KIPP Mathematica Study and Bragging Rights

After snarling at diCarlo earlier, I can generally agree with his on the one hand, on the other hand analysis of the Mathematica KIPP study. But I have some quibbles:

They show meaningfully large relative gains in all major subjects and on multiple assessments, as well as in other types of outcomes, such as student and parent satisfaction (as is often the case, longer-term outcomes remain an open question).

Understand here I’m talking not as a researcher (which I’m not), but a regular, reasonably well-informed person. Compared to our goals, the gains aren’t that large:

For the full matching sample of 41 KIPP schools, the average impact three years after enrollment is 0.36 standard deviations in math, which is equivalent to moving the KIPP students in our sample from the 44th percentile to the 58th percentile (Figure IV.1).38 Another way of interpreting these impact estimates is to compare KIPP effect sizes to national norms regarding the amount of student academic growth that takes place during middle school (Bloom et al. 2008). Expressed this way, our impacts suggest that on average, KIPP middle schools produce approximately 11 months of extra learning growth in math after three years. For comparison, in study districts there is a gap of 0.90 standard deviations between the average math test scores of black students and white students; students eligible for reduced-price school meals have math scores that are an average of 0.77 standard deviations lower than other students.

The average impact of KIPP after three years in reading (0.21 standard deviations) is somewhat smaller than that for math—equivalent to moving the KIPP students in our sample the 46th to the 55th percentile. This is consistent with a variety of other studies that have found reading scores to be more difficult to move than math scores. In other words, the size of the math impact produced by KIPP schools after three years is equivalent to about 40 percent of the local black-white test score gap and 47 percent of the local achievement gap between higher and lower income students.

(from the study, emphasis mine).

See, that’s what passes for awesome, stop the presses news in educational miracle stories. Not “After three years, KIPP kids have closed the achievement gap.” We aren’t getting, “In high school, KIPP students are getting average scores of 1800 on the SAT”. We aren’t getting “KIPP students are taking and passing 4-5 AP tests” or “KIPP kids are reading at high school level when they enter high school.”

Those would be “large gains”. What we get–and again, I agree this is better than anyone else has managed—is a slightly narrowed gap.

I am not dismissing these results. I’m just sayin’…..well, wait. I said it earlier:

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.

We can and should discuss the possibility of unmeasured factors such as peer effects, but it seems unlikely that these factors would come close to explaining away the estimated impacts.

Um. What? I looked diCarlo up—no, never been a teacher. Okay. Because the KIPP improvements look exactly like what low ability kids could do if problem children weren’t allowed to daily obliterate classroom learning environments. The improvements don’t look like better teaching, better curriculum, or higher expectations. They aren’t miracles. They are the results of motivated, low ability, kids with caring, committed parents working hard in a rigidly disciplined environment and few distractions.

And, as di Carlo notes, it’s the discipline and the longer school day, not the higher expectations or culture, that made the difference. That, too, sounds a lot like peer effects.

I guess some people think that KIPP’s approach works with the problem kids and turns them into hard workers? Yeah, I’m laughing at that idea.

To over-generalize a bit, critics sometimes seem unwilling to acknowledge that KIPP’s results are real no matter how well-documented they might be, whereas some proponents are quick to use KIPP to proclaim a triumph for the charter movement, one that can justify the expansion of charter sectors nationwide.

I know of no KIPP critic who denies the results are real. They all make much the same point—a point that the Mathematical study observes as well:

Students at three quarters of KIPP schools and parents at about half are required to make participation commitments before students enroll, as reported by principals. The “Choice and Commitment” pillar emphasizes that students and parents have a choice to enroll in a KIPP school and that everyone at the school (leaders, teachers, students and parents) make a commitment to do their part to achieve success. After the admissions lottery determines which students are to be offered admission (if applicable), one way KIPP schools implement this principle is by asking parents and students to sign commitment agreements during a home visit conducted by school staff. Almost half of KIPP principals (48 percent) report that their schools have such participation requirements for parents, and principals at more than three-quarters of schools (76 percent) report that students must sign a responsibilities agreement. Principals at KIPP schools in the matched comparison analysis are significantly more likely to report these participation requirements for parents (61 percent) than principals at all KIPP schools.

(emphasis mine)

To KIPP critics, any reluctance to concede that this commitment requirement isn’t all, or at least most, of the ballgame is just asinine, and insulting to boot. A big difference between KIPP critics and KIPP supporters is the degree to which each group believes that public schools could make the same gains, if they could restrict their population to parents and kids willing to accept home visits and sign commitment agreements. KIPP proponents think that the principals with just 2.5 years experience and brand new teachers that can be fired whenever the brand new principals say so contribute to the gains. KIPP critics demur.

It’s very difficult to put a number on this, but it’s safe to say that this model is not a good fit for a very large proportion of students, regardless of background.

Don’t pussyfoot, di Carlo, spell it out: it’s safe to say this model is not a good fit for white or Asian kids, regardless of background. In fact, no research I know of examines KIPP’s impact on white or Asian kids of any income level, because white or Asian parents are unlikely to ever find KIPP attractive.

It also isn’t a good fit for many low achieving black or Hispanic students, of course. But it’s worth remembering that, apart from Jay Mathews when he’s in super-booster mode, no one seriously argues that the KIPP model is acceptable for all but a fraction of a percentage of white or Asian students.

Ultimately, though, di Carlo continues to skate the larger issue. KIPP proponents are claiming that KIPP gets its results from superior teaching and management—and, not incidentally, use their claims and the gains to attack public schools. KIPP’s critics argue that the results are due to skimming the kids with motivated parents, attrition of the discipline problems returning to public schools, fewer special ed or ELL kids, and KIPP’s freedom to ignore constitutional requirements that public schools have to abide by. (I would add one more caveat: I am highly skeptical that the KIPP middle school kids are doing well in high school, or we’d hear of it. But that’s just me.)

On these points, the Mathematica study offers more support to the critics than the proponents.

Modeling Linear Inequalities

I committed to making a big leap forward in inequalities this year. They’ve always been low priority in my curriculum, nothing more than a subset of equations, even though as a programmer, I can come up with fifteen real-life examples of working with them—much more than I can for linear equations. But once I kicked off linear equations with modeling, I could see some obvious introduction points that would help them fall into place. I committed the time to design some new lessons and build some new handouts. And I completely forgot to take pictures of the boardwork, dammit.

