Monthly Archives: July 2012

The false god of elementary school test scores

Rocketship Academy wants to go national. Rocket Academy is a hybrid charter school chain that focuses solely on getting low income Hispanic elementary school students to proficiency. (Note: Larry Cuban has some excellent observations from his visit to a Rocketship Academy.)

First things first: I’ve checked the numbers every way I can think of, and Rocketship’s numbers are solid. They don’t have huge attrition problems that I can see. They are, in fact, getting 60% or higher proficiency in most test categories, and the bulk of their students are Hispanic, many of them not proficient in English. Of course, that brings up an interesting question–if they are proficient on the ELA tests, why aren’t they considered proficient in English? But I digress.

The larger point is this: getting high test scores on California’s elementary school math tests ain’t all that much to get worked up about. Here’s some data from the 2011 California Standards test in math:

I used two standards, because the NCLB obsession with “Proficient and higher” is, to me, moronic. I prefer Basic or higher. The blue line is the percentage of all California in grades 2-9 scoring Basic or higher in General Math, the red is the percentage of same scoring Proficient or higher.

So it gets a bit tricky here, because after 6th grade, the entry to algebra varies. In order to simplify it slightly, I’m ignoring the seventh grade algebra track (call it “accelerated advanced” path), which is about 40,000 students this year, fewer in previous years.

I combined 8th and 9th grade students in General Math and attached that result to the red and blue lines.

Then I separated two groups–the ones who took algebra in 8th grade, and the ones who took algebra later than that. The first group are those who entered algebra in 8th grade, passed it, and continued on the “average advanced” course path, culminating with Calculus senior year. The second group are those who took algebra for the first, second, or third time in high school and then continued on. For each group, I calculated percentages for Basic + and Proficient +.


  1. Through grade 6, the scores represent all students. In grade 7 and 8/9, general math scores reflect only those students who haven’t moved onto algebra. That’s probably why the proficiency levels drop to 50% and lower for the last two groups.In other words, the green and purple lines represent the advanced track students–most, but not all of the the strong algebra and higher math students. The turquoise and orange lines represent the weaker students taking algebra and higher.
  2. Roughly 80% of all students test at Basic or higher from second through sixth grade.
  3. Over 70% of the strong studentws test at Basic or higher from algebra through “summative math” (taken for all subjects after Algebra 2).
  4. The percentage of students testing proficient from second through sixth grade starts at 65%, rises slightly, and then drops steadily.
  5. In no course do more than 50% of the strong students in algebra and higher achieve a score of Proficient or higher.
  6. In no course do more than 50% of the weaker students in algebra or higher achieve a score of Basic or higher.

So the chart reveals that all California second through sixth graders, high and low ability, averaged higher scores on their tested subject than the strongest high school students did.

I used 2011 scores, and I may have made a minor error here or there, but the fall off has been in the scores for several years now, and it’s easy enough to check.

What could cause this? Why are California’s elementary school students doing so phenomenally well, and then fall apart when they get to high school? Let’s go through the usual culprits.

California’s high school math teachers suck.–Well, in that case, there’s not much point in demanding higher standards for math teachers, because California’s high school math teachers have had to pass a rigorous content knowledge test for over 20 years. California’s elementary school teachers have to pass a much easier test–which is much harder than anything they had to pass before 2001. In other words, try again.

The teachers aren’t covering the fundamentals! So when the students get to algebra, they aren’t prepared.–But hang on. Elementary school kids, the ones being taught the fundamentals, are getting good test scores. What evidence do you have that they aren’t being taught properly?

Well, they’re only getting good test scores because the tests are too easy!—dingdingding! This is a distinct possibility. Perhaps the elementary tests aren’t challenging enough. Having looked at the tests, I’m a big believer in this one. I think California’s elementary math tests, through seventh grade, are far less challenging to the tested elementary school population than are the general math and specific subject tests are to the older kids. (On the other hand, the NAEP scores show this same dropoff.)

However, while that might explain the disparity between the slower track math student achievement and elementary school, it doesn’t adequately address why the students in the “average advanced” track aren’t achieving more than 50% proficiency, does it?

Trigonometry is harder than memorizing math facts–We should take to heart the Wise Words of Barbie. Math achievement will fall off as the courses get more challenging. Students who excelled at their times tables and easily grasped fractions might still struggle with complex numbers or combinatorics.

So if you ask me—and no one does. Hell, no one has even really noticed the fall-off—it’s a combination of test design and subject difficulty.

Whatever the reason, the test score falloff has enormous implications for those who are banking on Rocketship Academy, KIPP, and all those other “proven” charters that focus exclusively on elementary school children.

Elementary school test scores are false gods. We have no evidence that kids who had to work longer school days simply to achieve proficiency in fifth grade reading and math will be, er, “shovel ready” for algebra and Hamlet. KIPP’s College Completion Report made no mention of its college students SAT scores, or indeed made any mention of demonstrated ability (e.g., AP tests), and color me a cynic, but I’m thinking they’d have mentioned both if the numbers were anything other than dismal.

So let’s assume that those Rocketship scores are solid (and I do). So what? How will they do in high school? Where’s the follow through? Everyone is banking on the belief that we can “catch them early”. Get kids competent and engaged while they are young, and it all falls into place.

