Monthly Archives: September 2012


I like my current principal more than any of my previous overlords—and I pretty much liked all of them as well. Of course, I never forget they are management, and like all long-term corporate survivors I consider management all-powerful, functionally (not personally) untrustworthy, and utterly irrelevant to my own job performance. They aren’t evil. It’s just baked into the job description. So this opening story isn’t a complaint, just an opening.

We were in a two hour staff meeting today and the principal wandered by. It struck me that until that moment I hadn’t even seen him for three weeks—I mean, literally seen him. I haven’t actually had a conversation with him since the first day of school. In that same period I’ve spoken to the AVP who interviewed me twice for a minute each time, just hi, how are you. I don’t even know the other two AVP’s names; they haven’t stopped by or introduced themselves. No administrator has even entered my room, much less watched me teach.

And this utter isolation from administrators is the norm, for me. I spent two years at my last job; the principal spent a grand total of 40 minutes in my classroom. 20 for evaluation, 20 with a district visitor, all 40 minutes during in the first year, although she didn’t actually give me the results of my eval until a 5-minute meeting the last day of school. She never set foot in my classroom the second year when students were present. Two AVPs spent, collectively, an hour in my room over the first year (about 30 minutes each, spread out over the year), and the AVP who did my eval the second year never spent a moment in my classroom and few even talking to me until the first observation.

My first year as a teacher, I taught at a ultra-progressive school; the principal gave me two hour long evals and a nice follow-up meeting for each. Except for those two evals, however, the administrators were never in my room and I did little more than nod hi to them periodically—it was a smaller school than the other two, so we ran into each other more frequently.

Is it like that for all new teachers? No. If a teacher’s classroom is out of control, the administrators will live there. If the teacher has highly sought after attributes (i.e., young and male) the administrators will do everything short of buying him hookers to win him over, and part of that winning over involves visiting his classroom, giving him lots of praise, extra earning opportunities, and seeking his input on everything short of buying new whiteboard erasers. No, I am not bitter, truly. That’s just how it rolls.

But if a newly hired teacher isn’t spectacularly bad or a hot commodity, he or she is ignored. This gives the administrator complete flexibility without the embarrassment of having to walk back any untoward comments, like praise or condemnation. The first evaluation can be noncommittal, leaving plenty of room to give a second bad one if the district needs to give a few extra teachers the boot, or if a new hot commodity has graduated and someone needs to be cut. (While I am not certain, tenured teachers seem to see administrators more often; maybe they have less to worry about and actively seek them out.)

As I’ve mentioned before, I’m not the hot commodity type, even though I’m a damn good teacher for just three years in. I’m not mad about this, more mildly chagrined and amused. I charge enough money per hour in my private tutoring sessions that my ego’s not at stake, and I’ve long since realized that teacher assessment is largely ideological.

So when eduformers talk about the importance of allowing administrators complete control over the hiring and firing of teachers, I’m like um, what? Are you insane? Principals are managers. They went into management because they find it appealing. That’s fine. It does not make them expert judges of teaching ability. In fact, it probably means they were entirely adequate but not stupendous teachers, because no matter how much you need the money, you don’t leave teaching if you’re stupendous. It’s a drug. And principals simply aren’t spending much time in classrooms; if they do, the other aspects of their job will suffer. PR outranks HR every time. How complicated is that?

Principals have considerable hiring autonomy; unless the district reallocates personnel, they interview and pick their own candidates. In my state they get fifteen months in which they can boot a teacher on a whim. A teacher can get sterling evaluations, be declared teacher of the year, and fired unceremoniously any time in the first two years—in some districts, it can take even longer to get tenure.

That strikes me as adequate time to give principals complete control over staff. After that, giving principals any control at all is spooky, in my view, but I guess most of the time limited firing ability works out because firing long-time teachers on a whim gets the rest of the staff pissed off. But giving them unlimited termination powers? Seriously? Why would we give government employees the autonomy of a small business owner?

If eduformers are absurd in their expectation for principals, progressives—and teachers themselves—aren’t any more realistic in their expectations. When I hear them going on and on about the importance of good leadership, I just yawn. A principal is—must be—focused on selling an image: to teachers, to parents, to the district, to the community. The extent to which he or she keeps the trains running on time is entirely dependent on which trains are carrying the most important passengers at that point in time. That’s their job.

Needless to say, I’ve stopped taking the evaluation process itself seriously. I’m interested in good feedback and suggestions—no, really! But the evaluation isn’t even remotely about me. The principal is interested in contract compliance (all teachers on the evaluation list undergo observation by October 20th. Check.) This evaluation process has nothing at all to do with whether or not the principal decides to keep me, either. It’s just cover.

And I’m fine with that. I just wish I didn’t have to go through the pretense every year that, in this observation, the administrator could suddenly discover that a teacher who has been utterly ignored for two to three months is in fact a wholly unsatisfactory teacher, one who is utterly failing to meet objectives. Really? Three months of nothing, followed by 30-40 minutes of observation, and suddenly the teacher is unsatisfactory? What sort of manager are you Sir or Madame Administrator, that you hadn’t figured that out before?

But in fact, a bad early eval that comes out of the blue is just a sign that the principal has someone else lined up for your job next year. I’d rather they do away with the extra effort, and the principal just had a form that said “Like/Don’t Like (circle one)”. But oh, well. Sorry, Sonny. Make sure the mortician fixes you up nice.

This is a good time to reiterate that at this point in time, given our current determination to delude ourselves about student ability, the existing teacher evaluation and tenure system is the best possible option. Mess with it at your peril. I’m personally certain the adjustments eduformers fantasize about will hurt low ability, low income kids. But that’s a different post.