Back to tacos and burritos, but this time I took away the “spend all the money” constraint. Stan could either make the purchase or he couldn’t. I gave them some starting combinations to test, and then they came up with their own.

By this time, they are old hands at modeling and easily came up with more true and false pairs. I then graphed all the points on the board, using blue for “True” values, and red for “False”.

“See that space between the TRUE and FALSE values? You can see pretty clearly there’s a line separating them, like this:

“Take a second. What might that line be?” I’m pleased to see several hands shoot up, but I pick on Karl, slinking away from my glance up front. “Karl?”

“I don’t know.”

“What if it wasn’t an inequality?”

“Well, then it’d be 3x + 5y = 60….oh. It’s the same line?”

“Yeah,” chimed in three other students.

“Yes, exactly. We are now working with linear inequalities, not linear equations. Solutions aren’t defined by a single point, but by entire regions. The line is the same in both equations and inequalities, but in an inequality, the line acts as a border between the TRUE and FALSE values. Everything on one side of the line is TRUE, and everything on the other is FALSE.”

From there, I give them one of the new handouts:

I’m really pleased with this one, as a first pass. The students plot the TRUE and FALSE values in different colors. Then they determine which of the linear inequality borders will correctly separate the regions. In one exercise, they become more familiar with solution regions, while also improving their ability to visualize lines from an equation (especially, god help me, positive and negative slopes).

Next, I give them a notes handout I’ve modified over the years.

as well as board notes a few days later:

I made two HUGE changes this year from previous years, changes I suspect most math teachers will recognize.

First, I abandoned “above and below the line” test for the solution region. This seems so obvious to math teachers, but it’s really only meaningful to about half the students. Worse, the test only works with slope intercept form, and has no validity in standard form. The purple math link above tells the student to solve the equation for y—yeah, because solving inequalities is such a breeze, particularly with negatives. It’s a kluge. I didn’t even mention that test.

Instead, I had them use (0,0) for a test value and had them test the value for all forms. MUCH better. No “hey, remember the first way I taught you? Above and below the line? It doesn’t work in standard form, so here’s another way!” Testing values always works.

(Liam in the comments pointed out that the test value can’t be on the border, and I do cover this. I don’t put it in my notes, though. I used to, but the kids would get very confused at the caveat. So now I wait until they are confident of the (0,0) point test and then introduce an example in which the point is on the border equation. I’m discovering that it sometimes takes me a couple years through before I figure out the best way to create fully complete notes.)

Second, I had them write “true” or “false” by the test point, and then shade the same or opposite side of the line. This gave them a visual and kinesthetic step in the process: One, test the inequality with (0,0). Two, write “true” or “false”. Three, shade the correct side of the line.

I’m sure in later years I’ll further hone this, but this was the first time I felt good about my linear inequalities unit. From there, systems of inequalities was an obvious step:

I did a day of modeling systems, but no, I didn’t go onto linear programming.. Instead, I moved onto practicing graphing without the models, and they did great.

I used one of my favorite worksheets as a quiz. The average grade was a B+. Check out this sample—see the “true” markings? By golly, they listened.

I was so emboldened by my success I went onto absolute values, which I usually only cover for tests. They did all right with that, too.

I’m grading the second unit test, covering linear equations, inequalities, and absolute values. So far, it’s looking very good.

Writing for free, but not as a Writer

I can write, but I am not a Writer. Not only am I not a Writer, but the conditions for Writers today are simply not that good, in part because there are people like me who write, but are not Writers.

— Razib Khan

I didn’t think the Nate Thayer hooha had any relevance to my life until I read Razib’s post and realized that I, too, am not a Writer, but someone who can write. Once I wrote a political website that started from scratch six weeks before an election and was selected for the Library of Congress Web Archive; not only wasn’t I paid, I actually forked out some funds for the domain name. I didn’t expect even a token payment when my two op-eds were published in top-ten circulation newspapers, so I wasn’t disappointed. I’ve spent hundreds of hours over the past year writing two essays, which both got a nice reception, for free. I was filling out an application today and was surprised to see how often I mentioned an unpaid writing project as an achievement worth mentioning on my resume.

I didn’t accept non-payment to build up my reputation as a Writer, so that some day I’ll be able to charge for my work, but because I want the validation that comes from a reputable source publishing my ideas, and I want an audience, whatever audience exists to read my ideas. Writing is just the means of creation of a package of ideas, and the ideas are what drive me to write.

Take this blog, which represents hundreds, and eventually thousands, of hours of unpaid writing time. Ideally, it will never be publicly linked to the person who wrote those op-eds and essays for free. It will not be picked up by Education Week and provide me an additional paycheck. I can’t use it on my resume, either. Yet this blog represents my greatest writing achievement and a source of considerable pride, a package of information and ideas validated by the growing audience and the recognition by advocates and reporters. Not in the slightest does it matter whether people know it’s me.

I like to think I write well. But I could never be a Writer. Never mind that I’m too slow, and too long, to do this for pay. Never mind that I love teaching and wouldn’t want to give it up. I don’t want to be a Writer because I’m not interested in telling someone else’s story. Advocacy groups would want me to support one particular position. News sites would want me to offer neutral analysis—except, of course, most education reporters are anything but neutral. Straight reporting would require too many tradeoffs in story selection and that I keep my opinions out of the story. Columnists (at least these days) have to find their place on the political spectrum and get a following, or they won’t be columnists. None of these functions sound appealing—assuming anyone would want me in a paid position in the first place, or that I could convince anyone to pay me to write for them.

So for someone like me, publication at a reputable, critically-acclaimed outlet offers exposure to a larger, or different, audience. The more that people read my work and realize that education is complicated, that pretty much every advocacy position is flawed, and that there aren’t any easy answers, the more I have achieved my goal—with or without money. The only payment that would further my goals would be, say, a book deal, and even then, it wouldn’t be the advance or the status of Writer that mattered, but the validation and the audience that comes with it.

