The worst example of curriculum dead wood?

One of the first things that hit me when I started teaching high school math was how much material there was to cover. There was no slack, no real time to slow down when students were having trouble. The most annoying part, though, was the number of topics that could easily have been cut, thus giving the students the time to master the important skills and concepts.

The example that really stuck with me was synthetic division, a more concise but less intuitive way of performing polynomial long division. Both of these topics are pretty much useless in daily life but polynomial long division does, at least, give the student some insight into the relationship between polynomials and familiar base-ten numbers. Synthetic division has no such value; it's just a faster but less interesting way of doing something you'll never have to do.

I started asking hardcore math people -- mathematicians, statisticians, physicists, rocket scientists*-- if they'd ever used synthetic division. By an overwhelming margin, the answer I got was "what's synthetic division?" Not only did they not need it; it made so little impression that they forgot ever learning it.

Which bring us to this passage from a recent Dana Goldstein post (discussed earlier):

The problem, according to [David] Coleman, is that American curriculum standards have traditionally been written by committees whose members advocate for their pet pedagogical theories, such as traditional vs. reform math.

Except, of course, that's not what happened here. As was the case with so many topics in mathematics, synthetic division remained in the curriculum because no one who knew what was going on had bothered to look that closely. Coleman has a clever narrative, but it doesn't fit the facts all that well.

Now I have a request for all the math geeks in the audience (and given that you're reading a blog called Observational Epidemiology...). Since we need to pare down the curriculum, what you choose to cut? Specifically, what mathematical topics that you learned in school can future generations do without?


* Literal rocket scientists -- JPL's just down the road.

Also posted in a slightly different form at Education and Statistics.

We need curriculum reform but we need to do it right

Dana Goldstein is arguably our best education writer and I have long argued that we need curriculum reform, but this post makes me nervous as hell:

Past attempts to develop national curriculum guidelines became mired in culture war controversy, but this latest effort--led by the states, not the federal government--has a real shot at influencing teaching and learning at the classroom level, and hopefully fostering a more rigorous academic culture in American public schools. If administrators and teachers implement the new standards faithfully, how will the curriculum evolve? Let's first look at math.

Currently, American students are taught just a little bit about a whole lot of mathematical topics each year; we have a curriculum with tons of breadth, but not much depth. Check out this chart Coleman showed us from education researcher Bill Schmidt. It demonstrates that while typical first-graders in high-achieving Western European and Asian countries learn just three concepts--quantity, measurement, and addition/subtraction of whole numbers--American first-graders must learn 14 topics, including polygons, circles, how to use a compass, and how to estimate.

The American curriculum may appear more rigorous, but our six-year olds are actually being denied the opportunity to master the foundational skills upon which the rest of their mathematical education will be based. The problem, according to Coleman, is that American curriculum standards have traditionally been written by committees whose members advocate for their pet pedagogical theories, such as traditional vs. reform math. "The only way to end a committee meeting is to let everyone get their stuff in," Coleman said. The result is that teachers feel rushed each year to move through an enormous list of standards. "Students and teachers bear all the weight of this," Coleman pointed out. "The standard writers are removed from this." The goal of the Common Core is, for the first time, to move American math standards in the simplified direction of our international peers.

.....

Before closing out, a few words on the nuts and bolts of the effort to implement the Common Core. The project is a partnership between a number of organizations, including the National Governor's Association; the Council of Chief State School Officers; Achieve, a non-profit testing group created by the governors; the ACT; the College Board; the State Higher Education Executive Officers; the American Association of School Administrators; and the Business Roundtable. The federal government is supporting the Common Core with about $350 million, most of which is dedicated to developing and implementing tests based on the new standards. Federal funds are also being used to create instructional materials and professional development sessions for teachers who will use the new curricula.

The other major supportor of the Common Core is the Gates Foundation, which expects to spend a total of $250 million "to develop next-generation instructional tools and assessments that will help states and school districts implement the standards."

Before I wade into the red flags, the suggestion that the curriculum needs to be greatly pared down is dead on. We do try to cover a ludicrous amount of material, much of it of little value. The explanation given here is too tidy (there are plenty of ways for undeserving concepts find their way into the standards), but it is, at least partially true.

