Some Followup on “A Note to My Fellow White People”

If you were interested, challenged or otherwise engaged by my Note to My Fellow White People, I have come across a bunch of other things recently you will be interested in:

Here is the other video he refers to in the video:

Also a propos is this recent opinion piece in the NYT by Ta-Nehisi Coates.

I was talking in general about white people receiving feedback about race, but several people who commented took it (very reasonably) in the direction of how to have conversations about race in the classroom. In which case I have the following strong book recommendation:

High Schools, Race, and America’s Future: What Students Can Teach Us About Morality, Community, and Diversity

I am cross-posting my review of this book on goodreads.com:

Full disclosure: the author of the book is my dad. The high school featured in the book is the one I both attended and taught at.

THAT SAID.

This is a beautiful book. The author is a (white, Jewish) professor of philosophy at a university. The book chronicles his venture into teaching a class about race and racism at his local racially diverse public high school. It offers a model of what a functioning, productive cross-race conversation about race and racism can look like, in an era where (depressingly) this is still a rarity. It makes a case for the civic value of integrated public education in an era where we seem to be forgetting that education even has a civic purpose.

It belongs broadly to the genre of teaching memoirs, along with books like Holler if You Hear Me. But two related features distinguish it in this genre:

(1) The author is a serious scholar. Unsurprisingly, then, the content of the course he taught features heavily in the book. So this teaching memoir also functions, with no cost to readability, as a scholarly book about race. (As an aside, I am very proud of him on the readability front. It was a real stretch for him to write a book whose style didn’t place a technical burden on the reader, and it took a lot of rewrites, and help from his editor, but he totally pulled it off!)

(2) The genre is characterized by taking students seriously as moral and psychological beings. That’s one of its strengths as a genre as a whole. But this is the first book I’ve read that takes students equally seriously as intellects. The author often writes with plain admiration for his students’ ideas. This may be my favorite feature of all. Developing students as minds is, after all, the point of education. So it strikes me as surprising that it’s so rare for a memoir about the lived experience of teaching to give such loving attention to what those minds produce.

What She Said

Three weeks ago Sue VanHattum and Kate Nowak recommended Bob and Ellen Kaplan’s Math Circle Training Institute. If you are looking for a PD opportunity this summer and you are interested in cultivating students thinking for themselves, I strongly second their recommendation.

This is a weeklong training on the campus of Notre Dame in South Bend, Indiana where you learn how to run a math circle in the spirit of the Kaplans. What that means is that you ask thought-provoking questions and you facilitate students discussing them. Heaven, right? The setup is that in the morning, the Kaplans run a math circle on you, and in the afternoon they bus in local kiddies for you to try out your thought-provoking questions on, and watch others do it, and give and receive feedback. At lunch and at night you hang out with like minded educators talking about math and education. The $850 includes room and board for the whole week.

I did this training in the summer of 2009 and it was a key step on my path to being the educator I am now. In 2007-8 I had come to the realization that my most central, pressing goal as an educator was to empower students to find their own mathematical curiosity, and I started stretching my pedagogical boundaries to find out what it would look and feel like to teach with this as the only goal. But I felt like I was reinventing the wheel. Reading the Kaplans’ book Out of the Labyrinth, I felt like I had found my comrades. Going to the Summer Institute, I felt like I had met them.

For example, Sue and Alex, and my fairy blogfamily Kate and Jesse Johnson. See what I mean?

Tangential to the math PD but also a wonderful benefit was the opportunity to spend a week on the Notre Dame campus. As a Jew I did not go into the experience expecting to be so moved by the shrines and sanctuaries of this Catholic institution, but I was. After my first experience with a labyrinth (the meditative kind), Alex McFerron said to me, “the Catholics really ace those sacred spaces.” True that.

Dispatches from the Learning Lab: Yup, Time Pressure Sucks

Continuing the series I began here and here, about snippets of new-feeling insight about the learning process coming from my new role on the student side of the desk…

This one is funny, because I knew it, I mean I knew it in my bones, from a decade working with students; but yet it’s totally different to learn it from the student side. I’m a little late to the blogosphere with this insight; I’ve been thinking about it since December, because it kind of freaked me out. Even though, like I keep saying, I already knew it.