None of this is to say I don’t sympathize with the Nate Thayers, the Writers who are seeing a near cataclysmic decline in income. The Atlantic is seeing record profits, a rare happy tale in a the recent publishing landscape. What does it mean if a publication can only achieve record profits by refusing to pay for the manufacture of its product? It’s one thing to occasionally pick up a well-written piece by an amateur who wants the audience. It’s quite another to just survey the landscape of written work and scavenge the pickings for the article that has the potential to increase their click—wait, we’re calling it “hits” now—count with an author who’ll value the exposure over cash. Is that the future of magazines without a deep pockets dilettante? Editorial vision and quality control secondary to manufacture?

If so, that will ultimately redound to people like me, who write but aren’t Writers, and who have done their bit to contribute to this situation, because one key aspect of our goal is “reputable outlet validating our work”. We’ll just have “hit”-whoring publications who will only care about quality after traffic, and billionaire mouthpieces that pay well, but require a certain viewpoint. And of course, to a certain extent, what else is new?—but really, it’s worse. The market is fragmenting even further, and the disintegration of another gold standard is nigh.

I find it increasingly difficult to get excited about technological innovations any more.

Why Charters Skim, and Why They Should Stop

Matthew DiCarlo of Shanker Blog deconstructs the larger meaning of the excellent Reuters article on selection practices of charter schools.

So, in the “traditional” model, public schools are supposed to be “general practitioners” – they must accept all students and serve them well. The charter/choice model, on the other hand, takes a somewhat different view – schools must accept those who apply, but different models will work well for different students. If we make schools compete for those students by giving their parents a choice, this will encourage schools to develop varying models, and to attract and retain those students for whom their approach is well-suited.
….For example, the flagship model of the charter movement is the high-cost, high-intensity approach of so-called “no excuses” schools, which rely on practices such as tutoring, extremely long school days and rigid discipline policies. But not all students, regardless of their backgrounds, thrive under these conditions, and so some of them leave (or don’t apply in the first place). Despite all the controversy about this selection and attrition, it is a crucial element of a choice-based system – students who don’t fit in well with a given approach will go elsewhere.
….In other words, one might speculate that the sheer extent to which raw absolute testing outcomes are judge and jury serves as an impediment to the “something for everyone” end goal of school choice. So long as these measures are the coin of the realm, operators will tend to compete and innovate for higher test scores, and there may be less incentive to cater to constituencies or develop/expand models that are not necessarily compatible with this priority. (emphasis mine)
…
These regular public schools take everyone they get, but there is a de facto screening process of sorts, by which entry into the schools requires income sufficient to live in the area. Put simply, if you can’t afford to live in a “good” school district, your children can’t attend its schools. That is one big reason why regular public schools are heavily segregated by race, ethnicity and income.

In brief: of course charters are selective. As specialists, that’s their job. And in each district, comprehensive schools act as the “general practitioners” who take all comers. But hey, before you get all righteous about it, public comprehensive schools in desirable districts are exercising choice, and this, too, is a bad thing we should fix.

I like DiCarlo’s work, but this line of thinking is disingenuous crap.

First, catch that guilt trip! All you folks opposed to charter schools, remember that public schools are viciously, ruthlessly, sorting by income. Sure, charters are sorting by ability, but only those kids shut out in the cold after geography does the job.

Then there’s diCarlo’s acknowledgement that while, in theory, each charter could specialize in teaching a different category of kids, in practice, they all want to raise test scores.

But hey, sorting’s reasonable—not the probably illegal methods outlined in Reuters, but the behavioral requirements sorting and academic expectations sorting and all the other tacit methods of getting rid of the unmotivated. Don’t get fussed about charter sorting unless you’re going to go nuclear over those dastardly rich folks keeping their schools free of pesky black or Hispanic poor people.

So let’s see. Public schools belong to districts. Any child in that district can attend the school. The public schools are ferociously bound by state, federal, and constitutional law. But because Americans self-segregate by income, these schools are morally equivalent to charter schools that take public funds, limit/select their population—and then brag about their success in raising test scores while pretending they aren’t selecting.

Yeah, not buying.

Di Carlo ignores the fact that charter school “success”, achieved by this selection, is used to condemn those “general practitioner” schools required to take the leftovers that none of the charters want. Charter school “success” at educating blacks and Hispanics is further used to pummel all schools, rich or poor, who have an achievement gap. Since charter schools can improve on the achievement gap, slightly (none of them have even come close to closing the gap), their “success” is portrayed as an indictment of all teachers, those lazy, fat, union-dependent slobs who just want to phone it in and teach “easy” kids and pretend that the other kids just can’t be taught. Moreover, the “general practitioner” schools forced to take all comers are portrayed as “failing schools” and face risk of closure for not doing as well as the “specialist” schools—except, remember, we’re pretending they aren’t specialists. But that’s okay, because we can start more charters to take on the kids that no one wants, but of course, those schools will “fail” as well—and, since they aren’t bound by the same rules as the true publics, they’ll be able to get away with all sorts of shenanigans.

It’s all based on a huge lie, but apparently di Carlo is okay with this because if we really wanted to change things, we’d force those rich and middle class districts to take their share of the kids no one wants—that is, “economic desegregation”.

Yeah, that’s not going to work. Parents are smarter than edupundits, and far more willing to acknowledge the obvious: school quality is primarily about the peers. Low income parents who compete for charter access do so not to get their kids better teachers, but to get them better classmates. Parents who buy or rent in districts with good schools are paying to keep their kids away from low income black and Hispanic kids—few suburban parents hold their kids’ teachers in particularly high regard (good lord, if they were any good, they’d have been something other than teachers). We tried economic desegregation with busing; it failed. Moreover, the achievement gap holds intact in good school districts; poor white kids still outperform wealthy black kids and tie with wealthy Hispanic kids pretty much everywhere. Not only would economic desegregation be woefully unpopular and drive parents out of public schools, it would fail to close the achievement gap. Bad idea in every way. But until then, apparently, di Carlo is cool with charter selection, dumping the kids no one wants back in the truly public schools.

Does no one find it troubling that charters are using any sort of selection on public funds? Apparently not. This is what bothers me the most. I am repulsed by schools like Bullis Charter suing their local district for public funds to run a quasi-private school, and the only difference betweeen Bullis and KIPP is that all the kids at Bullis are rich.

