Discovery Doesn’t Work

I had trouble in ed school because (well, at least in my view of it) I openly disdained the primary tenets of progressive education. I am pro-tracking, anti-constructivist, and pro-testing, all of which put me at odds with progressives. Here is the irony: I mention often that I am a squishy teacher (squishy=touchy feely). I am not just squishy for a math teacher, I’m the squishiest damn math teacher from my cohort at the elite, relatively progressive ed school that made my life very difficult. My supervisor, who knew me first as a student in a curriculum class, was genuinely shocked to learn that I didn’t talk at my kids in lecture form for 45 minutes or more, given my oft-expressed disagreement with discovery. Even my lectures are more classroom back and forth than me yammering for minutes on end. (In fact, my teaching style did much to save me at ed school, but that’s a different story.)

Here is what I mean by squishy: My kids sit in groups, not rows. When I set them to practicing, which is usually 20-35 minutes of class, they are allowed to work independently, in pairs, or as a group of four. I often use manipulatives to demonstrate important math facts. My explanations are, god help me, “accessible”. I don’t just identify the opposite, adjacent, and hypotenuse and then lay out the ratios. No, I’ve been mentioning opposite, adjacent and hypotenuse for weeks, whenever I talked about special rights. I introduce trig by drawing a line with a rise of 4, a run of 3, and demonstrate how every right triangle made in which one leg is 3 and the other 4 (that is, have a “slope” of .75) must have the same angle forming it. I spend a great deal of time trying to think of a way to help kids file away knowledge under images, concepts, pictures, anything that will help them access the right method for the problem or subject at hand. (For more info, see How I Teach and The Virtues of Last Minute Planning.)

However, I am not in any sense a constructivist as progressive educators use it. I use discovery as illustration, not learning method. I don’t let kids puzzle over a situation and see if they can “construct” meaning. I explain, give specific instructions, and by god, my classroom is teacher centered. I am the sage on stage, baby. And that’s why I got in trouble in ed school, despite my highly accessible, extremely concept-oriented teaching style; I routinely argued against constructivist philosophy, and emphasized the importance of telling kids what to do.

Anyway. I was incredibly excited to read an article that openly states the obvious: Putting Students on the Path to Learning: The Case for Guided Instruction. This article is just so dead on right. To pick one of many great excerpts–click to enlarge, but why can’t I copy text from pdf files any more?:

Yes. Low ability kids like discovery; it is less work for them, yet they feel they are doing something important—but in fact, they aren’t learning very much. High ability kids tend to be “for chrissake, give me the algorithm”, when they would be better off puzzling through the math for themselves.

The article talks about the importance of worked-out examples. I read the article this morning and had a worked out example on the board the same day—step by step factoring of a quadratic. Here’s the weird thing: the kids who need the help with factoring had to be prompted to use the example, but the kids who got factoring were clamoring for worked examples in the area they had trouble with.

This would be a great thing for notebooks. But how do you get the kids who need help to keep the notebooks?

Great article, that changed my teaching immediately. How often does that happen?

Homework and grades.

The NY Times rewinds the typical homework debate. The post gets predictable pro and con responses: “homework is ruining my kid’s life” vs. “homework is a necessary component to learning”.

As is often the case, the situation at hand involves middle and elementary school students. High school homework rarely gets much scrutiny, unless it’s high achieving students complaining (with a lot of justification) about the huge amount of work they have to stay on top of to stay competitive.

But outside the top 10%, homework’s impact on high school students is a much neglected issue, and it shouldn’t be. Few people seem to understand the inordinate influence homework has on student transcripts—and the results, for the most part, are near-fraudulent.

High school students are far less likely to do assigned homework and the consequences for non-compliance are much higher, because students who don’t do homework often fail—not for lack of demonstrated subject matter skills, but simply for not doing their homework.

Here’s a chart that pretty much any teacher in the country could produce, comparing achievement (test scores) to classwork and homework effort.

(from Reflections of a First Year Math Teacher)

Don’t be distracted by the positive correlation. This is for individual grades, so the individual points are what matter. Notice how many students work hard, yet have failing test results, and how many students don’t work much at all, yet ace the tests.

This graph reflects the reality I point out ad infinitum: effort is only tangentially related to achievement, and then only at the individual level. Students who try harder don’t do better than students who don’t try at all. The lurking variable, of course, is ability.

