More on Mumford

(Totally accidental pun, I promise. The man’s a disgusting sleaze, but he’s not stupid.)

So for some reason, the Clarence Mumford story broke this week. Odd, that.

A sample, just from my twitter feed:

Robert Pondiscio: “Cheating on teacher certification tests? Seriously?? Not exactly the highest bar to clear.”

Eduwonk: “The real scandal is the low-level of the Praxis test and why it continues to be used at all. The Praxis II is different, but the basic Praxis is much too low a bar given what we expect of teachers.”

Sarah Almy, Director of teacher quality at Education Trust: ““These are pretty basic tests….The fact that there were folks who felt like they needed to bring somebody else in in order to meet a very basic level of content knowledge is disturbing, in particular for the kids those teachers are going to wind up teaching.”

Walter Russell Mead: “Massive cheating scandal on teacher certification tests. Worse: tests are pathetically easy, only idiots could flunk.”

Here are the names of the people thus far indicted:

• Cedrick Wilson, ex-NFL player, paid someone to take his test. (Come on, aren’t you thinking it probably wasn’t the first time?)
• Shantell Larry Shaw: A biology teacher who took the biology certification test several times for other teachers, often just using their ids because “she looked like the teacher”.
• Carlo McClelland, of Meridian High School; reports suggest he paid someone to take the test.
• Jeryl Shaw Shantell Larry’s husband, paid for taking the test. I can’t find a picture, but Jeryl? Married to a black woman? Odds?
• Darcel Gardner paid someone to take the biology praxis test–during the same period Shantell Shaw was taking the biology tests.
• Then there’s ringmaster Clarence Mumford and his son.

Notice all these people are black. Which is what I predicted back in July, when this story first broke. Some of the other names are Jadice Moore, Felippia Kellogg (somehow, this Fox news story couldn’t find a picture of her), Dante Dowers, Jacklyn McKinnie. (A primary tester was John Bowen; I haven’t been able to find a picture of him, oddly, Fox News couldn’t find a picture of him, either.) If I do some bad ol’ stereotyping based solely on those names, I’d advise gamblers to bet on them being black, too.

I am pleased to be wrong about one thing—I thought it likely the testers who could easily pass the test would be white, but it appears that most of them are black, as well. Notice also that the Fox News story and many others make it clear that many of the people paying for the tests were already teachers, and that some of the tests were Praxis II. I’d written about that, too.

If you’re wondering why I am pretty sure that most, if not all, of the teachers paying for testers are black, here are some helpful graphics:

And yet, no one save little old me is even mentioning the race of the people involved, as if it’s this totally random factor, like you could find white teachers desperately paying thousands of dollars to pass these tests.

Robert Pondiscio, WRM, and Andy Rotherham and the many other people sneering about the people who need to pay someone else to pass the test, be very specific: Only 40% of African Americans can pass the Praxis I the first time. The other 60%? That’s who you are calling idiots.
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Let’s be clear what I am not saying. I am not excusing the fraud. I am not hinting that African Americans are incapable of passing the tests (this fraud ring shows clearly that they are not).

And since I’m prone to prolixity, I will bullet my points.

I am saying that reformers are:

• hammering constantly on the need for “higher standards”,
• sneering at the low standards on teacher credential tests,
• scoffing at grossly distorted stats suggesting that all teachers, regardless of content area, have low SAT scores,
• declaring that the only way to “restore credibility and professionalism to teaching” is to pull teachers from the top third of college graduates, ignoring the fact that high school content teachers are already drawn from the top half, as well as the fact that there’s no real need for elementary school teachers to be rocket scientists

And while they rant on endlessly on these talking points, they are ignoring the following unpleasantness:

• the low cut score on the basic content knowledge tests are put in place specifically to ensure that some small number of African American and Hispanic teachers will pass. The white averages are a full standard deviation higher; a huge boost to the cut scores in most credentialing tests wouldn’t bother the bulk of all teachers (white females, remember) in the slightest.
• research has turned up very close to empty in proving that teacher content knowledge has any relationship to student achievement. (Cite to research in my earlier article).
• research consistently shows that teacher race has a distressing relationship to student achievement–specifically, more than one study shows a positive outcome when black teachers teach black students. (again, cite in earlier article)
• Raising the cut scores will decimate the black and Hispanic teaching population.
• Many states dramatically increased the difficulty in elementary school credentialing tests after NCLB, yet research has not shown these new teachers to be far superior to the teachers who just passed the much easier (or non-existent) earlier tests. There hasn’t been research done specifically on this point. Hint. Oh, and by the way–those cut score boosts have already dramatically reduced the URM teaching population.

So reformers, when you call for higher content standards, when you say that teachers who can’t pass the test are idiots who should never be allowed in a classroom, you are talking about black and Hispanic teachers. When you demand that we need far more rigorous demonstrated content knowledge for teachers, you are merely making calls for changes that will decimate the already reduced URM teacher population.

And you are doing this with next to no evidence that your demanded changes will impact student achievement, merely on your own prejudice that smarter teachers would make better teachers.

Maybe you’re right. Maybe there’s a perfect research paper out there waiting to be written that will winkle out the lurking variables to prove that yes, we need smarter teachers and yes, it’s okay to annihilate the black and Hispanic teaching population in a good cause. Fine. Go find it.

Or maybe you just want to be snobby elites who don’t personally know anyone who scored below 600 on any section of the SAT, and think your own personal prejudices should substitute for education policy.

Whatever. Just learn and accept what you’re doing. You are calling for changes that will further homogenize an already white career category, closing off a major career option to over half of all blacks and Hispanics, for what is thus far no better reason than you think teachers should be smarter.

Got it? Own it. Or shut the hell up about it.

The Parental “Diversity” Dilemma

Ah, the eduformers have discovered the progressive charter:

Fueled by a confluence of interests among urban parents, progressive educators, and school reform refugees, a small but growing handful of diverse charter schools like Capital City has sprouted up in big cities over the past decade…These schools attract children of city workers, project residents, New York Times reporters, and government officials, and simultaneously attempt to address the weaknesses of “no-excuses” charter schools, progressive education, and school segregation: “Usually in the places that are all about accountability it doesn’t feel like there is a ton of learning going on as the primary outcome,” says Josh Densen, a former KIPP teacher who is set to open Bricolage Academy next year. “In schools where it’s all about learning, discovery, and projects and teamwork, there seems to me to be an absence of or a reluctance to have any kind of accountability.”

Russo, who’s a pretty even-handed education reporter, touches delicately and indirectly on the cause for the attention: progressive, “diverse” charters spring up in “diverse” environments precisely because the environments are diverse.

Look at the history of most progressive charters and you’ll find they are initiated by white people who fit into one or more of the following categories:

• Unnerved by the high percentage of low-achieving, low-income kids at their neighborhood school.
• Unwilling to risk the lottery system for the good schools in their district.
• Unable to afford private school, or a house in a homogenous suburb.
• Unsure their kids are going to be able to compete with the top kids in their neighborhood school (particularly in high school)
• Unhappy with the public school’s treatment of their idiosyncratic little snowflake.

These are people who would move to homogeneous environments, but can’t.

So a bunch of well-off but not super-rich white folks* who don’t want to or can’t move and don’t want to or can’t pay for private school live in a school district in which low-income black/Hispanic kids must be a part of their kids’ school environment. This is not optimal. However, if they can create a charter school and require a bunch of commitments, they can skim the cream off of this population, minimize the impact of low ability kids on their own child’s education, get their kids something close to straight As with far less work than they’d have to do in a public school, congratulate themselves on their tolerance and dedication to diversity, and all for less than the cost of a mid-tier private school. Such a deal.

Unlike low-achieving, majority URM charters, which are generally funded with billionaire grant money or for-profit charters, progressive charters are normally started by parents who are willing to fork out $10K or so apiece to get a charter school off the ground for their kids. Then, once they’ve got seed money, off they go in search of a reasonable amount of low income URM kids.

This kicks off a big hooha with the local school district. First, the charter will never be as “diverse” as the local school district. It will always run considerably behind in URMs. Then, the local school districts will accuse the charter of creaming just the motivated students, of URM attrition, of creating rules and expectations that are tough for the low-income (read Hispanic/black) parents to follow. Then there’s the yearly squabble as the local school district points out that the charters are pulling the public schools’ top achieving low income Hispanic/African American kids whilst leaving behind low incentive kids, special ed kids, English language learners, thus lowering the district school scores, while the charters congratulate themselves for their diversity, tolerance, humanity, generosity and high test scores. The local school district will often reject the charter’s extension, only to be overridden by lawsuits or the state. All done ostensibly in the name of good intentions and diversity, all done actually in the name of minimizing their own kids’ exposure to the lower achieving, poorly behaved low income blacks and Hispanics. (Of course, if the charter’s in a rich enough district, then they don’t even have to worry about finding URMs.)