So what is the answer? I think it starts by accepting that parents want peer effects, and that geographic limits on school districts are natural and normal. Within those limits, public schools (unlike charters) are required to accept all comers.

The answer continues by accepting that some kids have absolutely no desire to be in school, and these kids are disproportionately found in the lowest income communities and schools. While these kids deserve an education, any experienced veteran of low income public schools, whether administrator, teacher, or simple volunteer, can testify that these kids have a profoundly destructive impact on the classroom, on the teacher’s ability to teach and the students’ ability to learn.

So how do we fulfill our commitment to educate all children while still preventing these kids from doing any harm? First, allow public schools to permanently expel incorrigible students. Here, finally, is a legitimate role for charters: let them take the truly difficult kids, the incorrigibles, the willful destroyers. Let them enforce their behavior requirements or their educational agenda or whatever on kids who have no choice but to comply, because they can’t go back to public school.

This agenda, of course, will make it extremely difficult to recruit teachers. Charters will no longer be able to beguile high-achieving do-gooders with romantic tales of helping kids who “just need a chance”, who can pretend, for a few years at least, that they are educating the kids who public teachers just didn’t care about. Instead, they’ll need to pay big bucks to teachers willing to be enforcers to a dangerous population. No takers? Off the kids go to the alternative schools, where they can fill out worksheets.

As for those well-meaning philanthropists who want to give a boutique education to a few select low-income kids, let them start a private school.

What would such a policy entail? Well, the impossible. We would have to accept that permanently expelled students would be disproportionately black, Hispanic, male, and low-income—but that the students who benefit from this policy would also be disproportionately black, Hispanic, male, and low-income. Then we’d have to accept that this policy would not magically improve academic performance of low-income students, and that charter schools educating the toughest kids would have an even more dismal record of academic achievement. And none of that’s happening, which is why the Education Realist’s opinion is not heavily sought in educational circles, be they eduformer or progressive.

But consider what this would achieve. Poor kids would be given a secure and welcoming school environment without the requirement of a parent willing to enter a lottery. The kids who routinely destroy that safety and security would still be educated, but in a tougher and more restrictive environment, losing some rights due to their behavior. Knowledge of this dire fate might—just might—make more kids appreciative of the environment they have, and less likely to act out.

Giving all kids a safe, controlled environment in which they can learn and feel that the larger society cares about them, whether or not their parents do, is no small thing. Couple that with an incentive to behave, because otherwise a much tougher school awaits, and maybe a number of borderline kids will stay and “invest”, as TFA rather tediously puts it.

So what it comes down to, really, is who determines what kids should be expelled for the good of the majority. Right now, charter schools are making this determination and sending these kids back to the genuinely public schools, who have to take everyone. It’s time to look at giving public schools that determination, and leave charter schools to experiment with the genuinely hard to educate, as opposed to skimming the kids who want to learn. It will scale better, if nothing else.

On Graduation Rates and “Standards”

Stephanie Simon has a piece out on the increasing graduation rate (while I’m at it, mad props to Simon for the charter school piece, which probably did a lot to alert the general audience to charter selections), and various tweets are hailing the good news but—and this is the funny part—expressing concern that this increase rate might be due to schools lowering standards. Checker Finn has also written disapprovingly of credit recovery.

hahahahahaha. This is me, laughing.

Imagine you have forty 18 year olds, who all read and calculate at the 6th grade level, and another group of forty who all read and calculate at the 10th grade level. They are all high school seniors in a state that requires graduation competency tests. Of this overall collection of eighty, the following distribution is entirely unexceptional (and of course, not the only one possible):

1. Fifteen screwed around from the moment they entered high school, have a GPA in the tenths, and are currently in alternative high school filling out worksheets. No reason to worry about high school graduation tests, though, because they passed them first time out.
2. Fifteen are, on paper, identical to the previous group, except they haven’t passed any of their graduation tests and so some of their high school time is spent in test prep instead of worksheet completion.
3. Fifteen are far behind because they went to a charter school that prided itself on making kids repeat grades, and after two years of failure they went back to public school. They’ve passed the high school graduation tests, and have been doing well since they left the charter, GPAs of 2.0 or so. But they’re far behind, so are taking two hours every day to do online credit recovery.
4. Fifteen are at a charter school, where they have a 4.0 GPA with a bunch of AP courses on their transcripts, (thanks, Jay Mathews and your horrorshow of a Challenge Index) but haven’t passed the high school graduation tests.
5. Ten recovered from an early bad start, have a solid 2.5 GPA, but haven’t passed their state graduation tests. Half of them have IEPs and official learning disabilities (which means, of course, they aren’t in charters), and so they’ll just waive the requirement. The others will keep plugging away.
6. Ten have a solid 2.5 GPA after an early bad start and have passed their state graduation tests.

(Note: In case it’s not clear, the kids who can pass the state grad tests are the ones with tenth grade abilities, the ones who can’t are the ones with sixth grade abilities).

Any diverse high school district in the country, surveying its population in comprehensive, alternatives, online campuses, and charters, could assemble those eighty kids without breaking a sweat.

On the lower half of the ability spectrum, grades and credits are utterly pointless differentiators. Once you accept that we graduate thousands of kids who can’t read, write, or add, there’s no reason to cavil at the method we use to boot them out of the schoolhouse.

No, don’t yammer at me about persistence or compliance or god spare me “grit” of illiterates plugging away at school and therefore being more deserving of the diploma than the lazy but somewhat smarter kid. The concern about the increase was not about persistence or compliance or grit, but academic ability.

And so, rest easy, people. We are already graduating illiterates. The increased graduation rate is not achieved by teaching more kids more effectively, nor is it achieved by shovelling through the bottom feeders and thus devaluing high school diplomas. We are simply taking kids, whether near-illiterate or low but functional ability, who fell off the path that our other near-illiterate or low but functional ability kids stayed on, and putting them on a different conveyor belt.

