Isometries and Coordinate Geometry

Michael Pershan’s post on teaching congruence reminded me that way back in the beginning of summer, I’d been meaning to write up some of my geometry work, which I think is pretty unusual. Still on the list is the lesson sequencing, but here is some thoughts and sample problems on integrating Isometries and coordinate geometry.

To summarize my earlier work, explicated in Teaching Congruence, or Are You Happy, Professor Wu?, I was unhappy with the circular reasoning that geometry books present in congruence sections. Triangle ABC is congruent with Triangle DEF because all their sides and angles are congruent, and congruence is when the shapes have congruent sides and angles. Professor Wu’s writing taught me the link between congruence, similarities, and isometries (aka, transformations, or translations, rotations, and reflections). I’d previously skipped isometries, since the kids don’t need them much and they’re easy to figure out, but this discovery led me to use isometries as an introduction to congruence and similarity.

But all book chapters on isometries are very thin, or they rely on non-coordinate shapes, which is largely a waste of time. Was there any way I could bring back some other concept while working with isometries, particularly with my top students?

Which leads me straight to coordinate geometry. The most immediate tie-in is helping students figure out rotation, the most difficult of the transformations. A 90 degree rotation around a point involves perpendicular lines (“..and class, what is the relationship of perpendicular slopes, again? Class? Waiting!”). Moreover, the kids learn that the slope of the line connecting a point and its reflection must be perpendicular to the line of reflection. Finally, dilations involve all sorts of work with parallel lines. All of these reinforcements are excellent for weaker students, and are yet another reason to introduce transformations, even if only as a prelude to congruence.

But I wanted a meaningful connection for my top students, who usually grasp the basics quickly. What could I give them that would integrate algebra, coordinate geometry, and a better understanding of transformations?

Over the summer, I taught an enrichment geometry class to seventh graders whose parents got mad because I wasn’t assigning enough homework. My boss backed me–thanks, boss!—and the kids did, too—thanks, kids!—and not for the usual reasons (these are not kids who celebrate a lack of homework). The kids all told the boss that they were surprised that they weren’t able to just follow the pattern and churn out 50 problems of increasing difficulty in the same vein. “I have to really think about the problem,” said more than one, in some astonishment.

So, for example:

Homework: Reflect Triangle LMN [L: (-1,4), M: (0,7), N: (-4, 10) over line y=x+2. Prove it.

So we discussed the steps before they left. I actually posed it as a couple of questions.

1. If you sketched this and just estimated points the reflection, what would be the key information you’d need to pin down to go from “estimation” to “actual answer”?
2. Can you think of any coordinate geometry algorithms that might help you find these points?

And working with me, they came up with this procedure for each point:

1. Find the equation of the line perpendicular to the reflection line.
2. Find the solution to the reflection line and the perpendicular line. This solution is also the midpoint between the original point and its reflection.
3. Using the original point and the midpoint, find the reflection point.
4. Prove the reflection is accurate by establishing that the sides of the original triangle and the reflection are congruent.

And here it is, mapped out in Desmos—but honestly, it was much easier to do on graph paper. I just wanted to increase my own Desmos capability.

This is the cleaned up version. Maybe I should put the actual work product here. But I’m not very neat. Next time I’ll take pictures of some of the kids’ work; it’s gorgeous.

When we came in the next day, the kids excitedly told me they’d not only done the work, but “figured out how to do it without the work!” Sure, I said, and we then predicted what would happen with the reflection of y=x+3, y=-x + 4, and so on.

But what about reflecting it over the line y=-2x?

Gleesh. I didn’t have time during summer to investigate why the numbers are so ugly. The kids got tired after doing two points, and I told them to use calculators. But we did get it to work. We could see the fractions begin in the perpendicular line solutions, since we’re always adding .5x to 2x. But would it always be like that?

However, I’ve got one great activity for strong kids done–it reinforces knowledge of reflection, coordinate geometry, systems of equations, and some fairly messy algebra. Whoo and hoo.

Down side–for the first time in two years, I’m not teaching geometry this year!

All the more reason to document. Next up in this sequence is my teaching sequence. But if anyone has ideas about the translation that makes the second reflection have such unfriendly numbers, let me know.

Hey, under 1000!

Older Teachers

So I’m the opposite of “blocked”, lately. Lots of ideas and a laptop that’s annoying me. I had two, gave one away and the one I kept hangs so often (memory problems) that I get distracted waiting and watching Broadchurch (not too happy with who the murderer is obviously going to end up being on that one) or not watching Breaking Bad (me and four other people, apparently). Then I fall asleep because hey, it’s the first month of school and that’s how it rolls. So now I have four different ideas, plus two or three straightforward teaching writeups to do, and that’s not good because then I feel overwhelmed and start watching TV shows I’ve already seen 50 times (hello to the mother ship, L&O). I don’t know how actual bloggers do this. Fortunately, I’m just an essayist.

Then a friend who relocated for her job mentions that her husband, a 42 year old teacher, hasn’t yet found a job. I remember telling her when she first got the job to assume that he wouldn’t get hired (she makes enough for that not to be a problem), and she said that I wasn’t the only one to warn her. He has a lot of experience and two master’s, but in most inter-district (much less state) transfers, teachers lose next to all their seniority, so it’s not just about money. It’s a lot about money, but not all.

