Weekend blogging: before the man with no name, there was...

My first thought on first seeing Yojimbo years ago was that Kurosawa had been watching a lot of spaghetti westerns. Then I remember which came first...

This time it's different

Adriene Hill had a strangely schizophrenic story yesterday (CLASSROOM TECH: A HISTORY OF HYPE AND DISAPPOINTMENT). It came with the ominous title Classroom Tech: a History of Hype and Disappointment and the first half lived up to the claim:

That’s been the story of technology in the classroom, pretty much from the start. Great hope, ambition, and expense. Followed by disappointment.

Back in 1922, for instance, Thomas Edison thought he'd figured out the future of education.

“I believe that the motion picture is destined to revolutionize our education system,” he said, according to Larry Cuban's  Teachers and Machines: The Classroom Use of Technology Since 1920, “and that in a few years it will supplant largely, if not entirely, the use of textbooks.”

“Edison was a better inventor than prognosticator,” said Robert Reiser, Associate Dean for Research in the College of Education at Florida State University.

Films fizzled out. They were expensive. Projectors were unreliable. It was hard to find the right film for the right class.

Enter radio.

School boards and universities, even commercial networks like CBS and NBC, poured money into creating classroom broadcasts,  or  “textbooks of the air.” Then, said Reiser, “the enthusiasm died out.”

Next up were “teaching machines” with names like Cyclo Teacher, Instructocard, and the Edumator.

One of the best known was created by psychologist BF Skinner, in 1954. Here he is explaining the devices.

According to the 1962 book Teaching Machines and Programmed Learning, there were dozens of companies that made these devices in the early 60s.

Turns out buttons and levers weren’t a great way to learn.

Which brings us to television.

TV combined sight and sound, and could bring live events — like space missions — right into the classroom. It was also seen as one answer to the teacher shortage. The money poured in. The Ford Foundation invested millions into programming, according to Cuban's book. The federal government also pitched in cash. By 1971 more than $100 million had been poured into educational TV.

Again, the same story. “We see one medium after another coming along, a lot of enthusiasm for that medium, followed by disappointment in the extent to which that medium changed the nature of the instruction taking place in classrooms,” said Reiser.

So, when computers exploded into classrooms  in the early 80s, with basic video games like Oregon Trail.

And when, as Todd Oppenheimer writes in The Flickering Mind, the numbers of computers tripled between 1980 and 1982, and tripled again by 1984.

And when Time magazine ran a cover story called “Here Come the Microkids,” in 1982. Educators were skeptical.

At this point, for no apparent reason, the tone shifts radically.

But now, some are reconsidering. Maybe this time is different.

and

“We’re on the cusp now of that big revolution,” said Themistocles Sparangis, chief technology director at Los Angeles Unified School District. LA Unified has bet big on tech--a billion dollars big-- to give every student an iPad.

It turns out that Los Angeles schools Supt. John Deasy, who has a rather cozy relationship with Apple, paid more than he had to for those iPads and way more than he would have if other tablet makers had been allowed to bid. Furthermore, they didn't work as promised (particularly not the firewall) and -- here's the part that jumps out for me -- the team that put together the proposal didn't check the specs closely enough and later discovered the district had to come up with an additional $38 million for keyboards.

In past, I've used the term ddulites to describe people who are irrationally enamored with technology but who don't get the subtleties of thinking in terms of functionality. The LAUSD's iPad misadventure is a perfect example of the damage this approach can cause.

I firmly believe that educational technology can do great things, but the first step in achieving that potential requires keeping people like Deasy and Sparangis out of the process.

Bookable, readily bookable, semi-bookable, ebookable

While we're on the subject, Jeremy Kilpatrick of the University of Georgia has an interesting eye-witness take on the math reforms of the post Sputnik era. Check out the whole thing if you get a chance, but for now I'd like to focus on one section:

Lesson Two: Mathematical thinking is not bookable.

"Bookable" is a term used by publishers to describe the capability of a concept or mental process to be captured in print in a form that teachers will accept and can use. Many of the new math projects concentrated on bringing about reform primarily through the production of innovative materials. In particular, by providing sample textbooks for mathematics courses, the SMSG attempted to influence the commercial textbook publishing process, which would presumably then change how mathematics was taught. The SMSG author teams, by providing fewer problems for students to work, expected that those problems would be treated by teachers in greater depth and detail. The problem-solving process, however, proved not to be bookable. Books are not good at handling tentative hypotheses, erroneous formulations, blind alleys, or partial solutions. Teachers misunderstood what they were to do and called for more problems instead.

Max Beberman, in the new math materials he designed for the University of Illinois Committee on School Mathematics, attempted to incorporate into many lessons what he called guided discovery. Students would be led to see patterns in mathematical expressions and thus to arrive at generalizations that would not need to be made explicit in the materials (until a later lesson). The materials apparently worked well when restricted to teachers who had been trained in their use. When they were later published in the form of commercial textbooks, however, the guided discovery feature was greatly attenuated in order to capture a larger market.

Several recent curriculum projects have run into the same phenomenon. When efforts are made to encourage students to think about mathematical ideas rather than having them enshrined in a text, teachers who are not familiar with how those ideas might be handled criticize the books as incomplete and unsatisfactory. Textbooks are expected to contain authoritative rules, definitions, theorems, and solutions. Consequently, asking students to think about and formulate their own versions of these things rather than providing them ready-made can make a textbook unusable for many teachers.

There's an important point here but I don't think Kilpatrick quite nails it. For starters, speaking as someone who has recently been working with a number of students coming of different courses, grades and schools, I can attest that being familiar with the ideas doesn't always help and sometimes hurts (see Feynman for details). Until you've done it, you have no idea how distracting it can be to teach out of a text where the authors don't really understand the material.

In order to get get the concept into more usable form, let's introduce a couple of subcategories:

Semi-bookable.  These are concepts or mental processes that can be partly but not entirely captured in print in a form that teachers will accept and can use. For example, lots of people teach themselves a foreign language from a book, but the process is almost always supplemented by conversing and by listening to live or recorded speakers;

Readily bookable. Some ideas and processes are difficult to convey in print, either because they can be hard to express or because most textbook authors have a weak grasp of them and miss the subtleties. Feynman's critique hit this point heavily;

Ebookable. An idea or process that becomes much more readily or completely bookable with the introduction of other media.

I'll come back to this later, particularly with regard to why attempts to incorporate Pólya into math textbooks often go so badly.

What exactly are the stakes?

I want to be careful how I frame this, partly because it's a big, complicated question and partly because it would be easy to imply an extreme position that I do not hold.

All that said, there's a thought that's been nagging at me for years, particularly since I've been digging into the education reform debate. Over the Twentieth Century, America has swung from one pedagogical and curricular extreme to another. The data from these initiatives are confusing and inconclusive when we look at the various metrics we use to capture educational performance, but when we pull back and look at two of the big objectives we want the policies to accomplish, economic growth.and technological progress, it's difficult to see a clear relationship between how and what we teach kids and how well they do.

This table (from A Brief History of American K-12 Mathematics Education in the 20th Century by David Klein) really brought this home for me. One of the big and not entirely unreasonable drivers of the reaction to Sputnik was the belief that we had been neglecting math and science.

Percentages of U.S. High School Students Enrolled in Various Courses

School Year	Algebra	Geometry	Trigonometry
1909 to 1910	56.9%	30.9%	1.9%
1914 to 1915	48.8%	26.5%	1.5%
1921 to 1922	40.2%	22.7%	1.5%
1927 to 1928	35.2%	19.8%	1.3%
1933 to 1934	30.4%	17.1%	1.3%
1948 to 1949	26.8%	12.8%	2.0%
1952 to 1953	24.6%	11.6%	1.7%
1954 to 1955	24.8%	11.4%	2.6%

It has become fairly standard to use the number of and enrollment in advanced course as a measure of a school's quality. By this standard, American schools weren't just bad, they were horrible and they had been in steady decline for half a century. Looking at the numbers for the Thirties and Forties, this generation would appear to be woefully ill-prepared to deal with the STEM-heavy world of the late Twentieth Century, but of course they weren't. The students who graduated high school in the quarter century preceding Sputnik were responsible for an incredible period of across-the-board advances.