How? As Simon’s article makes clear, by spending lots and lots of money:

* Launching new schools designed to train kids for booming career fields, so they can see a direct connection between math class and future earnings

* Offering flexible academic schedules and well-supervised online courses so students with jobs or babies can earn credits as their time permits

* Hiring counselors to review every student’s transcript, identify missing credits and get as many as possible back on track

* Improving reading instruction and requiring kids who struggle with comprehension to give up some electives for intensive tutoring

* Sending emissaries door-to-door to hound chronic truants into returning to class

Notice that only one of the techniques used actually involved teaching the kids more—not that I’m in favor of forcing kids to give up electives for intensive tutoring (I still have nightmares). But most of the money spent involved forcing or coaxing the kids back to school—and while the kids are mostly low ability, they are no less and often considerably more intellectually able than kids who just happened to jump through the right hoops.

How does this happen, you ask? As I’ve said many times: grades are a fraud.

Or you could put it another way: the increased graduation rate is a triumph of administrators over teachers. Teachers, except those in majority minority urban schools, are flunking kids with little regard to ability and a whole bunch of regard to compliance, with no regard to administrative or societal cost. Administrators are spending money to work around teacher grades.

In this context, bleats about academic standards do seem a bit….well, silly, don’t they?

And now someone is going to say, “You’re absolutely right. We should be failing kids who don’t or can’t do the work, put teeth into the Fs. That’s the only way to raise academic standards.”

Sorry, that fool’s wrong, too. Higher standards are impossible. No, really. Common Core advocates, much like Mark Wahlberg at the end of Boogie Nights, are parading their favorite toy in front of a mirror in the desperate hope they’ll convince themselves, if no one else. (What, too much? Yeah, it’s late. I’m feeling bleak.) I very much doubt Common Core will ever be implemented (no test, no curriculum, baby), but if it is, nothing will change.

People assume that kids in the bottom half of the ability barrel are there because they suffered a deficit in environment, in parental attention and expectations, in teacher quality. Would that this were so.

Given all the money we’re spending on truancy officers, online credit recovery, counsellors to spot missing transcripts just to push kids through to a diploma, we might just want to consider teaching low ability kids less at a slower pace and stop pretending that they have a “deficit” that can be addressed by college level work and high expectations. We could create a hell of a curriculum for high school kids using nothing more than 8th grade math and vocabulary.

But we won’t do that for the same reason we won’t track, and for the same reason that adminstrators are spending a fortune coaxing kids back to school: namely, the racial distribution would make everyone wince.

Skills vs. Knowledge

E. D. Hirsch is all upset because teachers are deluded about the importance of knowledge (content), emphasizing skills such as critical thinking and written expression over content. A Common Core true believer, he is shocked, shocked I say! at the fact that most teachers think they are already implementing Common Core, but think its ability to impact achievement is minimal.

Fundamentally, the problem educators face is freeing themselves from the skills stranglehold. It is preventing them from understanding the Common Core standards, preventing them from meeting their own goals as professionals, and preventing them from closing achievement gaps between poor and privileged students.

We see evidence of it everywhere, especially in the MetLife survey. Nine in ten teachers and principals say they are knowledgeable about the Common Core standards, and a majority of teachers say they are already using them a great deal. At the same time, teachers, especially in later grades, are not all that confident about the effect the Common Core will have.
…..
The fact that so many teachers (62%) say the teachers in their school are already using the Common Core standards a great deal shows that these “thought leaders” are correct: most educators remain unaware of the massive changes that fully implementing the new standards will require. But everyone has been talking about these changes for more than a year. Clearly, the message is not getting through.

I have no dog in this hunt; I emphasize content knowledge in all my teaching subjects, but think Hirsch, who believes the achievement gap can be closed, is a tad deluded himself on its magical qualities. I also agree with the utter invincibility of the teacher population when it comes to resisting changes they don’t want to make, and let it be known that I join with my brethren in this resistance, because a cold, cold day in hell it will be before, say, I teach literacy in my trig class or come up with a project-based implementation of the power laws.

But I thought this graph interesting.

Hirsch on this graph, from the 2010 Met Life Survey:

I’ll let the executives off the hook for not knowing that the problem-solving and critical-thinking skills they are after depend on the knowledge that they (largely) dismiss. The teachers ought to know better. That just 11% think knowledge of higher-level science and math are essential for college and career readiness is appalling.

Okay. So the executives AGREE with the teachers, and DISAGREE with the thought leaders. But never mind, he’ll be noble and overlook their stupidity, because they were taught using this horrible skills-based method and it apparently didn’t serve them well. Oh, wait.

And please. Can we stop pretending? Trigonometry, chemistry, physics, and calculus are utterly non-essential for success in the real world. They are only essential for signaling to colleges that the student is a smart cookie, and as Ron Unz and Chris Hayes both point out, the value in that varies based on the student race and family SES (including where Mom and Dad went to school).

So can we give it a rest on the pieties?

Of course, now that I think on it, E. D. Hirsch is a thought leader, so I guess it makes sense he’d back his own against teachers and Fortune 1000 executives.

Modeling Linear Equations, Part 3

See Part I and Part II.

The success of my linear modeling unit has completely transformed the way I teach algebra.

From Part II, which I wrote at the beginning of the second semester at my last school:

In Modeling Linear Equations, I described the first weeks of my effort to give my Algebra II students a more (lord save me) organic understanding of linear equations. These students have been through algebra I twice (8th and 9th grade), and then I taught them linear equations for the better part of a month last semester. Yet before this month, none of them could quickly generate a table of values for a linear equation in any form (slope intercept, standard form, or a verbal model). They did know how to read a slope from a graph, for the most part, but weren’t able to find an equation from a table. They didn’t understand how a graph of a line was related to a verbal model—what would the slope be, a starting price or a monthly rate? What sort of situations would have a meaningful x-intercept?

This approach was instantly successful, as I relate. Last year, I taught the entire first semester content again in two months before moving on, and still got in about 60% of the Algebra II standards (pretty normal for a low ability class).

So when I began intermediate algebra in the fall, I decided to start right off with modeling. I just toss up some problems on the board–Well, actually, I start with a stick figure cartoon based on this lesson plan:

I put it on the board, and ask a student who did middling poorly on my assessment test, “So, what could Stan buy?”

Shrug. “I don’t know.”

“Oh, come on. You’re telling me you never had $45 bucks and a spending decision? Assume no sales tax.”