Geometry: Starting Off

The first day or two of geometry is always point line plane. We never really use it again. Geometry has mostly been subordinated to algebra in high school, as I’ve written before, and my geometry class is best thought of as algebra applications with geometry. Or is it the other way round? Purists see geometry as the medium for introducing proofs, logic, and construction. To which I say pish tosh. Most of them are never going to see those subjects again. “But if they don’t learn rigorous logic in geometry, they won’t be able to learn advanced math!” Yeah, that’s moronic nonsense. What is “solve for x”, if not a proof?

But I love history, so I always start by telling them to put their pencils down and just listen as I explain the significance of Euclid’s Elements and the wonder of a book written 2300 years ago. Three hundred years ago is older than our country. Euclid wrote Elements 300 years before the birth of Christ, so Christ’s contemporaries (the educated ones) thought of Euclid much the way we think of Alexander Hamilton or George Washington. Take seven additional chunks of people looking back 300 years and here we are. A book written that long ago was “in print” over 1000 years before “print” existed, and since then, is second only to the Bible in published editions—not just in the English language, which had to wait another 100 years after the Latin version was published, but in all languages.

As to writing another book on geometry [to replace Euclid] the middle ages would have as soon thought of composing another New Testament.–Augustus de Morgan

Why? Because he* nailed it. For over 2000 years, his model met the world’s requirements, and when the world finally found limits to his model, it wasn’t because he was wrong.

Euclid was nagged by his “fifth postulate”, which is easier to sketch than describe:

That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

If you’re not a mathematician—and I am not—you’re like, um, duh? What else is going to happen? The lines will meet up. But Euclid and other early mathematicians knew the fifth postulate wasn’t the same as the other four, and that’s almost certainly why he established the first 28 theorems without reference to it. For the next couple millennia, mathematicians tried to prove the fifth postulate using the other four, and failed. This collected history of effort around that single postulate ultimately led to the realization that there other, non-Euclidean geometries, many of which (if I understand this properly) begin with the negation of the fifth postulate. This discovery rocked the world, robbed it of a truth previously assumed absolute, and ultimately contributed a bit to Einstein’s theory of relativity.

And 2300 years ago, Euclid needed the fifth postulate to complete his model, furrowed his brow and said, “Yeah, hmm. Something’s not right about that one.”

I tell my students that I’m not a mathematician, and that they don’t need to be, either, in order to realize what a stunning achievement Elements is, and to realize the significance of math in our world that thousands of years ago, mathematicians knew enough to be bothered by a postulate that seemed obvious but was yet somehow different from the others needed for the model. That they, my students, are studying an incredibly old math, one that holds up for our ordinary requirements to this day, but also created the foundation for deeper, more complex models. That if they don’t like math, don’t like geometry, to at least appreciate it from a historical standpoint.

I am probably fooling myself a little bit, but the kids always seem interested. Which is all I’m looking for. Just to show I’m not making this up, here are my board notes:

(Yes, my board work sucks. It’s something I build as I go through a lecture most of the time, a document in progress. I’ve started taking pictures of my boardwork to get a better sense of what I said, what I emphasized, and what I could do to improve boardwork next time.)

Then I go onto undefined terms—not just the terms for geometry, but the meaning of undefined terms. Here, again, Euclid nails the building blocks for his model. (Geometry books give point, line, and plane as the three undefined terms, but I also spend time on “congruence” and “between”.)

Then I show how the building blocks of the undefined terms allow us to define everything else in the Eucliden model. I usually use ray, segment, and angle just to give the the idea.

This year, I decided I wanted to do more with 3-dimensional graphing (xyz) and introduced it as part of this lecture. First, the students learned to represent three dimensional planes without a coordinate system, and see for themselves what happened when two planes intersected. The kids had fun with that; here’s one of the best:

Then we went into more formal xyz graphing. I’m including more 3-d graphing this year to help prepare students for 3 variable systems next year, and also to give the students more variety in visualizing images. Click on the board work below to see that I draw in the rectangular prism, which helps students grasp the difference between 2-axis graphing, in which any two points are a diagonal in a rectangle, and 3-axis graphing, in which any two points are the vertices of a rectangular prism. I heard a lot of “ahas” as I went through this. Not sure what the next 3-d graphing activity will be, but I think I’ve started with a good foundation.

So that was the first day, really. Then I went into the meat of unit one: angle types, angle pairs, perimeter and area formulas, and as always, using these relationships to set up equations and solve with the ever loved algebra.

Here’s the first test. I think I caught all the glitches after I captured this. But I’m sure I missed something; I have a pathological tolerance for typos.

*I’m assuming it was just Euclid. More fun that way.

On the CTU Strike

Okay, unless I missed something, Rahm is CTU’s bitch.

Chicago, which is mostly broke, is hiring more teachers in languages, music and special ed, paying them more salary, paying them for supplies (still very little), paying them for suspensions, agreeing to limit their class sizes, paying their health premiums same as always, maybe even paying them for paternity leave. In return, they got….very little. They can hire new teachers over laid off teachers. They can use test scores for teacher evaluations—up to 30%.

I was enthralled by the CTU strike. Totally fascinated that an extremely overweight, frowsy, no-bullshit, way the hell left of center black woman virtually coldcocked a younger, relatively good-looking hard ass Democrat mayor who’s best buds with the big O.

I’m also pleased with the results, because the media was entirely on Rahm’s side. Harold Myerson and, much later, Eugene Robinson were the only major columnists who came out for the teachers. The Nation supported unions, for the most part. Everyone else slammed the unions hard. There were the cautious skeptics, like Kevin Drum, but almost no one criticized Rahm for being anything but too soft, while there were plenty of CTU beatdowns like this Charles Lane rant, which was truly depressing, since I normally like Lane.