Learning math under time pressure sucks. It sucks.

It sucks so much that I ACTUALLY STOPPED LIKING MATH for about 5 days in December.

I didn’t know this was possible, and I don’t think anyone who’s ever worked closely with me in a mathematical context (neither my students, colleagues, or teachers) will really believe it. But it’s true. It was utterly, completely unfun. There was too much of it and too little time. It was like stuffing a really delicious meal down your throat too quickly to chew, or running up the Grand Canyon so fast you puke. Beautiful ideas were everywhere around me and I was pushing them in, or pushing past them, so hard I couldn’t enjoy them; instead they turned my stomach, and I had the feeling that the ones I pushed past in a hurry were gone forever, and the ones I shoved in weren’t going to stay down.

I had some independent study projects to work on during winter break, and what was incredible was the way the day after my last final exam, math suddenly became delicious again. Engaging on my own time and on my own terms, that familiar sense of wonder was back instantly. All I had to do was not be required to understand any specific thing by any specific date, and I was a delighted, voracious learner again.

Now part of the significance of this story for me is just the personal challenge: most of the grad students I know are stressed out, and I entered grad school with the intention of not being like them in this respect. I was confident that, having handled adult responsibilities for a decade (including the motherf*cking classroom, thank you), I would be able to engage grad school without allowing it to stress me out too much. So the point of this part of the story is just, “okay Grad Program, I see you, I won’t take you for granted, you are capable of stressing me out if I let you.” And then regroup, figure out how to adjust my approach, and see how the new approach plays out in the spring semester.

But the part of the story I want to highlight is the opposite part, the policy implication. Look, I frickin love math. If you’ve ever read this blog before, you know this. I love it so much that most of my close friends sort of don’t feel that they understand me completely. So if piling on too much of it too quickly, with some big tests bearing down, gets me to dislike math, if only for 5 days, then the last decade of public education policy initiatives – i.e. more math, higher stakes – is nothing if not a recipe for EVERYONE TO HATE IT.

And, not learn it. Instead, disgorge it like a meal they didn’t know was delicious because it was shoved down their throat too fast.

In short. The idea of strict, ambitious, tested benchmarks in math to which all students are subject is crazy. It’s CRAZY. The more required math there is, and the stricter the timeline, the crazier. I mean, I already knew this ish was crazy, I’ve been saying this for years, but in light of my recent experience I’m beside myself. If you actually care about math, if you have ever had the profound pleasure of watching a child or an adult think for herself in a numerical, spatial or otherwise abstract or structural context, you know this but I have to say it: the test pressure is killing the thing you love. Its only function is to murder something beautiful.

If you teach, but especially if you are a school leader, and especially if you are involved in policy, I beg you: defend the space in which students can learn at their own pace. Fight for that space.

Take the Tests, Decisionmakers!

In case any of you missed this at f(t):

A school board member in Orange County, FL had the guts to sit for his state’s high-stakes test, the type of test a lot of decisionmakers are all in such a rush to have students’ futures and teachers’ livelihoods resting on.

Kate is asking her readers to call on NY Governor Cuomo to do the same thing.

This is effing brilliant. I say we take it up a notch. If you live in the US, pick an elected or appointed government official or purveyor of “education reform” who is rushing to rest more and more human futures on the results of a test, and call on them to take the test. I am not trying to be an organizer right now; I suppose it would be smart to make some strategic choices about whom to contact and via what medium (Kate: Cuomo / Twitter), but that’s not my style. I do have some nominations:

Arne Duncan
Bill Gates

Because these folks are operating at the national level, it’s not obvious which test to tell them to take. I want to say all of them, but maybe that’s just cuz I’m pissed off. Abnegating my role as organizer I’ll let you call it. Here’s one that’s easy:

NYC Mayor Michael Bloomberg

Take the NY Regents, mayor, and make the results public. I don’t care how you do, but I want you to know what you’re talking about when you make policy, and I want you to be willing to be scrutinized as you are insisting that students, teachers, and schools be.