Fine. Just let me know when the test scores back up that lovely vision.

Added in January 2014: Well, hey now. Growing Pains for Rocketship’s Blended-Learning Juggernaut.

Alas, it seems that Rocketship’s scores are declining, their model doesn’t scale, they are making decisions based on cost rather than learning outcomes and, my FAVORITE part:

Lynn Liao, Rocketship’s chief programs officer, said the organization has also received troubling feedback on how students educated under the original blended learning model fare in middle school.

“Anecdotal reports were coming in that our students were strongly proficient, knew the basics, and they were good rule-followers,” Ms. Liao said. “But getting more independence and discretion over time, they struggled with that a lot more.”

That graven image gets you every time, doesn’t it?

Black teachers, teacher quality, and education reform, revisited

In the interest of focus, I left a few things off my original post.

First, and most importantly: teaching is insanely complicated and non-linear. For me, it’s a free-form high-wire act on a daily basis, interspersed with bouts of intense mental activity outside of class as I try to figure out the best way to explain complicated subjects to kids who don’t want to be there and often don’t have the requisite skills to master the material. But for others, it’s a highly structured daily routine in which each lesson is planned out months in advance. I know many math teachers who have each problem worked out before they teach it (in many cases problems they’d done for years); I often make up my problems as I write them on the board, so I can carefully calibrate the difficulty level based on the students in that class. I know history teachers who have tremendous difficulty lecturing without index cards and can’t casually lecture on any topic in their curriculum without preparation; I can go from complete unfamiliarity to ready to talk in 2 hours.

Many non-teachers visualize their ideal teacher as someone more like me, except a lot younger–smart, fluid, an expert on anything a student might want to inquire about, and particularly an expert in the subject taught. Highly educated elites, in particular, have romantic notions of their little snowflakes being taught by a bright Harvard graduate who went to a top 50 school and wants to help the next generation be as enamored by learning as she is.

Given the tough times I have finding jobs, I encourage all those who hold these romantic notions to find the evidence that teacher IQ and general intelligence is dispositive in successful teaching. (It must be said, however, that principals don’t like teachers that are too smart. Or too old.)

Much as I’d like a world that makes it easier for me to find a job, though, I think the reality is much less comforting to those who want “smarter” teachers. Certainly, research has provided little comfort. When the best news available tells us that teachers in the 95% percentile get very small improvements over the very worst bottom-dwellers, and any improvement at all is considered great news because it’s so hard to find any teacher quality criteria that show any increase at all….well, it’s just possible that being smart ain’t all that.

I really understand the intuitive belief that smarter teachers are better teachers, because I used to hold the same notion, when I was a suburban parent. But that belief was shaken even before I became a teacher and realized that teachers weren’t complete morons and, furthermore, that the demonstrated knowledge requirements for teachers took a sharp increase after NCLB, particularly for elementary school teachers. Huge. So big that, if teacher competency were a factor, we should have seen some improvement in teacher outcomes. Instead, recent research shows, again, that experience boosts performance a bit and new teachers are still weakest of all. I’m open to having my mind changed on that one because no research has specifically tested on this point. But again, the boosts in demonstrated ability were huge in many states, and shouldn’t we have seen some improvement in performance?

But what we got for sure were far fewer black and Hispanic teachers.

Notice that the fraud ring involved existing teachers, teachers who were probably caught in the NCLB net and forced to re-qualify for existing positions. As always, ETS explains this with a helpful graphic (I’ve combined text and image from page 16. ETS has excellent data. That’s why everyone trying to push an educational policy ignores it.)

In 2001, NCLB required teachers to be fully credentialed, forcing many existing teachers with emergency credentials to pass a Praxis test. Many black teachers couldn’t. Hence, the fraud. This wasn’t simply a case of wannabe teachers, but actual teachers, teachers with jobs. What if they were considered competent teachers?

There’s a really interesting study idea: test the outcomes of the teachers who committed fraud, compare them to white and black teachers who passed the test legally. What if they do well?

I’m not fuming at the double standard revealed by the reformers who scream about “unqualified teachers” but duck and cover when black teachers are found to have committed fraud. I am, however, annoyed that reformers are constantly promoting a lie, or at least a fantasy unsupported by research, and they don’t even have the balls to hold consistently to that position. Instead, they wilt and run away from the Clarence Mumford case. They never seem to commit, exactly, to the qualifications teachers should have, and how the current tests fall short.

Why? Because failure to commit to a line in the sand allows them to skate on two points. First, the minute they draw that line, they will be ferociously questioned about the impact their standards will have on black and Hispanic teachers. Race is an area that reformers are absolutely determined to avoid, unless it’s an opportunity to call teachers racist for the uneven performance results, of course.

Furthermore, the minute they draw that competency line, they will be forced to confront the fact that, as I’ve said with some frequency, research doesn’t support their claims. It’s hard to argue for changes that will further obliterate the population of black and Hispanic teachers when you can’t prove being smart makes that much difference—and that the teacher’s race seems to matter.

So instead, reformers prate endlessly about incompetent, mediocre teachers who aren’t anything but white, of course, talking cheap about improving standards while fleeing in terror from the tiniest suggestion that raising teacher test scores will disparately impact black and Hispanic teachers.