So I thought I’d talk about older teachers. This is purely an opinion piece; I’m not even sure how much of it I’ll think in a year.

If you know any successful 40-something idealists who dream of “giving back to the community” by becoming teachers, ask if they have jobs lined up. If they don’t, ask them if they are spending a lot of money on their teaching credentials. If they are, tell them to go to a state school. It’s well documented that ed school selectivity is irrelevant in hiring decisions, and they’re going to have enough trouble finding jobs without worrying about loan forgiveness. I can’t really say I’m sorry I went to an elite ed school, but I never fail to consider it an example of luxury spending, as opposed to an educational investment.

Research on this subject is thin, but I did find one study on CPS principal hire/fire decisions on new teachers:

and

(Note: I suspect the bias against male teachers is at the elementary school level. At the high school level, I see a huge preference for male teachers that I’ve mentioned time and again.)

Anything else I say would be anecdotal. Check any teacher training cohort and see who’s last to sign with a school—assuming they have any candidates over 40, they’ll be the last hired, if they are so lucky. Read any story about “firing ineffective teachers” with deep skepticism. And giving administrators full hire/fire over all teachers would lead to a lot of forty-plus teachers losing their jobs. I saw three teachers, two of them in math, targeted and forced into retirement because the principal wanted “new blood” (the principal said as much, often, to anyone who would listen). All teachers have stories like that. All teachers know that the reason job applications ask about education credits is to weed out older applicants. And some teachers think it’s a great idea.

Lately, there’s been a push to reform pensions, push more money to teachers up front. After all, the thinking goes, it will be fairer to teachers who leave the profession:

First, districts should jettison their current approach to retirement benefits, in which teachers accrue relatively meager benefits through much of their careers, and then abruptly become eligible for much more as they near retirement age. In its place, districts should adopt retirement systems where benefits accrue smoothly, year after year, without sudden, arbitrary jumps late in a teacher’s working life. This would allow talented people to teach for part of their career, or teach in more than one district, without harming their retirement security. It would also end an unfair practice that places the majority of teachers on an insecure retirement savings path in order to support more generous pensions for the minority who work a full career in one system.

So we’ll make it easier for teachers to quit and get a little bit of money, and not have to pay as much in pensions. Saves money, right? Fine. Stop talking about fairness to new teachers, then, and focus on cost-savings.

Education reformers are profoundly clueless about what really drives teacher benefits and, I think, genuinely clueless about what really drives administrators. Paul Bruno has an interesting idea that teacher tenure is a perk. Bruno cites Mathew DiCarlo, who reviews the same study I linked in above from a different perspective (although he agrees that the discrimination against men and older teachers is troubling):

…there is little support for the idea that principals are just dying to fire at will – or that, once dismissed, teachers can easily be replaced by “better” alternatives – despite sometimes being taken for granted in our education debates. Although they are far from conclusive, and pertain only to probationary teachers, the descriptive results discussed above tentatively suggest that the supply of appropriate replacements may not always be quite as robust as is often assumed – and/or that there may be some other reasons for low dismissal rates that are not entirely a function of the difficulty of doing so.

What I take away from all this is complicated, but I think relevant. First, coupling the study with my own anecdata and that of many years in the workforce: principals, like all management, exercise their biases. Given the peculiar nature of teaching and its employment structure, I can build a good case that principals be prevented from doing this more than managers in the private sector. Managers pay a price in productivity if they fire good people purely because of their biases. Principals don’t, in the main. Productivity in schools is a complicated issue.

At the same time, most principals don’t fire teachers often because it’s incredibly hard to find new ones. Better the teacher who shows up on time and gets the job done than too many unknown quantities in any given year.

So a principal who is allowed to exercise biases could always defer to his or her particular preferences on a one-off basis, firing probationary or even tenured teachers for age, gender, race, or teaching philosophy, while in the main keeping teachers when in doubt because of the pain of hiring new teachers. Even more unnerving, that principal could keep genuinely weak teachers while firing/dumping good teachers that just happen to activate a bias. For example, keeping an ineffective new young teacher completely intimidated by her students, while dumping or threatening to dump a new older teacher who does a good job. (Not anything I’d have any experience with, nope.)

But wait, say reformers. Principals are constrained by productivity just as private sector management is! Yeah, this is me laughing at them: ha, ha. Of course, private sector management can exercise bias around the edges, and do. But in the case of older teachers, there’s that pesky money problem, too. Older workers in the private sector can adjust their salary if need be, if their value to the company isn’t as great as it once was. Teachers can’t. So take an existing bias against older teachers and toss in the added expense they usually represent, and the whole situation gets worse.

Ah, says the eduformers. That’s why we should revamp teaching entirely! Change the salary structure, don’t reward older teachers as much, and there’ll be less of a bias against them. Let teachers change districts! Let them move to different states! Let districts shift teachers around where they are most needed! (Hey, one of these things is not like the others.)