*****

Here’s what I love about this.

The last few years have felt to me like American schools are riding on top of a malfunctioning robot that is careening inexorably toward more and more insane school policy. The robot is being driven by an inflated sense of the importance and automatic legitimacy of numerical data. For a decade, a chorus of voices (many of people directly involved in the practice of education) have been crying out that this is madness,^[1] but the robot has only sped up.

During the same decade, and especially in the last few years before this fall, the language used by national political figures advocating for justice and progressive change has felt more and more tepid to me. The clearest instance of this is the way that Democrats and even some progressive advocacy groups have latched onto the phrase “middle class.” Y’all are giving up the fight, guys. If you feel you are not allowed to advocate for working people or (God forbid) poor people, that in order to be a legitimate public interest your cause has to be sanded down and shellacked with a patina of educated white-collarness, then the folks who are only looking out for the interests of rich people have already prevailed.

My mood in relation to this language was not unlike my mood when beholding current debates about education: the feeling that justice and sanity are speaking, but being ignored; and they cannot find the language that will make the powerful listen.

So, imagine my thrill when this fall a new language took over: the 99%. Whatever you think of the Occupy Wall Street movement, you have to give it credit for a complete reshaping of the vocabulary available to discuss economic inequality. It seemed like everywhere I went this fall, somebody was talking about either “the 99%” or “the 1%” or both. This is just what I was missing: a way of talking about economic justice that feels powerful and relevant. That interrupts the inexorable slide into tepid lameness that characterized the national discourse till now.

</Interlude>

What I’m getting at here is that we need ideas to interrupt the inexorable careening of the malfunctioning education reform robot, and Kate may just have found one. In the words of Rick Roach, the Orange County school board member who took the Florida tests,

“I can’t escape the conclusion that decisions about the FCAT in particular and standardized tests in general are being made by individuals who lack perspective and aren’t really accountable.”

You know I don’t love the word “accountable,” the way it is thrown around these days. But these are the folks who do love it. So if they love it so much, let’s make them accountable. What I really mean is this: the public defamation of public schools and teachers, and the concomitant policy initiatives, have been based on numerical data from tests whose contents are public, but this is the only public thing about them. Most critically, their development is opaque, the way the data is used is opaque, and the way that decisions get made about how the data is used is therefore not subject to legitimate public scrutiny, or even, in all probability, based on any real understanding of the tests. The decisionmakers don’t even know what taking the tests is like!

So, decisionmakers, take the tests! You are willing to force students to take them, to scrutinize the results, and to make important decisions about students, teachers, and schools on their basis. Finding out what you’re actually forcing on them, and opening yourself up to the same scrutiny, is the least you could do.

^[1]One of these voices was the television show The Wire, which aired well before the latest and most intense phase of this insanity, but which in spite of this develops a beautifully articulated critique of numbers-driven accountability in municipal institutions. Schools are included, but the brunt of the criticism is aimed at the police department and the city government. However, the essential problem is the same in all cases: when you demand numbers from people who are supposed to be doing a job requiring creative problem-solving and perseverance, you divert their attention from their actual work to the problem of giving you what you’re asking for. If you’ve never seen the show, you can get the whole thing from Netflix. You won’t be sorry. If you think I shouldn’t be citing a fictional television show regarding public policy, let me quote Mathnet: the names are made up but the problems are real. Not convinced? Read this.

Wasting for Stuporman

I dragged myself to Waiting for Superman last night.

What a confused movie.