Now the parts that make me apprehensive:

If you take on the paring without some serious thought, you can do more damage than good, and this example seems exactly the sort of thing that someone who hadn't given the subject much thought and who didn't know much about math might come up with;

And on the subject of the people behind the initiative, the list of partners seems rather light on mathematicians and scientists;

The emphasis here on elementary school is troubling. Historically, I believe it's the upper grades where we start to fall behind on international tests. Are we possibly fixing the part that works? This may be a small point but we've seen a long string of solutions that mainly affected areas which weren't actually affected by the problem. This does not inspire confidence;

The focus on international rankings is an even more troubling sign. TIMSS and PISA are too big a subject to go into this late in the evening, but there are a lot of reasons to worry about role that international tests play here. Just for a a brief overview, there are questions about
-- what these tests are really measuring,
-- where the problems with American scores are coming from,
-- what techniques really drove the successes in highly ranked countries,
-- whether those techniques would carry over to other cultures,
-- and finally the one closest to my heart, is there a possible downside to a country that built the world's greatest economy largely on creativity and unconventional problem solving suddenly doubling down on rote learning and regurgitation?;

Nor does the make up of the list of partners reassure me. I've already mentioned the lack of math and science people. As for the rest, the combination of politicians, administrators and businessmen seems awfully like the assortment that got us in this mess to begin with.

Curriculum reform is important but it's also difficult and I've grown rather cynical about the willingness and ability of most reformers to do the hard work and lay a solid foundation to support the big talk when it comes to difficult problems. Perhaps I judge these things too harshly but I haven't read anything here that makes me optimistic.

Is consistency too much to ask?

Paul Krugman points out a nasty trick:

In legal terms, the program is funded not just by today’s payroll taxes, but by accumulated past surpluses — the trust fund. If there’s a year when payroll receipts fall short of benefits, but there are still trillions of dollars in the trust fund, what happens is, precisely, nothing — the program has the funds it needs to operate, without need for any Congressional action.

Alternatively, you can think about Social Security as just part of the federal budget. But in that case, it’s just part of the federal budget; it doesn’t have either surpluses or deficits, no more than the defense budget.

Both views are valid, depending on what questions you’re trying to answer.

What you can’t do is insist that the trust fund is meaningless, because SS is just part of the budget, then claim that some crisis arises when receipts fall short of payments, because SS is a standalone program. Yet that’s exactly what the WaPo claims.

I wonder if the people who want to privatize social security have thought through exactly how bonds held in a 401(k) are different than the trust fund? Perhaps they are more awkward to default (in terms of not paying the bonds) on but governments have raided retirement accounts before. Add in the strange equivocation between "social security" and "social security/medicare" in terms of projecting cost growth (with the second) and targeting the first for reduction.

In general terms, I do not understand why there are such strong objections to income support for people in old age. The program isn't cheap but it widely benefits the majority of Americans (a lot). Why is it such a popular target for debate? Why not debate how high defense spending is relative to the rest of the planet? Or the amazing cost increases in medical care? Why are these not more pressing issues?

I really do not understand because this debate is eating up precious intellectual effort that really needs to be going into comparative effectiveness discussions for medicine.

Pre-blogging David Carr

I'm working on a couple of journalism posts (one about victimology and the other a reply to this post from Andrew Gelman). David Carr figures in both so I thought this would be a good time to provide some background with this clip.



I got this from Chait so I'll give him the last word:

That's actually repugnant. I don't actually think the sentiment reflects the general view of the Times, but I do think the Times deserves to be held accountable. If the newspaper lets reporter pop off on a talk show, then his opinions are going to represent the Times.

California Pension Reform

I have always had a fascination with California politics and we've talked a lot about personal finance. So I read this reform proposed by Jerry Brown with interest:

To deal with what have been widely seen as abuses of the retirement system, Mr. Brown said the pensions of all new employees should be based solely on their regular salaries, not taking into account any overtime or bonuses. For existing employees, he said the retirement benefits should be based on an average of the last three years’ salary.

I was always surprised that it was any other way. After all, employee base salary is a reasonably predictable variable for actuaries. Furthermore, base salary is likely to be more representative of the income that actually needs to be replaced in retirement and inflating that number can lead to very high liabilities. Finally, it creates the potential for unfairness as the ability to get overtime in one's final three years may depend on the discretion of the supervisor.

