and directors of nonprofits. It's worth noting, also, that the nonprofits we're talking about -- the Tiger Foundation and the Philanthropic Institute -- are both of the type generally referred to as the Nonprofit Industrial Complex; in other words, they're nonprofits who view themselves as primarily accountable to donors, rather than to the communities in which they work. Here's a text sample from the Tiger Foundation's "Who We Are" page:
Since inception, Tiger Foundation has pursued the dual mission of providing financial support to the top nonprofit organizations serving New York's neediest families, and training active and engaged philanthropists who serve on the foundation's board. Tiger Management was dedicated to maximizing the return on every investor dollar. Similarly, Tiger Foundation is dedicated to investing in nonprofit organizations in the five boroughs of New York City that maximize the social return on every contributed dollar.
I can understand why this is exactly what a Board made up largely of corporate officers and wealthy donors likes to hear -- but as someone whose primary involvement with Wesleyan was as a student rather than a donor, it makes me a little nervous to think our decision-making bodies are made of people who believe their primary responsibility is to donors.

You have to know that this isn't a representative sample of Wesleyan graduates. In fact, Wesleyan's embarrassingly small endowment is constantly being blamed on the fact that this isn't what most Wesleyan graduates look like. We're all going off to become social workers, and teachers, and community and union organizers, instead of going where the money is, the way all these nominees have.

Ultimately, I don't see any reason to vote for three more representatives of business and the nonprofit industrial complex to join a board that's already full of representatives of business and the nonprofit industrial complex. Boards of Trustees are not democratic institutions, and allowing us to choose from a list of pre-screened, pre-vetted candidates doesn't change that. This is a charade, and I'm not participating.

If you'd like some nominees that reflect the rest of the spectrum of Wesleyan graduates, I'm happy to submit a few.

Regards,
Per

Wednesday, April 14, 2010

In which feminists make jokes.

So I think it's fair to say that Sady "Sady fucking Doyle" Doyle went all Rahm Emanuel on this douchebag, who is pissed because he feels men aren't treated fairly by feminists -- basically, because he thinks feminism isn't about women, it's about equality, and therefore men shouldn't feel like they need women's approval to be real feminists. There's a whole argument to be had there about how if women don't like your feminism, it's probably not feminism, and about the epistemic privileging of the oppressed, but for right now, I want to talk about this shit:
Look, I have to tell you: your whole enterprise here, the whole long and short of it, appears to be an edifice designed to give you a platform that paws at discourse while denying the possibility of you ever getting called on anything. I mean the whole apparatus of the place. It’s like this constant recursion of LOLspeak/serious speak/LOLspeak, this Russian dolls style thing you’re so enamored with. It’s just a mechanism to introduce a self-limiting aspect on what you want to say; you want to be heard and to be taken seriously, but you want the out to be able to say that you were just goofing. Well, goof away, it’s the Internet, and it’s your dime, but understand that you are denying intellectual rigor when you do so.
Sady, in her first response, gave some pretty good attention to some of the reasons why she's allowed to make jokes if she wants to (it's a little alarming that this is something women have to defend), but I want to add a couple more reasons.
  1. Because of the humorless-feminist stereotype.
Over the years, I have noticed that sometimes, powerful people make really unpleasant jokes at the expense of women, or black people, or Jewish people, or Mexicans, or queer people. And when they do so, those people and their allies sometimes call them out on it. And almost always, when they do, we're told that the problem isn't in the joke -- no, the problem is that the victims of the joke were just too sensitive to get it, and were too caught up worrying about the fact that this joke was making light of very real hardships and dangers to get that it was funny.

So feminists get characterized, again and again, as humorless, because they're always cracking down on the enjoyment that normal, funny people get out of sexual assault; domestic violence; misogynist, racist, homophobic and transphobic stereotyping; violence against queer people; the grossness of queer people; and the grossness of fat people.

Almost all humor, people in marginalized communities are told, is at someone's expense -- it just happens that this time, it happened to be at your expense. But somehow these jokes never get turned around -- we don't actually end up hearing the jokes at the expense of men, or white people, or straight people. And when we do, without the context of oppression the meaning isn't the same -- I can hear jokes about straight white cis dudes without feeling threatened.

So what ends up happening is that many of the actual conflicts involving feminists (and, to a lesser extent, anti-racists and queers) are between some straight white dude making jokes, and some feminist earnestly telling him what's wrong with those jokes. And so feminism becomes the side of earnest, serious people getting in the way of fun-loving, if sometimes insensitive, dudes.

And that's not a fun side to be on. So it was nice to see, in this case, a real lady feminist getting criticized by a fake dude feminist for being too funny. And it's also a hopeful sign, that we might live in a society where people no longer feel that they have to trade in the funny for the feminism.
  1. Because humor is a really effective way of policing a space.
The two standard options for policing feminist spaces are to simply refuse to publish offensive comments and to be willing to seriously debate the ideas contained therein. Both of those have their merits, but they have their flaws as well.

In particular, refusing to publish them gives assholes an excuse to cry censorship, which can end up creating a conversation about censorship instead of a conversation about them being an asshole. But publishing them and seriously debating them lets them derail, and in the process sends a message to marginalized people that this is a space that cares more about the free speech rights of assholes than about their safety or comfort.

And to be fair, a little of both of those are done in the posts I linked above, but mostly, the guy's subjected to endless mockery. And rightly so -- because his ideas weren't serious criticisms, they were derailments. Humor enables us to send a clear message that particular types of discourse aren't welcome, without giving a real opportunity for people to cry foul -- it's exactly what anti-feminists have used against us for all these years.

And so the final result is, if I was planning on making an misogynist comments over at Tiger Beatdown, you can be pretty damn sure I'm not going to now. Because if I did, Sady Doyle would fucking end me.
 

CC0
To the extent possible under law, the person who associated CC0 with this work has waived all copyright and related or neighboring rights to this work.

However, he believes you have a moral obligation to comply with the restrictions of the Attribution-Noncommercial-Share Alike license.

Look here for clarification.