Tentatively. “He could just buy 9 burritos?”

“Yes, he could! See? Told you you could do it. How many tacos could he buy?”

“None.”

At this point, another student figures it out, “So if he doesn’t buy any burritos, he could buy, like,…”

“Fifteen tacos. Why is it 15?”

“Because that’s how much you can buy for $45.”

“Anyone have another possibility? You? Guy in grey?”

Long pause, as guy in grey hopes desperately I’ll move on. I wait him out.

“I don’t know.”

“Really? Not at all? Oh, come on. Pretend it’s you. It’s your money. You bought 3 burritos. How many tacos can you get?”

This is the great part, really, because whoever I call on, and it’s always a kid who doesn’t want to be in the room, his brain starts working.

“He has $30 left, right? So he can buy ten tacos.”

“Hey, now, look at that. You did know. How’d you come up with ten?”

“It costs $15 to get three burritos, and he has $30 left.”

So I start a table, with Taco and Burrito headers, entering the first three values.

“And you know it’s $15 because….”

He’s worried it’s a trick question. “…it’s five dollars for each burrito?”

I force a couple other unwilling suckers to give me the last two integer entries

“Yeah. So see how you’re doing this in your head. You are automatically figuring the total cost of the burritos how?”

“Multiplying the burritos by five dollars.”

“And, girl over there, in pink, how do you know how much money to spend on tacos?”

“It’s $3 a taco, and you see how much left you have of the $45.”

“And again with the math in your head. You are multiplying the number of tacos by 3, and the number of burritos by….”

“Five.”

“Right. So we could write it out and have an actual equation.” And so I write out the equation, first with tacos and burritos, and then substituting x and y.

“This equation describes a line. We call it the standard form: Ax + By = C. Standard form is an extremely useful way to describe lines that model purchasing decisions.”

Then I graph the table and by golly, it’s dots in the shape of a line.

“Okay, who remembers anything about lines and slopes? Is this a positive or a negative slope?”

Silence. Of course. Which is better than someone shouting out “Positive!”

“So, guy over there. Yeah, you.”

“I wasn’t paying attention.”

“I know. Now you are. So tell me what happens to tacos when you buy more burritos.”

Silence. I wait it out.

“Um. I can’t buy as many tacos?”

“Nice. So what does that mean about tacos and burritos?”

At this point, I usually get some raised hands. “Blue jersey?”

“If you buy more tacos, you can’t buy as many burritos, either.”

“So as the number of tacos goes up, the number of burritos…”

“Goes down.”

“So. This dotted line is reflecting the fact that as tacos go up, burritos go down. I ask again: is this slope a positive slope or a negative slope?” and now I get a good spattering of “Negative” responses.

From there, I remind them of how to calculate a slope, which is always great because now, instead of it just being the 8 thousandth time they’ve been given the formula, they see that it has direct relevance to a spending decision they make daily. The slope is the reduction in burritos they can buy for every increased taco. I remind them how to find the equation of a slope from both the line and the table itself.

“So I just showed you guys the standard form of a line, but does anyone remember the equation form you learned back in algebra one?”

By now they’re warming up as they realize that they do remember information from algebra one and earlier, information that they thought had no relevance to their lives but, apparently, does. Someone usually comes up with the slope-intercept form. I put y=mx+b on the board and talk the students through identifying the parameters. Then, using the taco-burrito model, we plug in the slope and y-intercept and the kids see that the buying decision, one they are extremely familiar with, can be described in math equations that they now understand.

So then, I put a bunch of situations on the board and set them to work, for the rest of that day and the next.

I’ve now kicked off three intermediate algebra classes cold with this approach, and in every case the kids start modeling the problems with no hesitation.

Remember, all but maybe ten of the students in each class are kids who scored below basic or lower in Algebra I. Many of them have already failed intermediate algebra (aka Algebra II, no trig) once. And in day one, they are modeling linear equations and genuinely getting it. Even the ones who are unhappy (more on that in a minute) are getting it.

So from this point on, when a kid sees something like 5x + 7y = 35, they are thinking “something costs $5, something costs $7, and they have $35 to spend” which helps them make concrete sense of an abstract expression. Or y = 3x-7 means that Joe has seven fewer than 3 times as many graphic novels as Tio does (and, class, who has fewer graphic novels? Yes, Tio. Trust me, it’s much easier to make the smaller value x.)

Here’s an early student sample, from my current class, done just two days in. This is a boy who traditionally struggles with math—and this is homework, which he did on his own—definitely not his usual approach.

Notice that he’s still having trouble figuring out the equation, which is normal. But three of the four tables are correct (he struggles with perimeter, also common), and two of the four graphs are perfect—even though he hasn’t yet figured out how to use the graph to find the equation.

So he’s doing the part he’s learned in class with purpose and accuracy, clearly demonstrating ability to pull out solutions from a word model and then graph them. Time to improve his skills at building equations from graphs and tables.

After two days of this, I break the skills up into parts, reminding the weakest students how to find the slope from a graph, and then mixing and matching equations with models, like this:

So now, I’m emphasizing stuff they’ve learned before, but never been able to integrate because it’s been too abstract. The strongest kids in the class are moving through it all much faster, and are often into linear inequalities after a couple weeks.

Then I bring in one of my favorite handouts, built the first time I did this all a year ago: ModelingDatawithPoints. Back to word models, but instead of the model describing the math, the model gives them two points. Their task is to find the equation from the points. And glory be, the kids get it every time. I’m not sure who’s happier, them or me.

At some point in the first week, I give them a quiz, in which they have to turn two different models into tables, equations, and graphs (one from points), identify an equation from a line, identify an equation from a table, and graph two points to find the equation. The last question is, “How’s it going?”

This has been consistent through three classes (two this semester, one last). Most of the kids like it a lot and specifically tell me they are learning more. The top kids often say it’s very interesting to think of linear equations in this fashion. And about 10-20% of the students this first week are very, very nervous. They want specific methods and explicit instructions.