It’s too bad, because if they stood up for their beliefs, we could have a meaningful discussion about where, exactly, the line is for teacher competency. One reasonable interpretation of the research thus far is that we are well above the line needed. Bad news for reformers, if so.

I keep wondering about one other possibility, which might explain why a low or failing score on a basic skills tests could nonetheless belong to an effective elementary school teacher.

Maybe they’re underperforming.

My years in test prep have shown me a number of oddities, including more than a few African American kids (by far, the smallest percentage of my demographic), who have a terrible time reading and thinking “on their feet” (that is, a general skills test), and can’t think abstractly at all, yet have very strong demonstrated abilities that they’ve internalized.

Two different African American girls have had exceptional writing skills with a strong demonstrated vocabulary (both got perfect scores on their essay), but struggled to break 500 on the SAT verbal. One of them got a 4 on the AP US History test. More than one boy (including some Hispanics) can do relatively complex math word problems beautifully but, given a simple equation, can’t isolate x. I had one kid who could not solve 4x -3 = 21, but if you asked him what number you could multiply by 4 and subtract 3, and get 21, he’d say “6” before I’d worked it out myself.

I’ve had more than a couple kids ask me why they were being tested on history when they’d never studied it in school. It took me a while to realize they thought the questions on the reading passage were questions they were supposed to know offhand. Their reading scores shot up (from say, the 3rd percentile to the 35th or 40th) when I explained that the big chunk of text on the right had the answers to the questions. They had no idea. And although they did better, they still complained that they wanted to be tested on “what they know” rather than “learn new stuff on the test”. Yes, that sort of thinking is completely alien to me and yes, it’s still pretty common.

In other words, I wonder if maybe crystallized vs. fluid intelligence impacts test scores on the bottom half of the bell curve. This might explain why relatively low skilled people have difficulty showing that knowledge on the test, but can be effective classroom teachers to young kids.

So I’m not as ready as I was five years ago to say that people who can’t pass a basic skills test don’t, in fact, have sufficient mastery of basic skills.

I’m not excusing the fraud. But it infuriates me that everyone’s ignoring it, because the conversations it would kick up are conversations we need to have—and, of course, they’re conversations we’re afraid to have.

Radio silence on Clarence Mumford

The Clarence Mumford case has gotten little traction outside its area. Save for the excellent Joanne Jacobs, probably the best pure education blogger around, none of the usual suspects have tweeted or blogged about it in the week since it happened.

Mumford, a former assistant principal, has been facilitating fraud in the Arkansas, Tennessee, and Mississippi teaching pool for 15 years or more. Teachers and prospective teachers who couldn’t pass the PRAXIS on their own sent him a few thousand dollars each. For that fee, he scheduled a test and created phony driver’s licenses for people who took the test instead.

I understand why the media is reluctant to touch this story, but the eduformer silence is deafening. Here’s devastating, damning evidence of an organized crime ring passing tests in the name of teachers aren’t actually qualified, proving a demand for teachers too weak to pass the credentialing tests, and…..nothing.

Me, I’m thinking race.

None of the articles I’ve seen mention that Mumford is black, although most articles provide the picture. The U.S attorney (also black) who brought charges against Mumford doesn’t provide the names or races of the teachers who gained or kept credentials. I will be extremely surprised if it does not turn out that most if not all of the teachers who bought themselves a test grade are black. (I am also betting that the actual testers are white, but am not as certain. It just seems that if black people were taking the test and guaranteeing passage, the fees would be higher.)

I suspect that everyone not talking about the Clarence Mumford is doing so because they, too, are pretty sure that the teachers paying for test passage are black, even though they’d hasten to holler “racist!” if anyone said this aloud. If I’m wrong, and it turns out that Clarence Mumford has been helping white teachers fake their credential scores, then when that news comes out I anticipate an avalanche of coverage. Everyone will be relieved.

Eduformers pushing for “more competent teachers” (read teachers with higher test scores) are doing their best to pretend away the enormously bad news about the end result if this push were successful. They push the bogus factoid about ed majors’ SAT scores, demand that our teachers be drawn from the top 30% of our college graduates, and do everything they can to promote the notion that teachers are as dumb as stumps.

If their audience were to visualize, without getting needlessly specific, that these low achievement scores were due to the overpopulation of some hapless bong-hitting Millennials who wandered through a state school reading nothing more than the Cheese Doodles packaging when they had the munchies and beer wasn’t sufficiently nutritious, why, that’s purely coincidental. If their audience were then to contrast this know-nothing pile of lazy do-nothings with the freshly-pressed penny bright Ivy League grads and conclude that, by golly, only the Best of the Best should be teachers, who should blame them? Certainly not the eduformers.

And so if this Mumford story were about white teachers, they’d be all over it. Look! Those damn teachers are morons! Burn them! See! Teachers are stupid!

But black teachers? Thud. Silence.