To which I say, again, eduformers, you aren’t reading the tea leaves. Finding teachers is the holy grail, not firing them. Most people don’t really have a clue about the enormous scale required to maintain millions of people in a job that has quite a few constraints on it—from regimented potty breaks to fingerprint checks to college degrees and competency tests.

So suppose we create the freedom to hire and fire at will, and we give teachers the same ability.

Let’s imagine some possibilities: A teacher can contract with three different districts to teach a popular AP US History course. Or maybe he’s just really good teaching math to low ability kids, and works three classes at two schools. Still other 50 year old teachers kick back and decide they have enough money. They want to teach three classes and then consult as a master coach in another district. Still others teach a couple classes and then go work in ed schools.

Not just 50-somethings, either. A lot of 5-year veterans decide they want to take off and raise their kids for a while, but are happy to put in a few classes here or there.

Meanwhile, very few teachers with any seniority or any talent are ever found at low income schools. No reason. Nothing to keep them there. In fact, any teachers with any talent have realized they have an easier life contracting out a couple classes a year part-time to a suburban district than teaching full-time in a low income district. Once districts are allowed to actually compete on salary, paying by negotiation instead of salary schedules, rich districts will compete heavily for desirable new teachers. Schools with undesirable kids, not matter how much money they have, will be forced to rely on teachers who view the work as a calling, not being able to count on seniority-bound teachers who probably would have switched elsewhere if they weren’t financially precluded from doing so.

In other words, if teachers are allowed to compete on skill and salary, the results might not exactly be what eduformers imagine. They appear to envision a world in which teachers are still committed to a district, with just a few more options on each side. I very much doubt that’s what will happen.

I do know that if districts and administrators were asked to consider a world in which everyone had more freedoms, they would almost certainly reject it out of hand. Charter schools operate on a very small level. That's part of the problem.

All of this goes back to older teachers. They’re a straw that almost everyone—principals, districts, reformers, well-meaning liberals who think they understand education, even a lot of genuine progressives—would like to remove, or redirect to some other area. But I'm not sure that one straw leaves without a bunch of others coming along. And very few people seem to understand what that could mean.

This is my fifth year of teaching, a job I love with a passion that surprises me. Yet I'm relieved that I qualify for both a pension and a lot of loan forgiveness at the end of this year because it's entirely possible I won't ever get tenure. I love my current school; it's the only one of my three that I say that about. I think they like me, but I'm expensive. I'm also old, and this district can keep teachers as temporary or probationary for a very, very long time (some teachers here have been temporary for seven years; in elementary school it's worse). Since I'm in math, it should move more quickly for me. But I'd be a liar and a fool if I didn't fear the possibility that right around the time I should be qualifying for tenure, the administration team will find some fault with my teaching, after x years of thinking I'm just fine, and blammo, I'm gone. I would never voluntarily leave this school, even if I didn't love it, because finding another job has routinely been a crapshoot that goes until less than a month before school starts. My usual line is "I've gotten this far because I look young for my age, but around the time I'm fifty-five I'm going to look forty-five and then it's game over."

And what, specifically, led to this maundering post, Ed? It's eval time, baby. And the principal who reviewed me last year took a new job. Keep your fingers crossed.

200,000 Views in 20 Months

I remember reading once that an extravert sees a star fall and says, “Wow, a falling star!” while an introvert sees the same star and says, “Wow, I am watching a falling star!”

So it’s not that my blog hit 200,000 page views, but my discovery of this milestone that matters.

Here’s the growth by month and other time units (click to enlarge):

My blog really took off in June 2012, which I associate with my starting Twitter, coupled with my growing readership among Steve Sailer fans. I had 7100 views in May of 2012. Cut those off, and I averaged about 12.5K views per month from June 2012 to August 2013. For this year alone, I’ve averaged 15.5K views per month through August.

This seems to me like a tremendous amount of activity from someone who has only 354 Twitter followers, although these followers are an influential crew, many of whom have many thousands of followers. My essays do not routinely see more than a few comments, although my regular commenters always have interesting things to say.

But I have no one to compare my activity to. I used to be able to use Quantcast for other wordpress bloggers, but something has changed at Quantcast and I’m too lazy to try and figure it out.

So I will just say again that I am stunned, truly, at these numbers, even if some of them are search spiders—are they still called that?

Primary referrers (click to enlarge):

First of all–Thanks, Steve! My referrers are very much on the HBD side of things. I don’t believe that hbdchick or Chateau heartiste has ever discussed one of my posts directly, but I’m on their blogrolls and get a huge amount of traffic. Thanks to both of them, too. Full disclosure: I can’t understand a single thing that hbdchick says (science is above my head), Roissy is a shocker to the unprepared. Discover Magazine links are from Razib Khan, Taki Magazine and VDare links are from John Derbyshire—thanks to both of them, too.

Joanne Jacobs is the only major education blogger who hits my top referrer list–thanks, Joanne! (The rest of the sites mentioned are where my pieces are linked in to the comments, not blogger referrals. About 25% of those are me citing my own pieces, the rest are other commenters.)

So if you look at my referrals, it looks like my work doesn’t get discussed or read much out of HBD circles.