From  Dewey Progressivism to New Math to Back-to-Basics to the modern reform movement, we have applied all sorts of theories to our kids' education. I'm sure that, if we thought through the problem, sharpened our analytic tools and devoted adequate resources to the question,  we could definitively say that for a given student and a given goal a certain approach is best.

I just wondering how big the magnitude of those differences will be compared to the impact of other public policy developments.

Adding in base 8, counting by ten, and other reform fixations

With all of the usual caveats about small samples, I've been reading up on education reform movements past and present recently and I've noticed something. There seems to be a tendency to latch onto some interesting but non-essential concept and impose upon it considerable, even central importance. Mastering these concepts is often seen as necessary conditions for truly understanding the material, despite the generations of students who had managed to get by without them.

Counting by certain intervals and ELA concepts like close reading, and the distinction between perspective and point of view are a couple of examples associated with Common Core, but the richest stake might well belong to the New Math movement of the post-Sputnik era. Some of the concepts were extremely important in higher level math courses (such as set theory). Others (such as performing operations in bases other than ten or two) seldom came up  even for mathematicians.

It's worth noting that both Richard Feynman and Tom Lehrer singled out working in other bases when criticizing New Math, Lehrer in song and Feynman in memorably scornful prose:

I understood what they were trying to do. Many [Americans] thought we were behind the Russians after Sputnik, and some mathematicians were asked to give advice on how to teach math by using some of the rather interesting modern concepts of mathematics. The purpose was to enhance mathematics for the children who found it dull.

I'll give you an example: They would talk about different bases of numbers -- five, six, and so on -- to show the possibilities. That would be interesting for a kid who could understand base ten -- something to entertain his mind. But what they turned it into, in these books, was that every child had to learn another base! And then the usual horror would come: "Translate these numbers, which are written in base seven, to base five." Translating from one base to another is an utterly useless thing. If you can do it, maybe it's entertaining; if you can't do it, forget it. There's no point to it.

Part of the standard narrative about New Math was that the new concepts being introduced were too advanced and unfamiliar for teachers to handle or parents to accept, but in many cases, the greater tension was between authors of the reforms and the people who actually understood the math.

A good day for a recommendation

There is, of course, no such thing as the military perspective -- no single person can speak for all the men and women who have served in the military -- but if you are looking for a military perspective, my first choice would be Lt. Col. Robert Bateman who writes eloquently and intelligently on the subject for Esquire. Here are Bateman's recent thoughts on Memorial Day.

When the guns fell silent in the Spring of 1865, they all went home. They scattered across the country, back across the devastated south and the invigorated north. Then they made love to their wives, played with their children, found new jobs or stepped back into their old ones, and in general they tried to get on with their lives. These men were no longer soldiers; they were now veterans of the Civil War, never to wear the uniform again. But before long they started noticing that things were not as they had been before.

Now, they had memories of things that they could not erase. There were the friends who were no longer there, or who were hobbling through town on one or two pegs, or who had a sleeve pinned up on their chest. There were the nights that they could not shake the feeling that something really bad was about to happen. And, aside from those who had seen what they had seen and lived that life, they came to realize that they did not have a lot of people to talk to about these things. Those who had been at home, men and women, just did not "get it." A basic tale about life in camp would need a lot of explanation, so it was frustrating even to talk. Terminology like "what is a picket line" and "what do you mean oblique order?" and a million other elements, got in the way. These were the details of a life they had lived for years but which was now suddenly so complex that they never could get the story across to those who had not been there. Many felt they just could not explain about what had happened, to them, to their friends, to the nation.

So they started to congregate. First in little groups, then in statewide assemblies, and finally in national organizations that themselves took on a life of their own.

The Mid-1860s are a key period in American history not just because of the War of Rebellion, but also because this period saw the rise of "social organizations." Fraternities, for example, exploded in the post-war period. My own, Pi Kappa Alpha, was formed partially by veterans of the Confederacy, Lee's men (yes, I know, irony alert). Many other non-academic "fraternal" organizations got their start around the same time. By the late 1860s in the north and south there was a desire to commemorate. Not to celebrate, gloat or pine, but to remember.

Individually, at different times and in different ways, these nascent veterans groups started to create days to stop and reflect. These days were not set aside to mull on a cause -- though that did happen -- but their primary purpose was to think on the sacrifices and remember those lost. Over time, as different states incorporated these ideas into statewide holidays, a sort of critical legislative mass was achieved. "Decoration Day" was born, and for a long time that was enough. The date selected was, quite deliberately, a day upon which absolutely nothing of major significance had occurred during the entire war. Nobody in the north or south could try to change it to make it a victory day. It was a day for remembering the dead through decorating their graves, and the memorials started sprouting up in every small town in the nation. You still see them today, north and south, in small towns and villages like my own home of Chagrin Falls -- granite placed there so that the nation, and their homes, should not forget the sacrifices of the men who went away on behalf of the country and never came back.

Here's one for the Unqualified Offerings crowd...

I'm taking this with a small grain of salt (there are a couple of things in the Georgetown report that concern me a bit), but with those caveats I think we can call this a point for Thoreau and company.

High Unemployment Major #1:
Information Systems
Unemployment rate for recent grads: 14.7 percent*
In the digital age, it may seem as though all bachelor's degrees in the computer science field would be a safe bet. But numbers from the Georgetown Report suggest that this is not the case. In fact, the report found that recent grads in this major faced an unemployment rate of nearly 15 percent.
Why the depressing job prospects? The simple answer: Too many job applicants, not enough spots. "The market is saturated for this industry," says Hallie Crawford, a job search expert and certified career coach.
With the rise of technology, many people have opted to pursue information technology paths, says Crawford. And the influx of new candidates for positions within this field has made the job market very competitive, she says.

Here's what I'm taking away from most of these stories and from what I'm hearing from people in the STEM job market:

The world of the STEM job hunter is brighter than that of the non-STEM crowd, but much dimmer than you've been told;

Because many of these specialties are fairly narrow, a small increase in supply or decrease in demand can gut the market (see above);

Even in hot, high-demand fields, fewer people are making big bucks than you might think. "Only 4 percent of software developers in the burgeoning app economy have made over a million dollars. Three-quarters of them made less than $30,000."*;

You hear stories about companies willing to do anything to acquire talented people and keep them happy. At best these examples are unrepresentative. At worst, they're fraudulent.

I would certainly encourage people with any interest in the field to go into one of the STEM fields. The subjects are interesting and you can probably get a pretty good job, but keep your expectations reasonable, your debt low and, whatever you do, don't believe the hype.


* I'm willing to bet you dinner that most of that 4% got a significant portion of that million through their talents as entrepreneurs, investors or managers.

Weekend blogging -- Memorial Day Roger Corman Marathon

I was having a cup of coffee and a cookie this evening at a place on Beverly I frequent a lot. The bakery's first rate, the coffee's good and I have no trouble picking up the wifi from the Starbucks next do. I happened to look at the theater across the street and the marquee read "Roger Corman and Joe Dante in Person." That sort of thing happens to you when you live in LA.

Unfortunately, none of the Poe films appear to be available for streaming but Hulu does have a few worth checking out. Roger Corman never made a bad film under the circumstances, and even when the circumstances were particularly dire, he always did something interesting.