I am completely against the current assault on pensions but that doesn't mean that we shouldn't look for places where intelligent reforms can happen.

All in all, it seems like a much saner approach. We'll see if it manages to gain any traction!

Another cautionary tale of corruption by metrics

This American Life has a great piece of radio up on their site. (You can get a free download if you hurry.) It's the account of a patrol man who started collecting evidence of rule-breaking in the department. The story itself is remarkable but what makes this piece extraordinary are the audio segments that the policeman covertly recorded, including the incredibly suspenseful confrontation near the end.

There are any number of interesting angles to this story but the one that caught my ear (at least with respect to the discussions we've been having here) is the role that metrics played.

Ira Glass

The New York Police Department declined our request to come onto the radio or to have the officers who supervised Adrian Schoolcraft, and who are heard on his recordings, to be interviewed about their side of all this. But the pressure on police commanders to get better numbers really goes back to 1994, when New York started tracking crimes with a system called CompStat. CompStat, for the first time, gave commanders timely, accurate data once a week on what crimes are happening, so they could send more cops to deal with it. Chances are you've heard of all this. It became one of the best known successes in modern policing. Serious crime has dropped an astonishing 77% in New York City since CompStat began in 1994. Other cities very quickly started imitating it-- DC, Philly, LA. Baltimore's version of CompStat ended up in a recurring plot line on the TV show The Wire, where street cops are told by the bosses to do anything to pump up their numbers. And the problem with CompStat, says Professor Eli Silverman, who studies the way police forces use numbers, is that the early success of CompStat created the expectation that numbers must get better every single year, no matter what.

Eli Silverman
In the beginning it was like an orange. You could squeeze juice from an orange in the beginning much more readily than you can as you extract juice from that orange. And now, it gets harder and harder to drive crime down, because you're compared to not how you were in '94, but how you were last year the same week. And when something's pushed to the excess that it is now, and numbers dominate the system, that's when you have negative consequences.

Specifically consequences like this:

Ira Glass
Then when the officer tried to file it that way, because he didn't have a name for the unauthorized driver, he couldn't file it at all. So the robbery went unreported. Rules go into effect in the 81st precinct that make it harder to report serious crimes. Officers are told that if there's a robbery, one of their supervisors has to come out to the scene themselves. And robbery victims are told that if they don't come into the police station, no crime report will be filed at all. After Graham Rayman started publishing these stories about Adrian Schoolcraft, retired cops and some on-duty cops started contacting him with their own anecdotes about crimes being downgraded from serious to much less serious-- the most shocking of these from a high ranking detective name Harold Hernandez.

Graham Rayman
He's a very distinguished detective. He was working in the 33rd precinct in Washington Heights. And one morning he comes into work and there's a guy who's accused of first degree rape sitting in his interview room. So he sits down and he looks at the guy. And he has a little twinge, and he says, have you ever done this before? And the guy said, yeah. And Hernandez says, how many times? And he says, oh, I don't know, seven or eight. And Hernandez says, where? And he goes, in this neighborhood. And Hernandez is now dumbstruck because there's been no report of a serial rapist-- sexual predator-- working the neighborhood.

Ira Glass
Like, no crimes have shown up. People haven't shown up saying they've been raped or assaulted.

Graham Rayman
He hasn't been notified. And he would be notified as a senior detective in the unit. It would be a very big deal. And so he says, can you give me the dates and locations? And the guy says, well, I can try, but you're going to have to take me around and I'll show. I'll show you. So he and a fellow detective get in the car and they drive around. And they look, and the suspect-- whose name is Darryl Thomas-- points out the locations. And then Hernandez takes his notebook and he writes down the locations. And then he goes back and he looks through stacks of crime complaints. And he finds them. And he realizes that they've been classified-- they've been downgraded. They've been classified either as criminal trespassing or criminal possession of a weapon-- both relatively minor crimes, given that the actual conduct in the narrative that the victims are describing is either first degree burglary, robbery, or sexual abuse, sexual assault. And he confronts his bosses about it. He confronts the precinct commander. And he confronts his detective squad commander. And everyone just shrugs. Meanwhile everyone's terrified that it's going to come out-- that these women are going to go to the press, and it's going to be a huge embarrassment, a huge scandal for the department. And if it had come out, it would have been a huge scandal for the department. But the department was able to keep it quiet. The District Attorney's office prosecuted Thomas and he went away for 50 years. But here's the interesting part-- they never publicized the case. There was never a press release issued about it. There was never a news article written about the case.