Have you ever been on the subway with a crazy person? I am from Boston, where I actually can’t remember this happening to me one time, although we do have crazy people; but it happens a lot in New York. You’ll be going from here to there and somebody on the subway car will just start discoursing, usually to no one in particular but as though they’re having a normal conversation. Sometimes angrily, which is always disconcerting to be around because if you’re simultaneously angry and totally disconnected from reality, who knows what you’ll do next. Often enough, though, it’ll be totally harmless. (Somehow, the time that the man next to me explained “when I cock my fist back, that’s potential energy; and when I throw it toward your face, that’s kinetic energy” managed to fit into the totally-harmless category. He was jovially illustrating a point. You could just tell.)

One of the most striking things about the discourse, though, whether harmless or angry, is that the person is usually speaking with conviction, but not making any sense. This is what it felt like to me watching Waiting for Superman.

Let me try to summarize this movie for you. SPOILER of sorts.

Geoffrey Canada (Harlem Children’s Zone) loved Superman when he was a kid. Davis Guggenheim (the filmmaker) decided to send his kids to private school. They have really cute kids in Boyle Heights, Harlem, the Bronx, and DC. Academic achievement in the US has not improved since 1971. In 2002 there was a moment when it looked like FINALLY THE SCHOOLS WOULD BE FIXED!!! because a republican (Bush) and a democrat (Teddy Kennedy) collaborated on a piece of legislation (NCLB). But it’s 8 years later and we still suck. People used to think that failing schools came from failing neighborhoods but now we realize it’s the OTHER WAY AROUND!! Our schools totally suck and that’s why our neighborhoods have crime and drugs. There are lots and lots of shitty teachers. Randi Weingarten is some kind of mediocrity nazi rallying the national teacher corps into a frenzy of mediocrity. The national Democratic party is basically owned by the teachers’ unions. Teacher tenure used to be useful, back when administrators were arbitrary and exploitative, but now all it does is keep useless, worthless humans in front of children. Even if you have a really kick-*ss teacher, you can’t pay them more money, even if you want to, because they already have a contract that says what you pay them. But then from out of the sky comes MICHELLE RHEE!! The public education bureaucracy prevents teachers from giving students the proper infusion of learning fluid. Michelle had a plan to save us all. Too bad the mediocrity nazis stopped her. US kids suck at math and think they rock, as we learn from Green Day. Tracking is evil because even though it’s supposed to be based on test scores, sometimes kids get tracked based on behavior. But actually, 50 years ago tracking was awesome because it reproduced the class structure, which was awesome. But the world has changed. Suburban schools have all the same problems as urban schools but the kids are higher-skilled so the grades are inflated. Urban schools have problems suburban schools don’t have to deal with. It’s really hard to be a teacher. Davis once made a movie about that. A great teacher is a work of art. Because all great teachers work for charter schools, the cute kids’ parents want them to go to KIPP, SEED and Harlem Success Academy, and basically they’ll DIE if they don’t get in. Bill [Gates] knows education.

There, that about covers it.

Then, as the credits roll, the film acts like this incoherent pastiche has added up to both a clear recipe for action and a movement. We get a summary of what Davis Guggenheim apparently thinks are the self-evident conclusions of the film –

The problem is COMPLEX
But the steps are SIMPLE
It starts with GREAT TEACHERS
More time in school
Getting the bureaucracy out of the way [I’m not remembering this word-for-word but this is the idea]
World-class standards
Real accountability

and a “change starts with you” message. Text “POSSIBLE” to such and such a number, we’re told.

I felt like the crazy person from the subway had just shown up on the corner wearing a PIRG t-shirt and holding a clipboard, trying to get me to sign a petition and donate money. And he was totally sure I was going to sign. It was really weird.

* * * * *

Let me be a little less coy about what I have to say about the content of this film.

Davis – I’m glad you got the draft in on time. You’re showing a lot of passion, but we’ve got to work on the clarity of your thesis and your evidentiary structure. In the meantime, you need to engage with some key sources of information you left out entirely:

1) Good teaching that is happening inside public schools.

You depict failing public schools, portrayed as the norm, and a handful of highly successful charter schools. This narrative makes successful public schools invisible. Have you never encountered one?

I have. Where I went to school, and where I learned how to teach. Unionized workforce and everything. And some of the best teaching you will see anywhere.