A Bucket Of Blood (1959)

Though Little Shop (also included here) gets more attention, I think this is the better movie, largely due to the rare lead by beloved character actor Dick Miller.




The Little Shop of Horrors (1960)

Still, you do have to give this one its props, shot in a couple of days for $30K. A pretty good little film in absolute terms but amazing when you realize what he had to work with.








The Terror (1963)

In some ways an even more impressive example of high speed, low cost movie making. Though there are differing accounts, most go something like this: when he realized that the film The Raven was going to wrap up three days early so he had Leo Gordon* write a script over the weekend. They started shooting that Monday, scheduling shots based on which part of the set was supposed to be torn down next.





* Gordon is more familiar to movie and TV fans as a menacing character actor in countless shows like Andy Griffith and Maverick, but he was also a highly successful self-taught writer. He had learned the craft while reading most of the books in the San Quentin library while serving time for armed robbery.

Can nobody work out the incentives?

I hate to do the both sides are out to lunch meme, but this response to the Levitt/Dubner/Noah Smith health care plan missed the main point: 

The L/D plan would, in its majestic equality, allow the affluent person with a well-stuffed savings account and the low wager-earner drowning in debt alike to set aside $1,000 for health care expenses and to take the risk of incurring 4 grand of debt through events they have little or no control over. Indeed, their always-smarmy tone (“if they are being prudent”) suggests that the point of the plan is not so much health care provision as setting up a cheap moral lesson in thrift, a lesson that not coincidentally will be much easier for people similarly situated to Levitt than for the ordinary working person in 2014 to pass.

But let’s assume arguendo that we should ignore questions of equity, and also assume that the only relevant question is trying to determine how to collectively spend health care dollars in the most efficient manner. Even on its own terms, the plan doesn’t make sense. The L/D wouldn’t disincentivize health care spending per se; it would massively disincentivize seeking cheap preventive care. If you get regular check-ups, it costs you money; if you save money by skipping checkups and get an illness that could have prevented, the costs are largely paid collectively. In other words, the L/D plan discourages the most cont-effective forms of care while doing little to discourage the least cost-effective. Even on its on terms, I don’t see how this plan makes any sense.

Cheap preventative care isn't where this system is going to go wrong.  Nor is it in the poor equality properties of the law, as some young people might end up ahead on total revenue (while others get crushed).  behind the veil of ignorance it isn't clear how it will all work out.

Now let's look at this plan:

On January 1 of each year, the British government would mail a check for 1,000 pounds to every British resident. They can do whatever they want with that money, but if they are being prudent, they might want to set it aside to cover out-of-pocket health care costs. In my system, individuals are now required to pay out-of-pocket for 100 percent of their health care costs up to 2,000 pounds, and 50 percent of the costs between 2,000 pounds and 8,000 pounds. The government pays for all expenses over 8,000 pounds in a year. 

So you have two efficiency problems here.  One is that you now have a whole bunch of extra paperwork and IT to track where people are on the cost spectrum.  Do we mail people bills after we determine if they have not hit the cap?  What about people will marginal addresses and living situations.  You are replacing a cheap system with average outcomes with one that is immediately more complicated to administer. 

But where this will go terribly wrong is for those people who go over 8,000 pounds per year.  Did you notice that piece where the government pays for all expenses over 8,000 pounds.  How do we know that these costs are acceptable?  After all, every single hip replacement might exceed 8,000 pounds in expenses.  How do we know if we are getting ripped off? 

So you end up needing to do the same schedule of acceptable costs as any socialized medical system has.  This rather removes the benefit of the free market in setting prices, as you have a single payer for all expensive conditions.  Will hospitals not offer free parking to get people to have a procedure at their (more expensive) hospital?  Why would the patient say no?  Altruism?

Even worse, this makes outcomes worse for patients with chronic conditions, at least until they hit the 8,000 pound ceiling in any year (and note the billing issues here -- if people have to pay and be reimbursed there can be a liquidity issue).  Now these people pay 4,500 pounds with a 1,000 pound subsidy.  Hopefully nobody will have trouble paying the 3,500 pounds per year?  That is around $450 a month -- what if the worker gets $5 an hour? 

And this gets back to the most important issue -- these people completely misunderstand the whole idea of insurance.  We insure against risks that exceed our ability to pay.  Is 3,5000 pounds a sum that every British person could pay without hardship?  A cost of zero would make it possible for everyone to be able to afford health care, regardless of financial circumstance.

Now, what I want to make exceedingly clear is that the nation with the highest private sector portion of payments also has the highest public sector as well, as even libertarian Megan McArdle notes:

A lot of people seem to think that "per-capita government spending" means "spending per person covered by government insurance." That's understandable, but wrong. "Per-capita government spending" means "government spending on health care per U.S. citizen." In other words, we spend as much to cover a fraction of our population as other governments spend to cover everyone. So pointing out that Medicare beneficiaries cost more on average than younger people is true but irrelevant. We spend more covering old people, poor people and veterans than many other governments spend to cover all those people, plus the rest of the population.

 So if you are advising the English on health care reform, why would you suggest the politically unpopular move of putting more "skin in the game" when the country that does the most of this ends up paying more money (out of government revenues) to cover fewer people?  And England allows private health care, so the benefits of a more private system (over and above current options) isn't absolutely clear. 

Finally, there is the issue of prioritization.  Is the NHS really the biggest policy challenge that the UK faces?  Is it in the top 10?  Now it is possible that innovation is under-supported by this approach.  Of course, they could simply increase research grants, if this was thought to be the most important issue.

But wouldn't issues like persistent unemployment and industrial decline be better places to focus efforts?  And how would increasing the government's expenditure on health care (likely financed by higher taxes) work to improve these issues?  Or is it expending political capital on an experiment that might well not work out to reduce costs? 

A pretty good one-page intro to New Math

Not what you'd call 'in  depth,' of course, but this primer by Calley Connelly of MSU Bozeman does a pretty good job hitting the major points and players.

Update: For something more in depth, try this and of course this.

Good grief! -- Sally Brown on New Math [Updated]

I have been working on a long piece on the parallels between the New Math of the Sixties and the Common Core math of today. As part of my research, I came across an amusing quote from a Peanuts strip of the time.

From Wikipedia:

In 1965, cartoonist Charles Schulz authored a series of Peanuts strips which detailed kindergartener Sally's frustrations with New Math. In the first strip, she is depicted puzzling over "sets, one to one matching, equivalent sets, non-equivalent sets, sets of one, sets of two, renaming two, subsets, joining sets, number sentences, placeholders." Eventually she bursts into tears and exclaims, "All I want to know is, how much is two and two?"

What surprised me was how well Schulz captured the terminology. The part about one to one matching was particularly apt.

[Found it]

The Aphorisms of Success

I've blogged a bit on corporate culture (and there are far more on the topic waiting to be written or rewritten). One of the aspects I should focus more on is the emphasis and, in some cases, the outright enforcement of aspirational language.

It is easy to satirize the steady stream of phrases like "achieving excellence," "amazing customers." and "maximizing impactfulness." A friend of mine, who was dean of business at a small college at the time, actually created an award called "the margins of excellence" (excellence apparently being a thing you don't want to hit dead on).

But there are bigger concerns than just looking silly. It is true that most of the time if properly applied, the combination of hard work and a reasonably positive attitude will often achieve impressive results, but it's not a deterministic relationship. When you ignore the caveats and the limits and completely commit yourself to the anything-is-possible rhetoric, the results can be disastrous.

I was recently reading some particularly embarrassing example on an education blog, I was reminded of the This American Life segment on Duke Fightmaster.