Am I painting this in the worst possible light? Probably, but it’s not all that pretty. Using taxpayer dollars for upscale liberals (they are, usually, liberals) who don’t want their kids in the overly “diverse” local schools or have a little snowflake who just isn’t good enough to compete in a more competitive public school, gaming the system and using their own dollars to bootstrap a plan to qualify for state and federal dollars? If you’re going to do it, then own it. We can argue about whether or not it’s appropriate to create charters for entirely low income populations, schools that skim the motivated kids without any disabilities or sped problems from the local public schools overloaded with all that and more and then take those kids and mercilessly beat information into them in the hopes of moving them to a better-educated life and middle class jobs. But at least, there, we are working with kids who have no other options, who are being funded largely by grants from billionaires who want to pat themselves on the back for helping the little people.

None of this means that the teachers aren’t hardworking and dedicated and that some low income kids are getting a much safer education than they otherwise would. (In high school, however, it does mean that the kids are all getting much, much better grades than they would be getting in their local comprehensive high schools, which gives them a huge advantage in college admissions.)

The eduformers have started to notice these progressive, “diverse” charters, as well as gentrifying urban schools, which spring from the same motivations. Mike Petrilli** has a book out (What, you didn’t know? You must not be on his Twitter feed.) celebrating the parents who seek out this choice for their kids, despite their concerns about performance and their own little snowflakes’ educations. Why, Petrilli himself suffered through the “diverse schools dilemma”. His own local school in Takoma Park had a student body in which THIRTY FIVE PERCENT of the students qualified for free lunch! I mean, that school almost qualified for Title I! Oh, the humanity. So you can see why Petrilli felt the need to write a book celebrating the parents who brave these schools full of the great illiterate unwashed, and showing them how to find schools that only looked bad on the outside, but weren’t, you know, actually bad.

In fairness, Petrilli, like all educational policy folks, is fixated on elementary and middle schools, which are far more segregated than high schools. So 35% probably seems like a rilly rilly high number to him. But I can list at least five high schools in my general vicinity that have are 65% free-reduced lunch and 65% ELL (mostly Hispanic) with a 30% population of white students, ranging from working class to well-off, a situation that’s becoming increasingly common in many suburbs. So Petrilli’s intro has already spotlighted him as a dilettante. I mean, gosh. 35%!!!

But Petrilli as a eduform policy wonk has been focused on pulling in whites to the reform movement for a while—in fact, I’m deeply skeptical that he ever really researched the issue for his own kids, given how neatly this book ties in with his clear policy goals. In his summary of takeaways from the 2012 election, #1 on his list is “don’t piss off the suburbs”. (And of course, Petrilli didn’t take any of his own advice, running away from the scarily “diverse” Takoma Park in favor of uprooting his family to an expensive house in the suburbs and sending his kids to lily white Wood Acres Elementary, a school he tsks tsks in the intro for being over 90% white. Really, who hands out book deals to people like this?)

So call me uncharitable, but I figure Petrilli and other eduformers are pushing “diversity” as a means of gently tempting house-poor or other economically stretched white folks into seeking out charters in order to further undercut public schools, while also reassuring the suburbs that the reform movement won’t drill and kill their kids to test heaven.

Of course, the real “dilemma” is one I wrote about earlier:

….why are charter schools growing like weeds?

I offer this up as opinion/assertion, without a lot of evidence to back me: most parents know intuitively that bad teachers aren’t a huge problem. What they care about, from top to bottom of the income scale, is environment. Suburban white parents don’t want poor black and Hispanic kids around. Poor black and Hispanic parents don’t want bad kids around. (Yes, this means suburban parents see poor kids as mostly bad kids.) Asian parents don’t want white kids around, much less black or Hispanic….So charters become a way for parents to sculpt their school environments. White parents stuck in majority/minority districts start progressive charters that brag about their minority population but are really a way to keep the brown kids limited to the well-behaved ones. Low income black and Hispanic parents want safe schools. Many of them apply for charter school lotteries because they know charters can kick out the “bad kids” without fear of lawsuits. But they still blame the “bad kids”, not the teachers, which is why they might send their kids to charter schools while still ejecting Adrian Fenty for Michelle Rhee’s sins.

As I’ve mentioned before, education reformers are now pushing suburban charters with strong academic focus, which are nothing more than tracking for parents who can’t get their public schools to do it for them.

And so the dilemma Petrilli and others write about involving both progressive charters and “gentrifying” public schools: how can white middle to upper class parents who can no longer afford to move to a homogeneous district sculpt the schools they want while minimizing the impact of the undesirable students?

Clearly, step one is for the parents to publicly congratulate themselves. They’re not avoiding diversity, they’re seeking it out! (They just don’t mention the part about controlling it.)

And then, wait patiently for step two: Eventually, all but the best low income students will either behave badly enough or get tired of the rules and leave the charter schools for the required-to-take-them comprehensives, and eventually, gentrification will be complete and all the low income students, good and bad, will go off to an exurb somewhere.

So all they have to do is cope until that happy day, and avoid the lawsuits. Tiptoe tentatively around the cultural issues in the meantime. If you want to worry, worry that you bet on the wrong neighborhood and that gentrification won’t take hold.

That’s the diversity dilemma, in a nut shell: a white parents strategy to minimize the impact of low income low ability students on their kids without the expense of a private school or a new house. If the economy or the housing market picks up, expect the trend to fade. Sorry, eduformers, but by and large, white folks like big high schools and full-service middle schools.

Anyway. Russo touches on another point directly: the upper middle class white funded charters are, in almost every case, progressive. They hire their teachers from straight from top-ranked ed schools, all of them thoroughly steeped in the tea of social justice, heterogeneous classrooms, complex instruction, and Freire. Teachers dedicated to closing the achievement gap not by drill and kill, but by shrinking the range by pulling the top-end in sharply. Not, to put it mildly, teachers who will provide an academically rigorous education.

What this means in practice is that progressive charters (and, probably, the gentrified publics) do not have a high-achieving white population–particularly at the high school level. The parents who start progressive charters are more likely to have idiosyncratic kids who would be labelled weird in their public school. Others, like the parents of Emily Jones in Waiting for Superman, are worried their kids wouldn’t track into the top group in their local suburban high school, and thus be stuck with the lower achieving kids. Still others just know their kids won’t work terribly hard and will get weaker grades at the local high school than they would at a progressive charter where they’d be the top students (and where, of course, they will be donating quite a bit of money for that sort of consideration). Parents with high achievers are either going to seek out academic charters (which are rare) or leave their kids in the comprehensive high school, where they are able to compete and perform at the top level.

You can see this reality reflected in the research on charter schools, with one of its key findings: Study charter schools’ impacts on student achievement were inversely related to students’ income levels.

Yep. Drill and kill works great for low ability kids, but heterogeneous complex instruction is a lousy way to teach a mixed ability classroom without many high achievers.

But that’s predictable, isn’t it? After all, progressive charters are a hybrid of the worst of both sides of the education debate. Progressive instruction and goals, social justice crap given full rein, all in an organizational structure designed to pull off exactly the sort of kids who wouldn’t benefit from it, courtesy of the reform movement.

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* I know many nice parents who send their kids to charters. I get it. But stripped of all the rationalizations, this is what’s left.

**I am normally a middling fan of Petrilli. He does come off a bit like a hyper-enthusiastic, gormless Richie Cunningham. But the minute he decided to move his family out to the homogenous zone, he should have dropped the book deal.

The End of Pi

No, not π. This is the English teacher speaking, although most of my English lit work is now in enrichment classes.

I’ve taught Life of Pi in my book club two or three times. For most of the book, I focus on literary terms: metaphors, similes, personification, metonymy, didactic (my lord, the amount of time Pi spends instructing the reader!), understatement and hyperbole. I also draw attention to Pi’s exceptionally unusual character. Adolescent readers have a distressing tendency to take everything they read at face value without thinking about what the events reveal. When Pi joins three religions, they don’t think, “What idiot is this?” They’re like, “Well, Pi was born a Hindu, but he really liked the Muslim religion, so he joined that, too. Then he became a Christian. His parents got really mad; they think he should just be Hindu.”

So I prod them a bit, ask them if they belong to three religions, and if they don’t think Pi’s a little odd for this and other reasons. Who is more reasonable, really, Pi or his perplexed parents? (who, ultimately, let him have his spiritual advisers). The early lessons focus on reading and appreciating the imagery, but also on gaining an understanding of the character in the first third or so of the book. Why, given what we know is going to happen, does the author spend so much time on zoos and religion?