I’ve written on the lurker in the teacher quality debate, but here’s some ETS data. (Cite, and I pulled out images of the relevant points in the gallery below)

The bullets, dressed up with details to drive the point home:

  • The white Millennial bonghitter with a 1.2 GPA who teaches sixth grade science after his parents booted him out of the basement ties the freshly-pressed hardworking black track star with a 3.8 GPA teaching special ed.* ( Cite)
  • The goofball wannabe manicurist who loafed through Podunk U and went into teaching kindergarten after the tenth of her problematic boyfriends dumped her outscores the idealistic black welfare daughter success story on a full scholarship to Harvard who went into teaching sixth grade English to “give back” to her community.* ( Cite)

(*on average, of course)

In so many words: “Improving teacher quality” by increasing test score mandates will result in a dramatic drop in black (and Hispanic) teachers.

Bumping the basement won’t even make a dent in the white teacher population, which is almost certainly meeting or exceeding any realistic score requirement.

And then, the irony: the research base offers little in the way of proof that “improving the teaching pool” (raising required test scores) will improve results.

Best news, from the most optimistic research:

  • “Quite striking” results show that teachers who score 2 or more standard deviations above average in math improved student gains by .068 of a standard deviation relative to average. (2sd is 95%ile).
  • Teachers who scored 2sd below average in math reduced achievement by .062 of a standard deviation.
  • Thus, the teachers from the 95% percentile or higher had a “whopping” improvement of .13 standard deviations over the teachers literally scraping the bottom.
  • No significant difference in reading scores.

And that’s the good news. RAND found “no evidence that [experience, education, scores on licensure examinations] have a substantial effect on student achievement.” (This report also has an excellent overview of the research (including the relatively cheery Clotfelter study above), starting on page 6.)

Meanwhile, there’s this rather unsettling, and recent, finding from Goldhaber’s Race, Gender, and Teacher Licensing:

Same-race matching effects dwarf most any information conveyed through the licensure test signal. We wish to point out that when teaching Black students, Black teachers in the lower end of the teacher test distribution are estimated to have impacts that are approximately the same as White teachers at the upper end of the distribution.

In summary, we find that evidence suggesting the uniform application of licensure standards for all teachers is likely to have differential impacts on the achievement of White and minority students. Specifically, we see that Black and other minority students appear to benefit from being matched with a Black teacher regardless of how well or poorly that teacher performed on the Praxis tests, and these positive effects due to matching with Black teachers are comparable in magnitude to having the highest-performing White teachers in the classroom. Removing the lowest of performers on the exam would necessarily remove some of the teachers that appear to be most effective for this segment of the student population.


Third, when isolating specific teacher-student interactions, we find evidence that Black teachers have more consistent success than White teachers in teaching minority students, and this matching effect is greatest in magnitude for Black teachers at the lower end of the licensure performance distribution.

Despite a decade or more of trying, the link between teacher cognitive ability and student outcome remains tentative at best, and appears to have a floor. Meanwhile, Goldhaber isn’t the first researcher to find that black students seem to do better with black teachers.

And so radio silence on the Mumford story, even though on the surface, it would seem to play right into their case for improving teacher quality. They can’t afford to be seen screaming for the removal of the thousands of African American teachers who would otherwise meet their criteria of “mediocre or worse”, and the mostly white population of eduformers certainly can’t afford to openly acknowledge that their demands for an improved teaching pool means a near decimation of the African American and Hispanic teaching pool–even without the unsettling lack of research to support their teacher quality fantasies. Because the optics, to put it mildly, suck.

Which is why they’re probably all secretly, desperately hoping the teachers are white so they can scream and point fingers. Because it’s fine to call white teachers stupid.

Note: I followed up on this post here:


Update: Hey, after 4 months, the Mumford case gets a bit more attention. I have periodically been checking for updates, and I don’t recall seeing Cedrick Wilson’s name mentioned before. So maybe an ex-NFL lineman makes it a bit more newsworthy.

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Math teachers’ feelings and other irrelevancies

Why Math Teachers Feel They’re Poorly Prepared.

I feel a rant coming on.

Why on earth would we care how math teachers feel about their abilities? They either are prepared or they aren’t, and that can be demonstrated through a test. As long as they are surveying teachers (in just two states, mind you, and about 20 counties), why not give them a test to capture their actual abilities?

This sort of research typifies that offered by both sides of the education policy debate: soft data, complete ignorance of any existing hard data, and intent determination to avoid collecting anything approaching meaningful data.

Just a few of the more annoying parts:

  1. “By relying on teachers’ reports of their own feelings of adequate preparation, we only get at their knowledge indirectly.”


    “Fortunately, this approach is sufficient to demonstrate how much variation there is in teachers’ content-specific knowledge, or at least in their feelings of adequate preparation.”

    How, exactly, is this approach sufficient to demonstrate variation? Any evidence that “feelings” about preparation is equivalent to, you know, actual preparation? It would have been useful to collect some knowledge (say a short multiple choice quiz) to see if any correlation between feelings and reality existed, for example.

  2. Commenting on the finding that many first to third grade teachers feel academically prepared to teach only their grade level, and no higher: “Is it reasonable for teachers to focus only on the topics that they will teach?”

    Great question. Except the author doesn’t answer it: “However reasonable such a position may appear, many of the more advanced topics for which teachers did not feel well prepared provide the mathematics background necessary to be truly well prepared to teach the more elementary topics at their grade level.”