Duke Fightmaster is not a man of half measures, and he believed in the aphorisms of success, that if he wanted something badly enough, he would have it. He was going to replace Conan O'Brien. Not by doing all the normal things like getting a production job at a local talk show, learning the business, working his way up. Instead, he would make himself into a talk show sensation from his own bedroom.

As you might guess, this did not go well.

Duke Fightmaster
I guess somewhere in my mind I just thought, you know, no matter how bad things get, I'll just kind of put my head down and keep going. And I knew that it was ridiculous, starting a talk show. I mean, I knew that, outwardly, people think I'm ridiculous.

And I remember just driving around like, "The show isn't going anywhere, I'm not going anywhere, I've wasted these last years." And I remember just driving around so depressed. And I just felt like I had broken-- and I had a breakdown where I just started crying in my car. And I just felt like I hit the core of my being and it was, "you're a loser." And I think that was part of my rock bottom.

Sarah Koenig
Did you quit after that?

Duke Fightmaster
No. No, I think I still went for another year after that.

You know, anyone who makes it in this life at anything, you always hear, has to go through hell. So I figured, "I'll just go through hell." I remember my friend who worked in real estate worked for one of those cheesy real estate motivators that used to yell out, "You have to have a break down to have a break through." So I was thinking, "OK, I've had my break down, so now I'm going to actually break through to some new level."

You really should listen to the whole thing

France and jobs

Sometimes the data just screams at you:

Since the late 1990s we have completely traded places: prime-age French adults are now much more likely than their US counterparts to have jobs.

This is for adults 25 to 54.  So maybe the USA might have some advantages above or below that age range.  But France has a world class medical system, high taxes, and a great deal of worker protection.  Enough protections that I can actually remember meeting French people in Quebec who moved there because their business model required too much worker churn to be viable in France. 

So we shouldn't necessarily say "they have it right".  There are good and bad things about the French model, and it hasn't always been a good thing to be a participant in the French economy.  However, what this does do is highlight how challenging it is to link US-style markets to general population employment. 

That has some real policy implications as it does remove a key trump card in the balance between business interests and social programs. 

When "best practices" aren't -- sometimes imitating the successful is a really bad idea

We started the week with a post on the much touted Relay Graduate School of Education. Yesterday we had a piece discussing the assumptions underlying the notion of "best practices." Here's where those two topics come together.

As I mentioned before, Relay GSE and its role in the reform movement is a complicated story. Not only are there a lot of moving parts; the moving parts have moving parts, so in this thread, I'm trying to open with a cursory bits for context then zoom in on one main aspect per post.

The cursory part: The following is a very good lesson intro but not a particularly good math lesson intro. The good part is is that the kids are having fun, they're ready to learn and they are associating positive emotions with the class. All of these things important and the instructor is managing them exceedingly well. The math part is considerably weaker. The opening is knowledge-, not process-based (no problem-solving or higher-order thinking) and the knowledge covered -- a mediocre mnemonic (since these are made-up words, they are easy to scramble or to forget entirely) for a formula most kids don't have that much trouble remembering -- is fairly trivial. Even the question around the 2:00 mark that got the dean so excited didn't show any significant connection with the material. (Questions you'd rather hear at that point include: "Why do they have to be right triangles?"; "What do we do with other shapes like rectangles?"; "Does this have anything to do with similar triangles?"; "If they give us both angles, how do we know which side is opposite?")

But I don't want to get too caught up in the criticisms. Though I have concerns, it is still clear that Corcoran is an extraordinarily talented teacher with a tremendous gift for entertaining and engaging students.



KIPP Academy's Frank Corcoran: Captain Hook from KIPP NYC on Vimeo.

He is also a potentially disastrous role model.

As I said in the last post:

In order for a best practices approach to make any sense whatsoever, the optimal level of the factors in question must remain basically the same from person to person, location to location, and sometimes even job to job. Those are extremely strong and in some cases wildly counterintuitive assumptions and yet they go unquestioned all the time.

For a young teacher, there is tremendous appeal to the idea of winning kids over with the big show. Today, they're ignoring your lessons, rolling their eyes at your advice and occasionally nodding off while you're talking; tomorrow, they're hanging on your every word. It hardly  ever works that way. One lesson almost never makes you anyone's favorite teacher.

On top of the question of effectiveness, there's often a real risk associated with the 'fun' lesson or hook. Not only does it break the normal structure and routine; it gives the students a relatively legitimate argument for non-cooperation ("if this is supposed to be fun and I'm not having fun, why can't I do something else?"). With time, teachers generally learn how to read classes and situations and discover ways of framing and executing these activities, but for an inexperienced teacher with a problem class, things can go badly.

Check out this passage from Michael Winerip's 2010 NYT article on Teach for America and keep in mind that there is an extremely high degree of overlap between the pedagogical methods taught by TFA and those taught by Relay.

The 774 new recruits who are training here are housed in Rice University dorms. Many are up past midnight doing lesson plans and by 6:30 a.m. are on a bus to teach summer school to students making up failed classes. It’s a tough lesson for those who’ve come to do battle with the achievement gap. 

Lilianna Nguyen, a recent Stanford graduate, dressed formally in high heels, was trying to teach a sixth-grade math class about negative numbers. She’d prepared definitions to be copied down, but the projector was broken. 

She’d also created a fun math game, giving every student an index card with a number. They were supposed to silently line themselves up from lowest negative to highest positive, but one boy kept disrupting the class, blurting out, twirling his pen, complaining he wanted to play a fun game, not a math game. 

“Why is there talking?” Ms. Nguyen said. “There should be no talking.” 

“Do I have to play?” asked the boy. 

“Do you want to pass summer school?” Ms. Nguyen answered. 

The boy asked if it was O.K. to push people to get them in the right order. 

“This is your third warning,” Ms. Nguyen said. “Do not speak out in my class.”

This is really bad. The lesson was not great to begin with -- there are better ways to get the concept across and the fun potential of lining up silently is limited -- but with the disruptions the time was almost entirely wasted (and wasting students' time is one of the worst things a teacher or administrator can do). And the damage almost certainly wasn't be limited to that one day. The teacher had her authority challenged, made empty threats, lost control of her classroom.

But it could have been worse. Kids have a natural tendency to push boundaries and the boundaries here were relatively tight. Now think about an activity that requires shouting and striking martial arts poses. In the video clip, we had an experienced and charismatic teacher with a medium sized class of well-behaved students in a school with strict discipline and a student body self-selected to be compliant and cooperative. Imagine what might have happened if someone like Ms. Nguyen had tried this in a tough school with thirty or forty students.

At the risk of oversimplifying, you can basically break this Relay clip down into two parts:

The dull content-driven part -- making concepts understandable, intriguing them with a challenging problems, getting them to make connections and engage in higher-order thinking -- plays an insignificant role in this clip. Corcoran may have done all of these things later in the lesson, he may even have done them very well, but in this clip there is simply nothing along these lines worth noting, let alone imitating;

Then there's the exciting performance-driven part. Corcoran is remarkably talented and he puts on an exceptional show, but like a lot of other impressive acts, you probably shouldn't try this on your own.

The two big assumptions behind 'best practices'

[Homonym alert -- another smart phone composition]

There is no notion better loved by scientific management types than 'best practices.' It has become one of the truly obligatory PowerPoint phrases and it is rare to hear a high-level executive lay out plans for fixing a large organization without promising to promote them. These days those executives often have titles like 'superintendent.' Scientific management is now extraordinarily popular in education circles, particularly in the education reform movement. This confluence of two of the major interests of this blog means there are some major threads starting that will allude to this topic quite a bit.

'Best practices' are often treated as a self-evidently good thing  – Who wouldn't want to be best? – – but the idea of finding optimal methods and strategies and applying them across an organization is based on two very big and difficult-to-justify assumptions.