Any story that up and bitchslaps the opinion leaders is a joy to behold. The elites are largely of one mind on education reform, even those who aren’t actually in the reform business; whether neo-liberal or conservative, it’s up with accountability and choice, down with unions who protect “bad teachers”. They really don’t seem capable of grasping that after 10-15 years of non-stop rhetoric on the supposed failure of public schools, they’ve barely moved the needle on public opinion, which isn’t sure whether the rhetoric is true and just not relevant, or a flat-out lie, or some of both. So when the polls showed the Chicago residents supporting the unions (Hispanics and blacks supporting by a substantial majority; whites were at 48%, which is much higher than I would have anticipated given how few white kids attend CPS), it was a hoot to watch everyone struggle to accomodate reality. Hard to call parents stupid when your big current issue is parental triggers, but really, what options are there?

The education reform movement and its growing body of elite adherents live in an echo chamber. Their political success, like NCLB and teacher evaluations via test scores, has been gained by a combination of federal fiat and public indifference for a cause that doesn’t affect most voters and sure sounds noble. Their own surveys reveal that public support for reform causes is soft, but they all keep talking as if they’re riding a wave of political outrage with just those nasty unions—not the teachers, just the unions—opposing the will of the people.

A Gallup poll reveals once again that more people think NCLB made public education worse than made it better, and a large majority thinks it made no difference or made things worse. And that’s when they are asked about education at the national level; everyone knows what Americans think of their local schools. Like Obamacare, education reform isn’t gaining fans with time.

But if I’m right about public indifference/rejection, 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. White parents don’t really want too many Asians around, either, but that’s the opposite of the “bad kids” problem.

Parents don’t care much about teacher quality. They care a lot about peer group quality.

They are right to worry. Before I became a teacher, I’d read other teachers talk about how just a few kids can really disrupt a classroom, moving management from a no-brainer to the primary focus of the day. Now I am one of those teachers. I’ve worked in several schools in which the overwhelming presence of low income students who didn’t care about their grades has utterly removed the “stigma of an F” from the entire population, causing panic in the upper middle income white parents who can’t quite afford private school yet live in a district that worries about lawsuits if they track by ability. Their kids, particularly the boy kids, start to adopt this opinion, and white failure rates start rising.

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.

I really can’t stress this point enough: charters have succeeded because of their ability to control students, not teachers. Comprehensive schools are bound by legal requirements and the constant threat of disparate impact lawsuits. It’s really that simple.

Charter schools don’t scale. What we should be doing, ideally, is “flipping” the populations. Charter schools can focus on one of three populations: low incentives, special ed, or non-native English speakers. Let the large comprehensives focus on the general population.

If comprehensive schools didn’t fear disparate impact lawsuits for expelling problem students and tracking; if free and appropriate education was dramatically limited in scope; if non-native English speakers were expected to learn English on their own, parents in “diverse” districts would become a whole lot less worried about their local schools and the charter movement would take a huge hit.

Wait, where was I? The CTU strike. But it’s related. The strike succeeded in large part because the reform Democrats were shocked to discover that the city population sided with the teachers. While I’m pleased at the outcome for the reasons outlined, costs are still a huge problem, particularly pensions. So what’s the answer?

Rick Hess compares the Chicago strike, brought about by Democrats, to the Wisconsin reforms (assuming they survive the courts). Democrats argue that reform can be achieved by working with unions; Governor Scott Walker just went after pension costs and won (again, so far).

I’m not sure I buy that distinction (although any article that calls Steven Brill a loser gets my vote). Rahm’s not a governor; he could only deal at the district level, and his ex-boss needs unions for his re-election bid. While he seemed to fold on everything, it may be that he had no options once the teachers walked out—again, because to reformers’ consternation, the parents and the public sided with the teachers. Walker had a legislature backing his play.

But I also wonder how much of the difference is due to the fact that Walker focused entirely on cost-cutting, without getting into accountability or merit. It’s one thing for the public to support teachers fighting for air-conditioning and against unfair evaluations, quite another to support their right to free guaranteed pensions on the taxpayers’ dime.

So here is my advice for Republicans:

  1. Focus on government worker pension pcosts. All government workers. No giving cops and firefighters a free ride. (The public supports this, too.)
  2. To the extent possible, scale back existing retirees’ benefits and pay, as opposed to focusing only on new and current workers.
  3. Instead of blaming teachers and unions, blame the frigging courts. They’re the huge obstacle to pension and union reform. Ask Arnold. Ask Scott Walker.
  4. Stop pushing charter schools and accountability. Start talking about the need to bring back tracking, and giving schools control over their environments. Talk about scaling back special education. Accept the Hispanic vote as a lost cause and start asking pointed questions about the cost of educating kids who can’t speak English.

As Rick Hess has noted elsewhere, parents see accountability as a problem for poor people, one they support rather like one supports Brussel sprouts—they taste like crap, but they’re supposed to be healthy. Neither political party is speaking to the hopes and fears of most parents.

So the CTU strike and its outcome, ideally, should resonate as a lasting symbol of the failure of education reform to win public opinion. This could be an opportunity for anyone willing to withstand disapproval by the elite machine that dictates acceptable opinions. That should be the job of Republicans in this environment. I’m afraid they’re not up to the task.

Binomial Multiplication and Factoring Trinomials with The Rectangle

I was reading about Joseph Nebus’s factoring method….

(okay, a brief note. Early in his writeup, Nebus (Joe? Joseph?) writes: “It’s a method for factoring quadratic expressions into binomial expressions, and I must admit, it’s not very good. It’s cumbersome and totally useless once one knows the quadratic equation.”