The day after the quiz, I address these concerns by pointing out that everyone in the room has been given these procedures countless times, and fewer than 30% of them remember how to apply them. The purpose of my method, I tell them, is to give them countless ways of thinking about linear equations, come up with their own preferred methods, and increase their ability to move from one form to another all at once, rather than focusing in on one method and moving to another, and so on. I also point out that almost all the students who said they didn’t like my method did pretty well on the quiz. The weakest kids almost always like the approach, even with initially weak results.

After a week or more of this, I move onto systems. First, solving them graphically—and I use this as a reason to explitly instruct them on sketching lines quickly, using one of three methods:

Then I move on to models, two at a time. Last semester, my kids struggled with this and I didn’t pick up on it until a month later. This last week, I was alert to the problems they were having creating two separate models within a problem, so I spent an extra day focusing on the methods. The kids approved, and I could see a much better understanding. We’ll see how it goes on the test.

Here’s the boardwork for a systems models.

So I start by having them generate solutions to each model and matching them up, as well as finding the equations. Then they graph the equations and see that the intersection, the graphing solution, is identical to the values that match up in the tables.

Which sets the stage for the two algebraic methods: substitution and combination (aka elimination, addition).

Phew.

Last semester, I taught modeling to my math support class, and they really enjoyed it:

Some sample work–the one on the far right is done by a Hispanic sophomore who speaks no English.

Okay, back at 2000 words. Time to wrap it up. I’ll discuss where I’m taking it next in a second post.

Some tidbits: modeling quadratics is tough to do organically, because there are so few real-life models. The velocity problems are helpful, but since they’re the only type they are a bit too canned. I usually use area questions, but they aren’t nearly as realistic. Exponentials, on the other hand, are easy to model with real-life examples. I’m adding in absolute value modeling this semester for the first time, to see how it goes.

Anyway. This works a treat. If I were going to teach algebra I again (nooooooo!) I would start with this, rather than go through integer operations and fractions for the nineteenth time.

On John Quincy Adams and His Photograph

Of late there’s been notice that John Quincy Adams was photographed once or twice (the link is to Razib Khan’s thoughtful post). I’m not sure why the meme started; the picture has been around for decades. These articles seemed to have kicked off the trend.

The two original articles I read paid little attention to the man himself.

This is the man who authored the Monroe Doctrine declaring the US closed for settlement, who was probably the greatest Secretary of State in our history at a time when Sec of State was the second most important job in government. When Andrew Jackson overreached by invading Florida, Adams seized the opportunity to acquire the territory. When the US got involved in an ill-advised Second War for Independence and got mostly trounced, Adams negotiated the Treaty of Ghent, giving Britain next to nothing and keeping what the US had. This man, as both president and ex-President, strongly supported American nationalism and growth, but nonetheless had a relatively sympathetic policy towards native Americans and was one of the great early anti-slavery activists in Congress, routinely fighting the gag rule and, of course, defending the rights of African slaves in the Amistad case; both his opposition to slavery and his support of native Americans mark a profound difference from his much lionized successor, slaveowner and Cherokee remover Andrew Jackson.

Many who see the picture marvel that photography was around to capture a man with such a strong relationship to the founding fathers—how amazing it was that we have a picture of a man who knew Washington and Jefferson. One of the founding fathers was his dad, of course, and he knew many of the early leaders well. But arguably, he was a founding father, less than a decade younger than Alexander Hamilton. Washington—the man, not the city—considered him an extraordinary young diplomat after reading his series of articles in support of Washington’s Proclamation of Neutrality. Hamilton and Jefferson fought passionately over domestic policy and saw foreign affairs largely in terms of their own ideological preferences (not that this is a bad thing), while their boss listened and decided, usually in Hamilton’s favor. But neutrality was Washington’s own priority, one he developed from his own experience and values, decidedly rejecting both of his key advisers’ advice. That the first president appointed JQA to his first diplomatic position as US minister to the Netherlands on the strength of that series, read his letters home carefully, and used phrases from those dispatches in his Farewell Address speaks to Quincy Adams’ impact on early US foreign policy.

Like his father, JQA was a cranky misogynist and an unpopular but not necessarily terrible one-term president. He shared the founding fathers’ early vision of the country as a republic, in which an elite and well-informed minority undid the will of the impassioned people, hence his acquiescence to the original Corrupt Bargain.

He had a massive stroke in the House Chamber while voting against a resolution to award medals to Mexican-American War generals (he opposed the war and its treaty saying it would only exacerbate sectional tensions and lead to civil war, and by golly, he was right), dying two days later. Abraham Lincoln was part of the delegation escorting his body home to be buried in Massachusetts.

And while we’re mentioning photographs of people who knew the founding fathers, how about a shout out for this lady on the right?

The socialite Dolly Madison carved the path for the ceremonial but none-the-less essential role for first lady, serving in that capacity for the widow Thomas Jefferson as well as for her husband James. While she didn’t personally cut down Washington’s portrait, she was unquestionably the person who identified it for rescue, along with a copy of the Declaration of Independence. She refused to leave Washington until the last minute when the British army was a few miles away, and rushed back to the city as soon as possible, understanding the importance of her symbolic presence.

But I digress.

Is there any tidbit of information in this Atlantic article or the Daily Mail piece even a tenth as interesting as any one of the facts I’ve outlined above? Both pieces are more interested in minutiae about the pebble in the man’s eye, and maybe a brief mention of hey, he knew the founding fathers!

Yes, it is insanely cool that this man lived long enough to be captured by photography—not because of who he knew, but because of who he was.

Spring 2013: These students aren’t really prepared, either.

I’m teaching Geometry and Algebra II again, so I gave the same assessment and got these results, with the beginning scores from the previous semester:

I’m teaching two algebra II classes, but their numbers were pretty close to identical—one class had the larger range and a lower mode—so I combined them.

The geometry averages are significantly lower than the fall freshmen only class, which isn’t surprising. Kids who move onto geometry from 8th grade algebra are more likely to be stronger math students, although (key plot point) in many schools, the difference between moving on and staying back in algebra come down to behavior, not math ability. At my last school, kids who didn’t score Proficient or Advanced had to take Algebra in 9th grade. I’d have included Basic kids in the “move-on” list as well. But sophomores who not only can’t factor or graph a line, but struggle with simple substition ought not to be in second year algebra. They should repeat algebra I freshman year, go onto geometry, and then take algebra II in junior year—at which point, they’d still be very weak in algebra, of course, but some would have benefited from that second year of first year.

