Wednesday, April 9, 2014

A Very Special Episode of Yarmulke Tales

I've included a lot of obscenities in this post, because that's how it happened.

The subway doors opened at 42nd Street and in walks this guy with a Department of Environmental Conservation t-shirt and lots of chains, lots of keys rattling around his pants. I'm sitting, he ends up standing right in front of me, but only for a second. He takes a look down at me and starts pushing people out of his way.

"Excuse me," he says, "I don't want to stand next to a Jew."

At this point I'm thinking, hey, that right there is some extra-ordinarily polite Jew hating.

Our t-shirt man clarifies: "I hate Jews. They fucking crucified God. Christ killers! Christ killers, I do not stand next to a Jew. No. Fuck you, fuck Jews. Heil Hitler! See you in Heaven, yeah, fuck you Jew. See you in Hell. I'll stick a cross up your ass. You're not a minority, you're the majority."

I mean dude's pointing at me while he's shouting at me from half-way across the car. I start chuckling which in retrospect isn't the best way to assure that crosses and my ass keep their distance.

"I should cut your heart out. I should fucking cut your heart out. I won't, I won't because I'm a Christian. I hope the Arabs kill you. Heil Hitler! Heil Hitler! etc."

When I changed jobs this school year I also changed commutes. I went from walking to work through the lovely Jewish/Dominican ghettos in which I reside to riding the subway for an hour everyday. And by my count this is like the fourth, or maybe fifth time that something like this has happened on the subway this year. There was the guy who threw a penny at me. There was that guy who just started yelling "Shalom" at me. And the lady who screamed "HE'S A JEW! HE'S A JEW! HE'S GOING TO KILL YOU!" while I was riding the C. (I was not.)

You might be thinking, hey, I didn't know that anti-Semitism is a problem in America. There's a good reason why this sort of thing isn't on your radar: it's really, really great to be a Jew in America.


Being a Jew in this country is a remarkably sweet deal, basically because we get to be well-educated white people. We weren't white when we got here, of course. It took a while to get things going, a story you can read about in "How Did Jews Become White Folks?"
As with most chicken-and-egg problems, it is hard to know which came first. Did Jews and other Euro-ethnics become white because they became middle-class? That is, did money whiten? Or did being incorporated into an expanded version of whiteness open up the economic doors to middle-class status? Clearly, both tendencies were at work.
These days, in this country, Jew is just another sort of white, and anti-Semitism has receded because you don't mess with white folks. After crazy dude got off the subway the lady sitting next to me reassured me that the guy was just some whack-job. But what makes him crazy, instead of hateful, evil? What makes him nuts is going after me, an upstanding member of the dominant class.

Jews are safe, rich even. Anti-Semitism is not part of the regular life of a Jew in this country, you don't have to gird yourself against it the way you do if you're black or brown...

...unless you go around wearing a yarmulke. Because then? Then all the whack-jobs come out. People stop you in the streets start telling you about their churches. They shout at you, threaten you bodily. They call you names, and who cares if they're crazy because crazy stabs just the same.

I mention all of this not to reinforce the notion of Jews as victims, because we're not worth your concern in America.* But I hope I'm not flattering myself in thinking that my experiences are instructive. I mean, for one you've got the sheer power of whiteness to admire. There are Jews walking around New York really everywhere, and they basically experience none of this stuff because they don't wear a yarmulke and can just slip in and disappear from view. There's all this hate out there for Jewish folks, but whiteness guards you against it in this country pretty much all the time. That's potent stuff.

* OK, one quick plug for anti-Semitism. Jews were knocked around Europe for a couple millenia, and the Holocaust was like a year ago. You think it just went away? Come on.

But the yarmulke reveals all truths, and it's a reminder that hate or prejudice doesn't have to be visible to exist. Check out Bonilla-Silva who showed that white students know how to express racially appropriate opinions on surveys, but revealed their prejudices more fully during subsequent interviews. And I expect that it's the same with Jews and other groups. Circumstance might drive expressions of prejudice away from public view, but it doesn't take much to reveal them.*

* As long as I've got your attention: "Negroes Are Anti-Semitic Because They're Anti-White." Food for thought.

This is only somewhat related, but a third grade student was singing a song in class today, and I asked him what he was singing. "I learned it in church," he said. He smiled. "You wouldn't know it because you don't go to church because you're..." and he runs up to me and actually starts rubbing me yarmulke with his palm.