The first is that you have or even can identify these behaviors. Determining "best" status usually requires a high degree of faith in your metrics and metrics almost never perfectly align with the properties they are supposed to measure. Even when handled by the most competent of people, things can go badly wrong.

And, as anyone who has worked for large corporations can tell you, the executives overseeing these programs often are not up to the job. Between various biases, office politics, and a widespread misunderstanding of how statistics works, the results are often far from "best."

Most corporate cultures strongly discourage employees from questioning whether or not a "best practice" is actually best, but at least the question does sometimes come up. The very idea of the next assumption often escapes people entirely.

In order for a best practices approach to make any sense whatsoever, the optimal level of the factors in question must remain basically the same from person to person, location to location, and sometimes even job to job. Those are extremely strong and in some cases wildly counterintuitive assumptions and yet they go unquestioned all the time.

Later in the week, we'll discuss how violating these assumptions can lead to trouble (and connect this topic with an earlier post).

Freakonomics

This piece of a review of the newest Freakonomics book is a bit harsh:

They take this as evidence that even intelligent politicians don't like hearing uncomfortable truths that challenge positions to which they are committed. But it seems more likely that Cameron, who is indeed an intelligent politician, noticed they were talking nonsense. After all, it's a ridiculous analogy. People don't go to the NHS and "pick out" their treatment. They are in the hands of doctors and other healthcare professionals who collectively try to find the best treatments for them, within limits. Healthcare is nothing like transportation. If it were, the NHS, whatever future problems it might be facing, could hardly have survived so long (and performed more efficiently than the rival US system, where many patients really are "picking out" their preferred treatments). Only two economists (or rather one-and-a-half economists) could be so arrogant and so ignorant as to think that this was how to talk to a future British prime minister about healthcare. I imagine that what Cameron was really thinking was: if these are the clever people, spare me from the stupid ones.

But it does get at a very real issue -- different markets operate in different ways.   Noah Smith and Paul Krugman point out the difficult link between theory and empiricism here.  It is true that very few health care markets are purely socialist or free -- they are classical mixed markets in most places.  That said, the English model is hardly a disaster. 

What I generally want to see when people suggest large countries radically change an existing system (upsetting many stakeholders and people who planned their lives around a set of rules) is that there will be relatively immediate benefits (i.e. it is politically viable) or long term improvements for the country (i.e. it is worth losing an election over as it makes people's lives better). 

Levitt clarified his ideas, but I think they still have some serious issues.  He suggests:

On January 1 of each year, the British government would mail a check for 1,000 pounds to every British resident. They can do whatever they want with that money, but if they are being prudent, they might want to set it aside to cover out-of-pocket health care costs. In my system, individuals are now required to pay out-of-pocket for 100 percent of their health care costs up to 2,000 pounds, and 50 percent of the costs between 2,000 pounds and 8,000 pounds. The government pays for all expenses over 8,000 pounds in a year.

Yet, ironically, this approach requires a real faith in effective government.  Why?  Because there will be people who need different amounts of subsidy (currently poor elderly, for example, or those whose illness prevents them from working).  Or it requires getting rid of universality, which might be a feature in the long run but has many bad features in the short run.  It adds in layers of billing and pricing, that health systems are often poor at generating (or at least the US systems seem to be).  People need to be able to get accurate price quotes, collections for debt needs to exist, and the hospital have to set up payment under difficult circumstances. 

It also requires the government to dynamically adjust the "payout" and the "thresholds" as prices change.  Will that be done by a central payments board?  How is that really different than the current English approach of determining cost effectiveness in general?    You are still using expert opinion to run the system, just in a different place.  And there could be some real concern that the "thousand pound" subsidy could be used to replace current benefits or drop over time as it is eroded by inflation. 

So what is the evidence that this radical reform will reduce total health care costs?  Because this is a case where we want to have a clear test of the theory before completely reforming a relatively functional system (it's mediocre for the OECD but one can go down from average, as well as up).  There are some examples of health care systems that might be more free market plus regulation oriented (say Singapore).  But why not the French model? 

I'd like for you all to take a look at something...

This is one of those big, complex stories that are themselves subplots of still bigger, more complex stories. These subjects tend to get out off if you approach them too ambitiously. The best way to handle them, at least for me, is to keep each post small and manageable, at least while you're laying the groundwork (blogs are good for that).

I've been meaning for a long time to write about Relay Graduate School of Education and its role in the education reform movement. Lots of moving parts here, but there's one very important part that I think we can pull out and address as a stand alone question:

Does getting a master's from Relay require graduate level work?

When you have a minute, check out Relay's website then watch a few of these videos. They're all short and relatively self-explanatory. I don't want to go into content, pedagogy, or applicability at this point (that can wait until later posts), but I do want to mention that the most interesting (hooking the lesson) is also the least representative.

Here are some of the videos which, as far as I can tell, are used as part the school's flipped classes:

Lesson plans*


Transitions


Wait Time


Clear and precise directions


Strong voice and positive framing


Hooking lessons


It's been a long time since I took a methods class but this looks a lot like what I remember from sophomore and junior level courses. Are these things you would normally see at a graduate level? I realize these videos are only part of the program but this description of the curriculum does nothing to allay my concerns:

The Relay GSE curriculum comprises two core components. First, graduate students learn core instructional practices in planning, delivery, and assessment of teaching and learning that are necessary for all teachers, regardless of the subject or grade level they are teaching. These practices are sometimes referred to in the education field as “general pedagogy.” Second, graduate students will learn how to teach their specific subject at one or more specific grade levels. Math teachers do not learn geometry, for example, but rather how to teach geometry and how students learn geometry. This is sometimes referred to as “pedagogical content knowledge.

Help me out on this one. Based strictly on the information Relay provides us, would you say this constitutes graduate or undergraduate level work?


*Not sure if intentionality (intensionality?) means what he thinks it means.

Quoting Pólya quoting Shaw

Along with Richard Feynman's "total temperature of the stars," this is my favorite comment on 'new math.'


From The Random Walks of George Pólya:

In the immediate post-Sputnik era Pólya had been an outspoken critic of the formalism of the School Mathematics Study Group (SMSG) and the “new math." He often cited an example taken from the SMSG geometry text that gave a theorem with proof—taking up half a page—stating that with three points on a line, one point must lie between the other two. He argued that though this is a necessary theorem for a foundations course in geometry, it has no place in an elementary text. He said that had he been asked to study the proof of such a theorem in high school, he would almost certainly have given up on mathematics, having concludcd that the subject is dumb! In support of this viewpoint— that there was excessive rigor in the “new math"—he was one of the signers of a manifesto on curriculum reform that appeared in The Mathematics Teacher and The American Mathematical Monthly decrying the direction of the reform movement of the 50's and 60's.

In talking about what he regarded as the excess of rigor in SMSG. he cited the oft‘repeated story about Isadora Duncan's proposal of something like marriage to George Bernard Shaw. She argued that their children would have his intelligence and her beauty. Of course, Shaw pointed out that the children might well have... Pólya suggested that SMSG had been put together by research mathematicians and high school teachers. on the assumption that the material would reflect the mathematical sophistication of the researchers. and the pedagogical skills of the high school teachers. But then, like Shaw, he pointed out that the material in fact reflected... The observation was unkind but there was, perhaps. some truth in it.

Weekend blogging -- Breaker Morant

I've always meant to see this one, even more so since I came across Edward Woodward's extraordinary work as the self-loathing agent Callan.

"Santa Ana winds blowin' hot from the north..."

Yes, it's been one of those weeks.

“There was a desert wind blowing that night. It was one of those hot dry Santa Anas that come down through the mountain passes and curl your hair and make your nerves jump and your skin itch. On nights like that every booze party ends in a fight. Meek little wives feel the edge of the carving knife and study their husbands' necks. Anything can happen. You can even get a full glass of beer at a cocktail lounge.”