    I think he’s saying that teachers can’t really be well-prepared to teach elementary topics unless they know advanced topics as well. Gosh. Wouldn’t it be nice if there were data to support that opinion? So far, the data on the relationship between teacher’s subject proficiency and teaching outcomes is, to say the least, a bit squishy. More importantly, there’s a huge difference between knowing a topic and being prepared to teach it. So a teacher could know how to find the area of a triangle but not feel comfortable teaching the derivation of the formula. This is a huge difference that the author completely ignores.

  3. “Teachers’ self-perceptions of their preparedness seem likely, if anything, to overestimate what they know and how well prepared they are rather than to underestimate it.”

    No data at all to support this bold assertion. I would intuitively argue (hey, the author can do it, so why can’t I?) that teachers, who are cautious critters of habit, are more likely to underestimate their knowledge and preparation, particularly in high school. I know this because I’m quite different from the average teacher in this regard. Tell me I’m teaching the history of technology or, god forbid, AP Calculus the next year, and I’d say, “Sure.” History of tech I wouldn’t start preparing for until three weeks before school started. AP Calc I’d spend the entire summer working on increasing my mastery, getting lesson plans from friends, and finding the critical teaching points in the subject. I know that I’d learn a huge amount the first year, that I’d do a decent but not great job my first year, be much better the second and subsequent years. Plus, I’d find it a fun intellectual challenge. Most teachers with my level of calc knowledge would, instead, say “Hell, no” to the offer. But then, I’m (literally) smarter and more flexible than the average teacher. This does not make me a better teacher, but I’m going to have an easier time stepping out of my comfort zone. From my perspective as an ex-techie, it’s hard to overstate the relative hide-boundedness of most teachers (I’m not saying this is a bad thing). So the author’s assertion that teachers would overstate their ability strikes me as not credible without further data.

  4. “In this section, we summarize what teachers have told us about their preparation in mathematics at the college level and as graduate students.”

    I have a degree in English and took no math in college a hundred years ago. All the math I’ve learned, I’ve learned on the job as a tutor–some of it as a teacher, but most while tutoring students in their coursework and on the Math 2c. (I’ve spent little time tutoring calculus, which is why I don’t know it well.)

    GRE Math score: 800. I am relatively certain I scored in the top 10% on two of the three required math credentialing tests, well higher than many math majors. My demonstrated math ability is probably in the top 10% of the entire college graduate population–certainly in the top 15%. Yet I would show up as one of these lamentably unqualified high school teachers who didn’t get a degree in math.

    Unless the author has evidence that, controlling for demonstrated ability, teachers who took math coursework in college do better than teachers who did not–that is, two teachers who got 800 on the GRE but only one of which majored in math have distinctly different outcomes in algebra instruction—then he shouold stop pretending that coursework is relevant. The author cites no such research, and I’m aware of none. Coursework is a proxy. It’s not the real thing.

    Of course, the author could have included a brief test with the survey so he could correlate, to some small degree, the performance of non math-majors to math majors on their chosen subject.

    Why would anyone take this data seriously? I genuinely don’t understand this. Why not survey math ability with a test and get hard data? But then, the hard data might be so discouraging for his side.

    Lest anyone take my ire amiss: I think most elementary school teachers close their eyes and think of England during their math segments. I’m not convinced their distaste makes a huge difference in outcomes. The country has dramatically increased teacher content knowledge requirements over the years, particularly in the last decade, particularly in elementary school. It hasn’t mattered a whip.

Is school too easy or too hard?

School is too easy?

I could not believe how many news outlets found this a compelling story. Did they not feel even the slightest sense of cognitive dissonance? How many “low test score” articles would it have taken for them to stop a minute and wonder if maybe the students aren’t the best judge?

Meanwhile, in the opinion column, Patrick Welsh has the real story, arguing that we are pushing students forward in math when they haven’t mastered the previous class. For example, my algebra II classes, in which 90% of the students got below basic or worse in Algebra I.

Welsh argues that more of these kids would be successful in math–and love it, too!–if we just moved slower. Well, maybe. Some kids have the ability to learn advanced math and just haven’t reached the cognitive development stage. But many kids may never have the cognitive ability to master advanced math.

Of course, we could just make kids take earlier math until they show mastery. But that would be “leaving kids behind” and the racial balance of the kids who were left back would be distressingly imbalanced.

Repeat after me: every educational policy that makes no sense has “disparate impact” pushing it along.

It’s not that only Hispanic and black kids have trouble in math; all math teachers have seen white and Asian kids who have no business taking algbra by junior year. It’s just that there are so much more of them.

We can blame both eduformers and progressives for this one. No one wants to acknowledge that ability matters.

Quick, someone, blame the teachers.

Why I teach enrichment, reasons #1138 and beyond

I teach summer school because compared to regular school it’s like free money.

But then, I teach enrichment classes in reading and composition, as well as PSAT prep, to kids whose parents make them show up and are too compliant to rebel–that is, I teach Asian first generation immigrants (Chinese, Korean, Indian, and the occasiohnal Vietnamese). I tease them about their compliance mercilessly, and they are, for the most part, fascinated by a teacher who tells them they should go home and watch more TV.

Brief anecdotes:

  • I gave them an essay question, “Should school grades be determined entirely by an end of year test?” All but two of the 18 students took positions emphatically in the negative, and all gave the same reason: kids would just goof around and cram at the end.