For this reason, teachers should not include homework as a significant part of a grade, and should never allow missing homework to lower a grade. (This means, English teachers, that if a student doesn’t do an assigned essay, you find another way to assess the student.)

But of course, teachers routinely include homework as 25, 35, 50% of the grade. Happens all the time, and no one calls teachers on this behavior because it’s so damn cheap and easy to argue that homework is essential, good for both discipline and achievement. Never mind that there’s no real evidence for the latter, and the former should not influence grading.

The “homework proxy for effort” skew is understandable, given that teachers really can’t grade students purely on demonstrated ability. Teachers would fail too many students if they set an absolute ability standard. (See the above chart again if you need reminding.)

Teachers tend to value effort anyway—it makes them feel needed. So this preference, coupled with the real dilemma imposed by teaching and assessing students whose skills are far below the required ability level, gives them license to reward effort, to some degree.

But the degree matters.

Boosting hardworking students’ grades just a bit (say from one grade’s “+” to another grade’s “-“) is fine. While some may raise an eyebrow at the idea of giving a failing student a D- because he shows up and tries, I not only forgive this, but engage in the practice frequently.

Giving a student with mediocre math skills an A or B simply because they work hard and finish all their homework is quite another matter and worst of all, giving a low grade to students with excellent test performance—in many cases even failing the student—is outright fraud.

This happens every day, although it’s drowned out by all the middle class parent whining about how much work their middle schoolers have.

In high school, teachers are assigning homework, students aren’t doing it, and teachers are giving lower grades—often failing students completely—even though their skills are strong, simply because they don’t do their homework. Teachers are a moralizing lot, by and large, and they are far more comfortable giving low grades, or outright failing, kids who don’t try and aren’t compliant than they are doing the same to hardworking kids with low skills.

This leads to astonishingly bizarre grade results. Two students might each have very weak algebra skills but one gets an A, because she goes to a school that weights homework as 50 or more percent of the grade and does extra credit, while the other fails at the same school simply for not doing his homework. Students who can read at basic proficiency can fail English for not doing their essays, while functionally illiterate students who earnestly string together sentences on books they didn’t understand get Bs.

Five of my algebra sophomore students last year scored Basic on their state tests–but failed algebra for not doing their homework. One of my best geometry students failed geometry last year for not doing his homework—at least, he was one of my best students until he left for alternative high school because he’d failed so many classes (all by not doing homework) that he can’t graduate on a normal schedule. Several of my top Algebra II students this year took Algebra II/Trig last year and scored basic—but, yes, failed for not doing their homework. Meanwhile, I have colleagues teaching AP Calculus to students who scored Below Basic on all their math state tests up to that point. How can that happen?

State universities don’t use test scores for basic admission, but grades. Which explains why remediation is such a huge problem, doesn’t it?

Of course, at this point in a conversation someone will say, condescendingly, that the students just need to learn how to put in some effort, go through the motions, and I have to fight the urge to go find a baseball bat. Really? We’re talking about a nationwide problem and some idiot treats this as a cheap sermon on morality and obedience? Seriously?

I mean, never mind the fraud that teachers are engaging in, failing competent students while giving good grades to functional illiterates. Consider the massive waste of money thrown away because so many teachers confuse homework obedience with academic achievement. And of course, because our nation is convinced that all kids must be on the college track, there’s so little room for error that one or two Fs ensure that a student is off-track and just marking time until alternative high school is an option.

Districts desperate to stop teachers from indiscriminately failing otherwise competent kids (compared to the kids who are passing) institute those policies that annoy eduformers and earn them lots of mocking catcalls—Fs can’t be less than 50%, homework can’t be more than 10% of the grade, and so on—but these policies make perfect sense when considered in light of the money districts lose to dropouts and quick credit factories that allow students to collect enough credits without learning a thing—even less than they learned from the teacher who gave them an F.

Never forget: grades are a fraud. And in homework, stop wondering about how much is given, and start asking about how much it’s worth to the grade. Because if it’s more than 5%, it’s too much.

Bad Teachers

The NY Post fumes about another “bad teacher” story, carefully designed to outrage all good taxpaying citizens as to the nefarious slugs collecting our hard-won taxpayer dollars.

I’m a process freak. When I read the Post story, my eyes went straight to the section that many others ] probably glossed over:

Accused in 2001 of making lewd comments and ogling eighth-grade girls’ butts at IS 347 in Queens, Rosenfeld was slapped with a week off without pay after the DOE failed to produce enough witnesses at a hearing.