I don't know how to wrap this up, but anyway it's besides the point. I've got to get moving, there's cleaning to be done, Passover starts on Monday and I've got to get ready.

Open Thread: The Changing Demographics of Teaching


It's conference time, which means that if you're connected to teacher-twitter you're going to see a lot of statistics being tossed around. It's always best to deal with the actual data and reports when trying to figure out what to believe. (For instance, last year I caught Treisman getting a little slippery with his slides.)

Are we not math teachers? Let's dig through some data, and shout out if you find something interesting or noteworthy. Make a graph and I'll toss it into the post. Ask a question, and we'll see if we can find the answer in some of the reports.

And here are links to some reports and data to think about.

Fast Facts about Trends in the Profession
NCEI: Profile of Teachers in the US
The Condition of Education: 2011

I'll start: it seems to me that we have fewer young teachers than we did in 2008. It looks as if the youth and inexperience of the profession peaked in 2008 and has been aging (slightly) since. Truth?

Friday, April 4, 2014

The Sticky, The Woodsicle, The Leg, and The Dogoala


Let's not bury the lede: yes, those are chocolate-filled blueberries and cheese-filled raspberries. A kid brought them in, we ate them, and they're gross.

OK but why? That's a slightly longer story, and I recommend that you start it over at Danielson's place. Basically, I gave kids an object to build a measurement system around. They named it, created a "made-up-of" (e.g. an inch) and a "made-out-of" unit (e.g. a yard). They made a measuring tape, they measured stuff with their units. 

Then we made square units to measure area with, and then cubic units to measure volume. Along the way a ton of good math happened -- fractions, scaling area, units, multiplication, measurement, volume concepts -- and a good time was definitely had by all.










Important questions for us were:
  • How should we make a helpful tape measure?
  • What's the best way to create a unit of area?
  • How come so many of the square small units fit into the square major units?
  • Ditto with cubes.
Important observations for me:
  • There was a strong desire to measure area in terms of the physical objects that were their measures of length.
  • Pretty much everyone had a moment while they were making a square or cubic unit where they went "Wait this is totally way too big." 
  • The kids couldn't keep "square" and "cubic" straight. That's a distinction they don't really make in their regular language, and I've seen the same thing with older kids calling a sphere a circle.
  • Measurement is simply a great context for fraction work.

Monday, March 31, 2014

Fundamentally Optimistic, Fiercely Critical

Reading much of the popular contemporary literature on race and racism written by men in this society, I discovered repeated insistence that racism will never end. The bleak future prophesied in those works stands in sharp contrast to the more hopeful vision offered in progressive feminist writing on the issue of race and racism. This writing is fundamentally optimistic even as it is courageously and fiercely critical precisely because it emerges from concrete struggles on the part of diverse groups of women to work together for a common cause, forging a politics of solidarity. 
[Source: "Killing Rage", bell hooks]

The Need For Non-Euclidean Geometry

I have argued against using whimsy to introduce complex numbers. You know what I mean by whimsy: "No square roots of negative? Let's invent them!" If you don't, go check out John and Betty.

One counter-argument, voiced in the comments and on twitter by MathCurmudgeon, is the Argument From Vi:
Historically, this is just not the way complex numbers were invented. They were invented out of need, in particular a need for real solutions to cubic equations.

But, no matter, maybe this sort of whimsical creation is just a regular practice of math, one that we could reasonably expect to resonate with our students. But where else is this sort of casual invention at play in the history of math? James Cleveland tentatively suggests that whimsy was responsible for the discovery of non-Euclidean Geometries.

But check out this 1824  letter from Prof. Gauss to a Taurinus who sent our cranky mathematician some of his geometric work:
"In regard to your attempt, I have nothing (or not much) to say except that it is incomplete. It is true that your demonstration of the proof that the sum of the three angles of a plane triangle cannot be greater than 180 degrees is somewhat lacking in geometrical rigor. But that in itself can easily be remedied, and there is no doubt that the impossibility can be proved most rigorously. But the situation is quite different in the second part, that the sum of the angles cannot be less than 180 degrees; this is the critical point, the reef on which all the wrecks occur. I imagine that this problem has not engaged you very long. I have pondered it for over thirty years, and I do not believe that anyone can have given more thought to this second part than I, though I have never published anything on it."