This preparation helps them make the most of the middle third, which is the book’s claim to fame, the reason Ang Lee made the movie in 3-D. We again focus on imagery and literary terms, practice writing analysis of said literary techniques and how they emphasize ideas,themes,and so on.

But then there’s the last third, which I’ve attached here–actually, I copied it from this site, but it didn’t have the font changes for the Japanese conversation.

I start by having the kids draw a sketch of the entire section (chapters 97-99). I encourage the kids who hate drawing by telling them that whatever they do, my sketch will be the worst. (They know my boardwork, so they believe me even before they see it.)

Why a sketch? Because after two-thirds of a plot-rich story, loaded with action, thoughts, and imagery, the sketch helps student see that the entire third section is three people talking in a room. All the insights, all the discoveries come through conversation. That is, the final third is much like reading a play, a profoundly important switch in a book thus far rich with imagery and thought with relatively little dialogue.

Right around here, we discuss the fact that Pi introduces a second story, that we now must question his original story. Enter the notion of “unreliable narrator” (I usually bring up The Murder of Roger Ackroyd).

So leaving aside event specifics, what patterns of interaction did the class notice about Pi and the investigators? We build a list:

• The Japanese insurance investigators are hungry and cranky.
• They speak their minds in Japanese, and their interactions are often very funny.
• Pi is hoarding food, something that the readers know he is still doing as an adult. (We discuss the hoarding impulse and why a prolonged bout of near-starvation would bring it on.)
• The Japanese men give Pi food, first grudgingly, then with more understanding of his need.
• Pi constantly challenges the investigators, making facially compelling arguments (that are nonethless ridiculous). These arguments nonetheless stop the investigators with frustrating frequency, because Pi won’t simply accept that a Bengal tiger in a lifeboat is ridiculous, that man-eating plants are absurd, and so on, but rather argues with seeming logic about other absurd realities.
• The frustrated investigators constantly remind Pi that they are investigating a tragedy, and Pi stops them again in their tracks by agreeing, and reminding them of what, exactly, he had lost. Over time, these reminders have their impact, and the investigators start their later questions by acknowledging his pain.
• Mr. Chiba, the assistant, is a good-humored and open man; Mr. Okamoto, the senior, is more analytical, and the more easily frustrated by Pi’s antics.

I make sure they see the humor for example, Mr. Okamoto’s irritation as shown by “[long silence]” when, dammit, the bananas do float, or the fake laughs, or Mr. Chiba’s offering of his uncle the bonsai master, and their pauses as he asks for more and more and, ultimately, all of their food. The kids see that humor is not really anything howlingly funny about any individual event, but the overall story of these increasingly frustrated investigators faced with a recalcitrant Pi. We talk about how it’s easier to see the impact of Pi’s behavior because of the POV change, from first person to third person limited omniscient (we know what the Japanese are thinking because of the translated dialogue). So it’s easier to realize how frustrating it is to deal with Pi.

Then we go through the specific events.

• The investigators ask Pi for an accounting of the events.
• Pi tells them the events as he recounted it later to the book’s author, and as we the readers read.
• The investigators are skeptical, and attack his logic. But Pi tries to build a logical chain by inference: if illogical events have happened elsewhere, they could have happened in the lifeboat.
• The investigators try to win his favor by giving him cookies, their lunch, chocolate bars, all while arguing with him and asking for a more realistic story that they can believe.
• After many cookies, chocolate, all the investigators’ lunch, Pi tells a second story, one that makes the reader wish devoutly for brain bleach, a story of horror, the degradation of humanity, and Pi’s own unwitting betrayal of his mother.
• The investigators don’t like that story either, and after further pushing, they give up. They realize that the sole survivor of the tragedy will not be able to enlighten them as to the cause of the sinking.
• Pi asks them a question: Given that neither story helps them resolve their investigation, which is the better story?
• Mr. Okamoto starts to analyze the question, but Mr. Chiba answers without hesitation that the first story, “the one with the animals”, is the better story. Mr. Okamoto approves of his underling’s answer privately, and chimes in with agreement.
• Pi thanks them, saying “and so it goes with god”. He starts to cry.
• The investigators sit in silence and wonder. After a while, they get up to leave, assuring Pi that they will look out for Richard Parker, the tiger at the center of the story they said was the better story.
• Pi offers them three cookies each. Up to this point, he has hoarded food and given it up (like the bananas) only to ask for it back.
• In a letter written years later, Mr. Okamoto restates his belief in Richard Parker.

It often takes some additional prodding, but after a while, my students notice that Pi did not ask which was the more believable story or the true story, but the better story. And yet, both Pi and the investigators behave subsequently as if the investigators have accepted the true story. Pi cries in clear relief. The investigators refer to Richard Parker.

Up to now, we do it as a class discussion, but I promise I’m not forcing them to “discover” what I want them to. In fact, many of the details I list above were original offered by my students, that I hadn’t originally seen (e.g., I hadn’t noticed the pattern break of Pi offering the investigators a cookie until a student pointed it out).

But now they break up into small groups (2-3) and I ask them this question: Why do the investigators accept Pi’s story? What answer does the text support?

I’ve taught this book three times, and in all cases, all my small groups come back unanimously with the same answer, the only answer I believe is possible after a close read of section three: Mr. Chiba and Mr. Okamoto declare “the story with the animals” the better story out of kindness, of sympathy for a young boy in tremendous pain, who they’ve come to admire, however grudgingly, for his ferocious determination and creative arguments. The students always point out the same key evidence—Mr. Chiba, the more empathetic and less purely analytical investigator, interrupts his superior to give the “right answer”, that his superior, Mr. Okamoto, says “Yes” in Japanese, signifiying approval of and consent to Mr. Chiba’s answer, abandoning his usual commitment to analysis and logic to reason his way to the correct answer.

So then we take the story as a whole. I point out that “dry, yeastless factuality” is a phrase that has appeared before, in a rather startling slam on agnosticism back in Chapter 22. Agnostics, it seems, are in danger of missing “the better story”….hey. That’s a term we’ve seen before. So Pi, and probably the author, is drawing a link between an insistence on facts and the refusal to choose, and choice is essential. We must choose. And we must choose the better story, to Pi. Hence his various comparisons of creation myths in Islam, Christianity, and Hinduism. So why does Pi return to this “yeastless factuality”, to a clearly religious context, when talking about his own stories and the choice he offers to the investigators?

Back to the groups, but despite lots of passionate discussion, the students aren’t sure if they have an answer. I tell them that there doesn’t have to be AN answer, but that they might find the notion of creation myth, understood broadly, to be helpful. I also tell them that I am leading them to my own preferred interpretation when I do so.

What continually hangs up the discussions, for good reason, is the book’s conflation of “better” with “true”. Which story is better? The one with the animals, of course. But which story is true? Is Pi relieved when the investigators choose the story with the animals simply because it speaks well of his story-telling? All my students reject that; Pi is clearly moved to tears because the investigators accept his story, in the absence of all relevance, as true, that they begin to discuss Richard Parker as a real being.

Each time I teach this book, we come to this impasse, and I always tell them that they can decide that the author meant true, not better, if they clearly qualify their interpretation with this decision.

At that point, coupled with my hint on “creation myth”, most of the kids come up with some form of this, which we then define as a group: Pi is struggling to survive his trauma, and comes up with a fantastic, beautiful story to mask the brutal reality. It’s more manageable to remember a hyena eating a still-living zebra than a Frenchman slicing up a Chinese sailor, the hyena breaking an orangutan’s neck preferable to the decapitation of his mother. The new story isn’t just a story of his survival, it’s his own “creation myth”, the creation of his own religion, the Life of Pi. He must have a basis, a religion, a credo in order to move forward with his life. He can’t live with the reality, that he was the brutal, savage, yet beautiful Richard Parker.

But all religions must have adherents, people who accept the creation myth. Hence the importance of the Japanese investigators. In refusing his original story, they show the rigid adherence to fact that Pi finds in all agnostics. Their insistence that he tell a “true” story forces him to tell the horrors he experienced. But the endlessly creative Pi, in the midst of his pain, finds one more logical way to ask the investigators for the validation he needs. Since the story of his survival has no relationship to the sinking of the ship, can they tell him which is the better story?