    I pointed out the implicit value system inherent in their answers: kids only care about grades, not about learning. I said tht this was a big problem, as I saw it, with their attitude towards school and it was something they might want to think about. However, I said, regardless of their opinion, they could make their essay much stronger by attributing this unattractive behavior to other students. “Regrettable as it is to consider, many students have no interest in learning, and are only interested in getting a good grade.” Now they have distanced themselves from the value system, while still holding onto their position and their argument—which had obvious merits.

    And I reminded them that my course had no grade. So why were they in the class? What was their purpose? I hoped they would focus on my big three: better thinkers, better writers, richer vocabularies.

  • Every year, we get a day off for the Fourth of July. Every year, I ask my class what the holiday celebrates. Every year, at least one kid doesn’t know. Every year, at least one of the kids who does know doesn’t know the year. And every year, that kid got an A in 8th grade US History. Every year, I point out that this is a symptom of a kid who wants to get an A, not learn about American history, and that all of the kids in this class have similar gaps—stunning ignorance in subjects where they learned to get the A and never thought about it again.

    And what I truly love about this class is that every year, this lecture makes a huge impression. The kids understand my point. They understand that I value knowledge, not grades, and for the first time, they realize the utter emptiness of an A achieved without actually learning anything.

  • Another “every year” conversation:
    “What courses are you signed up for?”

    Typical rising sophomore answer: “Calc A/B (or Math Analysis), Honors Chem, Spanish III, World History, English II.”

    “Why not Honors English or WHAP (World History AP)?”

    “It’s too hard.”

    Please remember that, the next time you hear about how Asians take tough classes. They don’t take tough classes. They take classes that everyone else (read, white people) find tough. The classes they find tough, they skip.

  • It is not at all uncommon to find exceptional writers. This is not encouraged by their parents.
  • One of my few classroom rituals is “do your two”. Students are required to read two detailed columns four times a week. The column must either be an opinion piece or informational reporting. It can be on any topic: sports, movies, politics, news. They have to report back. I then intersperse my opinions, ensure that they’ve read it accurately, and understood the purpose. Over the course of the summer, I observe the kids picking up more general content knowledge (the purpose of the exercise), but they also start building on each other. So one kid reports on the Euro status, and another kid sees an article two days later that they click on because of the first kid’s report. It’s a very useful exercise.

    Today, one of my students discussed a new study showing that most people don’t actually listen very well. (I’ll find the link later) This generated a fun discussion, culminating in my announcement that I liked to think my students listened to me. Was I wrong?

    Joey started suddenly, looked up, and said, “Uh, what?”

    Little punk.

Appropriate math questions

I had an interview for a middle school math position (why they called me, I dunno, I’m sure I was just filler), and had to bring a sample lesson plan.

I always create worksheets when asked to bring lesson plans, since it gives a better idea of how I teach. I read the standards and came up with this cartoon as a starting point:

I use buying decisions all the time in math classes, because the phrase “Pretend that it’s your money” has a near-magical effect on kids who would otherwise ignore word problems.

So I’d kick off a discussion by asking the kids to identify the difference between the two questions. Most kids of any ability will realize that the girl’s question has one answer, while the boy’s question has several.

From there, I drill down to the boy’s question. (click on the image for a slightly better view). Don’t get too quibbly on the definitions—math purists are insanely annoying.

Now, here’s the thing: this is not a lesson on functions. This is a lesson on variables and generating tables. It’s seventh grade math, not pre-algebra or algebra.

But in order to get kids to think about variables and tables, I find it’s helpful to start with a familiar situation and lead it back to math. In order to explain the difference between the girl’s question and the boy’s question, I have to introduce functions, which leads us to variables.

In my opinion, teachers don’t spend enough time leading kids through the process of identifying the definition of the unknowns (because trust me, if you say “identify the unknowns”, half the class says “Three Cheeseburgers!” and suddenly you’re in a Bill Murray skit.) and generating a table of solutions to the problem. Teachers see these as obvious, as mere activities that we use to solve problems. But low to mid ability kids see nothing obvious about defining variables and generating tables. I’ve been slowly realizing this over time, and it crystallized into my data modelling unit in my Algebra II class. This activity, which I drummed up for an interview (but will undoubtedly use at some point), was my attempt to move it back to a pre-algebra state.

Many teachers who only work with high ability kids would see this handout as ludicrously easy and in fact, I’d hand this worksheet to my top seventh graders and tell them to go it alone, while I talked the rest of the class through. Top kids should figure this out fairly quickly, and on day 2, when the rest of my kids are still practicing simple situations, they’d be on to more advanced scenarios (giving two points and figuring out the rule, giving them a table, and graphing).

But many teachers who work with lower ability kids work hard to find meaningful questions and yet miss the mark by making the question too complex. I was talking to one of my curriculum instructors, and he asked me about a lesson he was planning to give to middle school students in a low income district. He wanted to give kids fractions like 7/20, 8/25, 9/30 or 8/30, 9/35, 4/15 and have them just ballpark whether the fraction was greater or less than the obvious value nearby. So is 7/20 greater than or less than 1/3? and so on.