― Raymond Chandler, Red Wind: A Collection of Short Stories

The firefighters say they've never seen them coming in like this.

The SAT probably is unfair to the disadvantaged but not for the reasons you've been hearing

This is another one of those posts that I started weeks ago as part of the big SAT thread then didn't get around to posting. One of the big questions was the fairness of the test. I had alluded to the problem but usually as a side question. Part of the reason I didn't spend more time on the question was because of my specialty. Though I did originally certify to teach math and English, I've been focused almost entirely on the former for a number of years, and almost all of the prep work I've done with student has been on the math side.

If I had been working with the verbal part, I would have had to address some uncomfortable questions. The verbal SAT is a good, well-designed and informative test but there are inescapable concerns about its fairness.It is very difficult to design a verbal reasoning test that is not culturally biased. Language and culture are so intertwined that it is almost impossible to even discuss one with out considering the other. Cultural biases are not nearly as much of a concern on the mathematics side of the test.

Still, even in the reasonably objective and unambiguous world of mathematics, there are any number of ways in which background can give an unfair advantage. These include (but are by no means limited to) enrichment activities, role models, high-achieving schools and community culture, support and tutoring, and expensive prep classes.

This last item has become one of if not the central element in the SAT/fairness discussion. All stories on the subject seem to be contractually obligated to talk about expensive test prep courses and yet, as far as I can tell, they all frame the issue in a way that makes the criticisms completely invalid.

There are two fallacies in this standard line of argument: The first is based on confusion over absolute versus relative values; the second is based on a common but profoundly wrong concept of the test itself.

As an absolute statement it is true that if prep courses do any good at all then the ability to pay for them will provide an unfair advantage. The question on the table now, though, is not absolute. The people who are arguing for the elimination of the SAT are also arguing, sometimes implicitly, often explicitly, for grades to take a much larger role in the college selection process to take up the slack. This leads to a very different question: does having money give one a greater advantage on the SAT then it does on GPA?

Private tutoring centers are a huge national industry, and if you send your child to one for any length of time, the cost will probably be far greater than what you would've spent on an SAT prep course. We could, of course, have a long discussion about the intrinsic value of what is taught in one versus the other, but from an economic fairness standpoint, all we care about is the cost and the effectiveness in improving the given metric.

A valid argument here would start with a comparison of the ways that privilege can provide an unfair advantage on the SAT versus GPA, but what we've gotten so far is the pseudo-argument: A is worse than B because A is bad ("French Fries are so fatty; I think I'll have onion rings instead."). As far as I can tell, none of the many stories describing the potential impact of prep courses even mention the existence of the private tutoring industry.

The other fallacy here is the very wrong but very common belief that the SAT is some kind of mysterious black box, the secrets of which can only be revealed by one of the illuminated. I've already been through this at some length but just to reiterate, because of the stability of the tests and the large number of previous editions that the College Board has published, the SAT is one of the most transparent exams you're ever likely to take.

At least on the math side (which is the area I have some experience with), this transparency, along with the nature of the questions, makes the test surprisingly easy to teach and to teach yourself. In the latter case, it goes like this:

Take one of the old tests (don't worry about the time limit);

Check your answers;

Read the explanations for the ones you got wrong;

If you don't understand the explanations for some of those problems, take them to a teacher or administrator and ask for help (as a former teacher, I can tell you that educators love to see this kind of initiative and will go to great lengths to encourage it). There are also free after-school programs that would be glad to help (I volunteer at one of them);

Repeat the process. After you start breaking fifty or sixty percent, work on reducing your time.

If it's this easy, why does anyone bother with a pricey prep course? Well, for one thing, it's not that easy. We are talking about a tremendous amount of work and self-discipline. The courses provide structure and external discipline, not to mention a large dose of motivation and reassurance to counteract the test's foreboding reputation (a problem greatly compounded by journalists' tendency to talk about the exam in dark and mysterious terms).

To sum up, there is tremendous unfairness in our education system. The SAT is sometimes part of that unfairness, but neither for the reasons or to the extent you often hear.

A cyncial take

Kevin Drum asks:

Anyway, that's my question. There's already a perfectly good, perfectly simple way for ISPs to recover the cost of providing lots of bandwidth: just charge the customers who use it. Existing peering and transit arrangements wouldn't be affected, and there would be no net neutrality implications. So why not do it? What am I missing?

My cynical answer is that there are a lot of markets that are large but for which service is sub-optimal (think New York City)  If you charge users by bandwidth, the people in these markets would likely end up getting a discount because they are light user simply because it is nearly impossible to be heavy users.  But everyone would like some internet access.

So this is a way to have your cake and eat it as well.  In markets with bad service you make money as a gatekeeper.  In places with good service, you recover cash from the content providers who use the capacity. 

If you are wondering if this sounds a lot like a monopoly or a lack of competitive markets, you are probably correct.   After all, cell phones (which appear to still have a competitive market) had absolutely no trouble rolling out bandwidth based pricing.  Customers grumbled, but everyone gave up and adapted to it. 

Another one for the West Coast Stat Views lexicon: Jethro Models

[Part of an ongoing series]

The Jethro Model is a formal or informal model that leaves out a large number of necessary parts. The allusion was explained in a previous post.

From Anti-orthogonality at Freakonomics

In one of the many recurring gags on the Beverly Hillbillies, whenever Jethro finished fixing the old flatbed truck, Jed would notice a small pile of engine parts on the ground next to the truck and Jethro would nonchalantly explain that those were the parts that were left over. I always liked that gag and the part that really sold it was the fact that the character saw this as a natural part of auto repair: when you took an engine apart then reassembled it you would always have parts left over.

Sometimes I find myself having a Jed moment when I read certain pop econ pieces.

"What's that pile next to your argument?"

"Oh, that's just some non-linear relationships, interactions, data quality issues and metrics that won't reduce to a scalar. We always have a bunch of stuff like that left over when we put together an argument."

For a recent example, consider this quote from  George Mason University economist Robin Hanson (via Andrew Gelman):

If your main reason for talking is to socialize, you’ll want to talk about whatever everyone else is talking about. Like say the missing Malaysia Airlines plane. But if instead your purpose is to gain and spread useful insight, so that we can all understand more about things that matter, you’ll want to look for relatively neglected topics. . . .

Obviously, this is intended more as an observation than even an informal model, but we're still looking at a level of simplification that makes this rule pretty much meaningless; as soon as add any of the complexity of actual conversations, either with respect to why we converse or how we decide what to talk about, the whole argument just collapses. We converse for a long list of reasons. Sometimes we simply want company. Other times it's something more specific, to propagate our ideas, to amuse, to impress, to be liked, to establish individual and group identity, to get laid or, far more frequently, to convince ourselves that we could get laid if we wanted to. We could make similar list of reasons for picking conversational topics, but I think you get the point.

To reduce this down to social vs. informative motives and common vs. neglected topics, you either have to leave out important options or group together things so diverse as to make the definitions meaningless. What's more, by equating neglected topics with informative conversations, the model suggests some strange implications, such as that the person who just wants to be sociable will talk about racism and climate change, while the person who wants to be informative is more likely to discuss obscure distinctions between Phish bootlegs.

That's not to say that there's no extra value to bringing up neglected topics; it's just that Hanson's observation doesn't capture the fundamental relationships. I've been writing quite a bit recently on the importance of orthogonality and there's certainly a relationship between unique information and how much a topic has been discussed. Unfortunately there's also a great deal of collinearity. Lots of topics are relatively neglected because they don't contain that much interesting information.