At this point, I usually tell the students that the best part of the book, for me, lies in the extraordinary sympathy Mr. Chiba and Mr. Okamoto show Pi. Mr. Okamoto, the logical one, begins analytically but is saved by the more humane Mr. Chiba, who interrupts his boss to give the answer Pi so clearly craves. And then, as Pi cries quietly, Mr. Okamoto finds a way to reinforce the fact that better does indeed mean true, by reassuring Pi that they’ll be careful not to run into the tiger. These are the acts of kind men, men who were distracted by the demands of the job, frustrated by the fruitful inventions of this confusing survivor, but ultimately moved to help him take the first step past his pain. I always snuffle when Mr. Okamoto agrees with Mr. Chiba.

Then I pass out copies of this Yann Martel book club interview (pages 3 and 4), and let my students read the Wrongness.

They are outraged! Martel ignores the agency of the investigators and says they chose the “better” story because they responded to the more “transcendental” story, the one with the unreal elements. Martel wants readers to choose the unreal story because of their revulsion with the “true” story, but he wants the “better” story to have an unreal element to make it a more difficult choice.

“Wait. He’s basically making the whole story really about people and religion, rather than about Pi. He’s got this whole agenda!” said one of my strongest students one year.

“THANK you,” I growled.

And of course, the students are then bummed because they have spent all this time deciphering a story and coming up with a meaning that’s wrong.

“Who says so?” sez I.

“The author.”

” We can always focus on author’s intent, but when his intent conflicts with your own reading, and you’ve got the evidence to back it up, then the author’s just this guy, y’know? He doesn’t get the last word. This is why J.K. Rowling should be drummed out of civilized society, for acting like she’s the only interpreter of Harry Potter novels. As if there’s much to interpret in a damn Harry Potter novel in the first place. She should be skewered on Voldemort’s wand for her arrogance. Instead, when Salman Rushdie comes up with an interpretation clearly supported by the text, this lowlife fool explains patiently why he’s wrong—to friggin’ Rushdie, whose worst novel is of a quality that Rowling could only dream of. But I digress. Look. If Yann Martel wanted us to swallow his bilge, then he should have done a less excellent job with the Japanese investigators. There’s no way around it.”

“Are there other cases of authors being wrong about their work?”

“More specifically, are there other authors who I believe I can prove are wrong about their work? Sure. My favorite and earliest example (that is, the first case I realized I thought the author wrong) is William Faulkner and A Rose for Emily. Many people think Flannery O’Conner is wrong about her interpretation of A Good Man is Hard to Find; I’m not sure I’d go that far, but she definitely makes the grandma’s redemption case stronger than it is. And it’s very common in movies to see a different vision than the director and creative talents intended.”

So to finish the unit, I have them write a freeform essay on one of two topics. They can write up their own interpretation of the ending, or they can explain why they think Martel is wrong. OR right. Anyone who wants to argue that Martel is right because he’s the author can do it, but I tell them they still need to support from the text—or explain why I should ignore the text.

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This came up, of course, because of the movie. Reviews suggest that the adult Pi asks the question, “Which is the better story” of the author, not the adolescent Pi of the investigators. Rod Dreher says that the Japanese investigators reject the story with the animals and accept the horrible story—in other words, do exactly the opposite of what they did in the book.

It’s worth realizing these are not trivial changes. In the novel, no one other than the Japanese investigators got a choice. When the author is sent to Pi with the words, “This is a story that will make you believe in god”, the speaker refers to the “better story”, the story with the tiger. The author learns of the alternate version from additional research. The adult Pi has completely adopted his creation myth. His listeners are to believe in God because he has survived nearly a year on a lifeboat with a Bengal tiger, not because they are given a choice between a brutal, lifeless fact-based horror and a beautiful fantasy.

I suppose it’s inevitable that the interpretation of this book has been stuffed into the “Reader Response” funnel. Our just a tad short of narcissistic president wrote a letter telling the world that he and his daughter made the right choice of the “better story”, which makes him pretty much the equal of every book review , which also ended with the reviewer’s declaration of what he or she, personally, thought was the “better story”. Reader, do you believe in God, with no proof but the better story? Or are you one of those yeastless agnostics, dependent on fact and reason? Make your choice! Talk about how your response to the book is nothing more than a reflection of your finer qualities! Let us all bond together in congratulating ourselves on making the “better choice”, rather than critically analyzing and discussing the many fascinating ideas the book raises, often accidentally.

I don’t think Pi is a particularly excellent book, but the ending is its best part. It’s a shame that it’s been ruined by the Let’s Make Every Book All About Me school of faux critical analysis. (Ruined the book, that is. I can hardly blame Lee for playing to the bigger crowd.)

I believe the book offers considerably more profound insights if we accept that Pi’s survival is beautiful, regardless of how it happened, and that the kindness of two busy men faced with a young man trying to cope with horrors beyond their imagining is as much evidence of God as is the carnivorous island.

Kicking Off Triangles: What Method is This?

How do math teachers kick off a new unit? When possible, I like to do something with manipulatives, or some sort of activity that introduces interesting questions. Last year, I came up with a triangle activity that I’d originally conceived of for congruent triangles, and then realized it wouldn’t work. But something at the heart of the idea struck me as fascinating, and the single day activity was extremely successful. This year, I used it to kick off triangles.

As you read this (if you read this) ask yourself: is this a constructivist lesson, in which kids discover their own meaning, and the teacher is the “guide on the side”? Or an instructivist lesson, with the teacher as “sage on stage”, telling the students the facts?

I think describing key aspects of the lesson through my interactions with the class will help clarify the lesson. Or not. Maybe it’s just a goofy delusion.

Prep: I have several questions written on the white board:

1. What constraints exist in triangle construction?

2. Can a triangle be made out of any three lengths?
3. How many triangles can be made out of any specific three lengths?
4. How can we classify (group) triangles?
5. How many degrees in a triangle?

I also have some vocab words written out: constraints, properties, and room for more. I created seven of the bags, the Triangle Activity sheet, the Classifications graphic organizer. Planning this took a while until I realized I could leave the logic lesson (see below) for homework; then it all fell into place.

So first, I hand out the Triangle Activity Sheet and a bag for each group of kids (my kids sit in groups of 4, roughly arranged by ability, with strongest kids in the back):

So today we’re kicking off our triangle unit. I could lecture and give you an introduction, but I thought it might be fun to give you some specific memories about triangles to introduce the shape and help you understand that it’s a little more than ‘just take any three sides and put them together.’ So start off by emptying out the bag of everything EXCEPT the three identical paper triangles, okay?”

The kids obediently dump out the contents. They see paper fasteners (you know, those little gold things?), and strips of paper in various lengths and colors. The strips all have holes on each end, put there by a paper punch.

“Okay, first, I want you to know that this activity is going to create some really cheesy looking triangles, but it’s precisely because they are so cheesy that I like this exercise, because it proves an important point about triangles. So no giggling or mocking my strips of paper, okay? I spent hours making them.”

Naturally, a wiseass in the back of the room says “Oh, man, these are so flimsy and cheap! Who made this crap?” all to get the Killer Stare from his teacher.

“But before you start making triangles, I want you to NOT make triangles. Take a second to read the instructions in Part I.”

(Brief pause. But I do not make the rookie’s mistake, dear reader, of assuming that the kids are all obediently RTFM just because I provide them time and orders to do so.)

“Okay. Eddie, what do the instructions say?”

“Huh?”

“Alice?

“Um, what part again?”

“Craig, wanna go for a trifecta?”

“You just said it. We have to find strip combinations that DON’T make triangles. But we can’t bend them.” (Craig, btw, is the wiseass. He has redeeming qualities.)

“Exactly. See the holes on the end?” Wait for yeses, don’t get enough. “SEE THE HOLES ON THE END?”

“YES!”

Line those up. Some of the combinations will not extend sufficiently. Remember that you can change the angle measures, and try different lengths. Now. Turn over the instructions.” I listen and look for the half sheets to turn over. “Does everyone see the smaller of the two tables? When you find a combination of strips that can NOT make a triangle, you put the three lengths in this table. Got it? No, that wasn’t loud enough. One more time: You will put the strip lengths that do NOT form a triangle in this little table. All of you should keep your notes updated, but I’m going to collect one handout from each group. Ready? Louder?” YES! “Okay, go.”

I wander around the room, periodically reminding students that they can alter the angle measure, and within 5 minutes all student groups, even the weaker ones, have at least three combinations. I call on each group to provide an example, and we soon have 8 or 9 combinations on the board.

“Excellent! Now, I’m going to say a combination of strips that’s not here on the board, and I want to close your eyes and visualize those strips. Don’t say anything, just visualize. Close your eyes!”

“Okay, visualize the strips 2, 3, and 9. Don’t answer this question, just think: can you make a triangle with strips of 2 inches, 3 inches, and 9 inches? Think for a minute, don’t say anything. Okay, now: Put your thumb UP if you think you can, thumb DOWN if you think you can’t.” The bulk of the students have their thumbs down (this is a very strong class), and even many of the struggling students are visualizing correctly and have thumbs down. A few kids, no thumbs.