Wait, what was my point? Oh, yeah–this geometry class class is 10-12, so the students took one or more years of high school algebra. Some of them will have just goofed around and flunked algebra despite perfectly adequate to good skills, but a good number will also be genuinely weak at math.

On the other hand, a number of them really enjoyed my first activity: visualizing intersecting planes, graphing 3-D points. I got far more samples from this class. I’ll put those in another post, also the precalc assessment.

I don’t know if my readers (I have an audience! whoo!) understand my intent in publishing these assessment results. In no way am I complaining about my students.

My point in a huge nutshell: how can math teachers be assessed on “value-added” when the testing instrument will not measure what the students needed to learn? Last semester, my students made tremendous gains in first year algebra knowledge. They also learned geometry and second year algebra, but over half my students in both classes will test Below Basic or Far Below Basic–just as they did the year before. My evaluation will faithfully record that my students made no progress—that they tested BB or FBB the year before, and test the same (or worse) now. I will get no credit for the huge gains they made in pre-algebra and algebra competency, because educational policy doesn’t recognize the existence of kids taking second year algebra despite being barely functional in pre-algebra.

The reformers’ response:

1) These kids just had bad teachers who didn’t teach them anything, and in the Brave New World of Reform, these bad teachers won’t be able to ruin students’ lives;

2) These bad teachers just shuffled students who hadn’t learned onto the next class, and in the Brave New World of Reform, kids who can’t do the work won’t pass the class.

My response:

1) Well, truthfully, I think this response is moronic. But more politely, this answer requires willful belief in a delusional myth.

2) Fail 50-60% of kids who are forced to take math classes against their will? Seriously? This answer requires a willful refusal to think things through. Most high schools require a student to take and pass three years of math for graduation. Fail a kid just once, and the margin for error disappears. Fail twice and the kid can’t graduate. And in many states, the sequence must start with algebra—pre-algebra at best. So we are supposed to teach all students, regardless of ability, three years of increasingly abstract math and fail them if they don’t achieve basic proficiency. If, god save us, the country was ever stupid enough to go down this reformer path, the resulting bloodbath would end the policy in a year. We’re not talking the occasional malcontent, but over half of a graduating class in some schools—overwhelmingly, this policy impacts black and Hispanic students. But it’s okay. We’re just doing it for their own good, right? Await the disparate impact lawsuits—or, more likely, federal investigation and oversight.

Reformers faithfully hold out this hope: bad teachers are creating lazy students who could do the work but just don’t want to. Oh, yeah, and if we catch them in elementary school, they’ll be fine in high school.

It is to weep.

Hey, under 1000 words!

A new year begins—midyear

As I mentioned, my school runs a block semester schedule—we cover a year in a semester, four classes each semester. So Monday starts the new year.

I will be teaching Geometry and Algebra II again, although the geometry class will be 10-12 instead of the freshmen of my first semester. One Geometry, two Algebra IIs and, for the first time, pre-calculus.

Note that I am teaching four classes, which means no prep period, and 33% more pay. I am pumped. Okay, a little bit because of the pay, but mostly for two reasons.

Reason 1: Admins don’t give a teacher extra work unless they are happy with the teacher. I have now had two observation writeups so glowing that I keep checking back to see if the name is mine. I know I’m a good teacher. I’m just not used to the principal agreeing with me. More importantly, the administrators seem to like me for the right reasons. Both the principal, who did my observations, and the AVP of the master schedule (the one who reawakened my algebra terrors finally came to see me teach. We had a whole conversation.) both mentioned the quality of my explanations which, many will be surprised to learn, is rarely considered important by either administrators or ed schools. I don’t know why. They also like the fact that I pass most of my students, and keep low ability kids engaged, which is a skill of mine that all previous administrators have used for their own purposes, but never acknowledged as rare or useful. Anyway. I don’t know if they’ll keep me, but it’s very nice, if unusual, to be appreciated.

Reason 2: In my state, a math credential has two levels. One qualifies the teacher to teach through Algebra II, but a third test is required to teach Algebra II/Trig and beyond. I have passed all three tests, passed them first of all the subjects I’m qualified to teach, passed them before I went to ed school by a whole year. And yet, in my first three years of teaching, administrators have on several occasions given advanced math classes to other teachers, teachers who had not yet passed the third test, despite several attempts. Their decisions, done purposefully and in full awareness of the facts, then necessitated a letter home to the students’ parents, per NCLB, that their kids’ teacher was not qualified to teach the class. This is what is known as a penalty. And they took this penalty instead of giving me classes that I was actually qualified to teach. In one case, the administrator didn’t like the other teacher any better than me, had told him to his face he was a “useless brick”, and yet still gave him three Algebra II/Trig classes, giving me Algebra II, taking the penalty, instead of giving him A2 and me A2/Trig. She did not mean this as a personal affront, and I did not take it as such. Such madness as this is pretty normal, and it’s why teachers laugh hysterically when eduformers yammer on about giving principals complete control over hiring and firing. Anyway. As a result of these previous administrator decisions, I have never taught an advanced math class. Not once. Ever. I have no idea how to teach pre-calc. I have no idea how to talk to students who are taking a math class for some other reason than “I need it to graduate”. I have even less idea how to teach an entire class of people who–please, please, PLEASE god—know a positive slope from a negative one. I can’t wait.

I have a friend who is a professor at an elite public university, in a field that requires a lot of math. Back when I was first tutoring and learning math on the job, and got hired to teach a student pre-calc, I asked him “What topics are in pre-calc?” He sniffed, snootily, and said “Precalc isn’t a subject. It’s an administrative category.” I must have learned a lot of math in the intervening years, because I get the joke now.

I’ve got a book, so I’ll figure it out. But if any pre-calc teachers have broad topics to organize around, I’d love to hear about them.

In addition to teaching a full-schedule, no prep period, I start my yearly ACT class on Monday, and in a month I begin my AP US History review classes, two of them. I dropped my English enrichment class, though, so for the first time in seven years, my Saturday mornings are free. I love late winter/spring. But with all this extra money I may just take the summer off for the first time ever.