But instead of returning Rosenfeld to the classroom, the DOE kept him in one of its notorious “rubber rooms,” where teachers in misconduct cases sat idle or napped.

or

That let rubber-room granddaddy Roland Pierre make a mockery of the system. He finally retired at age 76 last year — 14 years after he was yanked from PS 138 in Brooklyn and never taught again. Criminal charges in 1997 that he molested a sixth-grade girl were dropped.

So….we don’t actually know if either of these guys are, in fact, oglers and molesters. We don’t know this because, perhaps, incompetent bureaucrats and law enforcement personnel (government workers, all) failed to make the case (just as the DA found insufficient evidence on Mark Berendt in 1994–and yes, Berendt, too, gets to retire with full benefits). Or, perhaps, we don’t know this because these guys aren’t actually guilty.

What we do know, according to the story, is the process for getting rid of bad teachers, as well as the process for putting sex offenders in jail, was followed. But the journalists who write “bad teacher” stories don’t agree with the outcome of that process. Journalists who write “bad teacher” stories have to mention the process, but they never blame the process. They blame the unions for doing the job they’re legally required to do, the teachers for not quitting or allowing themselves to be fired. But not the process. These stories always punch up the volume on the potential sex offender or near-abusive teachers, but it’s rare to see a “bad teacher” story that focuses on the effort to get rid of a teacher who just isn’t very good.

Eduformers, on the other hand, do blame the process. They don’t like it one bit. Eduformers often push the “bad teacher” sex offender stories, not because they think all teachers are sex offenders, but because, as they repeat ad nauseum, “we need to make it easier to fire bad teachers”. Gen up outrage to make it easier to fire sex offending teachers and hopefully the net will widen to pull in the other teachers the principal wants to fire as well.

But while eduformers do blame the process, they rarely talk about changing it. They want it gone. They point to the the process of firing teachers, which they clearly think is absurd, and call for a more executive approach, one that allows principals full discretion to fire “bad teachers”.

In fact, the process itself isn’t that ridiculous. In most districts, principals can visit classes any time they like. If they find a teacher asleep or reading the newspaper, they can write it up and put it in the teacher’s personnel file, where it can be used in the next evaluation. If students turn in absurd assignments that show the teacher is phoning it in, or record the teacher showing them movies daily, that, too, can be included in the evaluation. An aggressive principal can get a bad teacher fired—if, in fact, the teacher is a bad teacher.

But that’s not enough for eduformers. They don’t want a process, they want a system with executive control—one in which the principal is more powerful than the much-hated unions, one in which the principal gets to form his or her team and dump the naysayers. Dream on. I get the allure. It’s just not going to happen. Unions or no, teachers and principals are still paid with government money, and principals will never be able to have unilateral control as long as they’re spending taxpayer dollars. Because, just as there are really bad teachers, there are spectacularly awful principals¹, and the job carries authority to do real damage with real money. Eduformers either can’t or won’t understand the futility of their dreams.

I know that eduformers don’t understand math, despite their protestations about math teacher competence, because bad teachers are a non-issue when it comes to their contributions to educational costs. Imagine, for a moment, that 10,000 horrible teachers sit idle in New York City, teachers so awful that they are all banished to the rubber room and are collecting $100K/year. They would be taking up 5% of the city’s operations budget for education. In fact, there are fewer than a thousand horrible teachers sitting idle, and the money spent is a fraction of 1% of the budget. So spare me the sturm und drang. When it comes to waste in education, bad teachers are a rounding error.

If principals wanted to make firing bad teachers a priority, they would. The fact that they don’t speaks volumes not about the difficulty of firing bad teachers, but rather the low priority it is for principals.

So. Should it be easier to fire spectacularly incompetent teachers? Sure. Is that what eduformers are interested in? No.

What eduformers say they want is improved educational outcomes, and that improving teacher quality is essential. If that’s really what they want, then no problem, as far as I’m concerned: eduformers, you’re wrong. Give it up. Bad teachers aren’t causing the problems you’re worried about, and they really aren’t that much of a problem to begin with.