However, when you look at my outbound clicks, it’s a different story, supported by my most clicked images (not the same as my most linked images, which I didn’t include). From this aspect, it’s clear I’m read by a number of teachers who use my work.

Then there’s my aforementioned twitter follower list, which, small as it is, is filled with teachers, education policy wonks, both think tanks and professors, and education reporters—not people who routinely follow, say, Steve Sailer (although Steve, too, is followed by journalists and writers, of course). I assume they are reading my work? I’m not a devout tweeter, and use it primarily to send out my essays and responses to other education writing. I’m sure they don’t all agree with me, but clearly the education world at large, not just teachers, notices my existence. While I have no idea how to get twitter referrer stats, it’s Twitter that drives a lot of my ed world traffic. I get a lot of deeply appreciated retweet support from Charles Murray, David Pinsen, HBD Bibliography, and Paul Bruno (and there’s a “one of these things just doesn’t belong there” joke in that list somewhere), and if there’s a way to get a complete list to thank, I don’t know how. But thanks to everyone who retweets my work.

I apparently get mentioned on Facebook, but I don’t know how to find these mentions. Thanks to those of you who post about me.

But here’s the weird thing—the other thing that is clear from my referrer stats is that I get a whole lot of search engine traffic. WordPress gives me the most common searches:

Many people are looking for me, and find me. Whoohoo. It’s also clear that my pedagogy posts get a lot of reuse; this makes me very happy. But this is about 5500 posts, which is a long way from the over 30,000 hits I’ve gotten from search engines in the same time period (January 1, 2012 to now). What’s up with that?

I notice this a lot on a daily basis—I’ll be having a big day, based solely on search engine hits. But my blog is not even remotely SEO friendly. It’s clear that people are finding my work for various reasons, but I don’t know who or how.

Back in early May, I listed my most popular essays; you can compare them to the list below.

I remember the first time, back in the 90s, I read a list of the Best Selling Albums of all time and noticing that the list was a combination of recent hits and solid performers over time. I don’t think The Eagles ever had the best selling album in any given year, but Greatest Hits Volume I and Hotel California are well-represented among the top 30 albums. Of course, a musician can have a huge album that is also big over time (just ask Michael Jackson or Fleetwood Mac).

Anyway, that’s the analogy I see in my own essays. Some of them are huge at one point in time, then fall off. Others never had huge numbers, but are solid performers over time. I linked in some performance history—Escaping Poverty and Why Chris Hays Failes were very big by the end of last year, but neither have seen much action lately. The math teaching posts on my list, on the other hand, see unspectacular but solid numbers every month. The true puzzler is my #1 essay, still, Algebra and the Pointlessness of the Whole Damn Thing. It gets a huge amount of action, but I never see anyone mention it. Maybe so many people linked it in that the numbers are just google keeping up with its indexing.

I’m sure more knowledgeable people can explain some of this. I look forward to it.

Anyway. For the past year, this blog has so far exceeded my wildest dreams that I’m starting to think I need to upgrade my goals. Thanks, as always, for reading.

Title	Written	Views
Algebra and the Pointlessness of The Whole Damn Thing	08/12	5,896
Philip Dick, Preschool and Schrödinger’s Cat	04/13	5,408
Teacher Quality Pseudofacts, Part II	01/12	4,101
The Dark Enlightenment and Me	08/12	4,025
The myth of “they weren’t ever taught….”	07/12	3,966
Escaping Poverty	10/12	3,919
Homework and grades.	02/12	3,648
The Gap in the GRE	01/12	3,292
Kashawn Campbell	08/12	2,791
Why Chris Hayes Fails	06/12	2,713
The Parental “Diversity” Dilemma	11/12	2,330
Why Most of the Low Income “Strivers” are White	03/13	2,072
Dan Meyer and the Gatekeepers	08/13	1,968
An Alternative College Admissions System	12/12	1,913
SAT Prep for the Ultra-Rich, And Everyone Else	08/12	1,910
Jason Richwine and Goring the Media’s Ox	05/12	1,803
What causes the achievement gap? The Voldemort View	01/12	1,611
An Asian Revelation	06/13	1,473
Binomial Multiplication and Factoring Trinomials with The Rectangle	09/12	1,347
Teaching Polynomials	03/12	1,314
Teaching Algebra, or Banging Your Head With a Whiteboard	05/12	1,196
College Admissions, Race, and Unintended Consequences	08/13	1,170
Who I Am as a Teacher	07/13	1,132
Modeling Linear Equations	01/12	1,125
Plague of the Middlebrow Pundits, Revisited: Walter Russell Mead	03/13	1,101

These are my works that have over 1000 views; pretty soon I might have to have a higher cutoff. (why won’t it do the spacing properly? Makes me crazy.)

The Takeaway from the TFA Study

Jersey Jazzman’s list of cautions mirrors my own on the TFA study. I would add that the TFA skew towards middle school (in the study) makes a big difference; TFAers push testing excitement heavily in middle school, something that’s very tough to do with high schoolers.