“Ike, no thumb? Do you think you can make a triangle?” (Ike is in the front of the room and didn’t think to look around and get a thumbcount. He is chagrined.)

“Um, sure.” I hold up my hand to forestall the kids who want to correct him.

“Try it.” Ike tries to arrange the strips.

“No. You can’t.”

I add 2, 3, 9 on to the board. “Okay, Ike, how about 2, 3, and 3?”

“Yeah,” Ike says instantly.

“Yes, you can. That time you could see it, right?”

“Yeah. Two strips have to be longer than the other one or you can’t make a triangle. ”

“Very good! Anyone else see that?” A bunch of hands go up. “We’re going to formally learn this later, but Ike has articulated half of what’s called the Triangle Inequality Theorem. No need to write it down right now.” (I’m writing it on the board.) “In a triangle, the sum of two sides MUST be greater than the third side. There’s more to the theorem than that, but we’ll stop on this point, because I want you all to consider something. Before right now, how many of you thought you could just take any three lengths and make a triangle?” Most of the hands in the room go up, and most importantly, I see the top kids going “Hmm.” They realize that yes, indeed, they had thought that, which meant that this little exercise with no clear agenda had, in fact, taught them something. “Here’s what’s even stranger: before today, if I had asked you to make a triangle with a toothpick, a pencil, and a pogo stick, what would you have told me?”

“Wow,” said Mary. “You can’t.”

“You can’t. And you all would have instantly realized that, had you been given specifics, right?” Many nods, I own the class right now. “So this brings up something important about triangles: they have constraints. They have constraints that you have never considered, and yet if you had considered a triangle with specific questions, you would have instantly realized some of the constraints. Alan?”

“What’s a constraint?” I’m walking over to the vocabulary section while several students explain that it’s a restriction, or “something you can’t do”, and I write their definition on the board.

“So now, we’re going to build triangles. See Part two of the handout? Create triangles that meet the criteria. There are more than one combination of lengths for most, but not all, of the triangles listed. I recommend getting them all identified and lined up BEFORE you use the paper fasteners. And remember, if a hole breaks I’ve got more of the support doohickeys.”

So off they went, creating triangles with enthusiasm and precision. After 15 minutes, they all had completed tables that looked something like this:

Then I passed out this simple graphic organizer. Amazingly, many triangle classification graphic organizers (yes, there are a variety out there on the internet) miss the opportunity to visually emphasize the simplicity of triangle classification. For example, this one completely mucks it up, and this one buries the lede. This one is perfect, but it gives out all the information up front, when I wanted the kids to pull it together in a class discussion. I had already created mine which looks like a simpler version of the last, but really, how many ways are there to show it visually?

Now, some of you are saying, “WTF???? You need a GRAPHIC ORGANIZER to tell kids how triangles are classified?” Well, yes. I’m not a big fan of taking “math notes” for all but the very top kids. If a kid wants to take notes, fine. But
I hand out graphic organizers for most of the information I want kids to keep, so I can tell them what handouts to review for the test. If I want them to take down a page of notes (for example, coordinate geometry), I tell them specifically to copy down my board notes as is—and then, a few weeks later, I ask about those notes and check to see if kids have them (compliance rate this year close to 90%).

It takes about 8 minutes to go through the organizer; I look sternly at the top kids and stop them from blurting out the top-level categorizations, giving the mid-levels time to think and suggest. Then we complete the organizer working together; I tell the kids to put an example in each.

I hand out a triangle classification worksheet from KUTA (I used pages 2 and 3), and the kids work through it busily. The top kids rip through it the quickest; it’s not that hard. But this section here gave them opportunity to think:

Two of the triangle classifications aren’t possible, so when the top kids finished this, I made them write out why two classifications weren’t possible. This gave the less adept kids time to finish.

“So Jasmine, did you find a triangle type that wasn’t possible?” Jasmine stays silent, desperately hoping that someone else will shout out the answer, but I have poleaxed the usual suspects with a stare, and wait her out.

“Right….obtuse?”

“Very good! Why isn’t that possible?” Another long wait—an eternity to Jasmine, no doubt.

“They were in different circles?”

“And…”

“You..said that a triangle could be in only one circle?”

“I did! Clark, can you add to that?”

“A triangle can only be in one angle group?”

“Exactly. A triangle can only be classified by one angle type. Actually, if you put some information together, you may be able to figure out why a triangle can’t have both a right angle and an obtuse angle, but don’t worry about that now—we’ll work on that more tomorrow. Ellie, how about the other impossible triangle?”

“Right equilateral?”

“Good! Now that one is a bit tougher. Why isn’t it possible? Kevin?”

“Well, wouldn’t all the angles have to be equal, if all the sides are? And if they were all equal, the total degrees would be 270.”

“Very nice! We haven’t established all of the facts you used, but your reasoning is good. There’s another way, too. Maya?”

“The hypotenuse of a right triangle is the longest side, right?”

“Nice. Candy, can a triangle with three equal sides have a longest side?”

“No.”

“Does a right triangle have a longest side, class?” “YES!” “So can a right triangle have three EQUAL sides?” “NO!”

(okay, I know some of the weaker students don’t quite grok this, but I’m aiming for the top students now, so I’ll pick up the pieces later.)

“Okay. Very good. The big idea, again: every triangle fits into an angle classification and a side classification. All of them. Turn over your handout.”

“This is your homework. I’m going to go through it during our advisory, so don’t sweat it now. But this organizer reveals something critical about triangle classifications that I want you to think about tonight. Also, more logic. Don’t groan!”

[Groan. They do not like logic.]

“Okay, now put the graphic organizer away. Did everyone make a parallelogram? Everyone take the parallelogram they built, and any one triangle. Apart from the number of sides, what differences do you notice?”

It takes the kids a while to figure it out, even as the parallelograms collapse the minute they pick them up. I let them mull it for a while, and they do come up with some creative offerings. I hint at it by convincing them to move them around.

But I finally tell them to hold up each figure.

“Hey! Look at that!”

“That’s not a real difference! They’re just made differently!”

“Made differently? You made them! What did you do differently?”

“Nothing!”

“Okay! They were both made of index card stock and paper fasteners. So what’s keeping the triangle up?”

Silence.

“So take a look at the board, question 3. How many different triangles can be made from three specific lengths?”

Silence.

“Ooookay, how many different parallelograms can be made from two pairs of strips?”

“Lots,” says Angie promptly.

“Show me.” Angie takes her parallelogram and moves it from a rectangle to a steeply slanted parallelogram.

“Perfect! Now, which has the biggest area?” Silence. “Angie, stand up and show everyone your parallelogram in the super slanted position. Okay, now push it up a little bit. Class, what just happened to the area of the parallelogram?”

“Bigger,” says Ron.

“Angie, push it up more.”

“Oh, I get it,” Karinna says. “It always gets bigger if you make the….um. I don’t know how to explain it.”

“Think in terms of height. Angie, put it back to super slant.”

“Oh!” Ike says, “If it’s taller, it has a bigger area!”

“And where does that end? Angie, keep moving it..moving it….Craig?”

“When it’s a rectangle. Because after that, it’s going to start going down again.”

“Nice. So you see, guys, a parallelogram has an infinite number of areas, although the largest area is going to be when the sides are perpendicular to each other. No need to write that down; I am just making a point really about triangles. Back to our question. How many different triangles can be made from three specific lengths?”

Pause, then “Just one?” asks Ron.

“Everyone made a 5,5,9 triangle, right? Hold it up. Look around, everyone. See any variety? Or do they all look the same? ”

“But why?” asks Effie.

“It all goes back to Euclid. How many non-collinear points in a plane?”

I kid you not, the class gasped as they realized the connection. “THREE!”

“That’s right. Any three points define a unique plane. Only one possible plane. So the triangle has structural integrity and rigidity. The parallelogram does not. If I tell you the three lengths of a triangle, it’s mathematically possible to determine the area. Not so with a parallelogram. And there you have the reason I love this little exercise. You made these shapes. You can see the triangle hold up, the parallelogram collapse. You know there’s no trick. It’s just the triangle. So if you’re going to build a bridge, or a skyscraper, what shape is going to ensure your structure won’t fall down?”

“Triangles!”

“But look around this room. See any triangles?

God love ’em, they really do look around the room.

“How about squares, rectangles and parallelograms in this room?”

“They’re everywhere,” says Zeus.