Many, many math teachers have expelled much breath on the uselessness of factoring, as the skill is completely nullified by the quadratic formula (which I think what he means here). But when they make this comment, they are thinking as mathematicians, not as teachers. Mathematicians work with math to solve problems. Teachers teach math so their kids can demonstrate their knowledge on tests*—not just state tests, but college admissions tests and placement tests. And on these tests, the questions are designed for either factoring or the quadratic formula—and far more the former than the latter. All students must learn to factor trinomials if they are to escape remediation. The quadratic formula is optional. And if the test pragmatism isn’t enough of an argument, please know that students with limited integer operations skills will do better with factoring than the formula because they rarely have squares memorized and please, please believe me when I say that they will ALWAYS subtract 4ac from b squared, even if c is negative. End brief note.)

There are teachers who think this is a science, and teachers who know it’s an art based largely on the audience. And which kind of teacher you are is a religion, or an expression of personality (which I often think is the same thing).

So when I say that the method Nebus describes sounds extremely convoluted, I am simply a Jehovah’s Witness expressing doubt about the utility of the Amish rumspringa.

But many math teachers aren’t even aware of the box/diamond method, and many others who do use it don’t teach it in a fully integrated manner. So for the teachers of the artist mindset looking to find the right method for certain audiences, here’s an outline of the method.

I got the approach from CPM. I don’t know if it originated with CPM, so apologies if the original idea goes back earlier. CPM’s curriculum is insanely irritating: text heavy, lousy examples and insufficient practice. But in many cases, its approach to a topic provides a beautiful, fully integrated, and consistent framework that I steal without shame.

Factoring out common terms

I always introduce the generic rectangle when introducing or reviewing simple factoring (pulling out common terms). The area model uses the fact that the rectangle’s area is both the product of the length and width and the sum of the individual areas. You break up the side of the rectangle into as many different segments as there are terms.

So 8x + 18 is the sum of two areas, both created by a product of length and width. One side is used for both areas, so it must be a factor common to both areas. In other words, what is the greatest common factor of both terms?

Once you find the GCF, work backwards. What do I multiply by 2 in order to get 8x? Most students do well on this, but if they struggle, I show them how to divide in order to find the answer.

I don’t stress its use here, as I do during binomial multiplication; I just want students to be familiar with my use of it. At the same time, I always find a few students who struggle with factoring common terms and find the approach helpful.

Binomial Multiplication

I do not mention FOIL, although most of my students have learned it at one time or another. While I don’t require my students to use any particular method for tests, I require them to use the area model method for binomial multiplication at least for a day or two so they understand the underpinnings of the factoring method.

So obviously, binomial multiplication is the opposite of factoring; the terms go on the outside of the box and generate the individual areas. (x+2) is a segment of length of x and 2, (x+3) a segment of x and 3. I always point out that the lengths don’t need to be accurate or drawn to scale.

I demonstrate this method several times, up front. I explain the area concept again and how multiplication of length times width for each smaller rectangle is the same as the area of the larger rectangle. I don’t really expect my students to be able to repeat it back to me. What I expect, or hope, they will think is “Oh, okay, that makes sense”. Because from this point on, when they think of this method, I want them to remember that the method made sense to them, even if they don’t remember the specifics. That’s also why I don’t write any of this down—most of my students will toss any documentation, anyway. I work a variety of examples (at this point, a=1), picking students to walk through the process.

The kids have a handout with 20-30 problems (this is one of the few topics that kuta software doesn’t have a good handout for), but I don’t have my usual handout online. The original problems would all be a=1, b and c of all signs, because I want them to work dozens of problems and see the pattern, if they are able to. Then, on day 2, 3, and 4, I introduce difference of two squares (what happens to b?), a>1, and 2×3 or 3×3 polynomial multiplication—which works really well with this model, as the kids just make a bigger rectangle.

I wish I could say that this method eliminates the problem of (x+2)(x+3) = x2 + 6. Alas. However, when a student makes the mistake and I scowl and draw the rectangle, with no other explanation, 9 out of 10 kids making the mistake go “Oh, yeah.” That’s the win, such as it is.

Factoring Trinomials

So after a week or so of multiplication, I point out something interesting about the completed rectangle:

This is particularly interesting when we consider the two “middle” terms that add up to bx. We now know that they add to bx and multiply to the same product as ax2 and c.

Interesting, yes, but also useful. I remind the kids that distribution is the inverse of factoring, that distribution converts a product into a sum, while factoring turns a sum into a product. So if they are faced with a quadratic equation in ax2 + bx + c—say, for example, x2 + 9x + 14—how could they turn this sum back into a product?

I ask the kids, if I’d multiplied two binomials to get x2 + 9x + 14, what would have been in the box?

Factoring trinomials is the task of finding the numbers for the other half of the rectangle.

And thanks to the properties of the generic rectangle, we know that the terms we are looking for add to 9x and multiply to 14x2, the product of the first kittycorner.

So we use the “diamond” as a visual tool to help find those terms.

No matter what method a teacher chooses to teach, factoring comes down to that question: What do I multiply to get ac that I add to get b?

I teach the students to write out the factors in pairs, starting with 1 and the number itself (otherwise they tend to forget) and working up from there. Remember that I teach students who will often have a tough time remembering all the factors of 24, and pause on each term to remember the pair.

So once you find the terms that meet the requirements, you put them in the box. It doesn’t matter which goes where. I repeat that phrase a lot. I sometimes wonder if I should create a rule for where the terms go, just so I won’t get the question any more.

It’s worth stressing to your students that, while you’ve found the missing terms, you still have one more step! They’ll still forget, and this will bite them back when they start factoring trinomials in which a>1.

The last step involves finding the GCF for each row. This is where I get the payoff for introducing “single row” factoring much earlier. The students are familiar with the process; they’ve seen me explain that the outside terms are the GCF for a month or more, even if they didn’t use it themselves.