2) Teachers getting better.

It’s a shame that you left this image out of your narrative because this is the whole secret to successful education.

Where did you think great teachers come from? That they spring fully formed from the head of Zeus? Just about everybody who’s an accomplished teacher used to be an ineffective teacher, and as the maker of a documentary about first year teachers, I’m totally confused that you don’t seem to understand this. If you want to talk about great teachers, but don’t have anything to say about the conditions under which teachers become great, you are at a different stadium than where the game is happening.

(Hint, by the way: in order to become great, teachers need to make and then learn from their mistakes. What kind of environment fosters making and learning from your mistakes? Fear that you will lose your job over your kids’ test scores? Or maybe transparent, non-defensive collegiality? Okay, good job on that one, now the followup: what kind of education policies are going to create the environment that fosters growth?)

Conversely – where do you think incompetent burnouts come from? The League of Committedly Useless Humans? Do you think anybody gets up at 5:45 every day and gets in front of kids and wants to suck? I know hundreds of teachers, and I don’t know ONE who is honestly okay with doing a bad job. Be that as it may, teaching is actually very hard, a fact to which you pay lip-service, and that means that in a difficult situation and with an absence of support, it can be a pretty crushing experience. (I will go on record with this: teaching is way, way harder than math. Galois theory is a walk in the park next to figuring out how to alter your planning, presence, discussion facilitation, assessment, etc. to get better results for your kids. No contest.) Lots of folks leave the profession; plenty more stay on board and give up. If you want to decrease the amount of incompetence in front of kids, and you don’t have anything to say about how to support teachers in growing, then again, you’re at the wrong stadium.

* * * * *

A lot of the above has already been pointed out by others. Let me direct you to one excellent critique among many –

Ben Allen belongs to a category of person I think I pretty much always get along with: he’s a professional mathematician (a complex systems theorist) who spent time (3 years) teaching math in urban public school. So, when he talks about Waiting for Superman, I’m listening.

Ben calls attention to the absurd scene in which what education is “supposed to be” is depicted in a cartoon as a teacher opening up students’ heads and pouring in a liquid (“knowledge”), before this process gets interrupted by public education’s bureaucratic constraints. I’ll add that I used to use more or less this exact metaphor as a send-up of how people who don’t understand education imagine it works. Learning as some kind of IV drip.

* * * * *

Okay, I thought I was done but I have one more thing to say.

What’s with the creepy appropriation of civil rights language?

Creating Balance III / Miscellany

The Creating Balance in an Unjust World conference is back! I went a year and a half ago and it was awesome. Math education and social justice, what more could you want?

If you’re in NYC and you’re around this weekend, it’s happening right now! I’m going to try to make it to Session 3 this afternoon. It’s at Long Island University, corner of Flatbush and DeKalb in Brooklyn, right off the DeKalb stop on the Q train. I heard from one of the organizers that you can show up and register at the conference. I’m not 100% sure how that works given that it’s already begun, but I am sure you can still go.

* * * * *

I’ve just had a very intense week.

I want to get some thoughts down. I’m going to try very hard to resist my natural inclinations to a) try to work them into an overall narrative, and b) take forever doing it. Let’s see how I do.

(Ed. note: apparently not very well.)

I. Last spring I wrote

20*20 is 400; how does taking away 2 from one of the factors and 3 from the other affect the product? We get kids thinking hard about this and it would support the most contrivance-free explanation for why (neg)(neg)=(pos) that I have ever seen.

Without going into contextual details, let me just say that if you try to use this to actually develop the multiplication rules in a 1-hour lesson, all that will happen is that you will be dragging kids through the biggest, clunkiest, hardest-to-swallow, easiest-to-lose-the-forest-for-the-trees, totally-mathematically-correct-but-come-now model for signed number multiplication that you have ever seen (and this includes the hot and cold cubes). This idea makes sense for building intuition about signed numbers slowly, before they’re an actual object of study. It does not make any sense at all for teaching a one-off lesson explicitly about them. (Yes, the hard way. I totally knew this five months ago – what was I thinking?)