To further complicate matters, under the right circumstances, you can gain considerable social cachet by knowing interesting facts about little known topics. The "interesting" part can be a bit of a hurdle, but I know  people who do it which puts yet another hole in the model. As do people who bring up obscure topics for the primarily social purpose of making themselves seem distinctive or erudite.

Another problem with Jethro models is the way that their oversimplified, overgeneralized approach can enable self-serving hero/villain narratives. Andrew Gelman made a related point about many popular economics books and articles -- "What strikes me about this discussion is the mix of descriptive and normative that seems so characteristic of pop-microeconomics." You don't have to look hard to see that mix here -- you can almost hear the inspirational music in the background while reading this "if instead your purpose is to gain and spread useful insight, so that we can all understand more about things that matter, you’ll want to look for relatively neglected topics."

It should be noted that Robin Hanson spends a great deal of time on out-of-the-mainstream ideas. Without putting too fine a point on it, when someone who "has elected to have his head cryonically preserved in the event of medical death" depicts in such glowing terms people who discuss neglected topics, I can't help but suspect bias.

And given Hanson's tendency to portray himself as being above this sort of thing...

Yes, the House is still capable of bipartisan action...

...but what's interesting is where they choose to do it. Charter schools certainly aren't the least controversial issue facing congress and, if anything, they've become more so as stories have poured in about waste, huge payouts, discrimination, draconian discipline policies, and community protests. I don't want to demonize charters here -- there are a lot of good ones out there and I think they have an important role to play -- but they don't seem to be the sort of issue that could manage a 360 to 45 vote.

The answer lies, I think, in two factors: first, that it's easy to get a charter school bill in under the radar; and second, that charters have wide support on both the left and the right where it counts, in the media and among wealthy donors.

From the Hill:

The House on Friday passed bipartisan legislation to expand access to charter school funding.

Passed 360-45, the vote came in sharp contrast to the bitterly partisan debates this week over creating a select committee to investigate the 2012 Benghazi attack and holding former Internal Revenue Service official Lois Lerner in contempt of Congress.

A majority of Democrats — 158 in favor and 34 against — joined all but 11 Republicans in support of the measure.

The bill authored by House Education and the Workforce Committee Chairman John Kline (R-Minn.) and the panel's top Democrat, Rep. George Miller (Calif.), would consolidate the two existing federal charter school programs into one to award grants to state entities.

The measure would also authorize the secretary of Education to maintain a federal grant competition for charter schools that did not win state grants.

Republicans have touted the issue of school choice and access to charter schools as a way of limiting the federal government's role in education policy. Charter schools receive public funding, but operate independently and therefore are not subject to federal regulations.

"Expanding education opportunity for all students everywhere is the civil rights issue of our time," House Majority Leader Eric Cantor (R-Va.) said. "I say we help those students by expanding those slots so they can get off the waiting lists and into the classrooms."

Weekend blogging -- brought to you by the Good Wife

One of the small but ubiquitous changes the internet has brought is the end of the lost song. Before the mid-Nineties, the main ways to learn the names of songs was from the DJs who sometimes remembered to tell you who you were listening to or from the captions on videos that had a way of fading just as you remembered to look up. Songs you heard on TV shows and movies were generally lost causes. The irritating feeling that came from not being able to find or forget a song (specifically "Anna" but not the Beatles cover) was the basis of at least one sitcom episode. From Wikipedia:

In the Married... with Children episode "Oldies But Young 'Uns" (Season 5, Episode 17; airdate March 17, 1991), Al Bundy becomes obsessed with finding out the name of this song which has become his earworm (originally he can only tell people the nondescript misheard lyric "hmm hmm him").

It is still possible not to be able to find a song, but it doesn't happen often. If you can remember a fragment of a lyric or pin down where you heard it, you can usually be listening to it on Youtube in a couple of minutes.

On last week's The Good Wife, a distinct and very catchy beat kept running through the episode. As soon as it was over I went online and learned that the beat came from the equally catchy song "High On the Ceiling."






Once I got on the subject, I remembered an obscure song from Malcolm in the Middle. Googling the show's title and the word 'hockey' was enough to bring up the song.




"Little Buster" from the beloved coming of age anime FLCL was another potential earworm that proved easy to find.



I have to admit, I could never get into that show. The only anime I ever really connected with was Cowboy Bebop but that one won me over completely. It also had one of the great late 60s/early 70s opening titles. Even Lalo Schifrin would have been jealous.



Technically, this last one doesn't exactly belong on this list -- I was already a big fan if the song -- but I like this version a lot and, like all good covers, it reveal something interesting that you probably missed in the original.

A musical introduction to the old "new math"

The commonality between the current education reform movement and the Post-Sputnik era have been mentioned before. Among other similarities, both movements prided themselves on taking a rigorously scientific approach to education and yet some of their sharpest critics were the very scientists and mathematicians they were trying to emulate.

We've already talked about Richard P. Feynman's criticism of Post-Sputnik era math and science textbooks, particularly their attempts to be rigorous and realistic. Along similar lines, Tom Lehrer, who was either teaching math at Harvard or political science at MIT (depending on exactly when the song came out), had a great deal of fun with the topic in the song "New Math."

Two more for the West Coast Stat Views lexicon: The Jar Jar Binks Paradox and Mathematical Anosognosia

The Jar Jar Binks Paradox

Improving the reputation of something bad by adding an additional element that's even worse. The effect works by focusing criticism on one point, making the other elements look better by comparison, and by creating a more favorable narrative (____ would have been good if not for ______).

You could argue that the fatalities-per-mile metric was the Jar Jar Binks of Freakonomics' shoddy analysis of the risks of walking drunk vs. driving drunk. Just to be clear, walking drunk is very dangerous. It might even be more dangerous that driving inebriated, but Levitt's analysis was a collection of comically oversimplified assumptions and numbers pulled out of the air. (See here, here and here for critiques). By addressing criticisms of the fatalities-per-mile metric, Levitt was able to create the impression that the rest of the work was solid.


Mathematical Anosognosia

A condition that causes the false impression of comprehension when a concept is accompanied with familiar mathematical symbols and methods. This is often accompanied with a heightened sense of self-confidence and diminished sense of judgement and restraint. Those prone to this condition are often observed making sweeping pronouncements in fields they have no relevant background in. Though almost anyone working in a math-based field can suffer from Mathematical Anosognosia, physicists and economists seem most susceptible, Extreme cases have been known to produce NYT best-sellers.

More futures past -- Highway edition

The standard post to accompany this sort of clip either oohs and aahs over the more prophetic aspects or laughs at the less realistic, but I don't feel like either of those fits my reaction. What strikes me watching this is how fast-moving and, more importantly, ambitious people expected the future to be. This was particularly notable in the section describing road construction (living in LA no doubt contributes to my reaction).

When I look at the Post-War era, I almost always get this incredible sense of pent-up energy, as if the country couldn't wait to make up for all those years lost to the Depression and the War. People wanted to do big things. What's more, they wanted to do them as soon as possible and they were willing to pay whatever was required.

It would be interesting to try to attach some numbers to the attitudes, but just anecdotally it seems clear that when it comes to progress, we're now more tolerant of delay and less tolerant of cost. When an ambitious proposal (manned space exploration, hypersonic trains) does make the news, it almost invariably comes with a laughably low-balled cost, usually one or more orders of magnitude below reasonable.

We'd still like magic highways, just not enough to foot the bill.




Disney's Magic Highway - 1958

A distributional question

I have been under the weather for a bit (thus no posts) but I wanted to share a thought I have been having in reaction to the minimum wage discussion on the west coast.  People have tended to be worried about these increases, with much concern about economic damage.