Again, I work five or six problems with the class as a group each day. The kids have a page of 20-30 problems they work through; if they finish one page, I give them another with more complex problems. Anyone who can do the work peels off from the class discussion and works independently from the beginning, the rest are “released” after the class discussion. I put worked examples all over the whiteboards to give them models to follow. Many of my struggling students don’t move past a=1. Some of the weakest will only be reasonable competent at c>0 in the first go-round and struggle with finding the difference of two terms for a while. So over the next two-three days, the kids work on factoring at their own pace. The strongest kids are working a>1 by the last day (and their third page of problems), and working problems like x2 – 9x = 10, learning to set it equal to 0 and factor.

Here’s an example with c<0:

Here’s a>1—and this, by the way, is where anyone can benefit from the generic rectangle. Any other method of factoring a>1 trinomials is a pain in comparison:

I return to factoring throughout the year. Every so often I’ll declare it time to build on existing skills, so kids who had just gotten competent at c>0 can get more practice time on c1, and then the strongest kids start to identify patterns—identifying perfect squares, difference of two squares, and so on.

As time goes on, I give fewer worked examples and just the general outline below, to see how they do at moving from general to specific:

Next Steps

I have traditionally gone from this to completing the square and quadratic formula, then onto graphing parabolas. I am going to reverse these two topics this year. Teach factoring trinomials, then graph parabolas. Get that going well, and then move onto completing the square, quadratic formula, and then graphing those cases. See how that goes.

Finally, I can’t stress this enough: a quarter or more of my algebra classes are low ability kids, so if you’re thinking Jesus, two weeks or more for multiplying and factoring quadratics? then you aren’t teaching low ability kids or you’re just ignoring the fact that they’re flunking your class. My top kids are doing in depth work on the topic or, in some cases, moving onto another topic entirely.

I’ve been getting some people lately asking, or complaining, that “low ability” is vague. I’m sorry, but it’s not. Potter Stewart was right: you know it when you see it. If you want a specific metric, it’s a kid with cognitive abilities measured at the 50th percentile (say, IQ from 95-105, but that’s a guess). In other words, kids that are perfectly functional in the real world, but simply don’t have the interest or ability for advanced math. Kids with cognitive abilities any lower than that aren’t, as a rule, going to be able to even fake it in algebra, much less anything past that. There are always exceptions.

It’s the delusion of eduformers and progressives, one and all, that if teachers find the right approach, a low ability kid is transformed into a competent high ability kid. In reality, success in teaching low ability kids comes when they start to feel a sense of competence at some level of math. When a kid goes from staring blankly at a trinomial to thinking “Oh, yeah” when I draw the rectangle, that’s a big goddamn win. I believe a lot of kids in this category could learn specific high level math in the context of a concrete task, although I have no evidence of this. But we’d have to sort kids into different groups and sorting’s just one big no-no.

However, this method is helpful for kids of all abilities. High ability kids get a real kick out of seeing the link between the area model and the algebra, and I’ve rarely met a kid who didn’t appreciate the utility of this method for a>1.

I don’t have a handout per se for this whole method; what I’ve just laid out is 8-10 days of practice, followed by days interspersed here and there throughout the year. However, if I get a kid who comes in late, or who wants a specific tutorial, I have a document that I really need to rework, which is why I spent some time creating images for this writeup. But remember, all of this is religion and on factoring, I’m in a state of epistemic closure. Convert or live life as a heretic. I was going to say “Die, infidel”, but really, the current insanity in the mideast takes all the hyperbole out of that statement and thus all the fun.

*If you are a mathematician who is also a teacher, stop hyperventilating. It’s true. You know it is. Embrace the reality we live.

My math classes: are they prepared? Um. No. So what?

After over a month talking about policy, it’s fun to write about math classes for a change.

I’m teaching geometry, Algebra II, and Math For Kids Who Haven’t Passed The State Graduation Test Yet.

I’ve given this algebra readiness test to all my students for the past three years. I got it from a senior teacher at my last job, and it’s an excellent assessment of a students’ basic numeracy and first semester algebra skills. Can they substitute? work with negatives? multiply binomials? factor a quadratic? I don’t much care about second semester algebra (graphing parabolas, quadratic formula); my geometry students won’t need it, and my algebra II students will be reviewing the material again.

I know what some of you are thinking. “Why the heck are you giving your geometry and algebra II students a test in pre-algebra and first semester algebra? They already know that material, don’t they?”

This is me laughing at you naive folks. Ha ha!

Or, I could show you a graph of the results.

So the algebra II kids have taken a full year more of math than the geometry kids, and both groups have passed algebra. But the algebra II class is usually taken by kids who made it this far by their toenails, got low scores in both algebra and geometry. Geometry 9 is ninth graders who passed algebra the first time but chose not to take the honors course—and who aren’t in A2/Trig.

My Algebra II class is substantially stronger on average than last year’s class, which averaged around 20 wrong. I’ve got about 8 kids that got 0-2 wrong after finishing the test in ten minutes and should be taking A2/Trig, or even Honors. The Geometry 9 class is slightly stronger on average than my class from last year, which averaged around 12-13 wrong. My geometry classes last year were the strongest I’ve ever taught, but had a much weaker bottom than this class does. The strongest students in the Math Support class got 13-15 wrong, which is impressive.

For the uninitiated, there are two big pieces of info in this graph:

In all three classes but particularly the A2 and Geo, the range of scores on what should be an easy test is huge. The weakest students in both geometry and A2 got barely half right. I’m used to this—handling wide ranges in ability is probably my greatest strength as a teacher, although administrators don’t value it much. However, really think about that range and what it represents in terms of the ability gap within one classroom. And remember–this is a school that provides honors courses, so it tracks much more than my last two schools. The gap this year is considerably less than the scores from last year (which I can’t find, so you’ll have to take my word for it).