I told him that he was dramatically overestimating their ability, and recommended he start by doing the same thing with halves. So a list of numbers: 2/5, 9/17, 5/11, and so on. Greater than or less than one half? The kids who can do that quickly, move onto numbers around 1/4. Only after a few iterations should he give the strongest kids the exercise he was thinking of, which most of the kids wouldn’t be able to do, full stop. But he could build the weaker kids ability and fluency simply by getting them to think about greater or less than one half. I advised starting with the much simpler exercise. If I was wrong, he could have the more challenging activity ready to follow up, no harm done.

He took my advice and reported back. Most of the kids never got beyond the over/under 1/2, finding it challenging and meaningful. Most of the teachers he was working with had been sure the activity would be too easy.

I do think it’s important to set open questions for all kids, not just the top students, to let them tussle with before you settle into working problems for practice. However, the questions must be tailored to student ability, and math teachers dramatically overestimate the ability of their kids to work with these questions in a meaningful manner.

It gets old to be told that acknowledgement of low cognitive ability is “setting expectations low”. One of the comments on my “myth” post was “One question that I have is the extent to which students are playing Whack-a-Mole in order to get easy classes for a week or two.” My original response was rather rude, so I changed it to a simple “No”. It boggles my mind that anyone would think kids are faking it.

At this point, some teachers are remembering the time they taught their algebra intervention kids about logarithms, or complex numbers, or trigonometry cycles. I’m not saying you can’t teach it. They just won’t remember it. It will be as if they’ve never been taught.

Charter hypocrisy

I am not a blogger; I’m more of a writer who puts stuff on a blog. Well, actually, I’m an opinionator who is a decent writer and puts stuff on a blog. And at times like this, that’s irritating. I can’t write a pithy statement in a few minutes that get to the heart of the matter. With three different interesting things to write about, as well as a needed second half to my last post, which got a gratifying amount of attention, and a day job, I get overwhelmed and start watching reruns of The Mentalist. This is why I stopped writing for a year, and why I’m going to try and push past this.

Lots to think about in this Rick Hess post, but I wanted to focus on this complaint:

First up, people sometimes ask why I’m a little nervous about the Gates-sponsored urban “charter compacts,” pledges by charters to ensure their students are demographically representative of the community, or state efforts to apply teacher quality legislation to charters. Well, the problem is that each step along this path does a little more to import into the charter sector the pathologies and pettifogging bureaucracy that so hinder district schools.

And Hess gives an example of the Office of Civil Rights demanding that DC charters prove compliance in diabetes support, even if they don’t have any kids with diabetes.

Gotta admit, I don’t want teachers doing PD on diabetes services. I’d much rather they put the time into, you know, instruction. District schools don’t meet every need of every child, but use some schools to meet the needs of particular students. Rather than ask every charter to invest a lot of time and energy in training and planning that will apply to, at most, a tiny handful of children, I think it makes more sense to acknowledge that small, stand-alone schools aren’t equipped to meet every special need for every child, and to proceed accordingly.

Sure. That way, charter schools and their advocates could brag about how much more efficient they are than those loathsome, wasteful public schools.

I really don’t understand this sort of thinking. Charter schools are smaller and therefore can’t possibly scale. Many of their advocates are in favor of charters because the schools are allowed to skate the regulations that districts are bound by. Meanwhile, they continue their assault on public schools without acknowledging their circular thinking.

If charter schools had to follow the same crap that public schools did, they’d be less efficient. So they aren’t, in fact, more efficient, they are just designed to escape the inefficiencies, and have lots of powerful advocates to complain about the inefficiencies. Then, after getting those passes, they brag about the improved results, greater flexibility, and more effective cost structures of charter schools.

I’m not a fan of charters. They can’t possibly scale. They bleed off strong students in urban areas and middling students in suburban areas. Very few high school charters are any good, except the ones dedicated to academic excellence—actual excellence, not faked transcripts. (Think Pacific Charter, not Summit.)

But my contempt for charter advocates is in a whole different category. They are not willing, for example, to risk the wrath of parents with “disabled” kids by going after the mandates themselves. They are not willing to take on disparate impact by arguing that disruptive and unmotivated kids are a huge suck on the time and income of public schools.

So instead, they pretend that charter schools are superior simply on their own merits, not because they have a escape pod from the structural restrictions that plague public schools. Or they acknowledge these inconsistencies but nonetheless support charter schools as a “stopgap” of sorts (as Hess does).

By pushing for charters, these advocates pretend (or fool themselves) that they are interested in helping students, by getting around restrictions that were put in place to help students. Don’t like the restrictions? Argue against them and take the heat of millions of furious parents. But no, it’s much easier to argue for a magic bullet that conveniently, just as a total “wow, who’d have thought it?”, skates those same restrictions—and then, constantly denounce the schools that are bound by those restrictions as not caring about students.

Nice work if you can get it.

The myth of “they weren’t ever taught….”

A year or so ago, our math department met with one of the feeder middle schools to engage in a required exercise. The course-alike teachers had to put together a list of “needed skills” for each subject, to inform the teachers of the feeder course of the subjects they should cover.

One of the pre-algebra teachers looked at the algebra “needed skills” list and said, “Integer operations and fractions! Damn. Why didn’t I think of that?” and we all cracked up. End of Potemkin drill.