“Isn’t that weird? I don’t know if it’s human or just cultural, but we have a thing visually for rectangles. When was the last time you saw a triangular table of figures, or even a triangular dining room table? I was thinking of making the table on the back of this handout triangular, but it would distort the information! But even given our fondness for rectangles on the outside, we know to build and support our rectangles with triangles. And this goes back to the earliest times. Look at Roman architecture, and you can see triangles everywhere. When you leave the class, look outside at the classroom wall and the overhanging roof. You’ll notice struts holding it up, and what will the shape be?”

Bert: “But can’t you just add something to the rectangle to make it stay the same?”

“What, you mean like this?” I hold up two parallelograms that keep their shape:

“What’d I do?”

“Made triangles!” the class chorused.

“Indeed! Okay, for my last trick, take out the three identical triangles in the paper bag. See that each triangle has a different angle colored in? The Angle Addition Postulate says that if we align these angles so that each of them share a side with one of the others, the sum of their angles is equal to the sum of the larger angle that they form together.”

(I forgot to take a picture of this, but it’s a well known demonstration and I just stole an image off the web. Normally, you have one triangle and tear it into three parts, but I want to keep these bags as kits for future use.)

I wander round the room and check; all groups have their triangles arranged so that they can answer the key question.

“Okay. Your triangles are of all different shapes and sizes. But when you align their angles together, what do they form?”

“A straight line!”

“And how many degrees are in a straight line?”

“180!”

(I am getting very loud full-class responses here, not just the top kids in the back.)

“So the angles in a triangle add up to….”

“180 degrees!”

I wrap it up by going through the questions I posted on the white board, ensuring general understanding of the key concepts. And then.

“Okay, before we go through the homework, I want you to realize something. All this work you did today wasn’t proof of the facts you learned. They were demonstrations. You have demonstrated visually that a triangle has 180 degrees, that a triangle has rigidity, that the sum of two sides of a triangle must be greater than the third. And I like demonstrations! They are not to be sneered at. But don’t confuse a demonstration with proof. We’ll be proving some of these facts during the unit; in other cases, the proofs are more complicated than I want to go into. But don’t ever confuse a picture with a proof. A proof is an argument built with logic, facts, and definitions. But a picture or an experience is much easier to remember.”

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So, what do you think? Was this a “discovery” lesson, the classic progressive ideal that traditionalists sneer at? Was it constructivist or instructivist? Teacher-centered or student-centered?

Instructivist, teacher-centered…..and discovery-based.

Most progressive, constructivist “discovery” lessons are insufficiently sculpted. Check out the pictures of this lesson, which is clearly covering much of the same material that I did. But the kids are spending a lot of time creating triangles with a protractor and ruler. I don’t want them spending time on that right now, so I give them the strips. Moreover, the kids are spending a lot of time putting together a presentation, which they are then going to, well, present—and everyone is going to hear the same basic information 8 or 9 times, as each group presents their “findings”—which, in the happy talk, differs for each group but in reality is the same thing over and over again. Tons of wasted time, and if you ever see a classic group-work class, at least a third of the kids aren’t doing a thing (cf Boaler’s bias).

While I wouldn’t do such an open-ended lesson, my point isn’t to argue for my lesson’s merits. I want people to notice the difference between a classic constructivist, discovery-oriented lecture and one in which kids put things together or complete discrete tasks that lead to immediate, unambiguous findings that we then translate into facts. I’m still the sage at center stage, but the kids aren’t just listening. They have sense memories and are participating in long class discussion interspersed with tasks that they can all do.

A classic instructivist approach would be a lecture, in which the teacher gives notes and the students listen and take notes. I could, of course, have covered this material in about 15 minutes. The top kids would remember it. The bottom kids would not. Plus: boring.

I am not a fan of straight lecture every day—well, actually, I rarely but ever do a straight lecture. Even when I’m talking, I’m engaging in a class discussion to move things along. But for the teacheres who do lecture daily, why not vary the routine? Find some good activities that demonstrate essential principles, with some handouts. It takes a little work the first time, and you often have to modify the activity a few times until you find the right balance of tasks and fact delivery. But the end result is almost always an enjoyable activity that gets the same information across.

But the larger point is this: many people sneer at constructivist teaching. I am not a fan, either. But so long as we are teaching kids who don’t want to learn math, we need to accept that the lecture is just zooming right over the heads of 75% of most classes. I’d rather reach a larger audience.

Algebra Terrors

A day or so before the school year began, I went to an empty classroom that had a supply cabinet. This classroom was way better than mine. It was 3 or 4 feet wider, had shelving and a smart board. Now I didn’t care much about the smart board, but all smartboards have document cameras, which my room does not.

“Hey. This is a great room. Who gets it?”

“I guess the other new teacher.”

“When’s he coming?”

“I don’t think he’s even hired yet. You know, you should ask for this room! You’re here first.”

“Yeah, I think I will. It can’t hurt.”

So off I went to find an administrator, and the first one I I ran into was the AVP of discipline and scheduling. (As a sidenote, the conversation recorded below is the one of only two I’ve ever had with him.)

“Hi. Please don’t view this as a complaint of any sort, but I really like to teach with document cameras, and I notice that room 1170E has a smartboard. Hank (not his real name) suggested I ask if I could switch rooms?”

“To 1170E? Oh, yes, that’s for Ramon. I suppose I could switch rooms, but we’d need to change schedules as well. You see, we got the Promethean smartboard funding as part of our algebra initiative, and we committed to give those boards to teachers teaching Algebra I at least 60% of the time. If you’re interested….”

You know in Terminator 2, when Linda Hamilton has just finally broken out of her padded cell, broken Earl Boen’s arm, beaten the crap out of three security guards and is waiting for the elevator? Freedom is there, baby. She can taste it. She can get her son, escape to Mexico, stop the machines, save the world. All she needs is the ding of the elevator door.

Ding!

….and out of the elevator steps

Algebra I Arnold

NOOOOOOOOOOOOOOOooooooooooooooooo!
“I was told that you had expressed a strong preference to teach geometry and intermediate algebra. But I’m always happy to find interested algebra I teachers….”

“No, no, sir, no really. It’s fine. I do have a very strong preference to teach geometry and intermediate algebra, you were correctly informed, and I am happy with my current room. It’s fantastic. I can deal without a camera, it’s fine.”

“You’re sure?” Clearly, this man is an evil sadist. “You really do seem to like the document camera, and we prefer that the rooms go to teachers who will use them…”

No! No! I’ll stop! The machines can win! Take my son! Just don’t make me go back!!!

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It was just a bad scare. I’m teaching geometry and algebra 2. Well, Math Support, but even though the kids are weaker, I’d rather teach Math Support than Algebra I.

Math teachers think this story is very funny.

In retrospect, my second year of teaching was my most brutal, thanks to my schedule of all algebra I, all the time. I learned a lot. I never want to go back. Oh, sure, I’d like to teach one class of Algebra I, particularly to see if my data modeling lessons they work as well in algebra I as algebra II. But I do not want to be an “algebra I specialist”, and never, ever, EVER want to devote anything more than a class a year to algebra I. I’ve said it many times, but I’m always ready to bore folks: high school algebra I classes should convince anyone—from loopy liberal progressive to anti-teacher union tenure hating eduformer—that our educational policy is twisted and broken beyond all recovery.

So why bring it up now? Because until I saw this article, I’d forgotten the very worst part: A Double Dose of Algebra (ht: Joanne Jacobs).

Yes, I didn’t just teach straight algebra I classes. I taught a double class of Algebra Intervention. Let’s switch T2 characters for just a moment, shall we?

This is what happens when I’m reminded of that intervention class without time to prepare myself.

What is Algebra Intervention, or “double dose algebra”? Well, it’s this brilliant strategy of identifying kids who are really weak in math and increasing their hours of torture.

The best study of this approach, by Takako Nomi and Elaine Allensworth, examined the short-term impact of such a policy in the Chicago Public Schools (CPS), where double-dose algebra was implemented in 2003. …. Nomi and Allensworth reported no improvement in 9th-grade algebra failure rates as a result of this intervention, a disappointing result for CPS. The time frame of their study did not, however, allow them to explore longer-run outcomes of even greater importance to students, parents, and policymakers. (emphasis mine)

So double dose algebra didn’t work. Did that stop them? Hahahahah! Of course not! They just commissioned another study! One that would allow them to explore “outcomes of even greater importance” to students, like “will I make an extra $50,000 a year to compensate me for the time I spent in this tortuous hell?”

Using data that track students from 8th grade through college enrollment, we analyze the effect of this innovative policy by comparing the outcomes for students just above and just below the double-dose threshold. These two groups of students are nearly identical in terms of academic skills and other characteristics, but differ in the extent to which they were exposed to this new approach to algebra. Comparing the two groups thus provides unusually rigorous evidence on the policy’s impact.