The other news is, of course, that the average score for the geometry class should be 5-6 wrong, and the algebra II students should, in a world where we worry more about what kids learn than what their transcript says, knock the test out of the park.

About half the kids in both geometry and algebra II classes should not be taking formal college prep courses, but rather an interesting math applications course, in which they continue to apply what they’ve already learned, rather than pile on new stuff.

Oh, well. That’s what we get for pretending ability doesn’t matter.

I don’t want to sound cynical or discouraged. I’m pumped. They’re a great group of kids and are stronger on average than my last year’s kids, with lots of high achievers. But what’s “normal” for me is clearly not anything that reformers understand or anticipate when they talk about high expectations or proficiency for all.

The Sinister Assumption Fueling KIPP Skeptics?

Stuart Buck on KIPP critics:

It’s unwitting, to be sure; most of the critics haven’t thought through the logical implications of what they’re saying, and they would sincerely deny being racist in their thoughts or intentions. But even granting their personal good will, what they are saying is full of racially problematic implications. These KIPP critics are effectively saying that poor minority children are incapable of genuinely learning anything more than they already do. If poor minority children seem to be learning more, it can’t really be true; there must be some more sinister explanation for what’s going on.
Now here’s the key point: If selection and attrition is what explains KIPP’s good results, then that logically means that several hundred extra hours a year being instructed in reading, math, music, art, etc. do NOT explain KIPP’s good results. But wait a minute: what does that really mean?
Nothing less than this: several hundred hours a years instructing kids doesn’t actually make much difference. Recall that KIPP’s critics say that if KIPP’s students seem to be learning more, it must be an artifact of how KIPP selects kids and then pushes out the low-performers. In saying that, KIPP’s critics are implying, however unwittingly, that no amount of effort or study could possibly get poor urban minorities to learn anything more.

Okay, let me be clear that I am not speaking for any other KIPP critic. While I don’t talk much about KIPP, I am certainly one who thinks their results are due to attrition, creaming, and the benefits that accrue from a homogenous and motivated population.

But yeah. In a nutshell, I’m saying this:

IF you take low ability kids (of any race or income) and IF you select for motivation in the parents, at least, and IF you remove the misbehaving or otherwise highly dysfunctional kids who don’t share their parents’ motivation, and IF you enforce strict behavioral indoctrination in middle class mores and IF you give them hundreds of hours more education a year and IF they are in middle school and IF they are simply being asked to catch up with the material that middle to high ability kids learned fairly effortlessly—that is, elementary reading and math skills…..

…then they will have a slightly better test scores than similarly motivated low ability kids stuck in classes with the misbehavers and highly dysfunctional kids and fewer hours of seat time and less behavioral indoctrination into middle class mores, but their underlying abilities will still be weak and just as far behind their higher ability peers as they were before KIPP.

I’ve written before, improving elementary school or middle school scores is a false god when it comes to improving actual high school outcomes. Children who need tons of hours to get up to grade level fundamentally differ from those reading at or above grade level from kindergarten on, and this difference matters increasingly as school gets harder. High school isn’t the linear steps through increased difficulty that occurs in grades K-8, but a much different and far more difficult animal, now that we make everyone take college prep classes. There’s no evidence that KIPP students are learning more or closing the gap in high school, and call me cynical but I’m really, really sure we’d be hearing about it if they were. KIPP is not transforming low ability kids into high ability kids, or even mid-level ability kids.

I am comfortable asserting that hours and hours of additional education time does nothing to change underlying ability. I’m not a racist, nor am I a nihilist who believes outcomes are set from birth. I do, however, hold the view that academic outcomes are determined in large part by cognitive ability. The reason scores are low in high poverty, high minority schools is primarily due to the fact that the students’ abilities are low to begin with, not because they enter school with a fixable deficit that just needs time to fill, and not because they fall behind thanks to poor teachers or misbehaving peers.

That doesn’t mean we can’t improve outcomes, particularly in high school, when we do a great deal of harm by trying to teach kids what they can’t learn and refusing to teach them what they can learn. And it doesn’t mean we couldn’t tremendously improve elementary school outcomes in numbers, if not individual demonstrated ability, by allowing public schools to do what KIPP does—namely, limit classes to motivated kids of similar ability.

Paul Bruno, another KIPP skeptic (whose views in no way should be confused with mine), thinks it’s wrong to dismiss KIPP achievements, because they show that public schools for low income kids simply need much more money. I disagree. What KIPP “success” shows is the importance of well-behaved, homogeneous classes.

So here’s my preferred takeaway from KIPP and other successful charter schools:

Since it’s evident that much of these schools’ success stories come from their ability to control and limit the population, why are we still hamstringing public schools? Here’s a thought: how about KIPP schools take those really, really tough kids and only those kids? Misbehave too often in public schools and off you go to a KIPP bootcamp, where they will drill you with slogans and do their best to indoctrinate you into middle class behavior and after a while you’ll behave because please, god, anything to get back to the nicer public schools! You could also create KIPP schools for special ed kids–put the special ed kids with cognitive issues and learning disabilities in their own, smaller schools. Meanwhile, public schools could extend the school day a bit, help the kids catch up as much as possible while still making school fun. While the average test score might not improve much, this approach would keep a lot of kids engaged in school through elementary school instead of lost, bored, or acting out in chaotic classes disrupted by a few unmanageable or extremely low ability kids.

See, that would scale a lot better. Instead, we set up small schools for what is actually the majority of all low income students—reasonably well-behaved, of low to middle ability and, with no one around to lead them astray, willing to give school a shot. Only a few kids get into these schools, while the rest of them are stuck in schools where just a few misbehavers make class impossible and really low ability kids take up a lot of addtional teacher time. Crazy, that’s what it is. But what I just laid out is completely unworkable from an ideological standpoint, and as I just explained in an earlier post, school policy is set by ideology and politics, not educational validity. To say nothing of the fact that KIPP doesn’t want to teach “those” kids.