However, income and wealth in the United States are distributed with an extremely heavy tail, especially in terms of growth in the last 30 years.  This sort of growth, presuming a perfect market, is quite odd as I had always presumed human ability has a normal distribution.  The normal distribution is continuous and naturally presents several people of nearly the same ability behind the exceptional person (at least at the top end).  We can ignore the odd outlier -- if there was only one billionaire in the United States and they had had risen from poverty then we'd exclude them from any realistic analysis. 

But if we want to argue that current economic trends represent fairness, it turns out that we have some steep assumptions and observations to explain. These turn out to be crucial.

For example, when top wages are so high, why don't the companies hire the "next best executive" and split the surplus?  If ability is an innate (as opposed to learned ability), why don't we outsource all CEO jobs immediately to China (which would have more top performers as a function of a larger population)?  But this sort of wealth distribution seems like an odd way to end up given a normal distribution of ability, presuming one is talking about some sort of meritocratic environment.

Or how do we know we have an ideal marketplace now?  There have been a lot of commercial structures over history.  What makes us different than: a) Plato's Athens, b) the Roman Empire, c) Medieval England (say the anarchy period), or d) the Song dynasty in China?  They had markets too -- where the results of such markets just?  If the difference is due to corruption, government interference, and rent seeking, do we have a better balance now?  And how would we know, without making a consequentialist argument? 

It is actually a pretty deep question.

It may be a good thing that I missed this New York Times SAT article when it first came out...

If I had read all of their coverage at once, I'm afraid my head would have exploded.

From A New SAT Aims to Realign With Schoolwork
By TAMAR LEWIN

"The guessing penalty, in which points are deducted for incorrect answers, will be eliminated."

We been through this before

The SAT and the penalty for NOT guessing

On SAT changes, The New York Times gets the effect right but the direction wrong

but saying 'points' instead of 'fractions of points' is just inexcusable. I realize that the concept of expected value can throw people but even a NYT reporter should be able to distinguish between one and one fourth.

A Star Wars Day experiment

I know I'm mixing franchises here, but the recent coverage of Star Wars Day has left me with something of a Twilight Zone feeling. It's almost like waking up in a world where people have always celebrated an unofficial holiday commemorating some pretty good, if dated science fiction films of the Seventies and Eighties.

So I did some data collection, doing some Google searches (Web and News) over different custom time ranges and I found that, though the origins of the holiday date back to the late Seventies, the vast majority of the coverage seems to have started about the time Disney recently started seriously promoting the upcoming sequel. 

Try your own data gathering at home. You may get slightly different results but I think you'll find an exceptionally large jump this year. Wikipedia says "Observance of the holiday spread quickly due to Internet, social media, and grassroots celebrations," and I'm sure that interest in the upcoming film accelerated the process, but I have trouble believing that these factors alone could drive the increase we've seen. It's almost like major media conglomerates like Disney had some mysterious force that could cause journalists to promote their product. 

Weekend blogging -- perhaps the strangest Donald Sterling tie-in you'll see this week

Well, that worked out nicely. A few days ago, we ran a post about the similarities between the controversy over the NAACP accepting money from Donald Sterling and the moral dilemma at the heart of Shaw's Major Barbara. This morning I check out Hulu for the free selections from the Criterion Collection and I discover that the theme of the week is stage to screen and one of the selections is the 1941 adaptation of Shaw's play.

While I was at it, I also embedded a few other films from the collection, including one that I've always had a special connection to, Olivier's take on Richard III. I came across the film one night when I was ten or eleven. I had no idea what or whom I was watching, but I was fascinated nonetheless. I'm a big fan of Ian McKellen, but if you can only see one...

"The Heart of Algebra"

I'm working on a couple of bigger pieces on the SAT and one of the things that I've been looking at as part of the background work is this statement from the College Board discussing the changes in the math section of the test. Board president David Coleman quotes extensively from this and I'd be very much surprised if he hadn't been extensively involved in its writing. (the press releases very much have Coleman's voice.)

Reading these official statements after closely reviewing the old SAT test produces a couple of strange reactions. The first is a disconnect that comes from a list of changes that, with one or two exceptions, seem to describe the test we already have (work with systems of equations, analyze data, use percentages and ratios) and/or contradict other proposed changes (reduce the scope and add "trigonometric concepts").

The second  is a strange lost-in-translation feeling, as if the passages were almost saying something meaningful, but some key words had been omitted or put out of order. Perhaps the best example is this discussion of  linear equations and functions as "the heart of algebra." Coleman seems particularly enamored with this phrase -- he uses it frequently in interviews about the SAT -- but when I read through the press statement, I didn't see anything that made linear functions more important or fundamental than other polynomial functions (or rational functions or logarithmic or exponential functions for that matter).

Here's a little experiment. Read the passage below extolling the importance of equations and functions based on linear expressions. Then read it again but mentally strike out every occurrence of 'linear' except for the parenthetical phrase. I think you'll find it actually makes as much sense.

Heart of Algebra: A strong emphasis on linear equations and functions
Algebra is the language of much of high school mathematics, and it is also an important prerequisite for advanced mathematics and postsecondary education in many subjects. Mastering linear equations and functions has clear benefits to students. The ability to use linear equations to model scenarios and to represent unknown quantities is powerful across the curriculum in the postsecondary classroom as well as in the workplace. Further, linear equations and functions remain the bedrock upon which much of advanced mathematics is built. (Consider, for example, the way differentiation in calculus is used to determine the best linear approximation of nonlinear functions at a certain input value.) Without a strong foundation in the core of algebra, much of this advanced work remains inaccessible.

You might make a pretty good case for the central importance of polynomials (particularly if you want to get nerdy and bring in Taylor). You can make a great case for the central importance of functions. You can even make a crawl-before-you-walk case for focusing on linear expressions. But you have to make some sort of coherent argument.

Even the part about finding the slope of the tangent at a given point (that is what they're talking about, right? or am I missing something?) has an odd quality. It's difficult to see how using a derivative to help find the equation of a line makes linear equations the 'bedrock' of more advanced math. There are certainly examples where linear equations are used to find formulas and prove theorems in calculus and other more advanced fields, but the example in the parenthesis actually goes the other way. To me, the passage as a whole and the parenthesis in particular read as if the author had asked someone knowledgeable "where do we use linear equations and functions?" and had paraphrased the answer with only minimal comprehension.

What's so strange and somewhat sad about that possibility is the extraordinary pool of mathematical talent that was hanging around the halls when this was written. If you take a tests and measurements class, you soon realize that most of the good examples come from the SAT. The people who put the exam together are exceptionally good in a highly demanding field of statistics.

Not listening to people with experience and expertise is a noted characteristic of and perhaps even a point of pride with Coleman, who came into the field as a McKinsey & Company consultant and had no relevant experience in education or statistics.

When Coleman attended Stuyvesant High in Manhattan, he was a member of the championship debate team, and the urge to overpower with evidence — and his unwillingness to suffer fools — is right there on the surface when you talk with him. (Debate, he said, is one of the few activities in which you can be “needlessly argumentative and it advances you.”) He offended an audience of teachers and administrators while promoting the Common Core at a conference organized by the New York State Education Department in April 2011: Bemoaning the emphasis on personal-narrative writing in high school, he said about the reality of adulthood, “People really don’t give a [expletive] about what you feel or what you think.” After the video of that moment went viral, he apologized and explained that he was trying to advocate on behalf of analytical, evidence-based writing, an indisputably useful skill in college and career. His words, though, cemented his reputation among some as both insensitive and radical, the sort of self-righteous know-it-all who claimed to see something no one else did. 

Coleman obliquely referenced the episode — and his habit for candor and colorful language — at the annual meeting of the College Board in October 2012 in Miami, joking that there were people in the crowd from the board who “are terrified.”   

Given some of the changes we've seen in the test the College Board worked so hard to get right (the loss of orthogonality, the shoehorning in of "real-world" data), we may have some idea what they were scared of.