I had an interesting twitter exchange with Morgan Polikoff who, can I just say, makes me feel both ancient and unproductive, about the “significance” of the TFA improvement margin. He explained that hey, that’s what researchers have always used. Well, yeah. I know that. I’m not questioning the study’s use of that particular metric, I’m questioning the value of that particular metric.

Recently, the august NY Times declared that “Guesses and Hype Give Way to Data in Study of Education” but alas, all this knowledge “has another hurdle to clear: Most educators, including principals and superintendents and curriculum supervisors, do not know the data exist, much less what they mean.”

Y’all are going to tell us about it, right? While us teachers are supposed to just go “Wow, thanks! We’ll go put this in action!” (Now I sound like a typical teacher who values practice over data, which I actually don’t, and I find this very annoying.)

But in fact, teachers are actually reading more research than at any time in the past, if only because reformers are presenting us all as a bunch of incompetent buffoons whose results aren’t just equaled, but improved, by smarter, ambitious, desirable college graduates who are in it for the resume improvement. It’s just slightly possible, isn’t it, that when a bunch of teachers become familiar with “research practice”—created by people who usually have very little teaching experience or have been told to ignore that experience in favor of “research practice”—they might question that practice?

Note to those who want to start “educating” teachers on research: expect pushback if you try to sell “significant” improvement that translates to something like a couple questions more on a test. Here’s a small sample of what math teachers will want to know on this particular study: did the TFAers do better at teaching linear equations, factoring quadratics? Were the additional correct questions random, or specific to a content area? Was the improvement consistent over each subject taught, or specific to one subject? Did the classrooms have similar behavior referral rates? Mind you, we’ll see the “significance” as irrelevant either way, but at least we’ll know whether it’s “real”.

But accept the results as “significant” and here’s the big takeaway, hinted at by Dara Zeehandelaar of Fordham:

Both TFA and Teaching Fellows have less experience than their peers, are less likely to be minorities, more likely to have graduated from more selective colleges, less likely to be math majors but more likely to score higher on tests of math content. However, only years of experience and, for high school, math content knowledge were associated with higher student achievement. These findings add to the glut of research indicating that traditional certification programs could benefit from greater selectivity, indeed from a radical overhaul.

Dara is celebrating a future teaching force with fewer blacks and Hispanics. Me, I look at it from the opposite side of the mirror, where it reads something like this:

CAEP, the ed school accreditation organization, is setting new standards that include higher candidate selection benchmarks. Selective ed schools have been left some wiggle room, in that the cohort, not each individual candidate, has to have an average GPA over 3.0 and average test scores in the top third of a nationally normed achievement test. However, it will annihilate predominantly black/Hispanic teacher schools, which include no small amount of public universities. Only 6% of African Americans and 10% of Hispanics get over 600 on each section of the SAT, which is roughly the top 30% nationwide.

So if CAEP doesn’t blink, or ed schools don’t get creative, we will soon have almost no black and Hispanic teachers, since blacks and Hispanics who get over 600 on each section of the SAT go off to become doctors and lawyers and Wall Street hedge fund managers. While the test score requirements will almost certainly be loosened or eliminated as the import becomes clear, our nation will see a lot fewer black and Hispanic teachers. We’ve already cut into the supply back during the NCLB changes, and people are already scratching their heads about these “missing” minority teachers, as Mokoto Rich of the New York Times has termed this, blithely ignoring the reality right in front of her. If the CAEP standards have the intended effect, we’ll lose even more.

But that’s okay, right? Because sure, we’ll lose in the current generation, but the next generation, taught by those newer, brilliant teachers who really care about their kids and aren’t just doing it because it’s some pesky job will raise achievement! Blacks and Hispanics will score the same as whites and Asians! Stricter drug laws will eliminate addiction! Tougher gun laws will prevent Newtowns! Dogs and cats will live together in peace and harmony! Hell, Israel and Palestine will straighten things out.

So the TFA study gives us a preview of that brave new world. TFAers were three times as likely to be white; the control group of teachers had seven times as many blacks. And lo! you see the predictable one standard deviation difference in test score means between the groups. The TFA group is exactly the
highly qualified, selective crew of new penny bright teachers everyone says they want.

And you get .07 of a standard deviation difference in student outcomes.

Of course, we already knew that, since it was an example of what the clearinghouse on education research knows doesn’t work:

For example, Michael Garet, the vice president of the American Institutes for Research, a behavioral and social science research group, led a study that instructed seventh-grade math teachers in a summer institute, helping them understand the math they teach — like why, when dividing fractions, do you invert and multiply?

The teachers’ knowledge of math improved, but student achievement did not.

“The professional development had many features people think it should have — it was sustained over time, it involved opportunities to practice, it involved all the teachers in the school,” Dr. Garet said. “But the results were disappointing.”

So maybe we can add the TFA study to the clearinghouse as additional evidence that past a certain point (unknown), increased teacher ability doesn’t result in improved student achievement. Or are we going to still pretend that .07 of a standard deviation is 2.6 months of instruction, that, as Jerseyman says, the increase is actually “practically” instead of “statistically”, significant?