And now Lobachevsky:

"The fruitlessness of the attempts made since Euclid's time...aroused in me the suspicion that the truth...was not contained in the data themselves; that to establish it the aid of experiment would be needed, for example, of astronomical observations, as in the case of other laws of nature..."
Euclid's Postulates had been explicit for ages, and anyone could have just casually wondered what the world would look like if the fifth was false. That would be in the true spirit of mathematical whimsy -- "What if Euclid's Fifth Postulate was false?" -- but that's not what happened.

Instead, the existence of non-Euclidean geometries emerged from the need to explain why Euclid's parallel postulate couldn't be derived from the other four. Non-Euclidean geometries were posited out of the need to explain the failure of centuries of effort.

[Source: Euclidean and Non-Euclidean Geometries, Marvin Jay Greenberg]

Sunday, March 30, 2014

Betty and John's Bogus Journey



[See: The Book of John and Betty]

"Wait, what?" Betty said. "Just make another number up? Seriously?"

"Just make another number up! Make another number up!" John was hopping in place now, giggling while he chanted.

"What does that even mean?" Betty said. "I mean, I guess you can do whatever you want in math, sure, but why would we make up an answer to an impossible question?"

"Curiosity!" John said.

"Curiosity? What sort of curiosity are we talking about here? You tried squaring 1 and -1 and you didn't get -1. Great. That's proves it: my question had no answer. It's a great argument, simple and beautiful, so let's move on."

"Sometimes in math we just need to take a chance, Betty. Maybe for once in your life could you learn to take a chance?" John's eyes narrowed for a moment, but just for a moment and his smile returned. "We're having fun, aren't we!"

"Fine then, let's make up another number," Betty said, pacing away from John. "But while we're at it, I've got some other numbers to invent. I mean, you can't divide by zero, right? Let's make up a number for that. Let's invent a number that stays the same when you add five to it, and another number that's bigger than itself. Let's just throw new numbers at every impossibility in mathematics and call it a day."

"Oh, come off it, you big stickler," John said, tossing his yellow hair to the side. "You're completely ruining our afternoon, just like you ruin everything."

"Well why don't we invent a number to save our relationship, John, since that's your solution for everything!"

And suddenly trumpets sounded and the Heavens opened and the Lord Math Teacher descended upon the White Room where John and Betty fought. And a chalkboard appeared as well as chalk and John and Betty were verily impressed.

And the Lord Math Teacher spoke upon them, saying: "John, Betty, you are both loyal servants, and I wish to praise you for your hard work and grit. However, there indeed exists a difference between these numbers you wish to invent, Betty, and that which John has invented. Know it: John's number will lead to no further contradictions, while your numbers lead to contradictions, which is basically a no-go, for contradictions are impure in the eyes of the Lord."

"Lord Math Teacher? Lord?" Betty waved in the Lord's direction. "Excuse me? I have a question?"

"Umm, yes Betty."

"How do we know that inventing a square root of -1 won't lead to contradictions?"

"An excellent question, my daughter!" Lord Math Teacher replied. "Yes, and unfortunately proofs of non-contradiction are sort of dicey but I swear upon the heavens that Model Theory has some of the answers. I am the Lord Math Teacher, and I hope that answered your question."

And then the heavenly bell rang and the Lord departed.

And this answered all of Betty's questions and she was entirely satisfied with John and complex numbers for the rest of her days, verily.

"It's More Important To Defend Stupid Then To Correct It."

It’s pathetic, and it’s why the internet is such a broken, stupid, aggravating place. It’s why nothing ever changes. Because nobody who has any clout, visibility, or stature is willing to risk their position at the party. Because it’s more important to defend stupid then to correct it. But there’s no reform possible; if any of them find this post, they will ask the crowd, “should we take this criticism seriously, crowd?” and the crowd will soothingly reassure them. It’s all very elegant. And it’s exactly these people who will complain the most about the stupidity and the brokenness. They create the conditions they say they hate, and they live in them, and they deserve to.
This is Freddie deBoer explaining why he left a comment calling a paragraph "monumentally stupid" and why he hates calls for "being nice" on the internet. Temperamentally, I fall into the "why not be nice?" camp, but it's disturbing to think of that habit as a norm whose existence serves to protect my status on the internet.

Then again, there's probably a difference between people who get paid by publications to write things on the internet and some nobody teacher trying to think through his teaching life with friends. I'll stick to being nice until I grow up.

(By the way? That back and forth between Chait and Coates is great.)