One of the reasons that metric-centric systems can become so bad is that they almost always start out as something good. Compstat, like standardized testing, was a good thing and still is, if used properly. At some point though, people start to focus more on the metric, not because increased focus is helpful but because a metric-based approach is so seductively simple. When that happens the metric becomes an end rather than means (the map becomes the thing for all you Korzybski fans in the audience).

That's generally when things go to hell.

Felix Salmon on the implosion of Netflix

Felix Salmon has a great post up on Netflix. You should definitely read the whole thing but this passage in particular caught my eye:

In hindsight, it’s pretty clear that Netflix CEO Reed Hastings let the bubblicious stock price — it briefly topped $300/share at the beginning of the quarter — go to his head. The company was swimming in money! And so, in September, Hastings signed a deal to pay $30 million per movie for everything that DreamWorks creates, in return for the right to stream those movies a few months after they’re released on DVD. It’s known as the “pay-TV window”, and in order to wrest those rights from HBO, Netflix had to outbid HBO, which was reportedly paying something in the neighborhood of $20 million per movie.

There is a huge hype machine out there, powered by a symbiotic PR/press relationship and focused on selling tales of visionary CEOs. These stories are almost always incredibly distorted. In all but a handful of cases, these superstar CEOs are simply competent executives who had two or three good ideas and a great deal of luck.

When you're at the center of all that myth-making (as Hastings was), it can be difficult not to start believing it. When that happens, bad decisions inevitably follow. We've all heard about Hastings' disastrous attempts to wreck a perfectly good business model but I think this example (again from Salmon) might just be more telling:

Maybe the company shouldn’t have spent $40 million, over the course of the third quarter, buying back 182,000 shares at an average price of $218 apiece. (In the wake of today’s results, they’re trading in the $80s.)

While you're there, check out Salmon's tremendously informative discussion of the dynamics of Netflix's stock swings.

Is this an expression you want to see on the face of a woman holding a giant axe?

Just in time for Halloween (via TPM):

A Luddite Portfolio

Radio was supposed to kill newspapers, as were newsreels, slick magazines, television, and the internet. There was even a short-lived attempt to replace newspapers with fax machines. If we start from the Fessenden broadcast, the industry has been dying for ninety-five years and in that time any number of fortunes have been made publishing the damned things.

One of the memes we've heard ad nauseam in coverage of the Netflix story is that in order to survive, a company has to rush forward and grasp the future and divest itself of any vestiges of the out-of-date. This concept of CEO as bold futurist has great appeal, both for businessmen and business writers, but does always jumping on the latest technological bandwagon really work as an investment strategy?

Certainly, investing in cutting edge technologies can yield great returns (so can a winning lottery ticket), but it is by no means a sure bet. There are plenty of examples of innovative technologies that never went that far (the Teletouch transmission and the 8-track come to mind). There are also cases of old technologies that seem destined for obsolescence only to reinvent themselves (how many people in 1950 thought radio would remain viable a half century into the television age?) or that manage to survive as a niche product (did you know that you can still buy vinyl records at Target?).

A very good argument could be made that business writers get overly excited about the next big thing and since buzz can certainly pump up stock prices, there could very well be an undeserved premium on stocks associated with up and coming technologies. That would mean that the Luddite, by avoiding those overpriced stocks, could well have an advantage.

At the very least he would probably have unloaded Netflix when the CEO started talking about moving past DVDs, rather than waiting for the company to start to implode.

Tragic alignment

This NPR report about how the foster care system in South Dakota treats Native American families is an exceptionally powerful piece of journalism. It illustrates how bad things can get when the wrong forces align: poorly designed incentives, the corrupting power of money (in a fairly mild form), racism and class bigotry (also, I suspect, fairly mild), and the obliviousness of most journalists and other watchdogs to what goes in most of the country. This is not a story of bad people; that's what make it so tragic.