Both reformers and progressives push “improve teacher quality” as an easy mantra that really doesn’t have much basis in fact. However, reformers go farther. Reformers look at the existing state of affairs and see obvious failure, failure so manifest that it’s a simple matter to fix. Low test scores? Give them teachers who care. Smarter teachers. Higher standards. Over the past decade, their enthusiasm has been blunted a tad by the realization that at best, their “obvious” improvements, if you squint really hard and pretend peer environment is irrelevant, will improve outcomes a squidge around the edges. But still, they keep coming back for more. And so, they push this study as evidence that TFA works, not realizing that the study foretells the lackluster improvement they’ll see at the expense of a virtually closed career path for blacks and Hispanics.

That’s the takeway of the TFA study.

Can someone mention this to CAEP?

College Admissions, Race, and Unintended Consequences

Note: I wrote this before the SAT changed–again.

The Big Reveal on UC Berkeley’s holistic admissions process created much fuss, most of it on behalf of Asians who are clearly the victims of discriminatory behavior.

Most people don’t completely understand how this “problem” came about, and why the UC and other universities are discriminating against Asians. It’s not so much “affirmative action for whites” as it is unintended consequences of being forbidden to use affirmative action for blacks and Hispanics.

The GPA Demographic Footprint

In November of 1996, the UC system was told by the people of California that it was not allowed to consider race in admissions anymore. The UC system, like all universities in this country, wasn’t about to listen to the rabble. So, as Saul Geiser writes, the system went looking for a reason to reduce the weight given test scores.

Such differences in the demographic footprint of HSGPA and standardized tests are of obvious importance for expanding access and equity in college admissions, especially at those institutions where affirmative action has been curtailed or ended. … at those institutions where affirmative action has been challenged or eliminated, admissions officers have been forced to reevaluate the role of standardized tests as selection criteria.
…
The result has been a de-emphasis of standardized tests as admissions criteria at some institutions. …
UC introduced “comprehensive review,” an admissions policy that more systematically took into account the impact of socioeconomic factors, such as parents’ education and family income, on students’ test scores and related indicators of academic achievement. [note: this is the process described in the NY Times article]. UC also revised its Eligibility Index, a numerical scale which sets minimum HSGPA and test-score requirements for admission to the UC system; the revised index gave roughly three-quarters of the weight to HSGPA and the remainder to standardized tests. … Under this policy [of Eligibility in the Local Context], which also took effect in 2001, students’ class rank within high school was determined solely on the basis of their HSGPA in college preparatory coursework, so that the effect of this policy, too, was to diminish the role of standardized tests in UC admissions.

So de-emphasize those evil, racist tests that traditionally represent, in the typical progressive’s mind, a means of reinforcing the institutionalized hegemony of the white man’s values. Grades, in contrast, reflected the school’s values, the school’s priorities. So majority URM schools, both charters and inner city, can put whatever grades they like on classes that can be called whatever they want. UC officials made the change, along with Eligibility in the Local Context, so that majority URM schools could lie about their students’ academic abilities properly reflect the students’ diligence and abilities in subjects simply not valued by the institutional racists at the College Board.

The problem is, alas, that UC admissions made changes to their policy based on the “demographic footprint” of tests, but they forgot about the demographic footprint of grades.

Namely: Asians, particularly recent immigrant Asians, kill whites on grades. The test score advantage is getting (suspiciously) worse, but the grade advantage is huge.

That wasn’t part of the plan. Look, universities know the game as well as anyone: grades are a fraud. That’s why, until relatively recently, all universities weighted test scores as high or higher than grades.

If high school grades were objectively accurate, why does the University of California have an entry level writing requirement?—and why is that writing requirement either a test or a college level course? (And I have my own doubts of college level courses, but more on that later.) Why is remediation a huge issue in state colleges? If high school grades meant anything, schools could just accept students with high grades and hey, presto. Problem solved.

But Saul Geiser is a good researcher, and his study finds that HSGPA is as good or better a predictor of freshman GPA as test scores. Sure. But that brings up another point: Freshman GPA is pretty worthless, too. It’s a metric that goes back to a time when everyone took the same classes. It’s ancient. It predates the growing disconnect between grades and ability.

I’d go further and argue that in total, college GPA is worthless for much the same reasons that high school GPA is. We hear constant stories about grade inflation at elite schools, while public universities are under tremendous pressure to pass as many wholly unqualified blacks and Hispanics as they can, given the huge number that can’t even get past the remedial classes. How can grade point average mean anything in a world that requires some students to pass calculus and while others only take remedial math (which they can skip if they got an SAT score of 600+)?

If college grades were objectively accurate, the “mismatch theory“, for better or worse, couldn’t even be conceived of. If an A at Harvard is the same as an A at Berkeley which is the same as an A at Florida State, then lower ability students couldn’t get higher GPAs at Florida State and Richard Sanders shouldn’t be pushing his mismatch theory. Besides, what do you suppose the renewed push for a college exit exam is about? And in a world where we did require an exit exam, what would be the best predictor of passing rates—college grades or incoming SAT scores? Everyone knows that answer: unless the exit exam was rigged, we’d find that passing rates were best predicted by SAT scores, which would show a distressing, racially uneven, distribution.