What many progressives accuse eduformers of actually wanting is something quite different. Eduformers and their corporate funders are, say progressives, actively seeking to undermine all elements of the traditional educational power structure—unions and education schools—in order to remove teacher job protections and make education much cheaper. They want to turn teaching into a job like any other private sector job, with zero protections and guarantees, no pensions, getting turned out with a few weeks pay when a new boss comes in, no seniority rights. These protections, once guaranteed to many private sector workers, are now a sinecure of government jobs and need to be destroyed. Once teachers are stripped of the protections they have, say the progressives, eduformers will shrug and find a new culprit—and probably push for government to get out of schooling altogether.

I find this accusation extremely convincing. Many eduformers are no doubt well-meaning romantic fools being used by their corporate funders, while other eduformers are explicitly working towards this goal, openly or not.

The thing is, I’m not sure I disagree with that goal. Why should teachers and government workers be protected when private sector workers are not? Why should taxpayer dollars go straight from teacher paychecks to union funds that get handed directly to progressive causes that many teachers don’t support? While we can’t get better results with our current goals, we could undoubtedly get the same results for less money—not that much less, unless pensions got axed. But less.

If that’s the goal, then why not go for it directly? We could revamp the teaching job in all sorts of ways, many of which would give tons more power to good teachers in way eduformers can’t even dream of, cut costs, and—alas—send all the best teachers to the richest schools permanently.

Of course, if that is the goal, no one will admit it directly. Far more respectable to proclaim dedication to poor and underprivileged children everywhere and just incidentally–in the best interests of these children—go after those evil wicked teachers who are ruining childrens’ lives and our country’s future.

Just when I get to that point in the Machiavellian universe the progressives see, I shrug. Naw. Eduformers really are nothing more than naive dreamers who think they understand what’s wrong with our schools.

Not that their motives really matter. As long as they’re blaming teachers, they’re going to fail.

I’m not a fan of unions, so I do find it a tad ironic that I’m counting on unions and their invincibility to stop eduformers from further destroying our schools. At least I’m paying for it to the tune of a thousand or so a year.

¹Not my principal, however, who is a paragon of principals.

The Great Shift

A few years back, Charles Murray wrote Real Education, which he marketed as having four simple ideas:

1. Ability varies
2. Half of the children are below average
3. Too many people are going to college
4. America’s future depends on how we educate the academically gifted

Meanwhile, Mr. Teachbad describes The Great Shift:

It is my responsibility to always be engaging the child, rather than the child’s responsibility to learn how to shut….up, think, and do some thing he or she doesn’t love once in a while. This HUGE shift in responsibility away from students and families and onto teachers is a topic unto itself. It represents an enormous social capitulation and places an utterly unfair burden on teachers.

They’re both largely correct, although I quibble with them on the details. But they’re not just right, they’re correlated.

The American educational system refuses to acknowledge the basic truth behind Murray’s four ideas. I suspect that it would easily accept them if the import of Ideas #1 and #2 weren’t disproportionately allocated by race. Check out exclusively white or Asian high schools and you will find high schools that track ruthlessly, since they have no unsettling patterns in their bonehead classes. Schools whose bonehead classes have over-representation of underrepresented minorities get lawsuits and multi-generational court orders.

So while the educational system refuses to acknowledge reality, it can’t acknowledge reality anyway, because our legal system gets very cranky and starts talking about disparate impact. Our elites get even more upset because, hey, if we can’t move everyone up the ladder equally in our multi-racial, multi-cultural society, then there might be something wrong with the society, and racism is always their favorite culprit.

But regardless of the reason, here we are. If the system can’t accept that abilities vary, and that academic results are strongly linked to cognitive ability, then the system needs someone to blame. The kids can’t be blamed–and here, unlike Mr. Teachbad, I don’t think they should be. They’re not signing up to take trigonometry and poetry analysis and demanding excellent grades for no work. Not that it matters, though, since the system isn’t giving the kids a pass out of kindness but rather necessity. Blaming the kids leads to the obvious solution—take the kids out of the class and, if necessary, out of the school. Back to the disparate impact penalty box and the elites prating about racism and institutional legitimacy.

Government is supposed to protect kids from bad parents, so even if the parents are bad (again, not a major culprit), the public can’t be expected to pony up billions to run schools if the schools are going to shrug and say “wuddyagunna do? It’s the parents.”

That leaves teachers. Mr. Teachbad is correct. It’s extremely unfair. But we can’t resolve it without facing up to the core truths in Murray’s four ideas.

Why higher standards are impossible

Rigorous academic standards are impossible. Full stop. Sorry, Checker (barriers #3 and #4).