Anyway. The reality is that yes, a low ability kid, regardless of income or race, will not, on average, become a high or mid ability kid simply because he spends a lot of seat time working his butt off in a KIPP school. Sorry Stuart.

The Fallacy at the Heart of All Reform

Rick Hess  often tells education leaders to get over their “allergy” to policy. The first time I read this, I couldn’t  figure out what he was talking about, since education leaders are, for the most part, all about policy. (Teachers are another matter; they could give three nickels for policy.)

But Hess isn’t really mad at education leaders for not involving themselves in policy. He’s chastising them for  not agreeing with politicians on their current policy mandates:

Let me put it this way. If you were an elected official and were responsible for elementary schools where only half of kids are reading at grade level and high schools where only fifty percent of students are graduating, it’d be pretty understandable (and laudable, even) to think you can’t simply trust the educators to do the right thing.

Gosh. Those poor elected officials, trudging along, minding their own business, forced—yea, I say forced!–into the educational arena by the sheer incompetence of schools that can’t get their kids to read at grade level. Let us all bleed for them.

But while we are slitting our veins for a few ounces, some questions: what is this “grade level” he speaks of? And what are the academic expectations of a high school graduate? In fact, when did we declare that everyone should graduate high school, and why? When did we establish guidelines of what appropriate standards are? And aren’t those….you know, it kills me to bring it up, but aren’t those state responsibilities?

Yes, yes, I can hear the reply now. Of course it’s a state responsibility, constitution, blah blah blah. In fact the high school movement, the uniquely American push to increase access to a high school education, was a local movement. But the states want federal money, so naturally the federal government has an oversight role.

But when did the feds start giving the states money for education? Well, that would be when the states started incurring costs imposed upon public schools either by federal law or federal court fiat.

First up, of course, was the Elementary and Secondary Education Act’s Title I, designed to improve educational outcomes for the poor. More money would help the poor and close the achievement gap, so the thinking went–and still goes, although the Coleman Report, issued a year later, established that school spending had far less to do with student outcomes than student SES and background. But the expectation was set into law—all outcomes should be equal. No research, no science, no school has ever proven this out. It was just the sort of blithe expectation we had during the civil rights era that certainly seemed to be true. Unfortunately, when that expectation didn’t prove out, no one seemed to recall that we had no proof that it could ever be true. They just looked for someone else to blame. So the federal dollars came with more and more expectations, demanding an outcome that hadn’t ever been established as realistic to start with.

But Title I was just the start. In 1974, the Supreme Court, in Lau vs. Nichols, required the schools to educate kids in their native languages (ironically, this demand originated from the Asian community; bet they’re happy about that one now!). Then the Court told the schools that they have to educate illegal immigrants in Plyler vs. Doe, denying that there might be a “compelling state interest” in educating only those here legally. Don’t forget busing, disparate impact, free and appropriate education, inclusion….they cover all these court cases in ed school, did you know?

Meanwhile, Congress is busy declaring that children with mental and physical disabilities are guaranteed a free and appropriate public education, regardless of the cost, with a guaranteed Individualized Education Plan following when IDEA is passed in 1990.

So the feds are placing increasing burdens on the local school systems, often in the form of unfunded mandates, other times adding dollars with strings of steel.

These reforms were almost exclusively driven by progressives—liberals who believe that educational inequality is caused by unequal spending, white privilege, racism, prejudice, discrimination….you know that drill, too. Progressives were intent on improving access. While it’s likely that they, too, thought that access would end the achievement gap, they adjusted quickly when that expectation didn’t prove out. By the 80s, progressives in educational policy almost entirely anti-testing. They pooh-poohed SAT scores as racist and culturally biased. They instituted the multi-culti curricum, softened analytical requirements as much as possible whilst giving lip service to that all important “critical thinking”, declared tracking or other forms of ability grouping by demonstrated ability as another means of whites maintaining their institutional privilege, and declared that academic achievement could be demonstrated in many ways. To the extent possible, they ignored or downplayed demonstrated achievement in favor of a student’s effort, community service, and dedication to social justice.

So the original federal mandates were all initiated by progressives.

In contrast, the people we now call “reformers” (that I often refer to as “eduformers”) were largely conservatives. Checker Finn, Mike Petrilli, the Thernstroms, and Diane Ravitch before her switch—all policy wonks in Republican administrations or organizations (except Rotherham worked in a Democrat administration.)

The original reform movement originated as anti-progressive reform. Bill Bennett, in many ways the ur-Reformer, began his stint in the public eye by opposing or castigating many of the progressive mandates. He did his best to end native language instruction when he was Ed Sec, was pro-tracking, against affirmative action, and often castigated teacher unions as instruments of political indoctrination. Back in the 80s and 90s, Checker Finn lambasted the anti-tracking push and derided racial or economic integration as an end to itself, arguing that the important outcome was safe schools with effective teachers, not an obsession with numerical balance. Rare were the reformers who weren’t adamantly in favor of tracking, skeptical of mainstreaming special education kids, and opposed to bilingual education in native language. Educating illegal immigrants is possibly the only area in which reformers might have originally agreed with progressives (and consequently stand in stark disagreement with many parents).

They’ve softened this approach in recent years. For example, Mike Petrilli now writes about differentiation, and can be seen here telling a clearly skeptical, but not oppositional, Checker Finn about the way that differentiation avoids the bad old days of racially segregated approach of tracking. While many reformers used to openly oppose affirmative action, now they’re just really quiet about it, or promote charters for suburban families or selective public schools, both of which are just tracking in a different form (or reform, hyuk). No reformer has ever dared take on the special education mandates and the parental torrents of rage that would turn in his direction were he to be so foolish; instead, they’ll just talk up the charters that get to skate those mandates.