If you have a few minutes, follow the link and listen to the account. And while you're there, why don't you send a few bucks to NPR, journalists who actually do care about what happens to people the rest of the media overlook.

Interesting Trading Idea

The reformed broker has a great post on ten things not to do as an individual investor. Here is one that I think is worth keeping in mind in a more general sense:

"The market is all betting one way so of course I'm betting the other way." This works very well at major turning points, which are very rare. In truth, the herd usually outsmarts the remnant and you're much better off being an ordinary zebra in the middle of the pack than straying off on your own into a deep ravine where predators lurk. If there is a turning point you see coming and you want to exploit it, fine - just don't bet your life on it and deploy all your capital at once. Also, keep in mind that not everything mean-reverts, some things simply trend - some investments will simply never come back to where you wish to buy or sell them regardless of historic price points that might make sense to you. And being contrarian just for the sake of being different is not the same as being contrarian because you see something that others don't.

You see this tendency in a lot of fields. It is psychologically fulfilling to see oneself as the loner, who can see the truth that the rest of the herd so blindly overlooks. Unfortunately, there can be a very good reason that the herd is stampeding away from the vicious lion!

I've personally watched people lose money with the notion of mean-reversion (do we still think that AOL will revert back to its tech bubble peak?). I think we see the same phenomenon in academic research programs. It seems so cool to find this interesting and counter-intuitive finding that nobody else has seen. Because they are idiots. Or, perhaps (just perhaps), because I've managed to overlook something crucial to the whole process.

So if the finding seems to explain a complex phenomenon in a simple way . . . beware. There might be a reason that the herd is off chasing the complex solution and ignoring the counter-intuitive position.

A tweet from Matt Yglesias

Seriously amazing how much better digital over the air looks than "HD" cable with compression.

Isn't this the same argument Mark has been trying to make about Broadcast Cable?

UPDATE: See more here

The secret of (unintentional) comedy is timing

I don't know much about academic publishing so I'm probably missing some of the subtleties here but this certainly seems to be a situation I would have played differently. It's late 2008 and you're putting the finishing touches on a paper asking how so many American economists could have failed to see what a great idea the Euro was. Given the events outside your window, don't you think you would have dragged your feet a bit on the submission, or at least hedged your wording a bit?



Apparently these guys didn't. (via Krugman)

I could not disagree more

One of the things that makes cities tolerable is public land (as private parties cannot possibly own enough land for this effect) where there is green space to visit. Even if it is not always in use, the availability is of great psychological value. But this line of thinking could result in many fewer parks:

That’s not to say we should pave all the parks. But we should be thinking of something to actually do with them. Cities are full of people, and most of the country doesn’t have Southern California weather. There’s limited practical demand for just sitting around outside.

The reason we have to provide public parks is that developers can maximize profits by not including them. But if every developer omits including a park, you end up with no place for children to ever play. I worry that this is looking at a very small problem and risking creating a large one by trying to solve it.

Great catch from Jared Bernstein -- four years of your life for a lousy, stinking 0.1% a year

Bernstein has been doing exceptional work lately. Here he points out a genuinely shocking statistic:

Second point: again, Steve’s not at all alone in advocating for a more highly educated workforce, but he blows by an amazingly sobering statistic:

Achieving higher wages also requires a greater commitment to education; wages for those with college degrees rose 1.4 percent between 2000 and 2010, after inflation.

That’s not 1.4% per year—it’s 1.4% over 10 years! 0.1% per year…OMG—that’s the big freakin’ payoff!!

Now, there’s no question that college grads did better than high school grads, whose real wages fell by 2% over these years (see the data table below). And no question that we’re better off with a more skilled workforce. But a 1.4% median wage gain over 10 years for college grads is not part of the solution…it’s part of the problem.

I'd actually take this further. That 3.4% difference came with four years of lost wages and job advancement and, in many (most?) cases, serious debt. There seems to be a consensus that the country needs educated, tech-literate workers, but if we are serious about this, we need to do something about a system where getting a degree may actually be a losing proposition.

I'd start by scrapping the idea that we should make education accessible through subsidized and (God help us) nondischargeable loans. The current system of easy credit distorts the market in any number of truly ugly ways and takes undue advantage of the vulnerable and inexperienced. If we really want to we can find a better way to make college affordable.