Oklahoma’s recent fold is instructive. In 2005, the legislature voted in Achieving Classroom Excellence, a three-part implementation of tougher high school standards. High school graduates, beginning in 2012, would have to pass end-of-course tests in algebra, geometry, English, history, and science.

The math tests didn’t seem like cakewalks ( Algebra, Geometry) although the English test seems rudimentary.

But then, the state provided exemptions, which are an entirely different story. According to the exemption requirements, students could score an 18 on the ACT Math subtest (460 or thereabouts on the SAT) and a 15/17 on the English and Reading tests (430 ditto) in order to graduate. Any student who couldn’t pass the state tests faced a far friendlier standard–and a much lower one.

And yet, even with that low bye, Oklahoma is looking to end the requirement, because at least 6,000 students a year are at risk of not graduating.

Given that thousands of Oklahoma ACT testers can’t meet the exemption standard, which is above the mean for African Americans, and just at the mean for Hispanics and Native Americans, that’s not much of a shock.

I can never tell which side does more damage. Progressive educators set standards embarrassingly low while pretending to teach a challenging “idea-rich” curriculum. They think it’s demeaning to teach low ability kids what they need to know, so instead they “scaffold” advanced concepts and lead the kids through a mock-version of the real thing. So the kids “read” Hamlet, but in fact, all they do is watch a movie and talk about how they felt when their moms let them down. They are given difficult math problems to solve, in no particular sequence of instruction, but they don’t really have to solve them. It’s not the answer that’s important, it’s the process of thinking about the problem, didn’t you know?

And as frustrating and fraudulent as this behavior is, eduformers top progressives with their purely delusional insistence that all students can learn the same advanced curriculum.

Simple question: what is the algebra mastery rate for students with sub-100 IQs? What’s that? You don’t know? Well, it doesn’t have to be IQ. Pick the cognitive metric of your choice and take the bottom half. How are they doing in algebra?

You still don’t know?

Then kindly shut up about higher standards for all.

New Year Resolution

I went a year without writing anything for publication (or attempted publication) because I felt sure that anything I’d write would either be deemed too controversial or too specialized or too opinionated for someone who wasn’t an expert. I kept tossing around ideas but nothing seemed to pass that barrier.

But then, I did write anyway–in the comments sections of a hundred different blogs, spouting my opinions,  telling people they are idiots, whiners, or unrealistic dreamers, throwing in inconvenient facts.  As a commenter I am not nice and am often disrespectful, two qualities (“not nice” and “disrespectful”) that aren’t given nearly their due in online discourse.  Over time, snark and sarcasm with decent data can change a lot of minds. But while I’m a mean and disrespectful commenter, I am not, in fact, a mean and disrespectful person. No, really. And comments don’t leave much room to initiate ideas, to talk about the fun side of teaching, or bring up things that no blogger noticed.  So as a New Year’s resolution, I decided to try blogging.

It’s very dangerous for teachers to engage in any online discourse. I’ll take the usual precautions, but I wish there were clear rules about what teachers can and can’t do. Right now the rule is “If your administrator finds out and doesn’t like it, you’re in a lot of trouble”. I’m also not a natural blogger; I like the many to many discourse format of forums much better than blogging. Hence the resolution to blog, to keep me focused on writing something daily, or close to it.

Education is filled with unpleasant realities that “experts” routinely ignore. Some realities are ignored because the experts have a policy idea they want to sell (literally). Other realities are ignored because it’s ideologically inconvenient to everyone. Still others, however, are ignored because our world is constructed in such a way as to make those realities illegal, or at least actionable.  The National Association of Scholars published an anonymous article by a teacher who called some of these realities The Voldemort View–The View That Must Not Be Named. Hence I will call these realities Voldemortean and, well, name them anyway.

Many Voldemorteans speak with what almost seems like glee. They don’t mean it that way; it’s more a “Hah! got you!” to the ignoramuses who refuse to even acknowledge what must not be named. I will not. I don’t see the Voldemortean realities as good or bad. They just are. And we won’t get anywhere until we start focusing on what these realities mean.

But education has all sorts of other realities, particularly the realities of teaching, and I’ll write about those, too. I love teaching. I do it as my job, I do it in my spare time. For most of my life, I’ve been paid for providing information and giving advice–and, for most of my life, my clients ignored me, even though they agreed with me. In contrast, my student “clients” listen to me. Not every day, not every class, not all of them. But the percentages are much higher than I ever saw in corporate America. I’m hooked.