Wait. You checked the kids just below and just above the threshold? So you only compared the strongest intervention students with the weakest regular students? Well, golly. Did you, perchance, check how the weakest regular students did compared to the weakest intervention students? Was it substantially different from the gap between the strongest intervention and weakest intervention?

The benefits of double-dose algebra were largest for students with decent math skills” but below-average reading skills, perhaps because the intervention focused on written expression of mathematical concepts.

Guys, half of all regular high school algebra students can’t add fractions or work with negative numbers—that is, they do not have decent math skills. So what the hell is relevant about progress made by intervention students with “decent math skills”?

With the new policy, CPS offered teachers of double-dose algebra two specific curricula called Agile Mind and Cognitive Tutor, stand-alone lesson plans they could use, and three professional development workshops each year, where teachers were given suggestions about how to take advantage of the extra instructional time.

Eight days of PD. EIGHT DAYS! In three plus years of teaching, I’ve taken 1.5 days off for being sick. In one year of teaching algebra and algebra intervention, I was required to leave the classroom for 8 days. The PD was utterly useless. The lunches with the other math teachers, good—lots of conversations, sharing of lessons, venting, and so on. We would do better to just give us money and an extra half hour every month for lunch.

CPS also strongly advised schools to schedule their algebra support courses in three specific ways. First, double-dose algebra students should have the same teacher for their two periods of algebra. Second, the two algebra periods should be offered consecutively. Third, double-dose students should take the algebra support class with the same students who are in their regular algebra class. Most schools followed these recommendations in the initial year. In the second year, schools began to object to the scheduling difficulties of assigning the same teacher to both periods, so CPS removed that recommendation.

It wasn’t just the schools that objected, I’m betting. I taught intervention the first year it was offered by the school. Of the three intervention teachers, one (a TFAer) turned in her resignation in January purely because she felt beaten down by intervention. Another teacher, an algebra specialist, a near-phlegmatically calm Type B, burst into tears when she met with the principal to make absolutely sure she wasn’t given an intervention class the next year.

I was the third. I never complained. I was under continual pressure because I wouldn’t tolerate three kids who were deliberately disrupting the class. The administration hinted I was racist, that I was exaggerating their behavior, and only relented on the pressure when my induction adviser witnessed a middling incident of blatant misbehavior and blew a gasket when the AVP of discipline shrugged it off until he learned that she’d seen it. Admin got a long letter from her and started to make the kids’ lives hell.

The following year, the school dropped the requirement for consecutive periods and allowed two teachers to split the course, rather than requiring the same teacher to do both sections. That same year, the intervention teachers got called into a room by the district and were given a blistering come to jesus meeting in which they were informed that their pass rates better go way, way up until they were as good as the pass rates from last year, which were clearly a goal to be attained. Of course, that last year, when they were dumping all that pressure on me, they never said “Yeah, too many referrals but hey, your pass rate is awesome. You’re only failing two kids, who never show up. Great job!”

This year, the school has dropped the requirement that the students all be in the same class. Hey. That sounds familiar, doesn’t it?

The pressure on the teachers is tremendous. So the schools try to find a way to pay lip service to the method—we’re offering intervention for our weak students!—without all their teachers quitting on them simultaneously. Intervention is brutal on teachers.

The recommendation that students take the two classes with the same set of peers increased tracking by skill level. All of these factors were likely to, if anything, improve student outcomes. We will also show, however, that the increased tracking by skill placed double-dose students among substantially lower-skilled classmates than non-double-dose students, which could have hurt student outcomes.

In addition to the strain on teachers, intervention is a huge hassle for administration and has an unintended consequence that escapes the notice of people who haven’t talked to an AVP responsible for the master schedule. But the reality is that a group of kids who must take two classes back to back end up taking most, if not all, of their classes together.

Say a school has 10 freshmen English classes but only three of them are double block remedial and (please note, this will come up again) many of the kids who take double block algebra also require double block English. The intervention freshmen are in periods 3 and 4 for algebra intervention, and the only other double block English class they can take is 5 and 6, leaving periods 1 and 2 open. Only one freshman PE class available in period 1, so science (bio or general) has to go in period 2. All done. So all the kids in algebra intervention periods 3 and 4 who are also in double block English take all their classes together. For every intervention class, some 20-30 underachieving, low incentive kids are moving through their entire day together, in non-remedial and remedial classes both. Of course, since most intervention kids are weak in all their subjects, this means that their classes have a disproportionately high number of low achievers—all of whom spend their entire day together, socializing. Or planning ways to wreak havoc. The troublemakers in my class arranged signals that they would use to disrupt classes—all their classes. They’d pick a code word, and whenever the teacher said that word, they’d all start laughing loudly, or squeaking their shoes, or sneezing.

I’m a big fan of tracking. I am vehemently opposed to taking a group of low achieving kids who are already buddies, already with next to no investment in school, already really annoyed at having to take a double dose of math—and give them every single class together, so they can reinforce each other in noncompliance and have an entire school day to socialize.

And then this section, which caused more flashbacks:

Overall, 55 percent of CPS students scored below the 50th percentile and thus should have been assigned to double-dose algebra, but only 42 percent were actually assigned to the support class. In addition, some students took double-dose algebra, even though they scored above the cutoff on the exam.

You’re thinking, wait. Some of the weak kids didn’t get intervention, and some of the strong kids did? That’s a weird fluke, isn’t it?

And so, another anecdote.

My strongest intervention kids had taken Algebra I the year before. Each of these six kids had scored higher on their state test than my average score for all my non-intervention algebra students. Yes, you read that right. Six of my intervention kids were good enough for the top half of my non-intervention algebra class. Not just better than my worst. Better than HALF the 100 students in my non-intervention classes. Two of them had actually achieved Basic on the previous year’s test. I got them to bring in their test scores and show them to the AVP of Instruction, demanding they be put into normal algebra (leaving me out of it, of course). One of them was put into my regular algebra class, and got an A-. The other four missed Basic by just a few points and despite my asking on their behalf, were required to take intervention. This despite the fact that I had over a dozen non-intervention freshmen who’d scored Below Basic or Far Below Basic. None of it mattered.

I was so foolish as to write the AVP of Instruction saying randomly, casually, something like “Hey, okay, so I can’t move strong students out. But so long as I’m teaching an intervention class for really really weak students, could I move some of my weak non-intervention class IN? Some of them are even Resource (sped) students, so they could substitute the intervention class for their guided studies class, so it wouldn’t create a scheduling disaster (sped kids get a study hall). Here’s a list.”

AVP of Instruction wrote back, in all caps, “THESE STUDENTS ARE SOPHOMORES. SOPHOMORES CAN’T TAKE INTERVENTION.”

Three weeks later, as God is my witness, the AVP of Instruction sends me a note, “I’m moving Fred McInery [not his real name] into your intervention class. He is a weak math student who needs more support.”

I look up Fred. He is a sophomore. I am very excited, because I am a moron, and send her a note. “Hey, great! We’re putting sophomores in intervention now? Could we revisit my list? I really think it will help these extremely weak students succeed in math.”

She writes back in all caps, “THESE STUDENTS ARE SOPHOMORES. SOPHOMORES CAN’T TAKE INTERVENTION.”

WE HAVE ALWAYS BEEN AT WAR WITH EASTASIA.

That story is an amusing flashback, even if it is crazy-making. Here is a horrible one:

We shall call her Denise. She is a doll. She was in my intervention class and had extremely weak skills and was the propaganda child for intervention, the one that everyone is thinking of when they propose it, because she worked her ass off and actually became better at math. She was not “just below the cutoff point”, either, but an FBB child who surreptitiously counted on her fingers to add 4 + 2. But conceptually, she got it. In the first semester, she did so poorly she was one of my contract students. She improved dramatically on her test, missing Basic by just a point. She had the third highest state test score of my intervention students, and passed my class.

Not only didn’t the school move her on to Geometry, but they put her into intervention again. (Yes. Now they had a sophomore intervention class.) When Denise told me this, I went quietly berserk and emailed the AVP of Instruction. It is not the same AVP. This one is worse.

Keep in mind, this second year at the same school, I am teaching Geometry, thank all the gods, and have two of my last year’s intervention kids taking my class even though they received slightly lower state test scores than Denise. Five others of my kids have also moved on to geometry with lower state test scores. Denise and three others were kept behind. I email the AVP of Instruction—a different one, as last year’s AVP has been promoted to principal of another school. This AVP is much worse–and point out these facts. I do not point out that I can discern no organizing principle behind this decision, that I suspect a very disorganized AV principal behind it. I am very polite; hey, this is just some oversight? Want to make sure it gets cleared up.