I understand that GPAs are a useful metric because the people who use them filter the data through context—race, school, major, and so on. That’s fine, but not when you have the University of California claiming that HSGPA predicts four-year college outcomes when the university in questions sending easily half of its URM admits into remediation classes.

UC knows this. The whole GPA thing is just cover. What did a little lie matter, if it allowed them to bring in more blacks and Hispanics and thwart the will of California voters? The only people hurt would be the kids who didn’t get 4.0s.

Except that turned out to be a whole hell of a lot of kids with really good SAT scores, a whole lot of them white. So let’s look at four UC campuses:

Campus	Ranking	3.75+ GPA	Non-Res	SATR		SATM		SATW600
				% 600+	% 700+	% 600+	% 700+	% 600+	% 700+
Berkeley	1	79	540	38	36	28	56	34	46
San Diego	3	86	1530	42	15	41	42	46	22
Santa Barbara	5	75	228	41	13	47	24	44	17
Santa Cruz	7	33	16	26	6	31	7	24	7

The reality of demographic footprints being what they are, the kids represented by these numbers are almost exclusively white or Asian. Any black or Hispanic getting scores above 600 are usually going to a higher ranked private school. Keep in mind that these stats are leaving out UCLA, Irvine, and Davis, technically ranked second, fourth, and sixth, although the difference between UCSB, Irvine, and Davis metrics are primarily in the demographics.

In other words, a hell of a lot of kids are getting 2000+ SAT scores who aren’t getting into the top 3 schools, while a whole bunch of kids with 1800-2000 scores are. And the difference, for the most part, is grades. In the days before California banned affirmative action, the UCs weighted grades and test scores much closer to evenly—a 3.8 GPA with excellent test scores and a demanding schedule could easily get into Cal or UCLA. No more.

So the GPA edge led to unanticipated consequences and a huge advantage for Asians. But that was just one of the problems.

Changing the SAT

The UC system wasn’t content with just devaluing test scores, so they tried another change that had terrible blowback, again in the Asian category. First, in 2002, Richard Atkinson called for an end to the SAT and a greater use of the SAT Subject tests. By 2005, the SAT had been completely revamped, the College Board having clearly understood the hint.

While I can’t be certain, I think the original changes were intended to increase the number of blacks and Hispanics eligible by making the test burden lighter. At this point, the UC doesn’t appear to have been thinking about Asian overrepresentation. I’m not sure this was caused by anything other than Atkinson’s pet fancy, which is sad, given the consequences—which have gone well beyond Caliornia.

I haven’t been a fan of the new SAT. My sense has always been that it became much easier, and more amenable to swotters. But not until I worked on this piece did I realize how much easier, and how much more apparently coachable it is, particularly for those who take hundreds of hours of test prep. The College Board releases percentile ranks by race and ethnicity, but I can’t find the original files for anything before 2005. (If anyone can, then you’re a hell of a googler and send them my way.)

However, I found a book that cites exactly the file I want.

So in 1995, 14% of Asians, 5.8% of whites, and .6% of blacks scored over 700 in math, which means that the percentile for 700 was 86%, 94%, and 99%. In 2010 (confirm here), those percentiles were 77%, 94%, and 1%.

Only Asians got a lot smarter? Weird. Not impossible. A lot more Chinese and Koreans are taking the test. Not my pick as an explanation, though.

In 1995, the verbal percentile ranks for 700 were (I think) 98.2% Asian, 98.7% for whites, and 99+% for blacks. While this article doesn’t mention it, the 2010 rankings show that the corresponding 700 percentile rankings are now 92%, 94%, and 99%.

Have whites and Asians have gotten a lot smarter in verbal? No. If you won’t take my word for it, check out GRE scores during that time, which was very similar to the 1995 SAT throughout the 90s and before and after, did not see a corresponding increase in scores.

Or–my pick–the reading test has gotten a lot easier, which I’ve been telling to anyone who will listen, and, in my opinion, it’s gotten easier in a way that allows it to be coached more effectively. And the coaching has become more effective over time. Let’s look at all the data together, with a couple more years from the new SAT:

Year	Math 700 %ile		Verbal 700 %ile
	Asians	Whites	Asians	Whites
1995	86	94	98	99
2006	81	94	93	95
2010	77	94	92	94
2012	75	93	91	94

(Cite for 2006, 2012).

Weird. SAT scores are generally pretty stable. Until I started researching this, I had no idea that the Asian increase was that dramatic, and it is part of a series of discoveries over past year making me wonder if the big gap between Asian and white test prep use (and time spent in test prep) is doing more than just giving Asians a slight edge. This piece is long enough without bringing up the ACT, but I believe that a 700 M corresponds to a 32—or it used to, anyway—and notice that a 32 is only 85%ile for Asians. I have been working on these two essays for ten days or so, and I haven’t yet been able to find ACT percentiles by race over the past ten years or so. Reading and English appear to be roughly the same. However, almost three times as many Asians take the SAT as take the ACT.