So, for the first twenty to thirty years, progressives dramatically reformed public education through federal interventions. Conservatives opposed many of the initiatives. Progressives denounced opposition as racist and elitist. Conservatives tried to hold progressives responsible for these initiatives through accountability, and declared that parents needed more choice in schools, to get away from the forced control imposed by the progressive viewpoint. Progressives continued to denounce opposition as racist and elitist.

Finally, in the late 90s, conservatives figured out an effective strategy to gain support for their reforms. They took a card from the progressive deck, and demanded that the schools live up to the educational objectives the progressives had set for them. It wasn’t enough just to desegregate classes by race, income, language and learning status. The schools needed to demonstrate that they were teaching everyone equally, that there were “no excuses” for failure. Excuses were—wait for it—racist and elitist. Accountability became the club through which they could achieve choice, and choice would weaken public schools, thus weakening progressives and—not to put too fine a point on it—unions, whose political power the reformers saw as the primary opponent of their political objectives. By demanding equal performance and softening or eliminating their opposition to tracking, bi-lingual education, and all the other progressive hot spots, they could beat the progressives on their head with their own club.

They’d finally figured out the unassailable rhetorical approach. Who could oppose setting mandates requiring everyone—of all races, incomes, and abilities—achieve proficiency? Only racists and elitists. Who could oppose punishing such failure with consequences? Only racists and elitists. Who could oppose giving parents and their students a way to escape from these horrible schools that fail to educate their students to proficiency? Yes, progressives with their excuses of poverty and culture and isolation—they’re the racists. The same people who gave lip service to equality are now fighting the reformers’ efforts to achieve the reality—so not only are progressives elitist and racist, they’re hypocrites, too!

And so, the current reform movement set new federal mandates, which takes those original mandates of the 70s and 80s and shoves them down schools’ throats, hoisting any progressive opposition on its own petard. Unions who opposed accountability on behalf of the teachers, who know full well that equal outcomes are utterly impossible, could now be castigated as anti-education, fat, entitled organizations who protected all the terrible teachers preventing the nation from reaching the dream that progressives started, the dream that progressives have now abandoned, that reformers are finally helping the nation reach. Over time, this approach picked up some new democrats, who aren’t overly fond of unions and tend to sneer at the reputedly low educational achievement of teachers, and the billionaires who Diane Ravitch, now on the other side, excoriates regularly for finding a new hobby.

I’m no fan of progressives, so it’s pretty amusing watching them sputter. They can’t say, “WTF? We never thought everyone would actually achieve at the same level, dammit! We wanted everything to look equal, so that we could browbeat employers and colleges! Tests are racist!” Besides, it’s their idiotic mandates we’re all being forced to live up to now, and they had no more basis for demanding them than reformers do in enforcing them.

So here we are. Schools are stuck with the outcome of two different waves of political reform—first, the progressive mandates designed to enforce surface “equality” of their dreams, then the reforms mandated by conservatives to make the surface equality a reality, which they knew was impossible but would give them a tool to break progressives and, more importantly, unions.

From the schools’ point of view, all these mandates, progressive or “reform” are alike in one key sense: they are bent on imposing political and ideological mandates that haven’t the slightest link to educational validity.

No one has ever made an effective case that non-native speakers can be educated as well as native speakers, regardless of the method used. No one has ever established that integration, racial or economic, improves educational outcomes. No one has ever demonstrated that blacks or Hispanics can achieve at the same average level as whites (or that whites can achieve at the same level as Asians, although no one gets worked up about that gap), nor has anyone ever demonstrated that poor students can achieve equally with their higher-income peers. No one has ever established that kids with IQs below 90 can achieve at the same level as kids with IQs above 100, or examined the difference in outcomes of educating kids with high vs. low motivation. And the only thing that has changed in forty years is that anyone who points this out will now be labelled elitist and racist by both sides of the educational debate, instead of just one.

So back to Hess. Hess’s rationale for political interference starts with the premise that low test scores means failing schools. When Hess says that a politician whose district schools show half or more kids reading below grade level can’t trust educators to do the right thing, he is assuming that half or more kids reading below grade level is a bad result.

Hess is using exactly the same rationale that progressives did when they labelled schools racist/elitist/pick your ist for enrolling fewer blacks, Hispanics, poor kids or dyslexics in advanced classes. It’s the fallacy at the heart of all reform: that all kids can achieve equally.

We don’t know that this is true. In order to call test scores “low”, we assume that all populations can achieve to the same average ability. We don’t know that they can. All available evidence says that they can not, that race, special education status, and poverty are not excuses but genuine, reliable predictors of lower achievement.

But thanks to the combined efforts of progressives and eduformers and their blithe lack of interest in the validity of their expectations, schools are now stuck with mandates that force them to pretend that all students can achieve equally to the same average ability, even though no research supports this. When Virginia bit the bullet to acknowledge that race is in some way related to achievement (note: I don’t think race is a direct factor, just an unsettling proxy), they were browbeaten and hammered into backing down, although I was cheered to see they still used race for achievement goals.

Rick Hess is wrong in saying that education leaders are “allergic” to policy. They are “allergic” to mandates with no relationship to reality. And his sympathy for political leaders who are dragged in reluctantly, poor folks, to spare the kids from uncaring, dysfunctional schools is also misplaced. The problem isn’t the schools. The problem is the mandates—both progressive and reform. The problem is the imposition of political and ideological objectives into the educational world, screaming and howling and suing for five impossible things before breakfast.

*Yeah, I started writing this a month ago and got distracted.