I write three notes, all very polite, and finally, a month after school starts, Denise gets moved….to a regular Algebra class. I gnash my teeth, but Denise is thrilled and thanks me profusely.

I see Denise at the year-end, and ask how she’s doing. “Great. But I failed the first semester of geometry, so I’ll have to go to summer school.”

“What? They put you in geometry?”

“Yeah, they said you advised it. But they didn’t move me until, like, November, so I failed. But that’s okay. I did good second semester, and I’m going to pass it over the summer.”

I guess it worked out okay, ultimately. But had she been put in the geometry class originally, she’d have had her summer.

Double-dosing had an immediate impact on student performance in algebra, increasing the proportion of students earning at least a B by 9.4 percentage points, or more than 65 percent. It did not have a significant impact on passing rates in 9th-grade algebra, however, or in geometry (usually taken the next year). Double-dosed students were, however, substantially more likely to pass trigonometry, a course typically taken in 11th grade. The mean GPA across all math courses taken after freshman year increased by 0.14 grade points on a 4.0 scale.

(emphasis mine)

Clearly, most students did not do all that well. As the study acknowledges, the low-achieving students did not benefit at all from the intervention; the students most likely to benefit were those who just missed the cutoff. More on that later.

Here’s what the study doesn’t make clear: many high school algebra students never make it to trig. They take it twice in high school, then take geometry twice. Or they take algebra once, geometry twice, and algebra 2 without trig (that’s the class I teach). So are they only counting the students who made it to trig?

The more meaningful stat would be the percentage of double-dosed kids who made it to trig vs. the non-double-dosed kids who achieved same. Reading this passage, the study appears to be saying that all the kids made it to trig and hahahahahaha, no. Not happening.

And since that’s not happening, then who, exactly, is being compared in the GPA? All the kids, or just the ones that made it to trigonometry? Presumably, just that set, because otherwise, the GPA number isn’t worth much. Hey, the double dose kids who flunked algebra twice and made through geometry by their senior year had a GPA .14 points higher than the single dose kids who made it through trig. Whoo and hoo.

It is important to note that many of these results are much stronger for students with weaker reading skills, as measured by their 8th-grade reading scores. For example, double-dosing raised the ACT scores of students with below-average reading scores by 0.22 standard deviations but raised above-average readers’ ACT scores by only 0.09 standard deviations. The overall impact of double-dosing on college enrollment is almost entirely due to its 13-percentage-point impact on below-average readers (see Figure 3). This unexpected pattern may reflect the intervention’s focus on reading and writing skills in the context of learning algebra.

(emphasis mine)

Oh, yes. That’s what we do in these algebra intervention classes. We focus on reading and writing! We’re given a bunch of kids who add 8 to 6 on their fingers, and we figure their struggle comes from not being able to read the word problems. So we put up a word wall and teach them five new terms and suddenly their reading skills skyrocket wildly.

Or—and this is just a wild, random, thought—perhaps my last school isn’t the only school in which Set A = {names of students taking double dose algebra} and Set B = {names of students taking double dose English} and is a Venn diagram in the two circles largely overlap?

You say oh, don’t be silly, ER. Of course they’d account for the possibility that the double dose algebra kids are also getting a double dose of reading intervention! And then not mention it! And I say, you don’t read much educational research, do you?

Because keep in mind the conclusion of this research:

As a whole, these results imply that the double-dose policy greatly improved freshman algebra grades for the higher-achieving double-dosed students, but had relatively little impact on passing rates for the lower-achieving students.

Apart from that, Mrs. Lincoln, how’d you like the friggin’ play?

Look. None of my outraged noise makes any sense at all if you don’t realize that, in the world of high school math, the kids who benefited, according to this study, kids achieving just below the passing standard, are WAY ABOVE AVERAGE for that population, particularly in a Title I school. Intervention exists because these schools have dozens, if not hundreds, of algebra students who have taken the course three times and still score Far Below Basic. It does not exist to help kids just below the 50% mark in math get better scores in reading, marginally higher grades and ACT scores, and better Trig scores—if they get to trig, which the normal intervention kid does not.

What people fondly imagine algebra intervention to do is this: kids are just a little behind, you know? They just need some extra time learning integer operations and fractions. They didn’t learn it the FIRST FIFTEEN TIMES they were taught it, so all they really need is another hour or so a day and they’ll be right up there with the rest of them, all right? And if they aren’t, well, it’s those damn teachers who just don’t want to work with “those kids”, and we’ll just have to find more teachers who really, really care about these kids who just need a few hours more help than the others. (Yes. This is the myth of “They’ve never been taught…..”)

Meanwhile, forty percent of the freshman class comes in having taken algebra once and scored far below basic or barely below basic, and are randomly assigned to double block or no double block using a dartboard, from what I can see. The teachers are dealing with the same lack of basic skills in both double and single block algebra, and rapidly realize (if they didn’t know already) that the kids who don’t know integer operations and fractions have this gap because they aren’t terribly bright. They can’t come up with an intervention vs. non-intervention approach, because some kids in the intervention class don’t need support while some kids in the non-intervention class do. But in the non-intervention classes, the teachers only have to deal with 3-8 kids with low skills, while in the intervention classes it’s 14-15 out of 20. So the only thing different about the intervention classes is monstrously bad behavior and more time in hell.

All this, mind you, so that we can do research that reveals no real improvement in outcomes.

But I’m out of it, baby. It’s enough to make me believe in god. Death to algebra intervention.

But the nightmares, they won’t stop until it’s destroyed!

Midterms and Ability Indicators

Again with the big monster post (Escaping Poverty has eclipsed all but the top post of my old top 6, and my total blog view count as of today is 45,134), and again with the procrastination of success. I did not watch reruns while in hiding; it was All Election All the Time, and now I’m depressed. In the VDH typology, I’m a Near Fatalist, but an optimistic one. Like Megan McArdle, I think that the demographic changes will be offset by the inability of the Dems to manage a coalition with lots of demands but little else—and yes, I think, after a while, that the producers will wander over to the Republican side. If not, I will achieve total Fatalism.

Anyway. I got unnerved because I have many new followers, and I write about many things that may bore them because I don’t just write about policy. I have two posts almost completely done (okay, I didn’t just watch elections), but was actually intimidated to post them because they are about teaching math. Am I the only writer/blogger scared of the audience?

But I just graded midterms, and I thought I would mention something that may be illustrative to the people who are unhappy with my relatively frank discussion of race. As I wrote when I originally invoked the Voldemort View, (a notion proposed by an an anonymous teacher):

My top students are white, Hispanic, black, and Asian. My weakest students are white, Hispanic, and Asian. (No, I didn’t forget a group there.) Like all teachers, I don’t care about groups. I teach individuals. And the average IQ of a racial group doesn’t say squat about the cognitive abilities and the thousand other variables that make up each individual.

I wrote this at my previous school. So here’s what’s happening at my new school, in midterm results:

Freshman Geometry

Tied top scores: African American boy, Hispanic girl, white girl. Following right behind with one fewer right answer: two white boys. These five have consistently been the top achievers. The remaining top students are a mix of white and Hispanic (there are no other African Americans).

Low scores: two white girls, South Asian boy. Three Hispanic kids are next in line, but two of them took their time and did outstandingly well for their skill level, pulling off a D+.

The Asians in my class are all south Asian, and all but one are in the bottom half of the class, although one of those is clearly under achieving.

Keep in mind, however, that all the Asian kids are in the Honors Geometry class.

Intermediate Algebra

Top score: white senior boy, right behind him was a white sophomore boy, right behind him a Chinese junior girl and a Chinese sophomore boy, in that order. My top students, taking the tougher of the two courses I teach in one class, are a mix of whites, Asians (far east, mid-East, and south), and Hispanics (two girls, both in the top half of the top group). In the second half of the class, the top students are Chinese (but remember, this puts them in the middle of overall ability) and Hispanic.

Again, this is intermediate algebra; many of the top kids are taking Alg II/Trig.

But talking about race and cognitive ability can instantly annihilate a teacher’s career because of a flawed premise. A teacher who accepts that cognitive ability is real and explains much of the achievement gap must be a racist, sexist, or both. Racists can’t properly teach because their assumptions will color their outcomes. They’ll treat the black kids like they’re stupid, favor white kids, and assume all Asian kids are awesome math machines who can’t write. The sexists will be sighing impatiently at the girls who want more context and less competition and praising the eager beaver boys who want the facts and figures and that most horrible of all horribles, The Right Answer.

So, for what it’s worth, I offer my results to dispute that premise, and to restate: I don’t teach races, I don’t teach groups. I teach individual students.