One other thing to keep in mind—the number of native Chinese and Koreans taking the test has exploded. Are they fluent in English? Ask any university freshman at an elite school with a Chinese or Korean grad student instructor. So by any stretch, the Asian mean should have been dropping slightly, shouldn’t it? Which means either Asian Americans have gotten phenomenally better, the Chinese/Korean nationals are also getting high Verbal SAT scores, or….what? What explains this jump?

Whites had increased scores in reading, which I believe supports my contention that the 2005 changes were easier. Why did white math scores stay stable? That’s part of a longer post that’s all intuition on my part. Suffice it to say that the SAT math section is both shorter and easier. This helps people with high attention to detail who aren’t as intuitively strong in math. (yes, I know, the SAT supposedly tests higher math since 2005. Too long for this post, but I would disagree.) However, I do understand there could be other factors at work.

I’ll write more about various things that might be the cause of the extremely strange boost in Asian math and verbal scores in the next post, but for now, let’s leave it at this: UC had a big problem. The changes they had hoped might improve scores for blacks and Hispanics (my interpretation) had instead led to unimaginable increases in high Asian scores in the SAT.

More Subject Tests! No, wait. No Subject Tests!

The College Board obligingly did UC’s bidding in making the test easier (my read), but UC continued to follow Atkinson’s directive by requiring two optional subject tests. Previously, applicants had to take two required tests that were much easier than the others (Writing and Math 1C), and then one optional test. Now, the Writing and Math 1C tests were disallowed, and students had to choose two of the “harder” subject tests to take. This requirement handed Asians an enormous advantage over whites. To see why, just check out the percentile rankings of the subject tests—but before you do, close your eyes and stereotype like mad. What subject tests do you think Asians are more likely to take? Okay, now look. Get a load of those Chinese and Korean tests! Roughly half of all takers get an 800–and check out how many of the testers are native speakers. My goodness gracious.

Notice, too, the skew on the Math 2c test. I’ve tutored students in both the Math 2c and English Lit tests for around a decade. It is far easier to prep students for the Math 2c than it is the English Literature test. The test is considerably more difficult as well, because high schools directly cover the math subject matter, but don’t cover the English Lit subject matter, which relies far more on, dare I say, innate literary analysis skills.

In general, subject tests aren’t subjected (hahahaha) to the same scrutiny as the SAT. It’s well known, for example, that the score distributions are wacky, and that in certain tests–Physics, I’m looking at you–the lowest score is higher than the usual 200. I’m not a psychometrician, but I’d love to have someone make the College Board explain this document. Why, if more people finish the English test and get the same amount right, are the scores so much lower? Why, given the much higher accuracy rate of the Korean and Chinese listening tests, aren’t the tests made more difficult? But I digress.

And so, just a decade after Richard Atkinson called for an end to the SAT as an admissions tool and complete reliance on the Subject tests, UC does a complete 180, ending the use of subject tests in admissions. Asians knew instantly this was All About Them, and there was little attempt to deny it:

It was also noted that white students seem to be the winners under the new guarantee; this should be of concern to Council. BOARS Chair Rashid acknowledged that the percentage of white students does indeed go up and the percentage of Asian students goes down. The reason for this is that Asian students seem to be very good at figuring out the technical requirements of UC eligibility. If the subject exam is removed, even more white and Asian students meet the requirements of eligibility. Political perception is another concern. This proposal should also not be viewed as the ultimate solution to diversity. It was also noted that the numbers of females goes up under either scenario.

(emphasis mine.)

Please note that bolded comment. They aren’t saying drats, Asians are smarter. Or drats, we need diversity.

Read the rest of the memo to see the various hoops they jumped through in order to get this cover.

Back where it all started
You know what would have been much easier? Require four Subject tests: English Lit, Math 2c, American History, and a Science. Asians would still do well, but it would have been harder. Dump the SAT, dump or devalue grades. If nothing else, we’d be giving smart kids of all races a chance to show their stuff purely through test scores, imperfect as they may be, rather than the vagaries of teacher assessment.

But that gets UC right back to the problem it started with, the reason it emphasized GPA over test scores in the first place, the problem that it created just to give them a cover story for ignoring the will of the California voters (and, eventually, the constitution as interpreted by the Supreme Court). A test-score only admissions process would eliminate almost all blacks and Hispanics from consideration. The problem: every attempt to bring in more blacks and Hispanics leads to more Asians.

Problem? Why is it a problem? Shouldn’t the universities just let the chips fall where they may? If the schools are overwhelmingly Asian, so what?

Well, for starters, relying exclusively on grades leads to Kashawn Campbell at the low end—hell, Kashawn’s story singlehandedly reveals the need for test scores, the fraudulence of high school grades, and the sketchy nature of college grades in one neat little package.

But more importantly, a huge number of the Asians admitted are either nationals or first and second generation Chinese, Koreans, and Indians.

None of what I’ve written or will write is intended in any way to rationalize the discrimination against Asians. Quite the contrary. Any fair admissions process would lead to overrepresentation of Asians. But I hope to persuade readers that college admissions in its current form, in both private and public schools, is so corrupt that getting outraged about discrimination for or against any one demographic is pointless. Any outrage you find is counterbalanced by another, and no, it’s not as if it all works out.