All teachers working in low-ability populations go through a discovery process.

Stage One: I will describe this stage for algebra I teachers, but plug in reading, geometry, writing, science, any subject you choose, with the relevant details. This stage begins when teachers realize that easily half the class adds the numerators and denominators when adding fractions, doesn’t see the difference between 3-5 and 5-3, counts on fingers to add 8 and 6, and looks blank when asked what 7 times 3 is.

Ah, they think. The kids weren’t ever taught fractions and basic math facts! What the hell are these other teachers doing, then, taking a salary for showing the kids movies and playing Math Bingo? Insanity on the public penny. But hey, helping these kids, teaching them properly, is the reason they became teachers in the first place. So they push their schedule back, what, two weeks? Three? And go through fraction operations, reciprocals, negative numbers, the meaning of subtraction, a few properties of equality, and just wallow in the glories of basic arithmetic. Some use manipulatives, others use drills and games to increase engagement, but whatever the method, they’re basking in the glow of knowledge that they are Closing the Gap, that their kids are finally getting the attention that privileged suburban students get by virtue of their summer enrichment and more expensive teachers.

At first, it seems to work. The kids beam and say, “You explain it so much better than my last teacher did!” and the quizzes seem to show real progress. Phew! Now it’s possible to get on to teaching algebra, rather than the material the kids just hadn’t been taught.

But then, a few weeks later, the kids go back to ignoring the difference between 3-5 and 5-3. Furthermore, despite hours of explanation and practice, half the class seems to do no better than toss a coin to make the call on positive or negative slopes. Many students who demonstrated mastery of distributing multiplication over addition are now making a complete hash of the process in multi-step equations. And many students are still counting on their fingers.

It’s as if they weren’t taught at all.

But teachers are resilient. They redouble their efforts. They spend additional time on “warm-up” questions, they “activate prior knowledge” to reteach even the simple subjects that have apparently been forgotten, and they pull down all the kaleidoscopic, mathy posters and psychology-boosting epigrams they’d hung up in their optimistic naivete and paper the walls with colorful images formulas and algorithms.

They see progress in the areas they review—until they realize that the kids now have lost knowledge in the areas that weren’t being taught for the first time or in review, much as if the new activity caused them to overwrite the original files with the new information.

At some point, all teachers realize they are playing Whack-a-Mole in reverse, that the moles are never all up. Any new learning seems to overwrite or at best confuse the old learning, like an insufficient hard drive.

That’s when they get it: the kids were taught. They just forgot it all, just as they’re going to forget what they were taught this year.

All over America, teachers reach this moment of epiphany. Think of a double mirror shot, an look of shocked comprehension on an infinity of teachers who come to the awful truth.

End Stage One and the algebra specificity.

Stage Two: At this point, some teachers quit. But for the rest, their reaction to Stage One takes one of two paths.

Blame the students: The transformation from “these poor kids have just never been taught anything” to “These kids just don’t value education” is on display throughout the idealistic Teach for America blogs. It’s pretty funny to watch, since on many sites you have the naive newbies excoriating their kids’ previous teachers for taking money and doing nothing, while on other sites the cynical second-years are simultaneously posting about how they hadn’t understood the degree to which kids could sabotage their own destinies, or some such nonsense. Indeed, I once had a conversation with a TFAer at my school, and she said this to a word: “I’ve realized I’m a great teacher, but my students are terrible.”

Not that this reaction is unique to TFAers. Many experienced teachers who began their careers in a homogenous, high-achieving district that transformed over time into a Title I area with a majority of low income blacks or Hispanics have this response as well.

It’s easy to denounce this attitude, but teaching has taught me that easy is never a good way to go. These teachers are best served at a place like KIPP, where the kids who don’t work are booted. It’s not that the kids learn more, but at least the ones that stay work hard, and that allows the blamers to reward virtue. At comprehensive schools, the teachers who saw their student body population change over time respond by failing half or more of their classes.

These teachers please both progressives and eduformers, because they have high expectations. Their low-achiever test scores, however, are often (but not always) terrible.

Acceptance: Here, I do not refer to teachers who show movies all day, but teachers who realize that Whack-a-Mole is what it’s going to be. They adjust. Many, but not all, accept that cognitive ability is the root cause of this learning and forgetting (some blame poverty, still others can’t figure it out and don’t try). They try to find a path from the kids’ current knowledge to the demands of the course at hand, and the best ones try to find a way to craft the teaching so that the kids remember a few core ideas.

On the other hand, these teachers are clearly “lowering expectations” for their students.

Which is the best approach? Well, I’m an accepter. Not that I was ever particularly naive, but despite my realism, I was caught off-guard by just how much low ability students can forget. But as I’ve said before, that’s the challenge I see in teaching.

I could go into more on this, but this post is long enough. Besides, I don’t want to lose sight of the opening story and the pre-algebra teacher’s mockery of the entire point of the exercise. Of course they were teaching integer operations and fractions. Of course they were doing their best to impart an understanding of exponents and negatives. They didn’t need the list. They knew their job.

Teachers know something that educational policy folk of all stripes seem incapable of recognizing: it’s the students, not the teachers. They have been taught. And why they don’t remember is an issue we really should start to treat as a key piece of the puzzle.