II. I gave a workshop Wednesday night, for about 35 experienced teachers, entitled “Why Linear Algebra Is Awesome.” The idea was to reinterpret the Fibonacci recurrence as a linear transformation and use linear algebra to get a closed form for the Fibonacci numbers. Again, without going into details –

I gave a problem set to make participants notice that the transformation we were working with was linear. I used those PCMI-style tricks like giving two problems in a row that have the same answer for a mathematically significant reason. This worked totally well. Here is the problem set:

View this document on Scribd

Oops I guess I failed to avoid going into details. Anyway, the question was about how to follow this up. I went over 1-4 with everyone (actually, I had individual participants come up to the front for #3 and 4) at which point the only thing I really needed out of this – the linearity of the transformation – had been noticed by pretty much the whole room. One participant had gotten to #9 where you prove it, and I had her go over her proof.

I think this was valueless for the group as a whole. The proof was just a straight computation. You kind of have to do it yourself to feel it at all. It was such a striking difference watching people work on the problem set and have all these lightbulbs go off, vs. listening to somebody prove the thing they’d noticed. It almost seemed like people didn’t see the connection between what they’d noticed and what just got proved. I told them to take 5 minutes and discuss this connection with their table, but I got the feeling that this instruction was actually further disorienting for some participants.

I’m trying to put the experience into language so I get the lesson from it.

It’s like, there was something uninspired and disconnected about watching somebody formally prove the result, and then afterward trying to find the connection between the proof and the observation. Now that I write this down, clearly that was backward. If I wanted the proof (which was really just a boring calculation) to mean anything, especially if I wanted it to be at all engaging to watch somebody else do the proof, we needed to be in suspense about whether the result was true; either because we legitimately weren’t sure, or because we were pretty sure but a lot was riding on it.

This is adding up to: next time I do it, feel no need to prove the linearity. Let them observe it from the problem set and articulate it, but if there is no sense of uncertainty about it, this is enough. Later in the workshop, when we use it to derive a closed form for the Fibonacci numbers, now a lot is riding on it. If it feels right, we could take that moment to make sure it’s true.

III. As I work on my teacher class, something that’s impressing itself upon me for the first time is that definitions are just as important as proofs. What I mean by this is two things:

a) It makes sense to put a real lot of thought into motivating a course’s key definitions,

and maybe even more importantly,

b) Students of math need practice in creating definitions. You know I think that creating proofs is an underdeveloped skill for most students of math; it strikes me that creating definitions might be even more underdeveloped.

Definitions are one of the most overtly creative products of mathematical work, but they also solve problems. Not in quite the same sense that theorems do – they don’t answer precisely stated questions. But they answer an important question nonetheless – what do we really mean? And to really test a definition, you have to try to prove theorems with it. If it helps you prove theorems, and if the picture that emerges when you prove them matches the image you had when you started trying to make the definition, then it is a “good” definition. (This got clear for me by reading Stephen Maurer’s totally entertaining 1980 article The King Chicken Theorems.)

Anyway this adds up to an activity to put students through that I’ve never explicitly thought about before, but now find myself building up to with my teacher class:

a) Pose a definitional problem. Do a lot of work to make the class understand that we have an important idea at hand for which we lack a good definition.

b) Make them try to create a definition.

c) If they come up with something at all workable, have them try to use it to prove something they already believe true. I’ve often talked in the past about how trying to prove something you already believe true is very difficult, and that will be a problem here. However, unlike in the cases I had in mind (e.g. a typical Geometry “proof exercise”), this situation has the necessary element of suspense: does our definition work?

If they don’t come up with something workable, maybe give them a not entirely precise definition to try out.

d) Refine the definition based on the experience trying to use it to prove something.

I’ll let you know how it goes. I’m excited about it because it mirrors the process that advances mathematics as a discipline. But I expect to have a much better sense of its usefulness once I’ve given it an honest whirl.